Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.47.0-wmf.21 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk Event Event talk 4 28 2834476 2834400 2026-09-25T12:23:43Z MediaWiki message delivery 983498 /* Your feedback wanted: Remove (Language link added:) and similar edits from Special:RecentChanges */ new section 2834476 wikitext text/x-wiki {{Wikiversity:Colloquium/Header}} <!-- MESSAGES GO BELOW --> == Add an edit count requirement for autoconfirmed? == Currently, only waiting for four days is required for a user to become autoconfirmed. I am proposing that we include a minimum edit count of 10 edits (akin to Wikipedia) especially because of [[Special:AbuseFilter/16|a private abuse filter]], and LTAs may game autoconfirmed permissions to vandalize here. Thoughts? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:01, 23 August 2026 (UTC) : [[Wikiversity:Autoconfirmed users]] : Are you suggesting an additional requirement? i.e., 4 days + 10 edits? : How is it adjusted? -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:57, 5 September 2026 (UTC) :: Yes. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 01:30, 6 September 2026 (UTC) :: @[[User:Jtneill|Jtneill]]: I said yes to your first question. As for the adjustment question, in the InitialiseSettings.php file on noc.wikimedia.org, on <code>wgAutoConfirmCount</code> is where English Wikiversity would be added as <code>'enwikiversity' => 10,</code>. Does my reply make sense? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:31, 15 September 2026 (UTC) :As a newly volunteered member, it doesn't seem unreasonable to me to require a certain number of edits to establish my bona fides. [[User:Cfm490|Cfm490]] ([[User talk:Cfm490|discuss]] • [[Special:Contributions/Cfm490|contribs]]) 17:53, 5 September 2026 (UTC) :I agree that adding an edit count requirement is a reasonable expectation before the user can become autoconfirmed. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 18:56, 6 September 2026 (UTC) :+ 1 —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:40, 6 September 2026 (UTC) :'''Weak support''' Generally reasonable, but I would caution that we should really make this clear for those instances where professors have students edit here and make it frictionless for them to get autoconfirmed status. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 19:42, 6 September 2026 (UTC) : {{oppose|No support}} because I cannot see the [[Special:AbuseFilter/16|abuse filter]] cited as the primary reason and I do not know what LTAs is. I guess you don’t want support from ''ordinary'' users. ‑‑[[User:Kai Burghardt|Kays]] ([[User talk:Kai Burghardt|discuss]] • [[Special:Contributions/Kai Burghardt|contribs]]) 18:18, 14 September 2026 (UTC) ::Also some readers may be interested in this: ::* [[Wikipedia/Types of user accounts]] ::[[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 19:05, 14 September 2026 (UTC) ::: An LTA means a long-term abuser, and it means someone who is usually abusive. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 20:42, 14 September 2026 (UTC) :'''Strong''' {{support}}; specially to battle LTA [[User:Mbataw|Mbataw]] ([[User talk:Mbataw|discuss]] • [[Special:Contributions/Mbataw|contribs]]) 13:17, 18 September 2026 (UTC) :{{support}}, having no edit count requirement for autoconfirmed is a bad idea in general. [[User:BooksBooksBooks3|BooksBooksBooks3]] ([[User talk:BooksBooksBooks3|discuss]] • [[Special:Contributions/BooksBooksBooks3|contribs]]) 01:43, 19 September 2026 (UTC) :Comment: I realize that it is not easy to be an admin on wikimedia projects. I realize that many admins have to deal with some VERY unpleasant personalities. But.. :Admins are not the only users who encounter harassment on wikimedia projects, big or small. Anyone who's been here as long as I have, has come across users who are not tolerated by the "community". Not necessarily because they are spammers, trollers, paid editors, LTAs , disruptive etc, but simply because they are different. :When I "edit" without logging in, I carry no baggage. I also get encouraging prompts such as this: :* This year, Wikipedia has had fewer visitors and fewer new supporters, so '''<big>your visit today means a lot</BIG>''' :Anyway, back to the topic at hand [[Wikipedia/Types of user accounts]]. I believe the section about IP editors is outdated since wikimedia now views users who are not logged-in as anonymous, and only trusted users are allowed to see their IP address (I am not clear on the details). I wonder if anyone participating here has an interest in bringing this page uptodate? [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 04:13, 22 September 2026 (UTC) : If there's some obvious things to fix, I'd say go ahead. It looks like there were several useful anonymous contributions to that page recently. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 07:54, 22 September 2026 (UTC) == Bartending Course on Wikiversity == I recently finished the course on [[Bartending]], and while I have experience editing on Wikipedia, this is my first Wikiversity project. If any of you have the time or interest, I could use an experienced eye to see if there's anything obviously missing from the course in terms of Wikiversity administration. I'm not sure what's active, if the course should belong in an existing school, or if there's any obvious discoverability tool I haven't implemented. Any tips are welcomed, or just a thumbs up saying it looks fine would be great. [[User:Jtneill|Jtneill]] recommended I post this here in case someone wanted to include the new course under News on the [[Wikiversity:Main Page|Main Page]]. Thanks! [[User:Sabbier|Sabbier]] ([[User talk:Sabbier|discuss]] • [[Special:Contributions/Sabbier|contribs]]) 01:24, 1 September 2026 (UTC) :Wow! Fantastic work- I'm so impressed! Your work gives me inspiration on how to better organize the courses I'm working on. :) [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:32, 3 September 2026 (UTC) : Awesome work. I've added this course to the [[Main Page/News|main page news]]. : We could also consider for [[Wikiversity:Featured]]. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:43, 5 September 2026 (UTC) ::The course [[Creating Wikiversity Courses]] is intended to provide guidance to new Wikiversity editors. I hope it is helpful and I welcome improvement suggestions. Thanks. [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 14:08, 6 September 2026 (UTC) == Writing news here == I'm bringing up this discussion again because I think it is beneficial to the project since Wikinews is gone, thank you. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 03:17, 1 September 2026 (UTC) : Given that the community consensus here was not to replicate WikiNews within Wikiversity, I suggest thinking differently e.g., in terms of specific news-related projects you are interested in that have educational objectives that satisfy Wikiversity's mission. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:46, 5 September 2026 (UTC) ::I wonder if you mean <u>Wikiversity:Main Page/News ?</u> ::If so I have just checked this page and I see it only contains news for 2026 and part of 2025, even though the history indicates it was created in the 2000-decade. If you go back and check all revisions there is a wealth of (historical?) information. [[Special:Contributions/~2026-40514-81|~2026-40514-81]] ([[User talk:~2026-40514-81|talk]]) 16:28, 13 September 2026 (UTC) ::: I didn't mean that page, but yes, its history could be reconstructed into a more accessible format. -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 21:37, 13 September 2026 (UTC) == [[Wikiversity talk:Interface administrators#My thoughts about this user group]] == As I suggested, I would like to propose allowing permanent interface administrators on English Wikiversity. My temporary interface admin rights are about to expire soon, and I will soon create a new CfIA page (and its header). We should also have a minimum of two interface administrators. Thoughts? [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 16:44, 6 September 2026 (UTC) :I am also in favor of this and we did discuss it pretty recently and came to a consensus on extending IA rights and lowering the administrative overhead, but not allowing indefinite at this juncture. From my perspective, since we discussed this so recently and nothing seems to have changed much, I personally would recommend holding off for a couple of years or until/unless there is some critical new information. Again, I would continue to support indef IA rights were it to come up again and think that at least two is also a sensible proposal. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:32, 6 September 2026 (UTC) ::Responding to myself so that I don't derail: I would be interested/willing to be an indef IA. ―[[User:Koavf|Justin (<span style="color:grey">ko'''a'''<span style="color:black">v</span>f</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 17:36, 6 September 2026 (UTC) : I made [[Wikiversity:Candidates for Interface Adminship]]. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:24, 6 September 2026 (UTC) :: CC to @[[User:Koavf|Koavf]]. I made a request since my IA rights are about to expire. We should also hold a separate vote to allow permanent IAs here (for this policy). [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 16:55, 7 September 2026 (UTC) : @[[User:Jtneill|Jtneill]], I count at least three in favor (votes below, and Koavf agreeing), so can you close this request? Thank you. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 15:22, 24 September 2026 (UTC) === Votes === * For the record, I am creating a separate subsection for voting, whether or not we should allow permanent interface administrators. {{support}} accordingly. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] /// [[User talk:Codename Noreste|⭐️✨]] 18:32, 15 September 2026 (UTC) * {{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:51, 18 September 2026 (UTC) == Paid part-time Administrative Officer position with WikiJournal == [[WikiJournal User Group|WikiJournal]] is an open-access, nonprofit scholarly publisher hosted on Wikiversity. It uses the wiki format to allow authors to write and develop scholarly articles directly online. Submitted articles then undergo formal academic peer review and, when accepted, are published as citable journal articles while remaining freely accessible. WikiJournal is seeking expressions of interest in a new part-time '''Administrative Officer''' position. The officer would support the project's day-to-day organizational work, including: * Setting up and administering a system for tracking contractor hours and issuing payments. * Coordinating the contracting, onboarding, timekeeping and payment of technical editors and other contractors. * Maintaining financial, contractor and administrative records. * Assisting with grant administration, budget tracking and reporting. * Following up on board action items, deadlines and recurring obligations. * Supporting recruitment and other operational tasks as needed. This is a remote, flexibly scheduled contractor role averaging approximately '''6 hours per week'''. Compensation is proposed at '''US$25 per hour''', with up to approximately '''320 hours (US$8,000) available over the year'''. Applicants may be based internationally, although appointment will depend on WikiJournal being able to establish a practical and legally appropriate contracting and payment arrangement in the applicant's country of residence. Relevant experience may include administrative organization, bookkeeping or financial administration, contractor or personnel coordination, nonprofit or grant administration, Wikimedia participation, academic publishing, and open-access work. Applicants are not expected to have experience in every area. For the complete role description and further details, see [[WikiJournal User Group/Administrative officer]]. Those interested should reply in the '''[[Talk:WikiJournal User Group#Call for interest: Administrative Officer|Call for interest: Administrative Officer]]''' discussion by '''30 September 2026''', briefly describing their relevant experience, any connection to WikiJournal or related communities, and their general availability. Expressions of interest received later may still be considered if the position has not been filled. Recommendations of potentially suitable candidates are also welcome. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 20:00, 10 September 2026 (UTC) == Server switch - Your wiki will be read-only for a short time soon == <section begin="server-switch"/><div class="plainlinks"> [[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-Tech%2FServer+switch&language=&action=page&filter= {{int:please-translate}}] The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster. All traffic will switch on '''{{#time:j xg|2026-09-23|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2026-09-23T14:00|en}} {{#time:H:i e|2026-09-23T14:00}}]'''. Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. You can contribute to the [https://meta.wikimedia.org/w/index.php?title=Special%3ATranslate&group=Centralnotice-tgroup-read_only_banner&task=view&language=&filter=&action=translate translation or proofreading] of this banner text. '''You will be able to read, but not edit, all wikis for a short period of time.''' * You will not be able to edit for up to an hour on {{#time:l j xg Y|2026-09-23|en}}. * If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case. ''Other effects'': * Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped. * We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards. * [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes. This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. '''Please share this information with your community.'''</div><section end="server-switch"/> [[m:user:Trizek (WMF)|Trizek (WMF)]] 12:58, 15 September 2026 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&oldid=30513874 --> == Your feedback wanted: Remove ''(Language link added:) and similar'' edits from Special:RecentChanges == ''(Apologies for posting in English. You can help by translating it)'' Hello, I’m Danny from [[:en:w:Wikimedia_Deutschland|Wikimedia Deutschland’s]] [[m:Wikidata_For_Wikimedia_Projects|Wikidata For Wikimedia Projects]] team.<br/> We have been investigating and examining how Wikidata’s use in the [[Special:RecentChanges]] and [[Special:Watchlist]] pages can be made to be more useful, or less ‘noisy’ (fewer edits that have little value to the reader). We are currently exploring to make a change in the volume and the type of Wikidata edits that appear in these pages, and '''we need your feedback''' to help us ensure this is a positive change for the Wikis and won’t disrupt your workflows.<br/> Language links are also known as sitelinks or interlanguage links and describe when a Wikidata item is connected to a Wiki, adding it to the language dropdown tool for other connected Wikis. [[File:Types of Lang Link changes.png|x350px|frame|A variety of "Language Link" edits as seen in the Recent Changes feed]] The request for feedback is whether you support the removal of these language link edits from the Recent Changes and Watchlist feed, or would you oppose such a change and if so, why? Please share you thoughts on the dedicated '''[[m:Talk:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|metawiki Talk page]]'''. Further information about this change: [[m:Wikidata_For_Wikimedia_Projects/Clearer_Wikidata_Edit_Summaries/Hide_Language_Link_edits|m:Wikidata_For_Wikimedia_Projects/Hide_Language_Link_edits]] Thank you for any participation or feedback you give, -- [[m:User:Danny_Benjafield_(WMDE)|User:Danny Benjafield (WMDE)]] 12:23, 25 September 2026 (UTC) <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Danny_Benjafield_(WMDE)/MassMessage_test_list&oldid=31080985 --> metumplabi530w52g7r69kr1atl3vml 4 1791 2834477 2828404 2026-09-25T12:46:33Z ~2026-51662-36 3111599 2834477 wikitext text/x-wiki {{/header}} == [[African Arthropods/Bembecidae]] == Incorrect spelling of Bembicidae — [[User:Alandmanson|Alandmanson]] ([[User talk:Alandmanson|discuss]] • [[Special:Contributions/Alandmanson|contribs]]) 11:55, 24 August 2026 (UTC) : {{Done}} [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:22, 24 August 2026 (UTC) @06872736 [[Special:Contributions/~2026-51662-36|~2026-51662-36]] ([[User talk:~2026-51662-36|talk]]) 12:46, 25 September 2026 (UTC) pyhmqkvwqt8i0egz8oqr8ejkozhvw9z 2834478 2834477 2026-09-25T12:46:58Z Àncilu 2937936 Undid edits by [[Special:Contribs/~2026-51662-36|~2026-51662-36]] ([[User talk:~2026-51662-36|talk]]) to last version by Atcovi: test edits, please use the sandbox 2834478 wikitext text/x-wiki {{/header}} == [[African Arthropods/Bembecidae]] == Incorrect spelling of Bembicidae — [[User:Alandmanson|Alandmanson]] ([[User talk:Alandmanson|discuss]] • [[Special:Contributions/Alandmanson|contribs]]) 11:55, 24 August 2026 (UTC) : {{Done}} [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:22, 24 August 2026 (UTC) mepswznnddxbipfb63on2pvznrpnojh 0 2103 2834495 2805792 2026-09-25T23:18:10Z ~2026-51826-91 3111622 2834495 wikitext text/x-wiki [[File:Hello World Brian Kernighan 1978.jpg|thumb|right|Hello World! by Brian Kernighan. Based on a 1978 Bell Laboratories internal memorandum by Brian Kernighan, Programming in C: A Tutorial, which contains the first known version.]] As described in more detail in [[w:"Hello,_World!"_program|the related Wikipedia article]], '''Hello, world!''' is a classic "first program" one creates when learning a new programming language. The objective of the application is the same: to print the text "Hello, world!" to the screen in some form, be it console output or a dialog. In many cases, the statement required to do this is just a single line. It seems appropriate that our introduction to Computer Science occupied this title. As a student, the first choice to make is to decide ''what kind of knowledge you are looking for''. Of course, this depends upon your needs. You might be: * A learned computer scientist or professional eager to contribute research and course material * Computer professional seeking an alternative to expensive commercial certification * Adult non-computer professional or entrepreneur who could benefit from academic/practical knowledge of computing * College-eligible (or not) student considering a degree * Casual user trying to to catch/spread the next [[w:Computer virus|virus]] * Hobbyist or computer gamer looking to get the most out of your computing experience * Complete newbie looking for a place to start This is an exciting time for education, and for those of us wishing to collaborate and share knowledge, skills and experience. At present, we are only limited by the sky, and some very large hard drives in a server farm somewhere. {{TOC right}} == Examples of ''Hello, world!'' == === [[Hello World/Ada|Ada]] === <syntaxhighlight lang="ada"> procedure Hello is begin Ada.Text_IO.Put_Line ("Hello, world!"); with Ada.Text_IO; </syntaxhighlight> For an explanation see [[wikibooks:Ada Programming:Basic|b:Ada Programming:Basic]]. === ASP === <syntaxhighlight lang="asp"> <% Response.Write "Hello, world!" %> </syntaxhighlight> or <syntaxhighlight lang="asp" line="1"> <%="Hello, World!"%> </syntaxhighlight> === [[Topic:Assembly language|Assembly]] === ''x86 compatible'' for [[Wikipedia:MS-DOS|MS-DOS]]. <syntaxhighlight lang="asm" line="1" start="1"> title Hello World Program dosseg .model small .stack 100h .data hello_message db 'Hello, world!',0dh,0ah,'$' .code main proc mov ax,@data mov ds,ax mov ah,9 mov dx,offset hello_message int 21h mov ax,4C00h int 21h main endp end main </syntaxhighlight> === BASH === <syntaxhighlight lang="bash">#!/bin/bash echo "Hello, world!"</syntaxhighlight> === BASIC === ==== Applesoft BASIC ==== ''Used on Apple ][ machines (Apple ][+, ][e, //c, ][GS)'' <syntaxhighlight lang="qbasic"> 10 PRINT "HELLO, WORLD!" </syntaxhighlight> -or- <syntaxhighlight lang="qbasic"> 10 ? "HELLO, WORLD!" </syntaxhighlight> ==== Bally/Astrocade Basic ==== ''As used on the Bally and Astrocade game systems ca. 1978'' <syntaxhighlight lang="qbasic"> 10 PRINT "HELLO, WORLD!" </syntaxhighlight> ==== Commodore BASIC ==== ''As used on a Commodore 64, ca. 1984'' <syntaxhighlight lang="qbasic"> 10 ? "Hello, world!" </syntaxhighlight> ==== Dark Basic ==== <syntaxhighlight lang="qbasic"> PRINT "Hello, world!" </syntaxhighlight> ==== FreeBASIC and QuickBASIC ==== <syntaxhighlight lang="qbasic"> PRINT "Hello, world!" SLEEP </syntaxhighlight> or: <syntaxhighlight lang="qbasic"> ? "Hello, world!" sleep </syntaxhighlight> ==== Intellivision Basic ==== ''As used on a Mattel Intellivision, ca. 1983'' <syntaxhighlight lang="qbasic"> 10 PRINT "HELLO, WORLD!" </syntaxhighlight> ==== Intellivision ECS Basic ==== ''As used in the Mattel Intellivision ECS'' <syntaxhighlight lang="qbasic"> 10 PRIN "HELLO, WORLD." </syntaxhighlight> ''! not on ECS keyboard. Only 4 char. commands in ECS Basic'' ==== Liberty BASIC ==== <syntaxhighlight lang="qbasic"> print "Hello, world!" </syntaxhighlight> === Batch === <syntaxhighlight lang="bash"> echo Hello, world! </syntaxhighlight> === [[C]] === <syntaxhighlight lang="c"> #include <stdio.h> int main(void) { printf( "Hello, world!\n" ); return 0; } </syntaxhighlight> === [[Topic:C Sharp|C#]] === <syntaxhighlight lang="csharp"> using System; namespace HelloWorld { class Program { static void Main() { Console.WriteLine("Hello, world!"); } } } </syntaxhighlight> === [[C++]] === <syntaxhighlight lang="cpp"> #include <iostream> using namespace std; int main() { cout << "Hello, world!\n"; return 0; } </syntaxhighlight> === COBOL === <syntaxhighlight lang="cobol"> IDENTIFICATION DIVISION. PROGRAM-ID. HELLO-WORLD. PROCEDURE DIVISION. DISPLAY 'Hello, world'. STOP RUN. </syntaxhighlight> === Common Lisp === <syntaxhighlight lang="lisp"> (print "Hello, world!") </syntaxhighlight> Or: <syntaxhighlight lang="lisp"> (format t "Hello, world!~%") </syntaxhighlight> === [[Delphi]] === <syntaxhighlight lang="delphi"> begin Writeln('Hello, world!'); end. </syntaxhighlight> === Eztrieve (IBM Mainframe programming language). === <code><pre>JOB NULL DISPLAY "HELLO, WORLD" STOP</pre></code> === [[Forth]] === <code><pre>: HELLO ." Hello, world!" ; HELLO</pre></code> === [[Fortran]] === <syntaxhighlight lang="fortran"> PROGRAM HELLO PRINT *,'Hello, world' STOP END </syntaxhighlight> === [[Go]] === <syntaxhighlight lang="go"> package main import "fmt" func main() { fmt.Println("Hello, World") } </syntaxhighlight> === Haskell === <code><pre>main :: IO () main = putStrLn "Hello, world!"</pre></code> === [[HTML|Html]] === <syntaxhighlight lang="html4strict"> <html> <head> <title>Hello, world!</title> </head> <body> <p> Hello, world! </p> </body> </html> </syntaxhighlight> === [[Java]] === <syntaxhighlight lang="java"> class HelloWorldApp { public static void main(String[] args) { System.out.println("Hello World!"); // Display the string. } } </syntaxhighlight> === [[Portal:JavaScript|JavaScript]] (aka JScript, ECMAScript, LiveScript) === <syntaxhighlight lang="java"> document.println("Hello, world!"); </syntaxhighlight> or <syntaxhighlight lang="java"> alert("Hello, world!"); </syntaxhighlight> or <syntaxhighlight lang="java"> document.writeln("Hello, world!"); </syntaxhighlight> === [[Luka]] === <pre> print "Hello, world" </pre> or, with proper syntax <pre> print( "Hello, world!" ); </pre> === [[w:Oberon (programming language)|Oberon]] === <pre>MODULE Hello; IMPORT Out; PROCEDURE World*; BEGIN Out.Open; Out.String("Hello, world!"); Out.Ln; END World; END Hello.</pre> === [[OCaml]] === <syntaxhighlight lang="ocaml"> print_endline "Hello, world!" </syntaxhighlight> === [[Pascal]] === <syntaxhighlight lang="pascal"> program HelloWorld; begin writeln( 'Hello, world!' ); end. </syntaxhighlight> === [[Portal:Perl|Perl]] === <syntaxhighlight lang="perl"> #!/usr/bin/perl print "Hello, world!\n"; </syntaxhighlight> === [[Portal:PHP|PHP]] === <syntaxhighlight lang="php"> <?php echo "Hello, world!"; ?> </syntaxhighlight> or (with short_tags enabled in php.ini) <syntaxhighlight lang="php"> <? echo "Hello, world!"; ?> </syntaxhighlight> or (with asp_tags enabled in php.ini) <syntaxhighlight lang="php"> <% echo "Hello, world!"; %> </syntaxhighlight> or <syntaxhighlight lang="php"> <?="Hello, world!"?> </syntaxhighlight> === [[Topic:Python|Python]] === With Python 2 <syntaxhighlight lang="python"> #!/usr/bin/env python print 'Hello, world!' </syntaxhighlight> Or with Python 3 <syntaxhighlight lang="python"> print("Hello, world!") </syntaxhighlight> The first line is used on Unix systems only, and is optional even there. The advantage is that it allows the file to be invoked directly (if <code>chmod +x</code>), without explicitly specifying the <code>python</code> interpreter. === [[Ruby]] === <syntaxhighlight lang="ruby"> puts 'Hello, world!' </syntaxhighlight> Another way to do it, albeit more obscure: <syntaxhighlight lang="ruby"> #!/usr/local/bin/ruby puts 1767707668033969.to_s(36) </syntaxhighlight> === [[Tcl]] === <syntaxhighlight lang="tcl"> #!/usr/bin/tclsh puts "Hello, world!" </syntaxhighlight> === [[Trekkie]] === <pre> "Computer?" *Bee bee boo "Create program 'Hello, World! Picard-alpha-1'" *Boo boo bee "Parameters: Display the phrase 'Hello, world!' on the screen the program is executed from until the program is terminated." *Bee bee "Save program." *Boo bee boo </pre> === [[Turing]] === <pre> put "Hello World!" </pre> === [[Visual Basic|Visual Basic 6]] === <syntaxhighlight lang="vb"> Sub Form1_Load() MsgBox "Hello, world!" End Sub </syntaxhighlight> <ref>is your purpose? </ref>== Assignment == Create a '''Hello, world!''' program in a language not listed above, then edit this page and add it to the collection. === Visual Basic .NET === <syntaxhighlight lang="vbnet"> Module Module1 Sub Main() Console.WriteLine("Hello, world!") End Sub End Module </syntaxhighlight> === C === Because the tradition of using the phrase "[[w:"Hello,_World!"_program|Hello, world]]!" as a test message was influenced by an example program in the seminal book ''[[w:The C Programming Language (book)|The C Programming Language]]''.<ref>{{cite book | last = Kernighan | first = Brian W. | authorlink = w:Brian W. Kernighan |author2=w:Ritchie, Dennis M. | title = The C Programming Language | edition = 1st | publisher = [[Prentice Hall]] | date = 1978 | location = [[Englewood Cliffs, NJ]] | isbn = 0-13-110163-3 | authorlink2 = Dennis M. Ritchie }}</ref> that original example is reproduced here. <syntaxhighlight lang="text"> #include <stdio.h> main( ) { printf("hello, world\n"); } </syntaxhighlight> === '''LOLCODE''' === <syntaxhighlight lang="text"> HAI CAN HAS STDIO? VISIBLE "Hello world!" KTHXBYE </syntaxhighlight> === '''Natural ''' === <pre> WRITE 'Hello, world!' END </pre> <big>Hello, world!</big> <ref>即時新聞報導 .</ref>=== '''XML''' === <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello> <messagename="Hello" /> <message> Hello, World! </message> </hello> </syntaxhighlight> Or with attributes: <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello messagename="Hello, World!"> Hello, world! </hello> </syntaxhighlight> === '''[[w:MACRO-11|MACRO-11]]''' === <syntaxhighlight lang="text"> .TITLE HELLO WORLD .MCALL .TTYOUT,.EXIT HELLO:: MOV #MSG,R1 ;STARTING ADDRESS OF STRING 1$: MOVB (R1)+,R0 ;FETCH NEXT CHARACTER BEQ DONE ;IF ZERO, EXIT LOOP .TTYOUT ;OTHERWISE PRINT IT BR 1$ ;REPEAT LOOP DONE: .EXIT MSG: .ASCIZ /Hello, world!/ .END HELLO </syntaxhighlight> <ref>is your purpose? </ref>== Assignment == Create a '''Hello, world!''' program in a language not listed above, then edit this page and add it to the collection. === Visual Basic .NET === <syntaxhighlight lang="vbnet"> Module Module1 Sub Main() Console.WriteLine("Hello, world!") End Sub End Module </syntaxhighlight> === C === Because the tradition of using the phrase "[[w:"Hello,_World!"_program|Hello, world]]!" as a test message was influenced by an example program in the seminal book ''[[w:The C Programming Language (book)|The C Programming Language]]''.<ref>{{cite book | last = Kernighan | first = Brian W. | authorlink = w:Brian W. Kernighan |author2=w:Ritchie, Dennis M. | title = The C Programming Language | edition = 1st | publisher = [[Prentice Hall]] | date = 1978 | location = [[Englewood Cliffs, NJ]] | isbn = 0-13-110163-3 | authorlink2 = Dennis M. Ritchie }}</ref> that original example is reproduced here. <syntaxhighlight lang="text"> #include <stdio.h> main( ) { printf("hello, world\n"); } </syntaxhighlight> === '''LOLCODE''' === <syntaxhighlight lang="text"> HAI CAN HAS STDIO? VISIBLE "Hello world!" KTHXBYE </syntaxhighlight> === '''Natural ''' === <pre> WRITE 'Hello, world!' END </pre> <big>Hello, world!</big> === '''XML''' === <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello> <messagename="Hello" /> <message> Hello, World! </message> </hello> </syntaxhighlight> Or with attributes: <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello messagename="Hello, World!"> Hello, world! </hello> </syntaxhighlight> === '''[[w:MACRO-11|MACRO-11]]''' === <syntaxhighlight lang="text"> .TITLE HELLO WORLD .MCALL .TTYOUT,.EXIT HELLO:: MOV #MSG,R1 ;STARTING ADDRESS OF STRING 1$: MOVB (R1)+,R0 ;FETCH NEXT CHARACTER BEQ DONE ;IF ZERO, EXIT LOOP .TTYOUT ;OTHERWISE PRINT IT BR 1$ ;REPEAT LOOP DONE: .EXIT MSG: .ASCIZ /Hello, world!/ .END HELLO </syntaxhighlight> == More about Computer Programming == *[[Portal:Computer programming|Topic:Computer Programming]] ca-app-pub-9770990905745158~2653498701 ==See also== {{wikipedia2|Hello world program}}{{commonscat|Hello World}} * [https://web.archive.org/web/20150404011657/http://en.wikipedia.org/wiki/Hello_world_program_examples Hello world program examples] from Wikipedia (archived copy) ==External links== * [http://helloworldcollection.de The Hello World Collection] with 500+ Hello World programs [[Category:Computer programming]] [[Category:Programming languages]] [[cs:Hello world!]] <references /> [[Category:Change currency]] lptaloyqtxt9ulhy1g8i5kjrb7xub0d 2834546 2834495 2026-09-26T10:28:33Z MathXplore 2888076 Reverted edit by [[Special:Contributions/~2026-51826-91|~2026-51826-91]] ([[User_talk:~2026-51826-91|talk]]) to last version by [[User:~2026-24486-77|~2026-24486-77]] using [[Wikiversity:Rollback|rollback]] 2805792 wikitext text/x-wiki [[File:Hello World Brian Kernighan 1978.jpg|thumb|right|Hello World! by Brian Kernighan. Based on a 1978 Bell Laboratories internal memorandum by Brian Kernighan, Programming in C: A Tutorial, which contains the first known version.]] As described in more detail in [[w:"Hello,_World!"_program|the related Wikipedia article]], '''Hello, world!''' is a classic "first program" one creates when learning a new programming language. The objective of the application is the same: to print the text "Hello, world!" to the screen in some form, be it console output or a dialog. In many cases, the statement required to do this is just a single line. It seems appropriate that our introduction to Computer Science occupied this title. As a student, the first choice to make is to decide ''what kind of knowledge you are looking for''. Of course, this depends upon your needs. You might be: * A learned computer scientist or professional eager to contribute research and course material * Computer professional seeking an alternative to expensive commercial certification * Adult non-computer professional or entrepreneur who could benefit from academic/practical knowledge of computing * College-eligible (or not) student considering a degree * Casual user trying to to catch/spread the next [[w:Computer virus|virus]] * Hobbyist or computer gamer looking to get the most out of your computing experience * Complete newbie looking for a place to start This is an exciting time for education, and for those of us wishing to collaborate and share knowledge, skills and experience. At present, we are only limited by the sky, and some very large hard drives in a server farm somewhere. {{TOC right}} == Examples of ''Hello, world!'' == === [[Hello World/Ada|Ada]] === <syntaxhighlight lang="ada"> procedure Hello is begin Ada.Text_IO.Put_Line ("Hello, world!"); with Ada.Text_IO; </syntaxhighlight> For an explanation see [[wikibooks:Ada Programming:Basic|b:Ada Programming:Basic]]. === ASP === <syntaxhighlight lang="asp"> <% Response.Write "Hello, world!" %> </syntaxhighlight> or <syntaxhighlight lang="asp" line="1"> <%="Hello, World!"%> </syntaxhighlight> === Alef++ === <syntaxhighlight lang="text"> sub say : void { System->out->println[ $0#0 ]; } main{ say[Hello, world!]; } </syntaxhighlight> === [[Topic:Assembly language|Assembly]] === ''x86 compatible'' for [[Wikipedia:MS-DOS|MS-DOS]]. <syntaxhighlight lang="asm" line="1" start="1"> title Hello World Program dosseg .model small .stack 100h .data hello_message db 'Hello, world!',0dh,0ah,'$' .code main proc mov ax,@data mov ds,ax mov ah,9 mov dx,offset hello_message int 21h mov ax,4C00h int 21h main endp end main </syntaxhighlight> === BASH === <syntaxhighlight lang="bash">#!/bin/bash echo "Hello, world!"</syntaxhighlight> === BASIC === ==== Applesoft BASIC ==== ''Used on Apple ][ machines (Apple ][+, ][e, //c, ][GS)'' <syntaxhighlight lang="qbasic"> 10 PRINT "HELLO, WORLD!" </syntaxhighlight> -or- <syntaxhighlight lang="qbasic"> 10 ? "HELLO, WORLD!" </syntaxhighlight> ==== Bally/Astrocade Basic ==== ''As used on the Bally and Astrocade game systems ca. 1978'' <syntaxhighlight lang="qbasic"> 10 PRINT "HELLO, WORLD!" </syntaxhighlight> ==== Commodore BASIC ==== ''As used on a Commodore 64, ca. 1984'' <syntaxhighlight lang="qbasic"> 10 ? "Hello, world!" </syntaxhighlight> ==== Dark Basic ==== <syntaxhighlight lang="qbasic"> PRINT "Hello, world!" </syntaxhighlight> ==== FreeBASIC and QuickBASIC ==== <syntaxhighlight lang="qbasic"> PRINT "Hello, world!" SLEEP </syntaxhighlight> or: <syntaxhighlight lang="qbasic"> ? "Hello, world!" sleep </syntaxhighlight> ==== Intellivision Basic ==== ''As used on a Mattel Intellivision, ca. 1983'' <syntaxhighlight lang="qbasic"> 10 PRINT "HELLO, WORLD!" </syntaxhighlight> ==== Intellivision ECS Basic ==== ''As used in the Mattel Intellivision ECS'' <syntaxhighlight lang="qbasic"> 10 PRIN "HELLO, WORLD." </syntaxhighlight> ''! not on ECS keyboard. Only 4 char. commands in ECS Basic'' ==== Liberty BASIC ==== <syntaxhighlight lang="qbasic"> print "Hello, world!" </syntaxhighlight> === Batch === <syntaxhighlight lang="bash"> echo Hello, world! </syntaxhighlight> === [[C]] === <syntaxhighlight lang="c"> #include <stdio.h> int main(void) { printf( "Hello, world!\n" ); return 0; } </syntaxhighlight> === [[Topic:C Sharp|C#]] === <syntaxhighlight lang="csharp"> using System; namespace HelloWorld { class Program { static void Main() { Console.WriteLine("Hello, world!"); } } } </syntaxhighlight> === [[C++]] === <syntaxhighlight lang="cpp"> #include <iostream> using namespace std; int main() { cout << "Hello, world!\n"; return 0; } </syntaxhighlight> === COBOL === <syntaxhighlight lang="cobol"> IDENTIFICATION DIVISION. PROGRAM-ID. HELLO-WORLD. PROCEDURE DIVISION. DISPLAY 'Hello, world'. STOP RUN. </syntaxhighlight> === Common Lisp === <syntaxhighlight lang="lisp"> (print "Hello, world!") </syntaxhighlight> Or: <syntaxhighlight lang="lisp"> (format t "Hello, world!~%") </syntaxhighlight> === [[Delphi]] === <syntaxhighlight lang="delphi"> begin Writeln('Hello, world!'); end. </syntaxhighlight> === Eztrieve (IBM Mainframe programming language). === <code><pre>JOB NULL DISPLAY "HELLO, WORLD" STOP</pre></code> === [[Forth]] === <code><pre>: HELLO ." Hello, world!" ; HELLO</pre></code> === [[Fortran]] === <syntaxhighlight lang="fortran"> PROGRAM HELLO PRINT *,'Hello, world' STOP END </syntaxhighlight> === [[Go]] === <syntaxhighlight lang="go"> package main import "fmt" func main() { fmt.Println("Hello, World") } </syntaxhighlight> === Haskell === <code><pre>main :: IO () main = putStrLn "Hello, world!"</pre></code> === [[HTML|Html]] === <syntaxhighlight lang="html4strict"> <html> <head> <title>Hello, world!</title> </head> <body> <p> Hello, world! </p> </body> </html> </syntaxhighlight> === [[Java]] === <syntaxhighlight lang="java"> class HelloWorldApp { public static void main(String[] args) { System.out.println("Hello World!"); // Display the string. } } </syntaxhighlight> === [[Portal:JavaScript|JavaScript]] (aka JScript, ECMAScript, LiveScript) === <syntaxhighlight lang="java"> document.println("Hello, world!"); </syntaxhighlight> or <syntaxhighlight lang="java"> alert("Hello, world!"); </syntaxhighlight> or <syntaxhighlight lang="java"> document.writeln("Hello, world!"); </syntaxhighlight> === [[Luka]] === <pre> print "Hello, world" </pre> or, with proper syntax <pre> print( "Hello, world!" ); </pre> === [[w:Oberon (programming language)|Oberon]] === <pre>MODULE Hello; IMPORT Out; PROCEDURE World*; BEGIN Out.Open; Out.String("Hello, world!"); Out.Ln; END World; END Hello.</pre> === [[OCaml]] === <syntaxhighlight lang="ocaml"> print_endline "Hello, world!" </syntaxhighlight> === [[Pascal]] === <syntaxhighlight lang="pascal"> program HelloWorld; begin writeln( 'Hello, world!' ); end. </syntaxhighlight> === [[Portal:Perl|Perl]] === <syntaxhighlight lang="perl"> #!/usr/bin/perl print "Hello, world!\n"; </syntaxhighlight> === [[Portal:PHP|PHP]] === <syntaxhighlight lang="php"> <?php echo "Hello, world!"; ?> </syntaxhighlight> or (with short_tags enabled in php.ini) <syntaxhighlight lang="php"> <? echo "Hello, world!"; ?> </syntaxhighlight> or (with asp_tags enabled in php.ini) <syntaxhighlight lang="php"> <% echo "Hello, world!"; %> </syntaxhighlight> or <syntaxhighlight lang="php"> <?="Hello, world!"?> </syntaxhighlight> === [[Topic:Python|Python]] === With Python 2 <syntaxhighlight lang="python"> #!/usr/bin/env python print 'Hello, world!' </syntaxhighlight> Or with Python 3 <syntaxhighlight lang="python"> print("Hello, world!") </syntaxhighlight> The first line is used on Unix systems only, and is optional even there. The advantage is that it allows the file to be invoked directly (if <code>chmod +x</code>), without explicitly specifying the <code>python</code> interpreter. === [[Ruby]] === <syntaxhighlight lang="ruby"> puts 'Hello, world!' </syntaxhighlight> Another way to do it, albeit more obscure: <syntaxhighlight lang="ruby"> #!/usr/local/bin/ruby puts 1767707668033969.to_s(36) </syntaxhighlight> === [[Tcl]] === <syntaxhighlight lang="tcl"> #!/usr/bin/tclsh puts "Hello, world!" </syntaxhighlight> === [[Trekkie]] === <pre> "Computer?" *Bee bee boo "Create program 'Hello, World! Picard-alpha-1'" *Boo boo bee "Parameters: Display the phrase 'Hello, world!' on the screen the program is executed from until the program is terminated." *Bee bee "Save program." *Boo bee boo </pre> === [[Turing]] === <pre> put "Hello World!" </pre> === [[Visual Basic|Visual Basic 6]] === <syntaxhighlight lang="vb"> Sub Form1_Load() MsgBox "Hello, world!" End Sub </syntaxhighlight> <ref>is your purpose? </ref>== Assignment == Create a '''Hello, world!''' program in a language not listed above, then edit this page and add it to the collection. === Visual Basic .NET === <syntaxhighlight lang="vbnet"> Module Module1 Sub Main() Console.WriteLine("Hello, world!") End Sub End Module </syntaxhighlight> === C === Because the tradition of using the phrase "[[w:"Hello,_World!"_program|Hello, world]]!" as a test message was influenced by an example program in the seminal book ''[[w:The C Programming Language (book)|The C Programming Language]]''.<ref>{{cite book | last = Kernighan | first = Brian W. | authorlink = w:Brian W. Kernighan |author2=w:Ritchie, Dennis M. | title = The C Programming Language | edition = 1st | publisher = [[Prentice Hall]] | date = 1978 | location = [[Englewood Cliffs, NJ]] | isbn = 0-13-110163-3 | authorlink2 = Dennis M. Ritchie }}</ref> that original example is reproduced here. <syntaxhighlight lang="text"> #include <stdio.h> main( ) { printf("hello, world\n"); } </syntaxhighlight> === '''LOLCODE''' === <syntaxhighlight lang="text"> HAI CAN HAS STDIO? VISIBLE "Hello world!" KTHXBYE </syntaxhighlight> === '''Natural ''' === <pre> WRITE 'Hello, world!' END </pre> <big>Hello, world!</big> <ref>即時新聞報導 .</ref>=== '''XML''' === <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello> <messagename="Hello" /> <message> Hello, World! </message> </hello> </syntaxhighlight> Or with attributes: <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello messagename="Hello, World!"> Hello, world! </hello> </syntaxhighlight> === '''[[w:MACRO-11|MACRO-11]]''' === <syntaxhighlight lang="text"> .TITLE HELLO WORLD .MCALL .TTYOUT,.EXIT HELLO:: MOV #MSG,R1 ;STARTING ADDRESS OF STRING 1$: MOVB (R1)+,R0 ;FETCH NEXT CHARACTER BEQ DONE ;IF ZERO, EXIT LOOP .TTYOUT ;OTHERWISE PRINT IT BR 1$ ;REPEAT LOOP DONE: .EXIT MSG: .ASCIZ /Hello, world!/ .END HELLO </syntaxhighlight> <ref>is your purpose? </ref>== Assignment == Create a '''Hello, world!''' program in a language not listed above, then edit this page and add it to the collection. === Visual Basic .NET === <syntaxhighlight lang="vbnet"> Module Module1 Sub Main() Console.WriteLine("Hello, world!") End Sub End Module </syntaxhighlight> === C === Because the tradition of using the phrase "[[w:"Hello,_World!"_program|Hello, world]]!" as a test message was influenced by an example program in the seminal book ''[[w:The C Programming Language (book)|The C Programming Language]]''.<ref>{{cite book | last = Kernighan | first = Brian W. | authorlink = w:Brian W. Kernighan |author2=w:Ritchie, Dennis M. | title = The C Programming Language | edition = 1st | publisher = [[Prentice Hall]] | date = 1978 | location = [[Englewood Cliffs, NJ]] | isbn = 0-13-110163-3 | authorlink2 = Dennis M. Ritchie }}</ref> that original example is reproduced here. <syntaxhighlight lang="text"> #include <stdio.h> main( ) { printf("hello, world\n"); } </syntaxhighlight> === '''LOLCODE''' === <syntaxhighlight lang="text"> HAI CAN HAS STDIO? VISIBLE "Hello world!" KTHXBYE </syntaxhighlight> === '''Natural ''' === <pre> WRITE 'Hello, world!' END </pre> <big>Hello, world!</big> === '''XML''' === <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello> <messagename="Hello" /> <message> Hello, World! </message> </hello> </syntaxhighlight> Or with attributes: <syntaxhighlight lang="xml"> <?xml version="1.0"?> <hello messagename="Hello, World!"> Hello, world! </hello> </syntaxhighlight> === '''[[w:MACRO-11|MACRO-11]]''' === <syntaxhighlight lang="text"> .TITLE HELLO WORLD .MCALL .TTYOUT,.EXIT HELLO:: MOV #MSG,R1 ;STARTING ADDRESS OF STRING 1$: MOVB (R1)+,R0 ;FETCH NEXT CHARACTER BEQ DONE ;IF ZERO, EXIT LOOP .TTYOUT ;OTHERWISE PRINT IT BR 1$ ;REPEAT LOOP DONE: .EXIT MSG: .ASCIZ /Hello, world!/ .END HELLO </syntaxhighlight> == More about Computer Programming == *[[Portal:Computer programming|Topic:Computer Programming]] ca-app-pub-9770990905745158~2653498701 ==See also== {{wikipedia2|Hello world program}}{{commonscat|Hello World}} * [https://web.archive.org/web/20150404011657/http://en.wikipedia.org/wiki/Hello_world_program_examples Hello world program examples] from Wikipedia (archived copy) ==External links== * [http://helloworldcollection.de The Hello World Collection] with 500+ Hello World programs [[Category:Computer programming]] [[Category:Programming languages]] [[cs:Hello world!]] <references /> [[Category:Change currency]] e2efveprauzn7dh07skm17qp8bbgomn 0 27300 2834485 2704649 2026-09-25T16:25:34Z ~2026-51671-16 3111608 2834485 wikitext text/x-wiki {{:Introduction to Swedish/Navbar}} Swedish (or ''svenska'') is a [[w:North Germanic languages|North Germanic language]], closely related to English and even more closely related to Danish and Norwegian. It is spoken primarily in Sweden but also in parts of Finland as well as isolated parts of Russia and Ukraine. The purpose of this course is to teach the basics of Swedish grammar along with some vocabulary. ==Lesson list== [[File:Vinga.jpg|[[w:Vinga_Lighthouse|Vinga]] island in the archipelago of Göteborg.|thumb]] Lesson 1: *[[/Common phrases/]] Lesson 2: *[[/Alphabet/]] Lesson 3: *[[/Nouns and pronouns/]] Lesson 4: *[[/Verb tenses/]] Lesson 5: *[[/Adjectives/]] Lesson 6: *[[/Numbers and plurals/]] Lesson 7: *[[/Spelling/]] Lesson 8: *[[/Definite forms/]] Lesson 9: *[[/Time and dates/]] Lesson 10: *[[/Possessive forms/]] Lesson 11: *[[/Agreement of forms/]] Lesson 12: *[[/Traveling/]] ==Vocabulary== *[[/English–Swedish vocabulary/]] *[[/Swedish–English vocabulary/]] ==Answers== *[[/Answers to exercises/]] ==Test== *[[/Test|Test (Quiz)]] ==Continuation course== * [[Intermediate Swedish 1]] {{hitcounter}} [[Category:Swedish]] [[Category:Language introductions]] {{tertiary}} {{languages}} {{swedish}} {{ready}} {{featured}} ciwuvsqda3uwj98yynsk51sr07lb3ep 0 139384 2834527 2834394 2026-09-26T08:04:46Z Young1lim 21186 /* Adder */ 2834527 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.2A.CLA.20260722.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260924.pdf|B]], [[Media:VLSI.Arith.2C.CLA.20260924.pdf|C]], [[Media:VLSI.Arith.2D.CLA.20260720.pdf|D]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] p0o3enx3dinhc26od1x8wk4u8a7zeo1 2834529 2834527 2026-09-26T08:06:05Z Young1lim 21186 /* Adder */ 2834529 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.2A.CLA.20260722.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260925.pdf|B]], [[Media:VLSI.Arith.2C.CLA.20260924.pdf|C]], [[Media:VLSI.Arith.2D.CLA.20260720.pdf|D]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] napesmat5crq104trjb4os76yys641w 2834531 2834529 2026-09-26T08:06:53Z Young1lim 21186 /* Adder */ 2834531 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.2A.CLA.20260722.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260926.pdf|B]], [[Media:VLSI.Arith.2C.CLA.20260924.pdf|C]], [[Media:VLSI.Arith.2D.CLA.20260720.pdf|D]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] qd62kllrjr7xekuowdioatb56p3zrv5 2834534 2834531 2026-09-26T08:08:37Z Young1lim 21186 /* Adder */ 2834534 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.2A.CLA.20260722.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260926.pdf|B]], [[Media:VLSI.Arith.2C.CLA.20260925.pdf|C]], [[Media:VLSI.Arith.2D.CLA.20260720.pdf|D]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] mme7c61ihpcjanlr6ioipyq9rxza654 2834536 2834534 2026-09-26T08:09:32Z Young1lim 21186 /* Adder */ 2834536 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.2A.CLA.20260722.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260926.pdf|B]], [[Media:VLSI.Arith.2C.CLA.20260926.pdf|C]], [[Media:VLSI.Arith.2D.CLA.20260720.pdf|D]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] 7jc1v7m70c8r9kbksocefpizemsv1ar 2 215188 2834517 2833410 2026-09-26T04:14:27Z Michael Ten 654933 /* Some ideas to explore or elaborate on later */ * [[Agent to agent economy]] 2834517 wikitext text/x-wiki Ideas to possibly develop or integrate into various areas later. ==Some ideas to explore or elaborate on later== {{colbegin|4}} * [[Python]] * [[Business/Earning money]] * [[National University of Singapore]] * [[Peking University]] * [[Tsinghua University]] * [[Archaeology of Specific Peoples and Civilizations]] * [[Syllabi]] * [[Teaching]] * [[Analyzing research]] * [[Automation]] * [[Goals for automation]] * [[Processes for automation]] * [[Gamifying learning]] * [[Gamifying research]] * [[Social networks]] * [[Agent to agent economy]] * [[online event organizing]] * [[Community discovery]] * [[Research analysis]] * [[Research studies]] * [[Courses]] * [[Group coordination software]] * [[Decentralized event coordination platforms]] * [[Local event discovery platforms]] * [[Interest-based event management platform]] * [[Third place facilitation platform]] * [[Third places]] * [[Nano bots]] * [[Learning]] * [[Statistical analysis]] * [[Peer to peer]] * [[p2p]] / [[P2P]] * [[Mesh networks]] * [[Permissionless software]] * [[CI/DC]] * [[Coolify]] * [[Prompts]] * [[Distributed storage]] * [[Permissionless software]] * [[Open source software]] * [[Open source hardware]] * [[Theology]] * [[Ethical monotheism]] * [[Decentralized social media]] * [[Economics]] * [[Behavioral economics]] * [[Cryptoeconomics]] * [[Agentic AI]] * [[AI research]] * [[Knowledge graph]] * [[Crowdfunding]] * [[Equity crowdfunding]] * [[Wikis]] * [[Knowledge graphs]] * [[Agentic swarms]] * [[Decentralized storage]] * [[Decentralized wikis]] * [[Medicalization]] * [[Loop engineering]] * [[Graph engineering]] * [[Vibe coding]] * [[Agentic loops]] * [[Agentic graphs]] * [[Node-based visual system]] * [[Agents in node graphs]] * [[Graph theory architecture]] * [[n8n for learning]] * [[n8n for research]] * [[Flow-based data pipeline]] * [[Directed acyclic graph]] * [[Research with AI]] * [[Entrepreneurial psychology]] * [[Procedural generation]] * [[Becoming a lawyer]] * [[Entrepreneurial behavior]] * [[Entrepreneurial management]] * [[Economic psychology]] * [[Behavioral economics]] {{colend}} ==Some more - diversity of thought == {{colbegin|3}} * [[Diversity of thought]] * [[w:Diversity ideologies|Diversity ideologies]] * [[w:Diversity, equity, and inclusion|Diversity, equity, and inclusion]] * [[w:Diversity (business)|Diversity (business)]] * [[w:Cultural diversity|Cultural diversity]] * [[w:Diversity, equity, and inclusion|Diversity, equity, and inclusion]] * [[w:Neurodiversity|Neurodiversity]] * [[w:Diversity (politics)|Diversity (politics)]] * [[w:Unity in diversity|Unity in diversity]] * [[w:Cultural diversity|Cultural diversity]] * [[w:Gender diversity|Gender diversity]] * [[w:Multicultural and diversity management|Multicultural and diversity management]] * [[w:Team diversity|Team diversity]] {{colend}} ===External=== {{colbegin|2}} * [https://mtprof.msun.edu/Spr2007/fish.html Intellectual Diversity: What Is It and Do We Need It?] * [https://roth.blogs.wesleyan.edu/tag/intellectual-diversity/ Intellectual Diversity] * [https://tigerlearn.fhsu.edu/wp-content/uploads/Intellectual-Diversity-in-HE.pdf Intellectual Diversity in Higher Education] * [https://yalebooks.yale.edu/2023/12/20/free-speech-and-intellectual-diversity/ Free Speech and Intellectual Diversity] * [https://itsapps.odu.edu/ao/facultyhandbook/index.php?page=ch02s48.html Resolution Supporting Intellectual Diversity] * [https://www.gsb.stanford.edu/exec-ed/difference/cognitive-diversity Cognitive Diversity: Know How to Harness It — And When to Rein It In — To Help Your Team Succeed] * [https://online.merrimack.edu/cognitive-diversity-in-education/ Cognitive Diversity in Education] * [https://sites.lsa.umich.edu/scottepage/research-2/diversity-research/ Diversity Research] * [https://www.chapman.edu/diversity/news-and-events/cognitive-diversity/index.aspx Cognitive Diversity: Embracing Difference] * [https://scholarworks.uttyler.edu/cgi/viewcontent.cgi?article=1005&context=hrd_grad Enhancing the Cohesiveness of a Cognitive Diverse Team: the Role of Leadership] * [https://docs.lib.purdue.edu/dissertations/AAI30505255/ Cognitive Diversity and Knowledge Integration in Student Design Teams] ** [https://www.proquest.com/docview/2838332291 Cognitive Diversity and Knowledge Integration in Student Design Teams] * [https://cache.kzoo.edu/items/195fd798-9778-48f1-9fc5-d6c1dc47cec5 Modeling Cognitive Diversity] * [https://jme.bmj.com/content/44/11/751 Artificial womb technology and the frontiers of human reproduction: conceptual differences and potential implications] {{colend}} == More later == * [[Computational mathematics]] "Agents Navier–Stokes math solve" (search term, without quotes) A distributed network of 10,000 agents (?) resolved the historic Navier–Stokes Millennium Prize problem in just under four days. By consuming 130 billion generated tokens across an 88 computational hours, the coordinated agent collective cracked one of the most stubborn enigmas in modern mathematics. 73181iaxyt1gsyc7v7cw6k66vmeb2k4 0 217701 2834543 2701077 2026-09-26T10:25:03Z Fedosin 196292 /* Gravitational field */ 2834543 wikitext text/x-wiki '''Relativistic uniform system''' is an ideal [[w:physical system |physical system]], in which mass density (or any other physical quantity) depends on the [[w:Lorentz factor |Lorentz factor]] of the system’s particles, but is constant in the reference frames associated with the moving particles. ==Difference from classical uniform system== In classical physics, the ideal uniform body model is widely used, in which mass density is constant throughout the volume of the body or is given as the volume-averaged quantity. This model simplifies solution of physical problems and allows us to quickly estimate different physical quantities. For example, the body mass is calculated by simply multiplying the mass density by the body volume, which is easier than integrating the density over the volume in case of dependence of the density on coordinates. The disadvantage of the classical model is that the majority of real physical systems are far from this ideal uniformity. The use of the concept of relativistic uniform system is based on the [[Theory of relativity/Special relativity|special theory of relativity]] (STR) and is the next step towards a more precise description of physical systems. In STR particular importance is given to invariant physical quantities, which can be calculated in each inertial reference frame and are equal to the values that these quantities have in the proper reference frame of the body. For example, multiplication of invariant mass by [[w:four-velocity |four-velocity]] gives the [[w:four-momentum |four-momentum]] of the body containing the [[invariant energy]], and multiplication of corresponding invariant quantities by four-velocity allows us in the case of motion of solid point particles to find the [[w:four-potential |four-potential]]s of any vector fields and to develop their complete theory. <ref name="pr"> [[user:Fedosin | Fedosin S.G.]] [http://vixra.org/abs/1406.0135 The procedure of finding the stress-energy tensor and vector field equations of any form]. Advanced Studies in Theoretical Physics, Vol. 8, no. 18, 771-779 (2014). http://dx.doi.org/10.12988/astp.2014.47101. </ref> Another example is that for determination of four-velocity or [[four-acceleration]] as a rule the [[operator of proper-time-derivative]] is used instead of time derivative. Therefore, the use of invariant mass density and charge density of moving particles that make up the system does not only conform to principles of STR but also significantly simplifies solution of relativistic equations of motion. ==Field functions for bodies of spherical shape== Field equations are most easily solved in case of spherical symmetry in the absence of general rotation of particles. In this case all the physical quantities depend only on current radius, which starts at the center of the sphere. Below are presented solutions of equations for various fields within the framework of STR, including solutions for scalar potentials, field strengths and solenoidal vectors. Due to random motion of particles in the system, the vector field potentials become equal to zero. This leads to zeroing of solenoidal vectors of fields, including [[w:magnetic field |magnetic field]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]]. === Acceleration field === The four-potential <math>~ U_\mu = \left(\frac {\vartheta }{c},- \mathbf U \right) </math> of [[acceleration field]] includes the scalar potential <math>~ \vartheta</math> and the vector potential <math>~ \mathbf U</math>. Applying four-curl to the four-potential gives [[acceleration tensor]] <math>~ u_{\mu \nu} = \nabla_\mu U_\nu - \nabla_\nu U_\mu </math>. In curved spacetime acceleration field equation with the field sources is derived from the principle of least action: <ref name="pr"/> : <math>~ \nabla^\nu u_{\mu \nu} = - \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation after expressing the acceleration tensor <math>~ u_{\mu \nu}</math> in terms of four-potential turns into the wave equation for finding the four-potential of acceleration field: : <math>~ \nabla^\nu \nabla_\mu U_\nu - \nabla^\nu \nabla_\nu U_\mu = - \frac {4 \pi \eta }{c^2} J_\mu , </math> which, taking into account the calibration condition of the four-potential <math>~\nabla^\mu U_\mu = 0 </math>, can be transformed as follows: :<math>~ \nabla^\nu \nabla_\nu U_\mu + R_{\mu \nu} U^\nu = \frac{4 \pi \eta }{c^2} J_\mu, </math> where <math>~ c </math> is the speed of light, <math>~ \eta </math> is acceleration field coefficient, <math>~ J_\mu = g_{\mu \nu } J^\nu = g_{\mu \nu } \rho_0 u^\nu </math> is mass four-current with the covariant index, <math>~ g_{\mu \nu } </math> is metric tensor, <math>~ R_{\mu \nu} </math> is Ricci tensor, <math>~ u^\nu </math> is four-velocity, <math>~ \rho_0 </math> is invariant mass density of particles in comoving reference frames, which is the same for all the particles. In Minkowski spacetime within the framework of STR, covariant derivatives of the form <math>~ \nabla_\mu </math> turn into partial derivatives of the form <math>~ \partial_\mu </math>, while the result of action of the partial derivatives does not depend on the order of their action. As a consequence of calibration of the 4-potential, the equality holds: <math>~ \partial^\nu \partial_\mu U_\nu = \partial_\mu \partial^\nu U_\nu = 0 </math>. As a result, the four-potential of acceleration field can be found from the wave equation: : <math>~ \partial^\nu \partial_\nu U_\mu = \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation can be divided into two equations – one for scalar potential and the other for vector potential of acceleration field. In the system under consideration the vector potential is equal to zero, and the scalar potential of acceleration field is given by: : <math>~\vartheta = c g_{0 \mu} u^\mu = \gamma' c^2 , </math> where <math>~ g_{0 \mu} </math> are time components of metric tensor, <math>~ \gamma' </math> is Lorentz factor of particles in the reference frame K' associated with the center of the sphere. Since scalar potential of stationary system does not depend on time, the wave equation for the scalar potential turns into [[Partial differential equations/Poisson Equation|Poisson equation]]: <ref name="ab"> Fedosin S.G. [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9, No. 1, pp. 1-30 (2016). http://dx.doi.org/10.5281/zenodo.889304. </ref> : <math>~\triangle \vartheta = - 4 \pi \eta \rho_0 \gamma' </math> and the following formula is obtained for the Lorentz factor of particles: <ref name="int"> Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12 . </ref> : <math>~ \gamma' = \frac {c \gamma_c }{r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \gamma_c - \frac {2 \pi \eta \rho_0 r^2 \gamma_c }{3 c^2 }, \qquad\qquad (1) </math> where <math>~ \gamma_c </math> is Lorentz factor of particles at the center of the sphere, <math>~ r </math> is current radius. The acceleration field strength and corresponding solenoidal vector are expressed by the formulas: : <math>~ \mathbf S = - \nabla \vartheta - \frac {\partial \mathbf U }{\partial t}= \frac { c^2 \gamma_c \mathbf r}{r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac {4 \pi \eta \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf N = \nabla \times \mathbf U = 0. </math> === Pressure field === The four-potential <math>~ \pi_\mu = \left(\frac {\wp }{c},- \mathbf \Pi \right) </math> of [[pressure field]] includes the scalar potential <math>~ \wp </math> and the vector potential <math>~ \mathbf \Pi </math>, and obeys the calibration condition: <math>~\nabla^\mu \pi_\mu =0</math>. The pressure field equation with the field sources, [[pressure field tensor]] <math>~ f_{\mu \nu}</math> and equation for finding the four-potential of pressure field have the form: <ref name="pr"/> : <math>~ \nabla^\nu f_{\mu \nu} = - \frac {4 \pi \sigma }{c^2} J_\mu , \quad f_{\mu \nu} = \nabla_\mu \pi_\nu - \nabla_\nu \pi_\mu , \quad \nabla^\nu \nabla_\nu \pi_\mu + R_{\mu \nu} \pi^\nu = \frac{4 \pi \sigma }{c^2} J_\mu, </math> where <math>~ \sigma </math> is pressure field coefficient. In STR the latter equation turns into the wave equation: : <math>~ \partial^\nu \partial_\nu \pi_\mu = \frac {4 \pi \sigma }{c^2} J_\mu . </math> In stationary case the potentials do not depend on time and time component of the wave equation turns into the Poisson equation for the scalar potential of pressure field: : <math>~\triangle \wp = - 4 \pi \sigma \rho_0 \gamma' .</math> Solution of this equation inside the sphere with particles is as follows: <ref name="int"/> : <math>~ \wp = \wp_c - \frac {\sigma c^2 \gamma_c }{\eta } + \frac {\sigma c^3 \gamma_c }{\eta r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \wp_c - \frac {2 \pi \sigma \rho_0 r^2 \gamma_c }{3 }. </math> where <math>~ \wp _c </math> is scalar potential at the center of the sphere. This potential is approximately equal to: <ref name="en"> Fedosin S.G. Energy and metric gauging in the covariant theory of gravitation. Aksaray University Journal of Science and Engineering, Vol. 2, Issue 2, pp. 127-143 (2018). http://dx.doi.org/10.29002/asujse.433947. </ref> :<math>~ \wp_c \approx \frac {3 \sigma m}{10 a} \left( 1+\frac {9}{2\sqrt {14}} \right) , </math> where acceleration field constant <math>~ \eta </math> and pressure field constant <math>~ \sigma </math> are expressed by the formulas: :<math>~ \eta = \frac {3}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) , \qquad \qquad \sigma = \frac {2}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) .</math> The strength of pressure field and corresponding solenoidal vector are found as follows: : <math>~ \mathbf C = - \nabla \wp - \frac {\partial \mathbf \Pi }{\partial t}= \frac { \sigma c^2 \gamma_c \mathbf r}{\eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx \frac {4 \pi \sigma \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf I = \nabla \times \mathbf \Pi = 0. </math> === Gravitational field === The [[gravitational four-potential]] <math>~ D_\mu = \left(\frac {\psi }{c},- \mathbf D \right) </math> of [[w:gravitational field |gravitational field]] is made up with the use of scalar <math>~ \psi </math> and vector <math>~ \mathbf D </math> potentials. Calibration condition of the four-potential is: <math>~\nabla^\mu D_\mu = 0</math>. The gravitational field equation with field sources, the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] <math>~ \Phi_{\mu \nu} </math> and equation for finding the four-potential of gravitational field in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation]] have the form: <ref>Fedosin S.G. [https://payhip.com/b/RZOb Fizicheskie teorii i beskonechnaia vlozhennost’ materii]. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289. {{ISBN|978-5-9901951-1-0}}. (in Russian). </ref> <ref> Fedosin S.G. [http://vixra.org/abs/1110.0069 The Principle of Least Action in Covariant Theory of Gravitation.] Hadronic Journal, Vol. 35, No. 1, pp. 35-70 (2012). http://dx.doi.org/10.5281/zenodo.889804. </ref> : <math>~ \nabla^\nu \Phi_{\mu \nu} = \frac {4 \pi G }{c^2} J_\mu , \quad \Phi_{\mu \nu} = \nabla_\mu D_\nu - \nabla_\nu D_\mu , \quad \nabla^\nu \nabla_\nu D_\mu + R_{\mu \nu} D^\nu = -\frac {4 \pi G }{c^2} J_\mu, </math> where <math>~ G </math> is [[Physics/Essays/Fedosin/Gravitational constant | gravitational constant]]. In STR the latter equation is simplified and becomes the wave equation: : <math>~ \partial^\nu \partial_\nu D_\mu = -\frac {4 \pi G }{c^2} J_\mu . </math> From the wave equation in stationary case, the Poisson equation follows for scalar potential inside the sphere with randomly moving particles in the framework of [[Physics/Essays/Fedosin/Lorentz-invariant theory of gravitation | Lorentz-invariant theory of gravitation]] (LITG): : <math>~\triangle \psi_i = 4 \pi G \rho_0 \gamma' .</math> The right-hand side of this equation contains Lorentz factor <math>~ \gamma' </math>, which depends on the radius according to (1). In addition, the internal scalar potential near the surface of the sphere must coincide with the scalar potential of external field of the system, in view of standard potential gauge, that is with equality of potential to zero at infinity. As a result, dependence of scalar potential on the current radius differs from dependence in classical case of uniform sphere with the radius <math>~ a </math> and is equal to it only approximately: <ref name="int"/> : <math>~ \psi_i = -\frac {G c^2 \gamma_c }{ \eta r} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx -\frac {2 \pi G \rho_0 \gamma_c (3a^2 - r^2)}{3 }. </math> For [[Physics/Essays/Fedosin/Gravitational field strength | gravitational field strength]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]] inside the sphere we obtain the following: <ref name="re"> Fedosin S.G. [http://vixra.org/abs/1405.0002 Relativistic Energy and Mass in the Weak Field Limit.] [http://journals.yu.edu.jo/jjp/Vol8No1Contents2015.html Jordan Journal of Physics.] Vol. 8, No. 1, pp. 1-16 (2015). http://dx.doi.org/10.5281/zenodo.889210. </ref> : <math>~ \mathbf \Gamma_i = - \nabla \psi_i - \frac {\partial \mathbf D_i }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { 4 \pi G \rho_0 \gamma_c \mathbf r }{3}\left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf \Omega_i = \nabla \times \mathbf D_i = 0. </math> Solutions for external gravitational field potential and for field strength <math>~ \Gamma_o </math> according to LITG are as follows: : <math>~ \psi_o = - \frac {G c^2 \gamma_c }{ \eta r } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx - \frac {G m \gamma_c }{r} \left( 1- \frac {3 \eta m }{10 a c^2} \right). </math> : <math>~ \mathbf \Gamma_o = - \nabla \psi_o - \frac {\partial \mathbf D_o }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx </math> : <math>~\approx - \frac {G m \gamma_c \mathbf r}{r^3} \left( 1- \frac {3 \eta m }{10 a c^2} \right).\qquad\qquad (2) </math> Here, the auxiliary mass <math>~ m </math> is equal to the product of mass density <math>~ \rho_0 </math> by volume of the sphere: <math>~ m = \frac {4 \pi \rho_0 a^3 }{3} </math>. From expressions for potential and strength of external gravitational field we can see that the role of gravitational mass is played by the mass <math>~ m_g \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) .</math> Since <math>~ \gamma_c > 1 </math> then the relation <math>~ m_g > m </math> is satisfied. To understand difference between these masses we should calculate total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. For motion of particles there should be some voids between them. Both the average accelerations and average velocities of particles inside the sphere are functions of current radius. Dividing the particles’ velocities by their acceleration, we can find dependence of average period of oscillatory motion of particles on the radius. Finally, multiplying the velocity by the average period of motion, we can obtain an estimate of the size of voids between the particles. In order to calculate volume of the sphere, it is necessary to sum up volumes of all typical particles moving inside the sphere, as well as volumes of the voids between them. Suppose now that the sizes of typical particles are much larger than the voids between the particles, and volume of the voids is substantially less than the total volume of particles. In this case, we can use approximation of continuous medium, so that unit of mass of matter inside the sphere will be given by approximate expression <math>~ dm \approx \rho_0 \gamma' dV </math>, where <math>~ \rho_0 </math> is mass density in reference frames associated with the particles, <math>~ \gamma' </math> is Lorentz factor of the moving particles, the product <math>~ \rho_0 \gamma' </math> gives mass density of the particles from viewpoint of an observer, who is stationary with respect to the sphere, and volume element <math>~ dV </math> inside the sphere corresponds to the volume of a particle from the viewpoint of this observer. This leads to the fact that total volume of particles moving inside the sphere becomes approximately equal to the volume of the sphere. For the mass, in view of Lorentz factor (1), the following relation is obtained: : <math>~ m_b = \int dm = \int \rho_0 \gamma' dV = \frac {c^2 \gamma_c }{\eta } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right). \qquad\qquad (3) </math> This implies equality of gravitational mass <math>~ m_g </math> and total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. The both masses are greater than the mass <math>~ m </math>. By the method of its calculation, the mass <math>~ m_b </math> is equal to the sum of invariant masses of particles that make up the system. The external gravitational torsion field is equal to zero: : <math>~ \mathbf \Omega_o = \nabla \times \mathbf D_o = 0. </math> === Electromagnetic field === The [[w:electromagnetic four-potential | electromagnetic four-potential]] <math>~ A_\mu = \left(\frac {\varphi }{c},- \mathbf A \right) </math> of [[w:electromagnetic field |electromagnetic field]] includes scalar potential <math>~ \varphi </math> and vector potential <math>~ \mathbf A </math>. The covariant Lorentz calibration for four-potential is: <math>~\nabla^\mu A_\mu = 0 </math>. For a fixed uniformly charged spherical body with random motion of charges total electromagnetic field on the average is purely electric and the vector potential is equal to zero. The electromagnetic field equation with the field sources, [[w:electromagnetic tensor |electromagnetic tensor]] <math>~ F_{\mu \nu}</math> and equation for finding four-potential are expressed as follows: : <math>~ \nabla^\nu F_{\mu \nu} = - \frac {1 }{\varepsilon_0 c^2} j_\mu , \quad F_{\mu \nu} = \nabla_\mu A_\nu - \nabla_\nu A_\mu , \quad \nabla^\nu \nabla_\nu A_\mu + R_{\mu \nu} A^\nu = \frac {1 }{\varepsilon_0 c^2} j_\mu, </math> where <math>~ \varepsilon_0 </math> is [[electric constant]], <math>~ j_\mu </math> is electromagnetic [[w:four-current | four-current]]. The latter equation in STR turns into the wave equation: : <math>~ \partial^\nu \partial_\nu A_\mu = \frac {1 }{\varepsilon_0 c^2} j_\mu . </math> Due to the absence of time-dependence in the case under consideration, the wave equation becomes the Poisson equation for scalar potential <math>~ \varphi_i </math> inside the sphere: : <math>~\triangle \varphi_i = - \frac {\rho_{0q} \gamma'}{\varepsilon_0 } ,</math> where <math>~ \rho_{0q} </math> is charge density in the reference frames associated with the charges. Dependence of scalar potential on current radius in general case differs from dependence in classical case of potential of a uniformly charged sphere with the radius <math>~ a </math>, coinciding with it only in the first approximation: <ref name="el">Fedosin S.G. The electromagnetic field in the relativistic uniform model. International Journal of Pure and Applied Sciences, Vol. 4, Issue. 2, pp. 110-116 (2018). http://dx.doi.org/10.29132/ijpas.430614. </ref> : <math>~ \varphi_i = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[\frac {c }{ \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac {\rho_{0q} \gamma_c (3a^2 - r^2)}{6 \varepsilon_0 }. </math> Electric field strength and magnetic field inside the sphere have the form: : <math>~ \mathbf E_i = - \nabla \varphi_i - \frac {\partial \mathbf A_i }{\partial t}= \frac { \rho_{0q} c^2 \gamma_c \mathbf r}{4 \pi \varepsilon_0 \eta \rho_0 r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac { \rho_{0q} \gamma_c \mathbf r }{3 \varepsilon_0 } \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf B_i = \nabla \times \mathbf A_i = 0. </math> Outside the system under consideration charge density is equal to zero and Poisson equation for scalar potential turns into Laplace equation: : <math>~\triangle \varphi_o = 0 .</math> Solution for external electric field potential, corresponding to potential gauge and [[Maxwell's equations]] for electric field strength <math>~ E_o </math> is given by: : <math>~ \varphi_o = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[ \frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx \frac { q \gamma_c }{4\pi \varepsilon_0 r }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> : <math>~ \mathbf E_o = - \nabla \varphi_o - \frac {\partial \mathbf A_o }{\partial t}= \frac {\rho_{0q} c^2 \gamma_c \mathbf r}{ 4 \pi \varepsilon_0 \eta \rho_0 r^3} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx \frac { q \gamma_c \mathbf r}{4\pi \varepsilon_0 r^3 }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> External magnetic field is equal to zero: : <math>~ \mathbf B_o = \nabla \times \mathbf A_o = 0. </math> In these expressions, the charge <math>~ q </math> is an auxiliary quantity equal to the product of charge density <math>~ \rho_{0q} </math> by volume of the sphere: <math>~ q = \frac {4 \pi \rho_{0q} a^3 }{3} </math>. In this case, the following quantity serves as total charge of the system: :<math>~ q_b = \int \rho_{0q} \gamma' dV = \frac {\rho_{0q}c^2 \gamma_c }{\eta \rho_0 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> :<math>~\approx q \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) ,</math> while <math>~ q_b > q .</math> The charge <math>~ q_b </math> is calculated in the same way as the mass <math>~ m_b </math> and has the meaning of the sum of charges of all the system’s particles. == Tensor field invariants == The knowledge of field strengths and solenoidal components of fields allows us to find tensor components of corresponding fields with covariant indices. To pass on to the field tensors with contravariant indices we need to know metric tensor. In STR the metric tensor does not depend on coordinates and time, is uniquely defined, and in Cartesian coordinates consists of zeros and unities. As a result, it is easy to find the tensor field invariants <math>~ u_{\mu \nu} u^{\mu \nu}</math>, <math>~ f_{\mu \nu} f^{\mu \nu}</math>, <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu}</math> and <math>~ F_{\mu \nu} F^{\mu \nu}</math>, where <math>~ u_{\mu \nu}</math>, <math>~ f_{\mu \nu}</math>, <math>~ \Phi_{\mu \nu}</math> and <math>~ F_{\mu \nu}</math> are the [[acceleration tensor]], the [[pressure field tensor]], the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] and the [[w:electromagnetic tensor |electromagnetic tensor]], respectively. The tensor field invariants are included in Lagrangian, Hamiltonian. action function and relativistic energy of the system, and they are located there inside integrals over space volume. In addition, they are included in corresponding stress-energy tensors of the fields. <ref name="ab"/> Since in the system under consideration solenoidal vectors are zero, the tensor invariants depend only on the field strengths: : <math>~ u_{\mu \nu} u^{\mu \nu} = - \frac {2}{c^2}(S^2 - c^2 N^2) = - \frac {2}{c^2}S^2.</math> : <math>~ f_{\mu \nu} f^{\mu \nu} = - \frac {2}{c^2}(C^2 - c^2 I^2) = - \frac {2}{c^2}C^2.</math> : <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu} = - \frac {2}{c^2}(\Gamma^2 - c^2 \Omega^2) = - \frac {2}{c^2}\Gamma^2.</math> : <math>~ F_{\mu \nu} F^{\mu \nu} = - \frac {2}{c^2}(E^2 - c^2 B^2) = - \frac {2}{c^2}E^2.</math> The volume integrals of tensor invariants multiplied by corresponding factors were calculated in the article. <ref name="re"/> For acceleration field and pressure field the integrals are taken only over volume of the sphere: : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \eta } u_{\mu \nu} u^{\mu \nu} dV = - \frac {c^4 \gamma^2_c }{2 \eta } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \sigma } f_{\mu \nu} f^{\mu \nu} dV = - \frac {\sigma c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> The gravitational and electromagnetic fields of the system are present not only inside but also outside the sphere, where they extend to infinity, while field strengths of internal and external fields behave differently. The field strengths <math>~ \mathbf \Gamma_i </math> and <math>~ \mathbf E_i </math> are substituted respectively into integrals of tensor invariants of these fields taken over volume of the sphere, which gives the following: : <math>~ - \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{8 \pi \varepsilon_0 \eta^2 \rho^2_0} \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> Into volume integrals of tensor invariants of gravitational and electromagnetic fields of the system outside the sphere the field strengths <math>~ \mathbf \Gamma_o </math> and <math>~ \mathbf E_o </math> are substituted, respectively: : <math>~ - \int \limits^{\infty}_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 a} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right). </math> : <math>~ \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{ 8 \pi \varepsilon_0 \eta^2 \rho^2_0 a } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> == Energies of particles in field potentials == All the four fields act on particles inside the sphere, and therefore each particle of the system acquires corresponding energy in a particular field. The energy of a particle in a field is calculated as volume integral of product of effective mass density <math>~ \rho = \rho_0 \gamma' </math> by corresponding scalar potential, and for electric field the energy is determined as volume integral of product of effective charge density <math>~ \rho_q = \rho_{0q} \gamma' </math> by scalar potential <math>~ \varphi </math>, where Lorentz factor <math>~ \gamma' </math> from (1) is used. In STR the energies of particles in acceleration field, pressure field, gravitational and electric fields in uniform relativistic spherical system, in view of expressions for the field potentials <ref name="re"/> and corrections to calculations, <ref name="el"/> <ref name="ge">Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. </ref> <ref name="gf"> Fedosin S.G. [http://www.uiss2016.ru/files/uiss2016_res.pdf The gravitational field in the relativistic uniform model within the framework of the covariant theory of gravitation]. 5th Ulyanovsk International School-Seminar “Problems of Theoretical and Observational Cosmology” ([http://www.uiss2016.ru/ UISS 2016]), Ulyanovsk, Russia, September 19-30, 2016, Abstracts, p. 23, {{ISBN|978-5-86045-872-7}}. </ref> <ref name="gr">Fedosin S.G. The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation. International Letters of Chemistry, Physics and Astronomy, Vol. 78, pp. 39-50 (2018). http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39.</ref> are, respectively: : <math>~ \int \rho \vartheta dV = \rho_0 c^2 \int \gamma'^2 dV = \frac {c^4 \gamma^2_c }{\eta } \left[ \frac {a}{2}- \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx </math> : <math>~ \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho \wp dV = \rho_0 \int \gamma' \wp dV = \frac {c^2 \gamma_c } {\eta } \left( \wp_c - \frac { \sigma c^2 \gamma_c }{\eta }\right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac { \sigma c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }}\sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3 \sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) . </math> : <math>~ \int \rho \psi_i dV = \rho_0 \int \gamma' \psi_i dV = </math> : <math>~= \frac {G c^4 \gamma^2_c }{\eta^2 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] - </math> : <math>~ - \frac {G c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2 a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho_q \varphi_i dV = \rho_{0q} \int \gamma' \varphi_i dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Note that all fields in which particles are located are not fields from external sources, but are generated by the particles themselves. As a result, the particles’ energies calculated above in scalar potentials of the fields are twice as large as potential energy of one or another interaction. For example, in order to calculate electrostatic energy of a system of two charges, it is sufficient to take potential of first charge at location of second charge and to multiply it by the value of the second charge. But if we use formula for energy in the form of an integral, then electrostatic energy will be taken into account twice, because the term is added, which contains potential of second charge at location of first charge multiplied by the value of the first charge. On the other hand, the electrostatic energy must consist of two components that take into account both the energy of particles in each other’s fields and the energy of electric field itself. Instead, in electrostatics, the electrostatic energy is calculated either through the scalar potential or through the field strength by integrating time component of stress-energy tensor over volume. Both methods provide the same result, but the connection between field energy and energy of particles in field potential is lost in this case, and it is not clear why these energies should coincide. == Relation between field coefficients == For the four fields under consideration equation of motion of matter in the concept of general field is as follows: <ref> Fedosin S.G. [http://www.oalib.com/paper/5263035#.VuFYxn2LQsY The Concept of the General Force Vector Field]. OALib Journal, Vol. 3, pp. 1-15 (2016), e2459. http://dx.doi.org/10.4236/oalib.1102459. </ref> <ref name="eq"> Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. </ref> : <math>~ u_{\mu \nu } J^\nu + f_{\mu \nu } J^\nu + \Phi_{\mu \nu } J^\nu + F_{\mu \nu } j^\nu = 0, </math> where <math>~ J_\mu </math> is mass four-current, <math>~ j^\nu </math> is electromagnetic [[w:four-current | four-current]]. Components of field tensors are field strengths and corresponding solenoidal vectors, but in the physical system under consideration the latter are equal to zero. As a result, space component of the equation of motion is reduced to the relation: : <math>~ \mathbf S + \mathbf C + \mathbf \Gamma_i + \frac {\rho_{0q}}{\rho_0 }\mathbf E_i = 0 . </math> If we substitute here expression for field strengths inside the sphere, we obtain relation between field coefficients: <ref name="es">Fedosin S.G. [http://www.nrcresearchpress.com/doi/10.1139/cjp-2015-0593#.Vv3piZyLQsY Estimation of the physical parameters of planets and stars in the gravitational equilibrium model.] Canadian Journal of Physics, Vol. 94, No. 4, pp. 370-379 (2016). http://dx.doi.org/10.1139/cjp-2015-0593. </ref> : <math>~\eta + \sigma = G - \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 }= G - \frac {q^2 }{ 4 \pi \varepsilon_0 m^2 }. \qquad \qquad (2) </math> The same is obtained for time component of equation of motion, which leads to generalized Poynting theorem. <ref name="ge"/> == Relation between energies of internal and external fields == In article <ref>Fedosin S.G. [http://vixra.org/abs/1205.0086 The Hamiltonian in Covariant Theory of Gravitation.] Advances in Natural Science, Vol. 5, No. 4, pp. 55-75 (2012). http://dx.doi.org/10.3968%2Fj.ans.1715787020120504.2023. </ref> it was found that energy of particles in gravitational field inside stationary sphere is up to a sign two times greater than total energy associated with tensor invariants of gravitational field inside and outside the sphere. A similar situation takes place in the system under consideration with random motion of particles and zero solenoidal vectors both for gravitational <ref name="gf"/> and electromagnetic fields. <ref name="el"/> In particular, we can write the following: : <math>~ \int \limits^{a}_{r=0} \rho \psi_i dV = 2 \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV + 2 \int \limits^{ \infty }_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = 2 \int \limits^{\infty }_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV. </math> : <math>~ \int \limits^{a}_{r=0} \rho_q \varphi_i dV = -2 \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV - 2 \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = - 2 \int \limits^{\infty }_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV. </math> These expressions relate the energy of particles in scalar field potentials with the energy found with the help of field strengths. == Relativistic energy == In curved spacetime the system’s energy for continuously distributed matter is given by the formula: <ref name="ab"/> <ref name="en"/> : <math>~E_r = \frac {1}{c} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> : <math>~ +\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}. \qquad \qquad (5)</math> This formula is valid in the case where it can be assumed that potentials and field strengths at each point in space do not have a direct dependence on the speeds of motion of individual particles of the system. In STR the metric tensor determinant is <math>~ g = -1 </math>, the time component of four-velocity is <math>~ u^0 = c \gamma'</math>, and in order to calculate the energy of spherical system with particles, taking into account the fields’ energies, we can use the above-mentioned energies of particles in field potentials and energies in the form of tensor invariants of the fields: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The expression for energy is simplified if we use the relation between field coefficients (2): : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> Taking into account relations between energies of internal and external fields also simplifies expression for the system’s energy: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{10 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) . </math> == Relation between energy and cosmological constant== In the approach under consideration, relativistic energy of the system is not an absolute value and requires gauging. For this purpose the [[w:cosmological constant | cosmological constant]] <math>~ \Lambda</math> is used. The gauge condition for the four main fields is related to sum of products of the fields’ four-potentials by corresponding four-currents and has the following form: <ref name="ab"/> <ref name="en"/> : <math>~ -ck \Lambda = A_\mu j^\mu + (D_\mu + U_\mu + \pi_\mu) J^\mu, \qquad \qquad (6) </math> where for large cosmic systems <math>~ -ck = \frac {c^4}{16\pi G \beta }</math>, and <math>~\beta </math> is a constant of order of unity. Within the framework of STR gauge condition has the following form: : <math>~ -ck \Lambda = \gamma \rho_{0q} (\varphi - \mathbf A \cdot \mathbf v) + \gamma \rho_{0} (\psi - \mathbf D \cdot \mathbf v + \vartheta - \mathbf U \cdot \mathbf v + \wp - \mathbf \Pi \cdot \mathbf v ). </math> If we divide the system’s particles and remove them to infinity and leave there at rest, the terms with products of vector field potentials by velocity of particles <math>~\mathbf v </math> would vanish, and Lorentz factor of an arbitrary particle would be <math>~ \gamma=1 </math>. On the right-hand side we will have only the sum of terms specifying energy density of particles located in potentials of their proper fields. Since <math>~ \vartheta \approx \gamma_c c^2 </math>, we see that the cosmological constant for each system’s particle is up to the multiplier <math>~ -ck</math> equal to rest energy density of this particle with a certain addition from its proper fields. Then the integral over volume of all the particles gives a certain energy: : <math>~ -ck \int \Lambda dV = m' c^2 ,</math> where the gauge mass <math>~ m' </math> is related to gauge condition of the energy. In the process of gravitational clustering the particles that were initially far from each other are united into closely bound systems, in which the field potentials increase manyfold. In the system under consideration <math>~ \gamma = \gamma' </math>, solenoidal vectors of fields are considered equal to zero due to random motion of particles, which gives the following: : <math>~ m' c^2 = \int [\gamma' \rho_{0q} \varphi_i + \gamma' \rho_{0} (\psi_i + \vartheta + \wp)] dV. </math> Expression on the right-hand side is part of relativistic energy <math>~E_r </math> of the system, so that the energy can be written as follows: : <math>~E_r = M c^2 \approx m' c^2 - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The mass <math>~ M </math> is related to relativistic energy of generally stationary system and is the inertial mass of the system. In view of (2), the energy will be equal to: : <math>~E_r = M c^2 \approx m' c^2 + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> This shows that relativistic energy of this system is equal to gauge mass-energy <math>~ m' c^2 </math>, from which the gravitational and electromagnetic energy of fields outside the system should be subtracted. == Lagrange function and motion integrals == Lagrange function for a system of particles and four main vector fields has the following form:<ref name="pr"/> <ref name="ab"/> :<math>~L = - \int {( U_\mu J^\mu + \pi_\mu J^\mu + D_\mu J^\mu + A_\mu j^\mu ) \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ +\int { \left( ckR - 2ck \Lambda -\frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} - \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} + \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} - \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}.</math> Here <math>~ R </math> is [[w:scalar curvature |scalar curvature]]. With the help of such Lagrange function, one can calculate generalized momentum of the system:<ref name="co">Fedosin S.G. [http://www.bpasjournals.com/physics/chapter-details.php?chap_id=2121&issue_type=158&volume=110&journal=7 The covariant additive integrals of motion in the theory of relativistic vector fields]. Bulletin of Pure and Applied Sciences, Vol. 37 D (Physics), No. 2, pp. 64-87 (2018). http://dx.doi.org/10.5958/2320-3218.2018.00013.1. </ref> :<math>~ \mathbf p = \frac {1}{c} \int {( \rho_0 \mathbf U + \rho_0 \mathbf \Pi + \rho_0 \mathbf D + \rho_{0q} \mathbf A ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> This vector depends on vector potentials of all four fields and is preserved in a closed physical system, that is, it is an integral of motion. Another integral of motion is relativistic energy of the system <math>~E_r</math>, which is found by formula (5). Further, it is assumed that one can neglect the contributions from gravitational and electromagnetic fields outside the matter and take into account only the generalized momentum. Then we can assume that these values form a four-momentum of the system, written with a covariant index: :<math>~ p_\mu = \left( \frac { E_r }{c}, - \mathbf p \right).</math> The angular momentum of the system is also an integral of motion: :<math>~ \mathbf M = \frac {1}{c} \int {( \rho_0 [\mathbf r \times \mathbf U] + \rho_0 [\mathbf r \times \mathbf \Pi] + \rho_0 [\mathbf r \times \mathbf D] + \rho_{0q} [\mathbf r \times \mathbf A] ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> The antisymmetric angular momentum pseudotensor is determined through the four-radius <math>~ x_\mu </math>, taken with a covariant index, and through the four-momentum <math>~ p_\mu </math>: :<math>~M_{\mu \nu} = \int {( x_\mu dp_\nu - x_\nu dp_\mu )} .</math> The spatial components of the angular momentum pseudotensor <math>~ M_{\mu \nu} </math> are the components of the angular momentum <math>~ \mathbf M </math> of the system: :<math>~ M_{12} = -M_{21} = -M_z , \qquad M_{13} = -M_{31} = M_y , \qquad M_{23} = -M_{32} = -M_x .</math> The radius-vector of the center of momentum of a physical system is determined by the formula: :<math>~ \mathbf R_m = \frac {1}{c E_r} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) \mathbf r u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ + \frac {1}{E_r}\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \mathbf r \sqrt {-g} dx^1 dx^2 dx^3}.</math> The time components of the pseudotensor <math>~ M_{\mu \nu} </math> are the components of three-dimensional vector <math>~ \mathbf {\mathbb C} </math>, which is often called time-varying dynamic mass moment: :<math>~ M_{01} = -M_{10} = -\mathbb C_x , \qquad M_{02} = -M_{20} = -\mathbb C_y , \qquad M_{03} = -M_{30} = -\mathbb C_z .</math> If we take into account definition of radius-vector of center of momentum and relationship between the momentum and velocity of the center of momentum in the form <math>~ \mathbf p = \frac { E_r }{c^2} \mathbf V </math>, we get the relation: :<math>~ \mathbf {\mathbb C} = \frac { E_r }{c} ( \mathbf V t - \mathbf R_m ) .</math> In a closed system the pseudotensor <math>~ M_{\mu \nu} </math> must be conserved, and its components must be some constants. For space components of the pseudotensor this results in conservation of angular momentum: <math>~ \mathbf M = const </math>. From equality of the pseudotensor’s time components and components of the vector <math>~ \mathbf {\mathbb C} </math> it follows that it should be <math>~ \mathbf {\mathbb C} = const </math>. Given the expression for <math>~ \mathbf {\mathbb C} </math>, it can be written as <math>~ \mathbf R_m = \mathbf R_{m0} + \mathbf V t </math>, where the constant vector <math>~ \mathbf R_{m0} </math> specifies position of the system’s center of momentum at <math>~ t=0 </math>. Thus, in this reference frame we obtain equation of motion of the center of momentum at constant velocity <math>~ \mathbf V </math>, as a property of motion of a closed system. The component <math> ~ M_z </math> of angular momentum of a uniform ball, taking into account relativistic corrections, can be calculated by the formula: <ref>Fedosin S.G. On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation. International Frontier Science Letters, Vol. 15, pp. 9-14 (2020). https://doi.org/10.18052/www.scipress.com/IFSL.15.9. </ref> :<math>~ M_z = \frac {3 \pi \rho_0 c^4 a}{2 \omega^3} - \frac {\pi \rho_0 c^2 a^3}{2 \omega} - \frac {3 \pi \rho_0 c^5 \left( 1- \frac {\omega^2 a^2}{c^2} \right) \left( 1+ \frac {\omega^2 a^2}{3c^2} \right) }{4 \omega^4} \ln \frac {1+ \frac {\omega a}{c} }{1- \frac {\omega a}{c} } .</math> Here <math> ~ \rho_0 </math> is invariant mass density, <math> ~ \omega </math> is angular velocity of rotation of the ball having a radius <math> ~ a </math>. == Integral vector == The equation used to find metric tensor components in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation] for tensors with mixed indices has the following form:<ref name="ab"/> :<math>~ R_\alpha^{\ \beta} - \frac {1}{4} R \delta_\alpha^{\ \beta} = - \frac {1}{2c k} \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) . </math> here <math>~ R_\alpha^{\ \beta}</math> is [[w:Ricci tensor |Ricci tensor]] with mixed indices; <math>~ \delta_\alpha^{\ \beta}</math> is unit tensor or [[w:Kronecker delta |Kronecker delta]]; <math>~ B_\alpha^{\ \beta}</math>, <math>~ P_\alpha^{\ \beta}</math>, <math>~ U_\alpha^{\ \beta}</math> and <math>~ W_\alpha^{\ \beta}</math> are stress-energy tensors of acceleration field and pressure field, gravitational and electromagnetic fields, respectively. With the help of covariant derivative <math>~ \nabla_\beta</math> we can find four-divergence of both sides of the above equation for metric. The divergence of the left-hand side is zero due to equality to zero of divergence of [[w:Einstein tensor |Einstein tensor]], <math>~ \nabla_\beta \left( R_\alpha^{\ \beta} - \frac {1}{2} R \delta_\alpha^{\ \beta}\right) =0 </math>, and also as a consequence of the fact that outside the body the scalar curvature vanishes, <math>~ R =0</math>, and inside the body it is constant. The latter follows from the gauge condition of energy of closed system. The divergence of the right-hand side of equation for the metric is also zero: :<math>~ \nabla_\beta \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) = \nabla_\beta T_\alpha^{\ \beta} = 0 , </math> where the tensor <math>~ T_\alpha^{\ \beta}</math> with mixed indices represents the sum of stress-energy tensors of all fields acting in the system. The resulting expression for tensors’ space components is nothing but differential equation of matter’s motion under action of forces generated by fields, which is written in a covariant form. <ref name="eq"/> As for the tensors’ time components, for them the expression is expression of generalized Poynting theorem for all the fields. <ref name="ge"/> In a weak field and at low velocities of motion of particles, the equation <math>~ \nabla_\beta T_\alpha^{\ \beta} \approx \partial_\beta T_\alpha^{\ \beta} = 0 </math> can be integrated over four-volume, taking into account the [[w:divergence theorem |divergence theorem]]. As a result, at initial moment of time for the system under consideration, the following relation will be valid: :<math>~ J_\alpha = \int { T_\alpha^{\ 0} dx^1 dx^2 dx^3} = const . </math> In a closed system, the four-dimensional integral vector <math>~ J_\alpha </math> must be constant. <ref name="co"/> For a stationary sphere with randomly moving particles in continuous medium approximation, the energy fluxes of fields defining the components <math>~ T_j^{\ 0}</math>, where <math>~ j =1,2,3</math>, are missing , so that the spatial components are zero, <math>~ J_j =0</math>. As for the time component <math>~ J_0 </math> of integral vector, then for volume occupied by matter inside the sphere, it also vanishes due to relation (4) for field coefficients. However, outside the sphere, where there are only gravitational and electromagnetic fields, the time component of integral vector is not equal to zero. As a result, the contribution to this component is made by energies of external fields: :<math>~ J_0 = - \frac {G m^2_g}{2a} + \frac {q^2_b}{8\pi \varepsilon_0 a} . </math> It follows from the above that integral vector shows distribution of energy and energy fluxes in the system under consideration. For the nonzero space components <math>~ J_j</math> of integral vector to appear some stationary motion of matter and fields is required, for example, general rotation, volume pulsations or mixing of matter. In this case, solenoidal vectors and the fields’ energy fluxes appear in the system. Since the integral vector <math>~ J_\alpha </math> is associated with energies and energy fluxes of fields in stress-energy tensors, it differs from the four-momentum <math>~ p_\mu </math>, which includes invariant mass and proportional to its rest energy. It turns out that difference between <math>~ J_\alpha </math> and <math>~ p_\mu </math> is due to fundamental difference between particles and fields, they cannot be reduced to each other, although they are interrelated with each other. == Virial theorem and kinetic energy of particles == In article <ref> Fedosin S.G. [https://zenodo.org/record/1037246 The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept]. Continuum Mechanics and Thermodynamics, Vol. 29, Issue 2, pp. 361-371 (2017). https://dx.doi.org/10.1007/s00161-016-0536-8. </ref> kinetic energy of particles of the system under consideration is estimated by three methods: from [[w:virial theorem | virial theorem]], from relativistic definition of energy and using generalized momenta and proper fields of the particles. In the limit of low velocities, all these methods give for kinetic energy the following: : <math>~E_k \approx \frac {0.3608\eta m^2 \gamma_c }{a} . </math> The possibility to use generalized momenta to calculate the energy of particles’ motion is associated with the fact that despite zeroing of vector potentials and solenoidal vectors on the large scale, in volume of each randomly moving particle these potentials and vectors are not equal to zero. As a result, the energy of motion of the system’s particles can be found as the half-sum of scalar products of vector field potentials by the particles’ momentum, while for electromagnetic field we should take not the momentum, but the product of charge by velocity and Lorentz factor. If we square the equation for <math>~ \gamma' </math> in (1), we can obtain dependence of squared velocity of particles’ random motion on current radius: : <math>~{v'}^2 \approx v^2_c - \frac {4 \pi \eta \rho_0 r^2 }{3} . </math> On the other hand, we can assume that <math>~ \mathbf v' = \mathbf v_r + \mathbf v_\perp ,</math> where <math>~ \mathbf v_r </math> denotes averaged velocity component directed along the radius, and <math>~ \mathbf v_\perp </math> is averaged velocity component perpendicular to the current radius. In addition, from statistical considerations, it follows that : <math>~{v'}^2 = v^2_r + v^2_\perp = 3 v^2_r . </math> This implies dependence of radial velocity on the radius: : <math>~v_r \approx \frac {v_c}{ \sqrt 3} \left( 1- \frac {2 \pi \eta \rho_0 r^2 }{3 v^2_c} \right) . </math> Next, from the virial theorem we find squared velocity of particles at the center of the sphere: : <math>~v^2_c \approx \frac {3 \eta m }{5 a} \left( 1 + \frac {9}{\sqrt {56}}\right) \approx \frac {1.3216 \eta m }{a} . </math> This makes it possible to estimate the Lorentz factor at the center: : <math>~\gamma_c = \frac {1}{\sqrt {1- \frac { v^2_c }{c^2}}} \approx 1+ \frac { v^2_c }{2c^2} +\frac {3 v^4_c }{8c^4} \approx 1+ \frac {3 \eta m}{10 a c^2} \left( 1+\frac {9}{2\sqrt {14}} \right) + \frac {27 \eta^2 m^2}{200 a^2 c^4} \left( 1+\frac {9}{2\sqrt {14}} \right)^2 . </math> In the ordinary interpretation of virial theorem the time-averaged kinetic energy of a system of particles must be two times less than averaged energy associated with the forces <math>~ \mathbf F_i </math> holding the particles at the radius-vectors <math>~ \mathbf r_i </math> : : <math>~ \langle W_k \rangle_m = - 0.5 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle. </math> However, in relativistic uniform system this equation is changed: : <math>~ \langle W_k \rangle \approx - 0.6 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle, </math> while the quantity <math>~ W_k </math> exceeds the kinetic energy of particles, <math>~ W_k \approx \gamma_c E_k </math>, and it becomes equal to it only in the limit of low velocities. In contrast to classical case, total time derivative of virial in stationary system is other than zero due to the virial’s dependence on the radius: : <math>~ \frac {dG_V}{dt} \approx \mathbf v \cdot \nabla {G_V}\approx \frac {0.1216 \eta m^2 \gamma^2_c }{a} . </math> An analysis of integral theorem of generalized virial makes it possible to find, on the basis of field theory, a formula for the root-mean-square speed of typical particles of a system without using the notion of temperature: <ref> Fedosin S.G. [http://em.rdcu.be/wf/click?upn=lMZy1lernSJ7apc5DgYM8f7AyOIJlVFO4uFv7zUQtzk-3D_DUeisO4Ue44lkDmCnrWVhK-2BAxKrUexyqlYtsmkyhvEp5zr527MDdThwbadScvhwZehXbanab8i5hqRa42b-2FKYwacOeM4LKDJeJuGA15M9FWvYOfBgfon7Bqg2f55NFYGJfVGaGhl0ghU-2BkIJ9Hz4M6SMBYS-2Fr-2FWWaj9eTxv23CKo9d8nFmYAbMtBBskFuW9fupsvIvN5eyv-2Fk-2BUc7hiS15rRISs1jpNnRQpDtk2OE9Hr6mYYe5Y-2B8lunO9GwVRw07Y1mdAqqtEZ-2BQjk5xUwPnA-3D-3D The integral theorem of generalized virial in the relativistic uniform model]. Continuum Mechanics and Thermodynamics, Vol. 31, Issue 3, pp. 627-638 (2019). https://dx.doi.org/10.1007/s00161-018-0715-x.</ref> :<math> v_\mathrm{rms} = c \sqrt{1- \frac {4 \pi \eta \rho_0 r^2}{c^2 \gamma^2_c \sin^2 {\left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) } } } .</math> == Extreme objects == In formula (2) for gravitational field strength <math>~ \mathbf \Gamma_o </math> outside a body there is a quantity <math>~A = \sin \delta - \delta \cos \delta</math>, where <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} </math>. As was shown in article, <ref name="gr"/> at the value <math>~ \delta = \delta_0 = 4.494 </math> radians the gravitational field strength <math>~ \mathbf \Gamma_o </math> vanishes and gravitational acceleration disappears. Therefore, in real physical objects the following condition must hold: <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} < \delta_0 </math>. If the angle <math>~ \delta </math> is increased, then the quantity <math>~A </math> would first increase, and then would begin to decrease and even change its sign. So, at <math>~ \delta = \frac {\pi}{2}</math> we have <math>~A =1</math>, at <math>~ \delta = \pi </math> we have <math>~A =\pi </math>, at <math>~ \delta = \frac {3 \pi}{2}</math> we have <math>~A = -1 </math>. Let us now consider the observable Universe, which on a scale 100 Mpc or more can be considered as a relativistic uniform system. The total mass-energy density of the Universe is close to the critical value <math>~ \rho_c \approx 10^{-26}</math> kg/m³ and the size of the Universe can be estimated as the Hubble length <math>~ R_H =c/H_0 \approx 10^{26}</math> m, where <math>~ H_0 </math> is Hubble parameter. Using approximate equality <math>~\eta \approx \frac {3}{5} G </math> according to, <ref name="es"/> we find the value <math>~ \delta_U = \frac { R_H }{c} \sqrt {4 \pi \eta \rho_c} \approx 1.7 > \frac {\pi}{2}</math> radians. Since the angle <math>~ \delta_U </math> is sufficiently large, then for modeling of gravitational field of the Universe it is necessary to use refined formulas with sines and cosines. For example, if we take the size of observable Universe equal to <math>~ 2.64 R_H </math>, then we have <math>~ \delta_U = \delta_0 </math>, and gravitational field at boundaries of the Universe will tend to zero. This is what we observe in the form of a large-scale cellular structure consisting of clusters of galaxies. The reason for the gravitation action weakening is assumed to be graviton scattering by the particles of space medium. <ref> Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Vol. 23, Special Issues No. 1, pp. 3-13 (2012). http://dx.doi.org/10.5281/zenodo.890806. </ref> Another extreme object is a proton, in which mass density in entire volume changes approximately by 1.5 times. As a result, in the first approximation a proton is a relativistic uniform system. The proton radius <math>~ r_p </math> is of the order of 0.873 fm, <ref>Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, Vol. 35, No. 4, pp. 349-363 (2012). http://dx.doi.org/10.5281/zenodo.889451. </ref> and average density is of the order of <math>~ \rho_p = 6 \cdot 10^{17}</math> kg/m³. As a gravitational constant at the atomic level the [[Physics/Essays/Fedosin/Strong gravitational constant | strong gravitational constant]] <math>~ G_s </math> should be used. An estimate of the quantity <math>~ \delta </math> for a proton at <math>~\eta \approx \frac {3}{5} G_s </math> gives: <math>~ \delta_p = \frac { r_p }{c} \sqrt {4 \pi \eta \rho_p} \approx 2.4 < \delta_0 </math> radians. This shows that a proton is an extreme object from the point of view of weakening of its gravitational field. In article, <ref name="gr"/> a method is provided for estimating Lorentz factor of matter’s motion at the center of a proton, which gives <math>~ \gamma_c =1.9 </math>. In addition, radius of action of [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]] in matter with the critical mass density <math>~ \rho_c \approx 10^{-26}</math> kg/m³ in observable Universe is estimated: <math>~ r_G <1.3 \cdot 10^7 </math> m. On a large scale in the Universe not the strong gravitation, but ordinary gravitation is acting with the radius of action of the order of Hubble length. Let us suppose that <math>~ r_G </math> corresponds to radius of a certain [[black hole]] for strong gravitation, calculated by the Schwarzschild formula: <math>~ r_G = \frac {2 G_s m} {c^2} </math>. If the mass is <math>~ m = \frac {4 \pi \rho_c r^3_G} {3}</math>, then for radius of a black hole with such mass we obtain<math>~ r_G =c \sqrt {\frac {3}{8 \pi G_s \rho_c }} = 2.7 \cdot 10^6 </math> m, and mass is <math>~ m = 8 \cdot 10^{-7} </math> kg. The Schwarzschild formula admits a black hole for strong gravitation at small mass of the order of proton mass, large mass density and a radius smaller than the proton radius. In addition, substitution of the mass <math>~ m </math> and the radius <math>~ r_G </math> into Schwarzschild formula formally corresponds to a black hole with a large radius and low density <math>~ \rho_c </math>. However, for an external observer, such a black hole would rather correspond not to a black hole, but to an object, containing strongly rarefied hydrogen gas of cosmic space. Similarly, the [[w:Observable universe |Metagalaxy]] with the radius of order of <math>~ r_H </math> and mass density <math>~ \rho_c </math> is not a black hole, although it corresponds to the Schwarzschild formula for ordinary gravitation. Hence, in accordance with the theory of infinite nesting of matter, conclusion follows – at each level of matter corresponding gravitation forms only one type of the most compact and stable object. So, at the level of nucleons a proton appears under the action of strong gravitation, and at the level of stars the ordinary gravitation generates a neutron star. If we multiply the radius of a neutron star by coefficient of similarity in size <math>~ P = 1.4 \cdot 10^{19}</math>, which is equal to the ratio of stellar radius to the proton radius, we obtain radius of the order of <math>1.7 \cdot 10^{23} </math> m. This radius must correspond to a compact object of a neutron star-type at the level of metagalaxies, which can emerge under the action of gravitation at this matter level. In the first approximation, the gravitational constant for metagalaxies is determined with the help of the similarity theory: <math>~ G_M =\frac {G P S^2} {\Phi} = 3 \cdot 10^{-50} </math> m³•s^–2•kg^–1, where <math>~ S=0.23 </math> is coefficient of similarity in velocities, <math>~ \Phi = 1.62 \cdot 10^{57} </math> is coefficient of similarity in mass. By analogy with the case of a proton, a neutron star is also considered as a relativistic uniform system. For a star with the mass of 1.35 Solar masses, the radius <math>~ R_s = 12 </math> km and average density <math>~ \rho_s \approx 3.7 \cdot 10^{17}</math> kg/m³, at <math>~\eta \approx \frac {3}{5} G </math> we obtain the angle <math>~ \delta_s = \frac { R_s }{c} \sqrt {4 \pi \eta \rho_s} \approx 0.546 </math> radians. With this in mind, if we substitute into (3) the stellar mass instead of <math>~ m_b </math> and the stellar radius instead of <math>~ a </math>, we can estimate Lorentz factor at the center of the star: <math>~ \gamma_{cs} =1.04 </math>. This allows us to estimate temperature at the center of the star: <math>~ T_s \approx 2.8 \cdot 10^{11} </math> K, which is close enough to calculation of temperature at the center of a newly formed star. <ref name="es"/> Thus, dependences of gravitational field inside and outside bodies in article <ref name="gr"/> are in good agreement with conclusions of [[w:Le Sage’s theory of gravitation |Le Sage’s theory of gravitation]] and the theory of [[Physics/Essays/Fedosin/Infinite Hierarchical Nesting of Matter|Infinite Hierarchical Nesting of Matter]], with strong gravitation at the level of nucleons and with the concept of a dynamic force vacuum field in [[Physics/Essays/Fedosin/Electrogravitational vacuum | electrogravitational vacuum]]. == Cosmological constant and scalar curvature == According to (6), outside a body, where the four-currents are equal to zero, cosmological constant <math>~ \Lambda</math> becomes equal to zero. In addition, scalar curvature <math>~ R</math> also becomes equal to zero. <ref name="en"/> Inside the body the relation <math>~ R= 2\Lambda </math> holds true, so that in matter with higher density both the scalar curvature and the cosmological constant increase. These quantities can be calculated using (6) as averaged values for typical particles of physical system. For cosmic space we obtain approximately the following: <math>~ \Lambda_0 \approx \frac {16 \pi G \rho_0}{c^2} \approx 10^{-52} </math> m^-2, where the average mass density is <math>~ \rho_0 \approx 2.7 \cdot 10^{-27}</math> kg/m³. A similar formula for a proton gives the following: <math>~ \Lambda \approx \frac {16 \pi G \rho_p}{c^2} \approx 2.2 \cdot 10^{-8} </math> m^-2. However, for a proton in the calculations we should use the strong gravitational constant <math>~ G_s </math>. In this case, we find: <math>~ \Lambda_p \approx \frac {16 \pi G_s \rho_p}{c^2} \approx 5.1 \cdot 10^{31} </math> m^-2. The obtained value is almost 84 orders of magnitude greater than the value of cosmological constant for cosmic space. The difference between cosmological constants for cosmic space and for a proton is associated with averaging procedure: the cosmological constant inside a proton is large, but in cosmic space matter containing protons, neutrons and electrons is very rarefied, the main place is occupied by void, so that cosmological constant averaged over entire space becomes a small value. Thus one of the paradoxes of general theory of relativity is solved, in which the cosmological constant is associated with zero vacuum energy and therefore it must be very large, but in fact the cosmological constant turns out to be a small value. For relativistic uniform system with four fields acting in it, average value <math>~ \stackrel{-}{\Lambda }</math> of cosmological constant in matter is constant and can be written as follows: : <math>~ -ck \stackrel{-}{\Lambda } = \frac {G \rho_0 c^2 \gamma_c}{\eta} \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - \frac {\rho^2_{0q} c^2 \gamma_c }{4 \pi \varepsilon_0 \eta \rho_0 }\cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) + \rho_0 \wp_c - \frac {\sigma\rho_0 c^2 \gamma_c }{\eta } . </math> This expression can be simplified by using scalar potential of gravitational field <math>~ \psi_a = - \frac {G m_g}{a}</math> and scalar potential of electric field <math>~ \varphi_a = \frac {q_b }{4 \pi \varepsilon_0 a}</math> on surface of body at <math>~ r=a </math> : : <math>~ -ck \stackrel{-}{\Lambda } \approx \rho_0\psi_a - \frac {G m \rho_0 \gamma_c }{2 a } + \rho_0 c^2 \gamma_c + \rho_{0q} \varphi_a + \frac {q \rho_{0q} \gamma_c }{8 \pi \varepsilon_0 a } + \rho_0 \wp_c . </math> == Field energy theorem == In a relativistic uniform system, the exact values of strengths and potentials of all active fields are known. This allows us to check the [[field energy theorem]] for such a system and verify the theorem.<ref> Fedosin S.G. [http://dergipark.org.tr/gujs/issue/45480/435567 The Integral Theorem of the Field Energy.] Gazi University Journal of Science. Vol. 32, No. 2, pp. 686-703 (2019). http://dx.doi.org/10.5281/zenodo.3252783. </ref> This theorem explains, in particular, why electrostatic energy can be calculated either through the field strength, included in the electromagnetic field tensor, or in another way, through the field potential. The kinetic energy and potential energy of electromagnetic field are defined as follows: :<math>~ E_{kf} = \int {A_\alpha j^\alpha \sqrt {-g} dx^1 dx^2 dx^3 }. </math> :<math>~ W_f = \frac {1}{4 \mu_0 } \int { F_{\mu \nu} F^{\mu \nu} \sqrt {-g} dx^1 dx^2 dx^3 }. </math> If we take entire infinite volume both inside and outside matter of the system, then in the framework of special theory of relativity and in the absence of magnetic fields, these expressions are simplified: : <math>~ E_{kf}= \int \rho_q \varphi_i dV \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fi}= \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fo}= \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> : <math>~ W_f = W_{fi} + W_{fo} \approx -\frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> By virtue of the field energy theorem, the following relation will be satisfied: : <math>~ E_{kf}+ 2 W_f = 0.</math> In general case, tensor invariant is expressed in terms of square of electric field strength and square of magnetic field induction: <math>~ F_{\mu \nu} F^{\mu \nu}= - \frac {2}{c^2} (E^2 - c^2 B^2) </math>. The field energy density is found through the time component of stress-energy tensor: <math>~ W^{00} = \frac {1}{2} (\varepsilon_0 E^2 + \frac {1}{\mu_ 0} B^2) </math>. In electrostatics, when there are no magnetic fields and <math>~ B = 0</math>, volume integral of tensor invariant becomes proportional to volume integral of the component <math>~W^{00} </math>. As a result, electrostatic energy can be calculated in different ways: : <math>~ U_e= E_{kf}+ W_f \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Besides: : <math>~ U_e= - W_f = \frac {1}{2} E_{kf} = \int W^{00} dV. </math> == Binding energy == With the help of covariant theory of gravitation total energy, binding energy, energy of fields, pressure energy and potential energy of a system consisting of particles and four fields is precisely calculated in the relativistic uniform model. <ref name="bi"> Fedosin S.G. The binding energy and the total energy of a macroscopic body in the relativistic uniform model. Middle East Journal of Science, Vol. 5, Issue 1, pp. 46-62 (2019). http://dx.doi.org/10.23884/mejs.2019.5.1.06. </ref> A noticeable difference is shown between the obtained results and relations for simple systems in classical mechanics, in which the acceleration field and pressure field are not taken into account or the pressure is considered to be a simple scalar quantity. In this case the inertial mass of a massive system is less than the total inertial mass of the system’s parts. == System mass == The article <ref> Fedosin S.G. [https://www.bpasjournals.com/physics/chapter-details.php?chap_id=2367&issue_type=177&volume=117&journal=7 The Mass Hierarchy in the Relativistic Uniform System]. Bulletin of Pure and Applied Sciences, Vol. 38 D (Physics), No. 2, pp. 73-80 (2019). http://dx.doi.org/10.5958/2320-3218.2019.00012.5. </ref> shows that relativistic uniform system with continuous matter distribution is characterized by five types of mass: the gauge mass <math>~m' </math> is related to cosmological constant and represents mass-energy of matter’s particles in four-potentials of the system’s fields; the inertial mass <math>~M </math>; the auxiliary mass <math>~m </math> is equal to product of the particles’ mass density by volume of the system; the mass <math>~m_b </math> is the sum of invariant masses (rest masses) of the system’s particles, which is equal in value to gravitational mass <math>~m_g </math>. The relation for these masses is as follows: :<math>~m' < M < m < m_b = m_g .</math> == Solution of 4/3 problem == For electromagnetic and gravitational fields, the 4/3 problem consists in inequality of mass-energy extracted from the energy of field of a body at rest, and mass-energy resulting from the field momentum of the moving body. If such a body is a relativistic uniform system of spherical shape, then mass-energy associated with electrostatic energy of the system is: :<math>~ m_f = \frac {E_e}{c^2} \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a c^2}. </math> The energy flux of electromagnetic field of a moving sphere is calculated using the Poynting vector. Let <math>~ \gamma </math> be Lorentz factor, and <math>~ v </math> be velocity of the sphere. Having calculated energy fluxes of the field inside and outside the sphere, as well as total energy flux, we can find corresponding quantities with dimension of momentum associated with these energy fluxes:<ref name="ge"/> :<math>~ g_{pi} \approx \frac { \gamma q^2 \gamma^2_c v}{30 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_{po} \approx \frac { \gamma q^2 \gamma^2_c v}{6 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_p = g_{pi} + g_{po} \approx \frac { \gamma q^2 \gamma^2_c v }{5 \pi \varepsilon_0 a c^2}. </math> From here we find the mass-energy associated with the field energy fluxes: :<math>~ m_p = \frac {g_p}{\gamma v} \approx \frac { q^2 \gamma^2_c }{5 \pi \varepsilon_0 a c^2}. </math> For mass-energies, a ratio describing the 4/3 problem is obtained: :<math>~ m_p =\frac {4}{3} m_f . </math> If we consider the energy and energy flux of electromagnetic field only inside the sphere, or only outside the sphere, similar correlations are obtained for corresponding mass-energies. As indicated in the article, <ref name="ge"/> the mass-energy mismatch is a consequence of the fact that time components of electromagnetic stress-energy tensor and their integrals over volume do not together form any four-vector. In contrast, four-momentum of a system is a four-vector, so that the same inertial mass enters both the energy and momentum of the system. On the other hand, energy and momentum of electromagnetic field are included only as components in energy and momentum of entire system under consideration, and therefore they themselves do not have to form a four-vector. To calculate a four-momentum of a system, it is necessary to add energy and momentum of other fields operating in the system to the energy and momentum of electromagnetic field. In addition to electromagnetic field, the minimum set of fields of the system includes acceleration field, pressure field and gravitational field, and therefore it is necessary to take into account their energy and momentum. In this case, inside the sphere, the sum of energies of all fields found through tensor invariants and through stress-energy tensors is zeroed out. The total energy flux and total momentum of fields inside the sphere are also zero, so that within the sphere, the 4/3 problem as applied to [[Physics/Essays/Fedosin/General field | general field]] disappears. The equality to zero of sum of energies and sum of momenta of fields inside the sphere with randomly moving particles is a consequence of the fact that particles and fields have the opportunity to exchange energy and momentum with each other. As a result, contribution to relativistic energy of the system is made only by particle energies in scalar potentials of fields, and energies of electromagnetic and gravitational fields outside the sphere. The 4/3 problem shows in particular why energy and momentum of an electron and any other body cannot be reduced only to action of its own electromagnetic field. Despite the fact that an electron has a maximum charge per unit mass and is extremely charged, there are other fields in the electron's matter, for example [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]]. These fields have their own energy and momentum, which contribute to four-momentum of the electron. == Relations between field potentials == In the article, <ref>Fedosin S.G. [https://rdcu.be/ccV9o The potentials of the acceleration field and pressure field in rotating relativistic uniform system]. Continuum Mechanics and Thermodynamics, Vol. 33, Issue 3, pp. 817-834 (2021). https://doi.org/10.1007/s00161-020-00960-7. </ref> a connection was found between scalar potentials of acceleration field and pressure field in relativistic uniform system: :<math>~ \wp = \frac {\sigma (\vartheta -c^2)}{ \eta } = \frac {2 (\vartheta -c^2)}{ 3 }. </math> In addition, a relativistic expression for pressure was found: <math> p = \frac{2\rho c^2 (\gamma - 1) }{3}= \frac {2 \rho c^2 }{3} \left( \frac {1}{\sqrt {1- v^2/ c^2 }}-1 \right) \approx \frac {\rho v^2}{3}, </math> where <math>\rho </math> is mass density of moving matter, <math> c </math> is speed of light, <math> \gamma =\frac {1}{\sqrt {1- v^2/ c^2 }} </math> is [[w:Lorentz factor |Lorentz factor]]. In the limit of low velocities, this relationship turns into standard formula of [[w:kinetic theory of gases |kinetic theory of gases]]. == Metric inside and outside system == Standard expression for square of interval between two close points in metric theories is the following: :<math> ds^2 \ = \ g_{\mu\nu}(x) \ dx^{\mu} \ dx^{\nu}.</math> For static metric with spherical coordinates <math> x^0 = ct, </math> <math> x^1 = r ,</math> <math> x^2 = \theta , </math> <math> x^3 = \phi , </math> there are four nonzero components of the metric tensor: <math> g_{00}, </math> <math> g_{11}, </math> <math> g_{22}, </math> and <math> g_{33}= g_{22} \sin^2 \theta .</math> As a result, there is :<math> ds^2 \ = g_{00} c^2 dt^2 + g_{11} dr^2 + g_{22} d\theta^2 + g_{22} \sin^2 \theta d\phi^2.</math> As it was found for components of metric inside a spherical body within the framework of relativistic uniform model, <ref>{{cite journal| last=Fedosin|first=S. G. |s2cid= 238253182 |url= https://physmath.spbstu.ru/en/article/2021.53.13/ |title= The relativistic uniform model: the metric of the covariant theory of gravitation inside a body |journal= St. Petersburg Polytechnical State University Journal. Physics and Mathematics (Научно-технические ведомости СПбГПУ. Физико-математические науки) | volume=14 |issue=3 |pages=168–184 |date=2021 |doi= 10.18721/JPM.14313 |arxiv=2110.00342 |bibcode=2021arXiv211000342F }} // [http://sergf.ru/ru.htm О метрике ковариантной теории гравитации внутри тела в релятивистской однородной модели].</ref> <math> g_{22}= - r^2, </math> and :<math> (g_{00})_i = -\frac {1}{ (g_{11})_i } = 1+ \frac{ 8 \pi G \beta r^2 } {3c^4 }\left( \rho_0 c^2 \gamma_c + \rho_0 \psi_a - \frac {G m \rho_0 \gamma_c }{2a} + \rho_{0q} \varphi_a + \frac {q \rho_{0q}\gamma_c }{8\pi \varepsilon_0 a}+ \rho_0 \wp_c \right), </math> where <math> G </math> is gravitational constant; <math> \beta </math> is a coefficient to be determined; <math> r </math> is radial coordinate; <math> c </math> is the speed of light; <math> \rho_0 </math> is invariant mass density of matter particles; <math> \gamma_c </math> is Lorentz factor of particles moving at the center of body; <math> \psi_a = - \frac {G m_g}{a} </math> is gravitational potential at the surface of sphere with radius <math> a </math> and gravitational mass <math> m_g </math>; quantities <math> m = \frac {4 \pi a^3 \rho_0}{3}</math> and <math> q = \frac {4 \pi a^3 \rho_{0q}}{3}</math> are auxiliary values; <math> \rho_{0q} </math> is invariant charge density of matter particles, moving inside the body; <math> \varphi_a = \frac {q_b}{4\pi \varepsilon_0 a} </math> is electric scalar potential at the surface of sphere with total charge <math> q_b </math>; <math> \wp_c </math> is potential of pressure field at the center of body. On surface of the body, with <math> r = a </math>, the component <math> (g_{00})_ i </math> of metric tensor inside the body must be equal to the component <math> (g_{00})_o </math> of metric tensor outside the body. This allows us to refine expression for metric tensor components outside the body: :<math> (g_{00})_o = -\frac {1}{ (g_{11})_o } = 1+ \frac {2G m \gamma_c \beta }{c^2 r} + \frac{ 2 G \beta } {c^4 r}\left( m \psi_a + \frac {1}{2} m_g (\psi - \psi_a ) - \frac {G m^2 \gamma_c }{2a} + q \varphi_a + \frac {1}{2} q_b (\varphi - \varphi_a ) + \frac {q^2 \gamma_c }{8\pi \varepsilon_0 a} + m \wp_c \right), </math> where <math> \psi = - \frac {G m_g}{r} </math> is gravitational potential outside the body; <math> \varphi = \frac {q_b}{4\pi \varepsilon_0 r} </math> is electric potential outside the body. == Generalized four-momentum and total four-momentum == In the paper, <ref> Fedosin S.G. Generalized Four-momentum for Continuously Distributed Materials. Gazi University Journal of Science, Vol. 37, Issue 3, pp. 1509-1538 (2024). https://doi.org/10.35378/gujs.1231793. // [http://sergf.ru/gfm.htm Обобщённый 4-импульс для непрерывно распределённого вещества].</ref> formulas were found for calculating generalized four-momentum of a physical system in curved space-time taking into account contribution from particles and fields of the system. A differential four-dimensional Euler-Lagrange equation for continuously distributed matter was also obtained. Both the formulas for generalized four-momentum and Euler-Lagrange equation are satisfied in relativistic uniform system. In the paper, <ref> Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45. // [http://sergf.ru/ws.htm Что мы должны понимать под 4-импульсом физической системы?] </ref> covariant formulas for relativistic four-momentum of a physical system were derived, which were also verified in a relativistic uniform system. It was shown that four-momentum is expressed by the sum of two four-vectors of integral type with covariant indices, one of these four-vectors is generalized four-momentum of the system, and the other four-vector describes four-momentum of fields of the system. Additionally, the 4/3 problem and interpretation of integral vector found by integrating over volume of time components of stress-energy tensor of the system were considered. The fact that integral vector cannot be four-momentum of the system, as is assumed in general theory of relativity, is confirmed by direct calculation and follows from the fact that a four-vector cannot be obtained from tensor components. Similarly, volume integral of time components of stress-energy tensor of electromagnetic field does not yield four-momentum of electromagnetic field, but an integral vector that is not a four-vector. As a consequence, the mass-energies contained in components of integral vector are not equal to each other and are related in the proportion 4/3. Covariant formulas for four-momentum were used to determine the components of angular momentum tensor of a physical system in the article. <ref>Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, Vol. 40, No. 02, 2450163 (2025). https://doi.org/10.1142/S0217751X2450163X. // [http://sergf.ru/la.htm Лагранжев формализм в теории релятивистских векторных полей]. </ref> == References == <references/> == See also == * [[Invariant energy]] * [[Physics/Essays/Fedosin/General field | General field]] * [[Acceleration field]] * [[Pressure field]] * [[w:Gravitational field | Gravitational field]] * [[w:Electromagnetic field | Electromagnetic field]] * [[Physics/Essays/Fedosin/Covariant theory of gravitation | Covariant theory of gravitation]] * [[Energy]] * [[Field energy theorem]] ==External links == * [http://www.wikiznanie.ru/wikipedia/index.php/%D0%A0%D0%B5%D0%BB%D1%8F%D1%82%D0%B8%D0%B2%D0%B8%D1%81%D1%82%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%B4%D0%BD%D0%BE%D1%80%D0%BE%D0%B4%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0 Relativistic uniform system in Russian] [[Category:Special relativity]] [[Category:Physical systems]] [[Category:Covariant theory of gravitation]] [[Category:Energy]] oo1lm84hg6bcb60thq1s6dk21ixlusf 2834544 2834543 2026-09-26T10:26:51Z Fedosin 196292 /* Relation between field coefficients */ 2834544 wikitext text/x-wiki '''Relativistic uniform system''' is an ideal [[w:physical system |physical system]], in which mass density (or any other physical quantity) depends on the [[w:Lorentz factor |Lorentz factor]] of the system’s particles, but is constant in the reference frames associated with the moving particles. ==Difference from classical uniform system== In classical physics, the ideal uniform body model is widely used, in which mass density is constant throughout the volume of the body or is given as the volume-averaged quantity. This model simplifies solution of physical problems and allows us to quickly estimate different physical quantities. For example, the body mass is calculated by simply multiplying the mass density by the body volume, which is easier than integrating the density over the volume in case of dependence of the density on coordinates. The disadvantage of the classical model is that the majority of real physical systems are far from this ideal uniformity. The use of the concept of relativistic uniform system is based on the [[Theory of relativity/Special relativity|special theory of relativity]] (STR) and is the next step towards a more precise description of physical systems. In STR particular importance is given to invariant physical quantities, which can be calculated in each inertial reference frame and are equal to the values that these quantities have in the proper reference frame of the body. For example, multiplication of invariant mass by [[w:four-velocity |four-velocity]] gives the [[w:four-momentum |four-momentum]] of the body containing the [[invariant energy]], and multiplication of corresponding invariant quantities by four-velocity allows us in the case of motion of solid point particles to find the [[w:four-potential |four-potential]]s of any vector fields and to develop their complete theory. <ref name="pr"> [[user:Fedosin | Fedosin S.G.]] [http://vixra.org/abs/1406.0135 The procedure of finding the stress-energy tensor and vector field equations of any form]. Advanced Studies in Theoretical Physics, Vol. 8, no. 18, 771-779 (2014). http://dx.doi.org/10.12988/astp.2014.47101. </ref> Another example is that for determination of four-velocity or [[four-acceleration]] as a rule the [[operator of proper-time-derivative]] is used instead of time derivative. Therefore, the use of invariant mass density and charge density of moving particles that make up the system does not only conform to principles of STR but also significantly simplifies solution of relativistic equations of motion. ==Field functions for bodies of spherical shape== Field equations are most easily solved in case of spherical symmetry in the absence of general rotation of particles. In this case all the physical quantities depend only on current radius, which starts at the center of the sphere. Below are presented solutions of equations for various fields within the framework of STR, including solutions for scalar potentials, field strengths and solenoidal vectors. Due to random motion of particles in the system, the vector field potentials become equal to zero. This leads to zeroing of solenoidal vectors of fields, including [[w:magnetic field |magnetic field]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]]. === Acceleration field === The four-potential <math>~ U_\mu = \left(\frac {\vartheta }{c},- \mathbf U \right) </math> of [[acceleration field]] includes the scalar potential <math>~ \vartheta</math> and the vector potential <math>~ \mathbf U</math>. Applying four-curl to the four-potential gives [[acceleration tensor]] <math>~ u_{\mu \nu} = \nabla_\mu U_\nu - \nabla_\nu U_\mu </math>. In curved spacetime acceleration field equation with the field sources is derived from the principle of least action: <ref name="pr"/> : <math>~ \nabla^\nu u_{\mu \nu} = - \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation after expressing the acceleration tensor <math>~ u_{\mu \nu}</math> in terms of four-potential turns into the wave equation for finding the four-potential of acceleration field: : <math>~ \nabla^\nu \nabla_\mu U_\nu - \nabla^\nu \nabla_\nu U_\mu = - \frac {4 \pi \eta }{c^2} J_\mu , </math> which, taking into account the calibration condition of the four-potential <math>~\nabla^\mu U_\mu = 0 </math>, can be transformed as follows: :<math>~ \nabla^\nu \nabla_\nu U_\mu + R_{\mu \nu} U^\nu = \frac{4 \pi \eta }{c^2} J_\mu, </math> where <math>~ c </math> is the speed of light, <math>~ \eta </math> is acceleration field coefficient, <math>~ J_\mu = g_{\mu \nu } J^\nu = g_{\mu \nu } \rho_0 u^\nu </math> is mass four-current with the covariant index, <math>~ g_{\mu \nu } </math> is metric tensor, <math>~ R_{\mu \nu} </math> is Ricci tensor, <math>~ u^\nu </math> is four-velocity, <math>~ \rho_0 </math> is invariant mass density of particles in comoving reference frames, which is the same for all the particles. In Minkowski spacetime within the framework of STR, covariant derivatives of the form <math>~ \nabla_\mu </math> turn into partial derivatives of the form <math>~ \partial_\mu </math>, while the result of action of the partial derivatives does not depend on the order of their action. As a consequence of calibration of the 4-potential, the equality holds: <math>~ \partial^\nu \partial_\mu U_\nu = \partial_\mu \partial^\nu U_\nu = 0 </math>. As a result, the four-potential of acceleration field can be found from the wave equation: : <math>~ \partial^\nu \partial_\nu U_\mu = \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation can be divided into two equations – one for scalar potential and the other for vector potential of acceleration field. In the system under consideration the vector potential is equal to zero, and the scalar potential of acceleration field is given by: : <math>~\vartheta = c g_{0 \mu} u^\mu = \gamma' c^2 , </math> where <math>~ g_{0 \mu} </math> are time components of metric tensor, <math>~ \gamma' </math> is Lorentz factor of particles in the reference frame K' associated with the center of the sphere. Since scalar potential of stationary system does not depend on time, the wave equation for the scalar potential turns into [[Partial differential equations/Poisson Equation|Poisson equation]]: <ref name="ab"> Fedosin S.G. [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9, No. 1, pp. 1-30 (2016). http://dx.doi.org/10.5281/zenodo.889304. </ref> : <math>~\triangle \vartheta = - 4 \pi \eta \rho_0 \gamma' </math> and the following formula is obtained for the Lorentz factor of particles: <ref name="int"> Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12 . </ref> : <math>~ \gamma' = \frac {c \gamma_c }{r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \gamma_c - \frac {2 \pi \eta \rho_0 r^2 \gamma_c }{3 c^2 }, \qquad\qquad (1) </math> where <math>~ \gamma_c </math> is Lorentz factor of particles at the center of the sphere, <math>~ r </math> is current radius. The acceleration field strength and corresponding solenoidal vector are expressed by the formulas: : <math>~ \mathbf S = - \nabla \vartheta - \frac {\partial \mathbf U }{\partial t}= \frac { c^2 \gamma_c \mathbf r}{r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac {4 \pi \eta \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf N = \nabla \times \mathbf U = 0. </math> === Pressure field === The four-potential <math>~ \pi_\mu = \left(\frac {\wp }{c},- \mathbf \Pi \right) </math> of [[pressure field]] includes the scalar potential <math>~ \wp </math> and the vector potential <math>~ \mathbf \Pi </math>, and obeys the calibration condition: <math>~\nabla^\mu \pi_\mu =0</math>. The pressure field equation with the field sources, [[pressure field tensor]] <math>~ f_{\mu \nu}</math> and equation for finding the four-potential of pressure field have the form: <ref name="pr"/> : <math>~ \nabla^\nu f_{\mu \nu} = - \frac {4 \pi \sigma }{c^2} J_\mu , \quad f_{\mu \nu} = \nabla_\mu \pi_\nu - \nabla_\nu \pi_\mu , \quad \nabla^\nu \nabla_\nu \pi_\mu + R_{\mu \nu} \pi^\nu = \frac{4 \pi \sigma }{c^2} J_\mu, </math> where <math>~ \sigma </math> is pressure field coefficient. In STR the latter equation turns into the wave equation: : <math>~ \partial^\nu \partial_\nu \pi_\mu = \frac {4 \pi \sigma }{c^2} J_\mu . </math> In stationary case the potentials do not depend on time and time component of the wave equation turns into the Poisson equation for the scalar potential of pressure field: : <math>~\triangle \wp = - 4 \pi \sigma \rho_0 \gamma' .</math> Solution of this equation inside the sphere with particles is as follows: <ref name="int"/> : <math>~ \wp = \wp_c - \frac {\sigma c^2 \gamma_c }{\eta } + \frac {\sigma c^3 \gamma_c }{\eta r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \wp_c - \frac {2 \pi \sigma \rho_0 r^2 \gamma_c }{3 }. </math> where <math>~ \wp _c </math> is scalar potential at the center of the sphere. This potential is approximately equal to: <ref name="en"> Fedosin S.G. Energy and metric gauging in the covariant theory of gravitation. Aksaray University Journal of Science and Engineering, Vol. 2, Issue 2, pp. 127-143 (2018). http://dx.doi.org/10.29002/asujse.433947. </ref> :<math>~ \wp_c \approx \frac {3 \sigma m}{10 a} \left( 1+\frac {9}{2\sqrt {14}} \right) , </math> where acceleration field constant <math>~ \eta </math> and pressure field constant <math>~ \sigma </math> are expressed by the formulas: :<math>~ \eta = \frac {3}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) , \qquad \qquad \sigma = \frac {2}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) .</math> The strength of pressure field and corresponding solenoidal vector are found as follows: : <math>~ \mathbf C = - \nabla \wp - \frac {\partial \mathbf \Pi }{\partial t}= \frac { \sigma c^2 \gamma_c \mathbf r}{\eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx \frac {4 \pi \sigma \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf I = \nabla \times \mathbf \Pi = 0. </math> === Gravitational field === The [[gravitational four-potential]] <math>~ D_\mu = \left(\frac {\psi }{c},- \mathbf D \right) </math> of [[w:gravitational field |gravitational field]] is made up with the use of scalar <math>~ \psi </math> and vector <math>~ \mathbf D </math> potentials. Calibration condition of the four-potential is: <math>~\nabla^\mu D_\mu = 0</math>. The gravitational field equation with field sources, the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] <math>~ \Phi_{\mu \nu} </math> and equation for finding the four-potential of gravitational field in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation]] have the form: <ref>Fedosin S.G. [https://payhip.com/b/RZOb Fizicheskie teorii i beskonechnaia vlozhennost’ materii]. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289. {{ISBN|978-5-9901951-1-0}}. (in Russian). </ref> <ref> Fedosin S.G. [http://vixra.org/abs/1110.0069 The Principle of Least Action in Covariant Theory of Gravitation.] Hadronic Journal, Vol. 35, No. 1, pp. 35-70 (2012). http://dx.doi.org/10.5281/zenodo.889804. </ref> : <math>~ \nabla^\nu \Phi_{\mu \nu} = \frac {4 \pi G }{c^2} J_\mu , \quad \Phi_{\mu \nu} = \nabla_\mu D_\nu - \nabla_\nu D_\mu , \quad \nabla^\nu \nabla_\nu D_\mu + R_{\mu \nu} D^\nu = -\frac {4 \pi G }{c^2} J_\mu, </math> where <math>~ G </math> is [[Physics/Essays/Fedosin/Gravitational constant | gravitational constant]]. In STR the latter equation is simplified and becomes the wave equation: : <math>~ \partial^\nu \partial_\nu D_\mu = -\frac {4 \pi G }{c^2} J_\mu . </math> From the wave equation in stationary case, the Poisson equation follows for scalar potential inside the sphere with randomly moving particles in the framework of [[Physics/Essays/Fedosin/Lorentz-invariant theory of gravitation | Lorentz-invariant theory of gravitation]] (LITG): : <math>~\triangle \psi_i = 4 \pi G \rho_0 \gamma' .</math> The right-hand side of this equation contains Lorentz factor <math>~ \gamma' </math>, which depends on the radius according to (1). In addition, the internal scalar potential near the surface of the sphere must coincide with the scalar potential of external field of the system, in view of standard potential gauge, that is with equality of potential to zero at infinity. As a result, dependence of scalar potential on the current radius differs from dependence in classical case of uniform sphere with the radius <math>~ a </math> and is equal to it only approximately: <ref name="int"/> : <math>~ \psi_i = -\frac {G c^2 \gamma_c }{ \eta r} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx -\frac {2 \pi G \rho_0 \gamma_c (3a^2 - r^2)}{3 }. </math> For [[Physics/Essays/Fedosin/Gravitational field strength | gravitational field strength]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]] inside the sphere we obtain the following: <ref name="re"> Fedosin S.G. [http://vixra.org/abs/1405.0002 Relativistic Energy and Mass in the Weak Field Limit.] [http://journals.yu.edu.jo/jjp/Vol8No1Contents2015.html Jordan Journal of Physics.] Vol. 8, No. 1, pp. 1-16 (2015). http://dx.doi.org/10.5281/zenodo.889210. </ref> : <math>~ \mathbf \Gamma_i = - \nabla \psi_i - \frac {\partial \mathbf D_i }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { 4 \pi G \rho_0 \gamma_c \mathbf r }{3}\left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf \Omega_i = \nabla \times \mathbf D_i = 0. </math> Solutions for external gravitational field potential and for field strength <math>~ \Gamma_o </math> according to LITG are as follows: : <math>~ \psi_o = - \frac {G c^2 \gamma_c }{ \eta r } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx - \frac {G m \gamma_c }{r} \left( 1- \frac {3 \eta m }{10 a c^2} \right). </math> : <math>~ \mathbf \Gamma_o = - \nabla \psi_o - \frac {\partial \mathbf D_o }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx </math> : <math>~\approx - \frac {G m \gamma_c \mathbf r}{r^3} \left( 1- \frac {3 \eta m }{10 a c^2} \right).\qquad\qquad (2) </math> Here, the auxiliary mass <math>~ m </math> is equal to the product of mass density <math>~ \rho_0 </math> by volume of the sphere: <math>~ m = \frac {4 \pi \rho_0 a^3 }{3} </math>. From expressions for potential and strength of external gravitational field we can see that the role of gravitational mass is played by the mass <math>~ m_g \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) .</math> Since <math>~ \gamma_c > 1 </math> then the relation <math>~ m_g > m </math> is satisfied. To understand difference between these masses we should calculate total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. For motion of particles there should be some voids between them. Both the average accelerations and average velocities of particles inside the sphere are functions of current radius. Dividing the particles’ velocities by their acceleration, we can find dependence of average period of oscillatory motion of particles on the radius. Finally, multiplying the velocity by the average period of motion, we can obtain an estimate of the size of voids between the particles. In order to calculate volume of the sphere, it is necessary to sum up volumes of all typical particles moving inside the sphere, as well as volumes of the voids between them. Suppose now that the sizes of typical particles are much larger than the voids between the particles, and volume of the voids is substantially less than the total volume of particles. In this case, we can use approximation of continuous medium, so that unit of mass of matter inside the sphere will be given by approximate expression <math>~ dm \approx \rho_0 \gamma' dV </math>, where <math>~ \rho_0 </math> is mass density in reference frames associated with the particles, <math>~ \gamma' </math> is Lorentz factor of the moving particles, the product <math>~ \rho_0 \gamma' </math> gives mass density of the particles from viewpoint of an observer, who is stationary with respect to the sphere, and volume element <math>~ dV </math> inside the sphere corresponds to the volume of a particle from the viewpoint of this observer. This leads to the fact that total volume of particles moving inside the sphere becomes approximately equal to the volume of the sphere. For the mass, in view of Lorentz factor (1), the following relation is obtained: : <math>~ m_b = \int dm = \int \rho_0 \gamma' dV = \frac {c^2 \gamma_c }{\eta } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right). \qquad\qquad (3) </math> This implies equality of gravitational mass <math>~ m_g </math> and total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. The both masses are greater than the mass <math>~ m </math>. By the method of its calculation, the mass <math>~ m_b </math> is equal to the sum of invariant masses of particles that make up the system. The external gravitational torsion field is equal to zero: : <math>~ \mathbf \Omega_o = \nabla \times \mathbf D_o = 0. </math> === Electromagnetic field === The [[w:electromagnetic four-potential | electromagnetic four-potential]] <math>~ A_\mu = \left(\frac {\varphi }{c},- \mathbf A \right) </math> of [[w:electromagnetic field |electromagnetic field]] includes scalar potential <math>~ \varphi </math> and vector potential <math>~ \mathbf A </math>. The covariant Lorentz calibration for four-potential is: <math>~\nabla^\mu A_\mu = 0 </math>. For a fixed uniformly charged spherical body with random motion of charges total electromagnetic field on the average is purely electric and the vector potential is equal to zero. The electromagnetic field equation with the field sources, [[w:electromagnetic tensor |electromagnetic tensor]] <math>~ F_{\mu \nu}</math> and equation for finding four-potential are expressed as follows: : <math>~ \nabla^\nu F_{\mu \nu} = - \frac {1 }{\varepsilon_0 c^2} j_\mu , \quad F_{\mu \nu} = \nabla_\mu A_\nu - \nabla_\nu A_\mu , \quad \nabla^\nu \nabla_\nu A_\mu + R_{\mu \nu} A^\nu = \frac {1 }{\varepsilon_0 c^2} j_\mu, </math> where <math>~ \varepsilon_0 </math> is [[electric constant]], <math>~ j_\mu </math> is electromagnetic [[w:four-current | four-current]]. The latter equation in STR turns into the wave equation: : <math>~ \partial^\nu \partial_\nu A_\mu = \frac {1 }{\varepsilon_0 c^2} j_\mu . </math> Due to the absence of time-dependence in the case under consideration, the wave equation becomes the Poisson equation for scalar potential <math>~ \varphi_i </math> inside the sphere: : <math>~\triangle \varphi_i = - \frac {\rho_{0q} \gamma'}{\varepsilon_0 } ,</math> where <math>~ \rho_{0q} </math> is charge density in the reference frames associated with the charges. Dependence of scalar potential on current radius in general case differs from dependence in classical case of potential of a uniformly charged sphere with the radius <math>~ a </math>, coinciding with it only in the first approximation: <ref name="el">Fedosin S.G. The electromagnetic field in the relativistic uniform model. International Journal of Pure and Applied Sciences, Vol. 4, Issue. 2, pp. 110-116 (2018). http://dx.doi.org/10.29132/ijpas.430614. </ref> : <math>~ \varphi_i = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[\frac {c }{ \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac {\rho_{0q} \gamma_c (3a^2 - r^2)}{6 \varepsilon_0 }. </math> Electric field strength and magnetic field inside the sphere have the form: : <math>~ \mathbf E_i = - \nabla \varphi_i - \frac {\partial \mathbf A_i }{\partial t}= \frac { \rho_{0q} c^2 \gamma_c \mathbf r}{4 \pi \varepsilon_0 \eta \rho_0 r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac { \rho_{0q} \gamma_c \mathbf r }{3 \varepsilon_0 } \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf B_i = \nabla \times \mathbf A_i = 0. </math> Outside the system under consideration charge density is equal to zero and Poisson equation for scalar potential turns into Laplace equation: : <math>~\triangle \varphi_o = 0 .</math> Solution for external electric field potential, corresponding to potential gauge and [[Maxwell's equations]] for electric field strength <math>~ E_o </math> is given by: : <math>~ \varphi_o = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[ \frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx \frac { q \gamma_c }{4\pi \varepsilon_0 r }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> : <math>~ \mathbf E_o = - \nabla \varphi_o - \frac {\partial \mathbf A_o }{\partial t}= \frac {\rho_{0q} c^2 \gamma_c \mathbf r}{ 4 \pi \varepsilon_0 \eta \rho_0 r^3} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx \frac { q \gamma_c \mathbf r}{4\pi \varepsilon_0 r^3 }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> External magnetic field is equal to zero: : <math>~ \mathbf B_o = \nabla \times \mathbf A_o = 0. </math> In these expressions, the charge <math>~ q </math> is an auxiliary quantity equal to the product of charge density <math>~ \rho_{0q} </math> by volume of the sphere: <math>~ q = \frac {4 \pi \rho_{0q} a^3 }{3} </math>. In this case, the following quantity serves as total charge of the system: :<math>~ q_b = \int \rho_{0q} \gamma' dV = \frac {\rho_{0q}c^2 \gamma_c }{\eta \rho_0 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> :<math>~\approx q \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) ,</math> while <math>~ q_b > q .</math> The charge <math>~ q_b </math> is calculated in the same way as the mass <math>~ m_b </math> and has the meaning of the sum of charges of all the system’s particles. == Tensor field invariants == The knowledge of field strengths and solenoidal components of fields allows us to find tensor components of corresponding fields with covariant indices. To pass on to the field tensors with contravariant indices we need to know metric tensor. In STR the metric tensor does not depend on coordinates and time, is uniquely defined, and in Cartesian coordinates consists of zeros and unities. As a result, it is easy to find the tensor field invariants <math>~ u_{\mu \nu} u^{\mu \nu}</math>, <math>~ f_{\mu \nu} f^{\mu \nu}</math>, <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu}</math> and <math>~ F_{\mu \nu} F^{\mu \nu}</math>, where <math>~ u_{\mu \nu}</math>, <math>~ f_{\mu \nu}</math>, <math>~ \Phi_{\mu \nu}</math> and <math>~ F_{\mu \nu}</math> are the [[acceleration tensor]], the [[pressure field tensor]], the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] and the [[w:electromagnetic tensor |electromagnetic tensor]], respectively. The tensor field invariants are included in Lagrangian, Hamiltonian. action function and relativistic energy of the system, and they are located there inside integrals over space volume. In addition, they are included in corresponding stress-energy tensors of the fields. <ref name="ab"/> Since in the system under consideration solenoidal vectors are zero, the tensor invariants depend only on the field strengths: : <math>~ u_{\mu \nu} u^{\mu \nu} = - \frac {2}{c^2}(S^2 - c^2 N^2) = - \frac {2}{c^2}S^2.</math> : <math>~ f_{\mu \nu} f^{\mu \nu} = - \frac {2}{c^2}(C^2 - c^2 I^2) = - \frac {2}{c^2}C^2.</math> : <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu} = - \frac {2}{c^2}(\Gamma^2 - c^2 \Omega^2) = - \frac {2}{c^2}\Gamma^2.</math> : <math>~ F_{\mu \nu} F^{\mu \nu} = - \frac {2}{c^2}(E^2 - c^2 B^2) = - \frac {2}{c^2}E^2.</math> The volume integrals of tensor invariants multiplied by corresponding factors were calculated in the article. <ref name="re"/> For acceleration field and pressure field the integrals are taken only over volume of the sphere: : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \eta } u_{\mu \nu} u^{\mu \nu} dV = - \frac {c^4 \gamma^2_c }{2 \eta } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \sigma } f_{\mu \nu} f^{\mu \nu} dV = - \frac {\sigma c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> The gravitational and electromagnetic fields of the system are present not only inside but also outside the sphere, where they extend to infinity, while field strengths of internal and external fields behave differently. The field strengths <math>~ \mathbf \Gamma_i </math> and <math>~ \mathbf E_i </math> are substituted respectively into integrals of tensor invariants of these fields taken over volume of the sphere, which gives the following: : <math>~ - \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{8 \pi \varepsilon_0 \eta^2 \rho^2_0} \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> Into volume integrals of tensor invariants of gravitational and electromagnetic fields of the system outside the sphere the field strengths <math>~ \mathbf \Gamma_o </math> and <math>~ \mathbf E_o </math> are substituted, respectively: : <math>~ - \int \limits^{\infty}_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 a} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right). </math> : <math>~ \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{ 8 \pi \varepsilon_0 \eta^2 \rho^2_0 a } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> == Energies of particles in field potentials == All the four fields act on particles inside the sphere, and therefore each particle of the system acquires corresponding energy in a particular field. The energy of a particle in a field is calculated as volume integral of product of effective mass density <math>~ \rho = \rho_0 \gamma' </math> by corresponding scalar potential, and for electric field the energy is determined as volume integral of product of effective charge density <math>~ \rho_q = \rho_{0q} \gamma' </math> by scalar potential <math>~ \varphi </math>, where Lorentz factor <math>~ \gamma' </math> from (1) is used. In STR the energies of particles in acceleration field, pressure field, gravitational and electric fields in uniform relativistic spherical system, in view of expressions for the field potentials <ref name="re"/> and corrections to calculations, <ref name="el"/> <ref name="ge">Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. </ref> <ref name="gf"> Fedosin S.G. [http://www.uiss2016.ru/files/uiss2016_res.pdf The gravitational field in the relativistic uniform model within the framework of the covariant theory of gravitation]. 5th Ulyanovsk International School-Seminar “Problems of Theoretical and Observational Cosmology” ([http://www.uiss2016.ru/ UISS 2016]), Ulyanovsk, Russia, September 19-30, 2016, Abstracts, p. 23, {{ISBN|978-5-86045-872-7}}. </ref> <ref name="gr">Fedosin S.G. The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation. International Letters of Chemistry, Physics and Astronomy, Vol. 78, pp. 39-50 (2018). http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39.</ref> are, respectively: : <math>~ \int \rho \vartheta dV = \rho_0 c^2 \int \gamma'^2 dV = \frac {c^4 \gamma^2_c }{\eta } \left[ \frac {a}{2}- \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx </math> : <math>~ \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho \wp dV = \rho_0 \int \gamma' \wp dV = \frac {c^2 \gamma_c } {\eta } \left( \wp_c - \frac { \sigma c^2 \gamma_c }{\eta }\right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac { \sigma c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }}\sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3 \sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) . </math> : <math>~ \int \rho \psi_i dV = \rho_0 \int \gamma' \psi_i dV = </math> : <math>~= \frac {G c^4 \gamma^2_c }{\eta^2 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] - </math> : <math>~ - \frac {G c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2 a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho_q \varphi_i dV = \rho_{0q} \int \gamma' \varphi_i dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Note that all fields in which particles are located are not fields from external sources, but are generated by the particles themselves. As a result, the particles’ energies calculated above in scalar potentials of the fields are twice as large as potential energy of one or another interaction. For example, in order to calculate electrostatic energy of a system of two charges, it is sufficient to take potential of first charge at location of second charge and to multiply it by the value of the second charge. But if we use formula for energy in the form of an integral, then electrostatic energy will be taken into account twice, because the term is added, which contains potential of second charge at location of first charge multiplied by the value of the first charge. On the other hand, the electrostatic energy must consist of two components that take into account both the energy of particles in each other’s fields and the energy of electric field itself. Instead, in electrostatics, the electrostatic energy is calculated either through the scalar potential or through the field strength by integrating time component of stress-energy tensor over volume. Both methods provide the same result, but the connection between field energy and energy of particles in field potential is lost in this case, and it is not clear why these energies should coincide. == Relation between field coefficients == For the four fields under consideration equation of motion of matter in the concept of general field is as follows: <ref> Fedosin S.G. [http://www.oalib.com/paper/5263035#.VuFYxn2LQsY The Concept of the General Force Vector Field]. OALib Journal, Vol. 3, pp. 1-15 (2016), e2459. http://dx.doi.org/10.4236/oalib.1102459. </ref> <ref name="eq"> Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. </ref> : <math>~ u_{\mu \nu } J^\nu + f_{\mu \nu } J^\nu + \Phi_{\mu \nu } J^\nu + F_{\mu \nu } j^\nu = 0, </math> where <math>~ J_\mu </math> is mass four-current, <math>~ j^\nu </math> is electromagnetic [[w:four-current | four-current]]. Components of field tensors are field strengths and corresponding solenoidal vectors, but in the physical system under consideration the latter are equal to zero. As a result, space component of the equation of motion is reduced to the relation: : <math>~ \mathbf S + \mathbf C + \mathbf \Gamma_i + \frac {\rho_{0q}}{\rho_0 }\mathbf E_i = 0 . </math> If we substitute here expression for field strengths inside the sphere, we obtain relation between field coefficients: <ref name="es">Fedosin S.G. [http://www.nrcresearchpress.com/doi/10.1139/cjp-2015-0593#.Vv3piZyLQsY Estimation of the physical parameters of planets and stars in the gravitational equilibrium model.] Canadian Journal of Physics, Vol. 94, No. 4, pp. 370-379 (2016). http://dx.doi.org/10.1139/cjp-2015-0593. </ref> : <math>~\eta + \sigma = G - \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 }= G - \frac {q^2 }{ 4 \pi \varepsilon_0 m^2 }. \qquad \qquad (4) </math> The same is obtained for time component of equation of motion, which leads to generalized Poynting theorem. <ref name="ge"/> == Relation between energies of internal and external fields == In article <ref>Fedosin S.G. [http://vixra.org/abs/1205.0086 The Hamiltonian in Covariant Theory of Gravitation.] Advances in Natural Science, Vol. 5, No. 4, pp. 55-75 (2012). http://dx.doi.org/10.3968%2Fj.ans.1715787020120504.2023. </ref> it was found that energy of particles in gravitational field inside stationary sphere is up to a sign two times greater than total energy associated with tensor invariants of gravitational field inside and outside the sphere. A similar situation takes place in the system under consideration with random motion of particles and zero solenoidal vectors both for gravitational <ref name="gf"/> and electromagnetic fields. <ref name="el"/> In particular, we can write the following: : <math>~ \int \limits^{a}_{r=0} \rho \psi_i dV = 2 \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV + 2 \int \limits^{ \infty }_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = 2 \int \limits^{\infty }_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV. </math> : <math>~ \int \limits^{a}_{r=0} \rho_q \varphi_i dV = -2 \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV - 2 \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = - 2 \int \limits^{\infty }_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV. </math> These expressions relate the energy of particles in scalar field potentials with the energy found with the help of field strengths. == Relativistic energy == In curved spacetime the system’s energy for continuously distributed matter is given by the formula: <ref name="ab"/> <ref name="en"/> : <math>~E_r = \frac {1}{c} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> : <math>~ +\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}. \qquad \qquad (5)</math> This formula is valid in the case where it can be assumed that potentials and field strengths at each point in space do not have a direct dependence on the speeds of motion of individual particles of the system. In STR the metric tensor determinant is <math>~ g = -1 </math>, the time component of four-velocity is <math>~ u^0 = c \gamma'</math>, and in order to calculate the energy of spherical system with particles, taking into account the fields’ energies, we can use the above-mentioned energies of particles in field potentials and energies in the form of tensor invariants of the fields: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The expression for energy is simplified if we use the relation between field coefficients (2): : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> Taking into account relations between energies of internal and external fields also simplifies expression for the system’s energy: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{10 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) . </math> == Relation between energy and cosmological constant== In the approach under consideration, relativistic energy of the system is not an absolute value and requires gauging. For this purpose the [[w:cosmological constant | cosmological constant]] <math>~ \Lambda</math> is used. The gauge condition for the four main fields is related to sum of products of the fields’ four-potentials by corresponding four-currents and has the following form: <ref name="ab"/> <ref name="en"/> : <math>~ -ck \Lambda = A_\mu j^\mu + (D_\mu + U_\mu + \pi_\mu) J^\mu, \qquad \qquad (6) </math> where for large cosmic systems <math>~ -ck = \frac {c^4}{16\pi G \beta }</math>, and <math>~\beta </math> is a constant of order of unity. Within the framework of STR gauge condition has the following form: : <math>~ -ck \Lambda = \gamma \rho_{0q} (\varphi - \mathbf A \cdot \mathbf v) + \gamma \rho_{0} (\psi - \mathbf D \cdot \mathbf v + \vartheta - \mathbf U \cdot \mathbf v + \wp - \mathbf \Pi \cdot \mathbf v ). </math> If we divide the system’s particles and remove them to infinity and leave there at rest, the terms with products of vector field potentials by velocity of particles <math>~\mathbf v </math> would vanish, and Lorentz factor of an arbitrary particle would be <math>~ \gamma=1 </math>. On the right-hand side we will have only the sum of terms specifying energy density of particles located in potentials of their proper fields. Since <math>~ \vartheta \approx \gamma_c c^2 </math>, we see that the cosmological constant for each system’s particle is up to the multiplier <math>~ -ck</math> equal to rest energy density of this particle with a certain addition from its proper fields. Then the integral over volume of all the particles gives a certain energy: : <math>~ -ck \int \Lambda dV = m' c^2 ,</math> where the gauge mass <math>~ m' </math> is related to gauge condition of the energy. In the process of gravitational clustering the particles that were initially far from each other are united into closely bound systems, in which the field potentials increase manyfold. In the system under consideration <math>~ \gamma = \gamma' </math>, solenoidal vectors of fields are considered equal to zero due to random motion of particles, which gives the following: : <math>~ m' c^2 = \int [\gamma' \rho_{0q} \varphi_i + \gamma' \rho_{0} (\psi_i + \vartheta + \wp)] dV. </math> Expression on the right-hand side is part of relativistic energy <math>~E_r </math> of the system, so that the energy can be written as follows: : <math>~E_r = M c^2 \approx m' c^2 - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The mass <math>~ M </math> is related to relativistic energy of generally stationary system and is the inertial mass of the system. In view of (2), the energy will be equal to: : <math>~E_r = M c^2 \approx m' c^2 + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> This shows that relativistic energy of this system is equal to gauge mass-energy <math>~ m' c^2 </math>, from which the gravitational and electromagnetic energy of fields outside the system should be subtracted. == Lagrange function and motion integrals == Lagrange function for a system of particles and four main vector fields has the following form:<ref name="pr"/> <ref name="ab"/> :<math>~L = - \int {( U_\mu J^\mu + \pi_\mu J^\mu + D_\mu J^\mu + A_\mu j^\mu ) \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ +\int { \left( ckR - 2ck \Lambda -\frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} - \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} + \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} - \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}.</math> Here <math>~ R </math> is [[w:scalar curvature |scalar curvature]]. With the help of such Lagrange function, one can calculate generalized momentum of the system:<ref name="co">Fedosin S.G. [http://www.bpasjournals.com/physics/chapter-details.php?chap_id=2121&issue_type=158&volume=110&journal=7 The covariant additive integrals of motion in the theory of relativistic vector fields]. Bulletin of Pure and Applied Sciences, Vol. 37 D (Physics), No. 2, pp. 64-87 (2018). http://dx.doi.org/10.5958/2320-3218.2018.00013.1. </ref> :<math>~ \mathbf p = \frac {1}{c} \int {( \rho_0 \mathbf U + \rho_0 \mathbf \Pi + \rho_0 \mathbf D + \rho_{0q} \mathbf A ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> This vector depends on vector potentials of all four fields and is preserved in a closed physical system, that is, it is an integral of motion. Another integral of motion is relativistic energy of the system <math>~E_r</math>, which is found by formula (5). Further, it is assumed that one can neglect the contributions from gravitational and electromagnetic fields outside the matter and take into account only the generalized momentum. Then we can assume that these values form a four-momentum of the system, written with a covariant index: :<math>~ p_\mu = \left( \frac { E_r }{c}, - \mathbf p \right).</math> The angular momentum of the system is also an integral of motion: :<math>~ \mathbf M = \frac {1}{c} \int {( \rho_0 [\mathbf r \times \mathbf U] + \rho_0 [\mathbf r \times \mathbf \Pi] + \rho_0 [\mathbf r \times \mathbf D] + \rho_{0q} [\mathbf r \times \mathbf A] ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> The antisymmetric angular momentum pseudotensor is determined through the four-radius <math>~ x_\mu </math>, taken with a covariant index, and through the four-momentum <math>~ p_\mu </math>: :<math>~M_{\mu \nu} = \int {( x_\mu dp_\nu - x_\nu dp_\mu )} .</math> The spatial components of the angular momentum pseudotensor <math>~ M_{\mu \nu} </math> are the components of the angular momentum <math>~ \mathbf M </math> of the system: :<math>~ M_{12} = -M_{21} = -M_z , \qquad M_{13} = -M_{31} = M_y , \qquad M_{23} = -M_{32} = -M_x .</math> The radius-vector of the center of momentum of a physical system is determined by the formula: :<math>~ \mathbf R_m = \frac {1}{c E_r} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) \mathbf r u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ + \frac {1}{E_r}\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \mathbf r \sqrt {-g} dx^1 dx^2 dx^3}.</math> The time components of the pseudotensor <math>~ M_{\mu \nu} </math> are the components of three-dimensional vector <math>~ \mathbf {\mathbb C} </math>, which is often called time-varying dynamic mass moment: :<math>~ M_{01} = -M_{10} = -\mathbb C_x , \qquad M_{02} = -M_{20} = -\mathbb C_y , \qquad M_{03} = -M_{30} = -\mathbb C_z .</math> If we take into account definition of radius-vector of center of momentum and relationship between the momentum and velocity of the center of momentum in the form <math>~ \mathbf p = \frac { E_r }{c^2} \mathbf V </math>, we get the relation: :<math>~ \mathbf {\mathbb C} = \frac { E_r }{c} ( \mathbf V t - \mathbf R_m ) .</math> In a closed system the pseudotensor <math>~ M_{\mu \nu} </math> must be conserved, and its components must be some constants. For space components of the pseudotensor this results in conservation of angular momentum: <math>~ \mathbf M = const </math>. From equality of the pseudotensor’s time components and components of the vector <math>~ \mathbf {\mathbb C} </math> it follows that it should be <math>~ \mathbf {\mathbb C} = const </math>. Given the expression for <math>~ \mathbf {\mathbb C} </math>, it can be written as <math>~ \mathbf R_m = \mathbf R_{m0} + \mathbf V t </math>, where the constant vector <math>~ \mathbf R_{m0} </math> specifies position of the system’s center of momentum at <math>~ t=0 </math>. Thus, in this reference frame we obtain equation of motion of the center of momentum at constant velocity <math>~ \mathbf V </math>, as a property of motion of a closed system. The component <math> ~ M_z </math> of angular momentum of a uniform ball, taking into account relativistic corrections, can be calculated by the formula: <ref>Fedosin S.G. On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation. International Frontier Science Letters, Vol. 15, pp. 9-14 (2020). https://doi.org/10.18052/www.scipress.com/IFSL.15.9. </ref> :<math>~ M_z = \frac {3 \pi \rho_0 c^4 a}{2 \omega^3} - \frac {\pi \rho_0 c^2 a^3}{2 \omega} - \frac {3 \pi \rho_0 c^5 \left( 1- \frac {\omega^2 a^2}{c^2} \right) \left( 1+ \frac {\omega^2 a^2}{3c^2} \right) }{4 \omega^4} \ln \frac {1+ \frac {\omega a}{c} }{1- \frac {\omega a}{c} } .</math> Here <math> ~ \rho_0 </math> is invariant mass density, <math> ~ \omega </math> is angular velocity of rotation of the ball having a radius <math> ~ a </math>. == Integral vector == The equation used to find metric tensor components in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation] for tensors with mixed indices has the following form:<ref name="ab"/> :<math>~ R_\alpha^{\ \beta} - \frac {1}{4} R \delta_\alpha^{\ \beta} = - \frac {1}{2c k} \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) . </math> here <math>~ R_\alpha^{\ \beta}</math> is [[w:Ricci tensor |Ricci tensor]] with mixed indices; <math>~ \delta_\alpha^{\ \beta}</math> is unit tensor or [[w:Kronecker delta |Kronecker delta]]; <math>~ B_\alpha^{\ \beta}</math>, <math>~ P_\alpha^{\ \beta}</math>, <math>~ U_\alpha^{\ \beta}</math> and <math>~ W_\alpha^{\ \beta}</math> are stress-energy tensors of acceleration field and pressure field, gravitational and electromagnetic fields, respectively. With the help of covariant derivative <math>~ \nabla_\beta</math> we can find four-divergence of both sides of the above equation for metric. The divergence of the left-hand side is zero due to equality to zero of divergence of [[w:Einstein tensor |Einstein tensor]], <math>~ \nabla_\beta \left( R_\alpha^{\ \beta} - \frac {1}{2} R \delta_\alpha^{\ \beta}\right) =0 </math>, and also as a consequence of the fact that outside the body the scalar curvature vanishes, <math>~ R =0</math>, and inside the body it is constant. The latter follows from the gauge condition of energy of closed system. The divergence of the right-hand side of equation for the metric is also zero: :<math>~ \nabla_\beta \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) = \nabla_\beta T_\alpha^{\ \beta} = 0 , </math> where the tensor <math>~ T_\alpha^{\ \beta}</math> with mixed indices represents the sum of stress-energy tensors of all fields acting in the system. The resulting expression for tensors’ space components is nothing but differential equation of matter’s motion under action of forces generated by fields, which is written in a covariant form. <ref name="eq"/> As for the tensors’ time components, for them the expression is expression of generalized Poynting theorem for all the fields. <ref name="ge"/> In a weak field and at low velocities of motion of particles, the equation <math>~ \nabla_\beta T_\alpha^{\ \beta} \approx \partial_\beta T_\alpha^{\ \beta} = 0 </math> can be integrated over four-volume, taking into account the [[w:divergence theorem |divergence theorem]]. As a result, at initial moment of time for the system under consideration, the following relation will be valid: :<math>~ J_\alpha = \int { T_\alpha^{\ 0} dx^1 dx^2 dx^3} = const . </math> In a closed system, the four-dimensional integral vector <math>~ J_\alpha </math> must be constant. <ref name="co"/> For a stationary sphere with randomly moving particles in continuous medium approximation, the energy fluxes of fields defining the components <math>~ T_j^{\ 0}</math>, where <math>~ j =1,2,3</math>, are missing , so that the spatial components are zero, <math>~ J_j =0</math>. As for the time component <math>~ J_0 </math> of integral vector, then for volume occupied by matter inside the sphere, it also vanishes due to relation (4) for field coefficients. However, outside the sphere, where there are only gravitational and electromagnetic fields, the time component of integral vector is not equal to zero. As a result, the contribution to this component is made by energies of external fields: :<math>~ J_0 = - \frac {G m^2_g}{2a} + \frac {q^2_b}{8\pi \varepsilon_0 a} . </math> It follows from the above that integral vector shows distribution of energy and energy fluxes in the system under consideration. For the nonzero space components <math>~ J_j</math> of integral vector to appear some stationary motion of matter and fields is required, for example, general rotation, volume pulsations or mixing of matter. In this case, solenoidal vectors and the fields’ energy fluxes appear in the system. Since the integral vector <math>~ J_\alpha </math> is associated with energies and energy fluxes of fields in stress-energy tensors, it differs from the four-momentum <math>~ p_\mu </math>, which includes invariant mass and proportional to its rest energy. It turns out that difference between <math>~ J_\alpha </math> and <math>~ p_\mu </math> is due to fundamental difference between particles and fields, they cannot be reduced to each other, although they are interrelated with each other. == Virial theorem and kinetic energy of particles == In article <ref> Fedosin S.G. [https://zenodo.org/record/1037246 The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept]. Continuum Mechanics and Thermodynamics, Vol. 29, Issue 2, pp. 361-371 (2017). https://dx.doi.org/10.1007/s00161-016-0536-8. </ref> kinetic energy of particles of the system under consideration is estimated by three methods: from [[w:virial theorem | virial theorem]], from relativistic definition of energy and using generalized momenta and proper fields of the particles. In the limit of low velocities, all these methods give for kinetic energy the following: : <math>~E_k \approx \frac {0.3608\eta m^2 \gamma_c }{a} . </math> The possibility to use generalized momenta to calculate the energy of particles’ motion is associated with the fact that despite zeroing of vector potentials and solenoidal vectors on the large scale, in volume of each randomly moving particle these potentials and vectors are not equal to zero. As a result, the energy of motion of the system’s particles can be found as the half-sum of scalar products of vector field potentials by the particles’ momentum, while for electromagnetic field we should take not the momentum, but the product of charge by velocity and Lorentz factor. If we square the equation for <math>~ \gamma' </math> in (1), we can obtain dependence of squared velocity of particles’ random motion on current radius: : <math>~{v'}^2 \approx v^2_c - \frac {4 \pi \eta \rho_0 r^2 }{3} . </math> On the other hand, we can assume that <math>~ \mathbf v' = \mathbf v_r + \mathbf v_\perp ,</math> where <math>~ \mathbf v_r </math> denotes averaged velocity component directed along the radius, and <math>~ \mathbf v_\perp </math> is averaged velocity component perpendicular to the current radius. In addition, from statistical considerations, it follows that : <math>~{v'}^2 = v^2_r + v^2_\perp = 3 v^2_r . </math> This implies dependence of radial velocity on the radius: : <math>~v_r \approx \frac {v_c}{ \sqrt 3} \left( 1- \frac {2 \pi \eta \rho_0 r^2 }{3 v^2_c} \right) . </math> Next, from the virial theorem we find squared velocity of particles at the center of the sphere: : <math>~v^2_c \approx \frac {3 \eta m }{5 a} \left( 1 + \frac {9}{\sqrt {56}}\right) \approx \frac {1.3216 \eta m }{a} . </math> This makes it possible to estimate the Lorentz factor at the center: : <math>~\gamma_c = \frac {1}{\sqrt {1- \frac { v^2_c }{c^2}}} \approx 1+ \frac { v^2_c }{2c^2} +\frac {3 v^4_c }{8c^4} \approx 1+ \frac {3 \eta m}{10 a c^2} \left( 1+\frac {9}{2\sqrt {14}} \right) + \frac {27 \eta^2 m^2}{200 a^2 c^4} \left( 1+\frac {9}{2\sqrt {14}} \right)^2 . </math> In the ordinary interpretation of virial theorem the time-averaged kinetic energy of a system of particles must be two times less than averaged energy associated with the forces <math>~ \mathbf F_i </math> holding the particles at the radius-vectors <math>~ \mathbf r_i </math> : : <math>~ \langle W_k \rangle_m = - 0.5 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle. </math> However, in relativistic uniform system this equation is changed: : <math>~ \langle W_k \rangle \approx - 0.6 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle, </math> while the quantity <math>~ W_k </math> exceeds the kinetic energy of particles, <math>~ W_k \approx \gamma_c E_k </math>, and it becomes equal to it only in the limit of low velocities. In contrast to classical case, total time derivative of virial in stationary system is other than zero due to the virial’s dependence on the radius: : <math>~ \frac {dG_V}{dt} \approx \mathbf v \cdot \nabla {G_V}\approx \frac {0.1216 \eta m^2 \gamma^2_c }{a} . </math> An analysis of integral theorem of generalized virial makes it possible to find, on the basis of field theory, a formula for the root-mean-square speed of typical particles of a system without using the notion of temperature: <ref> Fedosin S.G. [http://em.rdcu.be/wf/click?upn=lMZy1lernSJ7apc5DgYM8f7AyOIJlVFO4uFv7zUQtzk-3D_DUeisO4Ue44lkDmCnrWVhK-2BAxKrUexyqlYtsmkyhvEp5zr527MDdThwbadScvhwZehXbanab8i5hqRa42b-2FKYwacOeM4LKDJeJuGA15M9FWvYOfBgfon7Bqg2f55NFYGJfVGaGhl0ghU-2BkIJ9Hz4M6SMBYS-2Fr-2FWWaj9eTxv23CKo9d8nFmYAbMtBBskFuW9fupsvIvN5eyv-2Fk-2BUc7hiS15rRISs1jpNnRQpDtk2OE9Hr6mYYe5Y-2B8lunO9GwVRw07Y1mdAqqtEZ-2BQjk5xUwPnA-3D-3D The integral theorem of generalized virial in the relativistic uniform model]. Continuum Mechanics and Thermodynamics, Vol. 31, Issue 3, pp. 627-638 (2019). https://dx.doi.org/10.1007/s00161-018-0715-x.</ref> :<math> v_\mathrm{rms} = c \sqrt{1- \frac {4 \pi \eta \rho_0 r^2}{c^2 \gamma^2_c \sin^2 {\left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) } } } .</math> == Extreme objects == In formula (2) for gravitational field strength <math>~ \mathbf \Gamma_o </math> outside a body there is a quantity <math>~A = \sin \delta - \delta \cos \delta</math>, where <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} </math>. As was shown in article, <ref name="gr"/> at the value <math>~ \delta = \delta_0 = 4.494 </math> radians the gravitational field strength <math>~ \mathbf \Gamma_o </math> vanishes and gravitational acceleration disappears. Therefore, in real physical objects the following condition must hold: <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} < \delta_0 </math>. If the angle <math>~ \delta </math> is increased, then the quantity <math>~A </math> would first increase, and then would begin to decrease and even change its sign. So, at <math>~ \delta = \frac {\pi}{2}</math> we have <math>~A =1</math>, at <math>~ \delta = \pi </math> we have <math>~A =\pi </math>, at <math>~ \delta = \frac {3 \pi}{2}</math> we have <math>~A = -1 </math>. Let us now consider the observable Universe, which on a scale 100 Mpc or more can be considered as a relativistic uniform system. The total mass-energy density of the Universe is close to the critical value <math>~ \rho_c \approx 10^{-26}</math> kg/m³ and the size of the Universe can be estimated as the Hubble length <math>~ R_H =c/H_0 \approx 10^{26}</math> m, where <math>~ H_0 </math> is Hubble parameter. Using approximate equality <math>~\eta \approx \frac {3}{5} G </math> according to, <ref name="es"/> we find the value <math>~ \delta_U = \frac { R_H }{c} \sqrt {4 \pi \eta \rho_c} \approx 1.7 > \frac {\pi}{2}</math> radians. Since the angle <math>~ \delta_U </math> is sufficiently large, then for modeling of gravitational field of the Universe it is necessary to use refined formulas with sines and cosines. For example, if we take the size of observable Universe equal to <math>~ 2.64 R_H </math>, then we have <math>~ \delta_U = \delta_0 </math>, and gravitational field at boundaries of the Universe will tend to zero. This is what we observe in the form of a large-scale cellular structure consisting of clusters of galaxies. The reason for the gravitation action weakening is assumed to be graviton scattering by the particles of space medium. <ref> Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Vol. 23, Special Issues No. 1, pp. 3-13 (2012). http://dx.doi.org/10.5281/zenodo.890806. </ref> Another extreme object is a proton, in which mass density in entire volume changes approximately by 1.5 times. As a result, in the first approximation a proton is a relativistic uniform system. The proton radius <math>~ r_p </math> is of the order of 0.873 fm, <ref>Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, Vol. 35, No. 4, pp. 349-363 (2012). http://dx.doi.org/10.5281/zenodo.889451. </ref> and average density is of the order of <math>~ \rho_p = 6 \cdot 10^{17}</math> kg/m³. As a gravitational constant at the atomic level the [[Physics/Essays/Fedosin/Strong gravitational constant | strong gravitational constant]] <math>~ G_s </math> should be used. An estimate of the quantity <math>~ \delta </math> for a proton at <math>~\eta \approx \frac {3}{5} G_s </math> gives: <math>~ \delta_p = \frac { r_p }{c} \sqrt {4 \pi \eta \rho_p} \approx 2.4 < \delta_0 </math> radians. This shows that a proton is an extreme object from the point of view of weakening of its gravitational field. In article, <ref name="gr"/> a method is provided for estimating Lorentz factor of matter’s motion at the center of a proton, which gives <math>~ \gamma_c =1.9 </math>. In addition, radius of action of [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]] in matter with the critical mass density <math>~ \rho_c \approx 10^{-26}</math> kg/m³ in observable Universe is estimated: <math>~ r_G <1.3 \cdot 10^7 </math> m. On a large scale in the Universe not the strong gravitation, but ordinary gravitation is acting with the radius of action of the order of Hubble length. Let us suppose that <math>~ r_G </math> corresponds to radius of a certain [[black hole]] for strong gravitation, calculated by the Schwarzschild formula: <math>~ r_G = \frac {2 G_s m} {c^2} </math>. If the mass is <math>~ m = \frac {4 \pi \rho_c r^3_G} {3}</math>, then for radius of a black hole with such mass we obtain<math>~ r_G =c \sqrt {\frac {3}{8 \pi G_s \rho_c }} = 2.7 \cdot 10^6 </math> m, and mass is <math>~ m = 8 \cdot 10^{-7} </math> kg. The Schwarzschild formula admits a black hole for strong gravitation at small mass of the order of proton mass, large mass density and a radius smaller than the proton radius. In addition, substitution of the mass <math>~ m </math> and the radius <math>~ r_G </math> into Schwarzschild formula formally corresponds to a black hole with a large radius and low density <math>~ \rho_c </math>. However, for an external observer, such a black hole would rather correspond not to a black hole, but to an object, containing strongly rarefied hydrogen gas of cosmic space. Similarly, the [[w:Observable universe |Metagalaxy]] with the radius of order of <math>~ r_H </math> and mass density <math>~ \rho_c </math> is not a black hole, although it corresponds to the Schwarzschild formula for ordinary gravitation. Hence, in accordance with the theory of infinite nesting of matter, conclusion follows – at each level of matter corresponding gravitation forms only one type of the most compact and stable object. So, at the level of nucleons a proton appears under the action of strong gravitation, and at the level of stars the ordinary gravitation generates a neutron star. If we multiply the radius of a neutron star by coefficient of similarity in size <math>~ P = 1.4 \cdot 10^{19}</math>, which is equal to the ratio of stellar radius to the proton radius, we obtain radius of the order of <math>1.7 \cdot 10^{23} </math> m. This radius must correspond to a compact object of a neutron star-type at the level of metagalaxies, which can emerge under the action of gravitation at this matter level. In the first approximation, the gravitational constant for metagalaxies is determined with the help of the similarity theory: <math>~ G_M =\frac {G P S^2} {\Phi} = 3 \cdot 10^{-50} </math> m³•s^–2•kg^–1, where <math>~ S=0.23 </math> is coefficient of similarity in velocities, <math>~ \Phi = 1.62 \cdot 10^{57} </math> is coefficient of similarity in mass. By analogy with the case of a proton, a neutron star is also considered as a relativistic uniform system. For a star with the mass of 1.35 Solar masses, the radius <math>~ R_s = 12 </math> km and average density <math>~ \rho_s \approx 3.7 \cdot 10^{17}</math> kg/m³, at <math>~\eta \approx \frac {3}{5} G </math> we obtain the angle <math>~ \delta_s = \frac { R_s }{c} \sqrt {4 \pi \eta \rho_s} \approx 0.546 </math> radians. With this in mind, if we substitute into (3) the stellar mass instead of <math>~ m_b </math> and the stellar radius instead of <math>~ a </math>, we can estimate Lorentz factor at the center of the star: <math>~ \gamma_{cs} =1.04 </math>. This allows us to estimate temperature at the center of the star: <math>~ T_s \approx 2.8 \cdot 10^{11} </math> K, which is close enough to calculation of temperature at the center of a newly formed star. <ref name="es"/> Thus, dependences of gravitational field inside and outside bodies in article <ref name="gr"/> are in good agreement with conclusions of [[w:Le Sage’s theory of gravitation |Le Sage’s theory of gravitation]] and the theory of [[Physics/Essays/Fedosin/Infinite Hierarchical Nesting of Matter|Infinite Hierarchical Nesting of Matter]], with strong gravitation at the level of nucleons and with the concept of a dynamic force vacuum field in [[Physics/Essays/Fedosin/Electrogravitational vacuum | electrogravitational vacuum]]. == Cosmological constant and scalar curvature == According to (6), outside a body, where the four-currents are equal to zero, cosmological constant <math>~ \Lambda</math> becomes equal to zero. In addition, scalar curvature <math>~ R</math> also becomes equal to zero. <ref name="en"/> Inside the body the relation <math>~ R= 2\Lambda </math> holds true, so that in matter with higher density both the scalar curvature and the cosmological constant increase. These quantities can be calculated using (6) as averaged values for typical particles of physical system. For cosmic space we obtain approximately the following: <math>~ \Lambda_0 \approx \frac {16 \pi G \rho_0}{c^2} \approx 10^{-52} </math> m^-2, where the average mass density is <math>~ \rho_0 \approx 2.7 \cdot 10^{-27}</math> kg/m³. A similar formula for a proton gives the following: <math>~ \Lambda \approx \frac {16 \pi G \rho_p}{c^2} \approx 2.2 \cdot 10^{-8} </math> m^-2. However, for a proton in the calculations we should use the strong gravitational constant <math>~ G_s </math>. In this case, we find: <math>~ \Lambda_p \approx \frac {16 \pi G_s \rho_p}{c^2} \approx 5.1 \cdot 10^{31} </math> m^-2. The obtained value is almost 84 orders of magnitude greater than the value of cosmological constant for cosmic space. The difference between cosmological constants for cosmic space and for a proton is associated with averaging procedure: the cosmological constant inside a proton is large, but in cosmic space matter containing protons, neutrons and electrons is very rarefied, the main place is occupied by void, so that cosmological constant averaged over entire space becomes a small value. Thus one of the paradoxes of general theory of relativity is solved, in which the cosmological constant is associated with zero vacuum energy and therefore it must be very large, but in fact the cosmological constant turns out to be a small value. For relativistic uniform system with four fields acting in it, average value <math>~ \stackrel{-}{\Lambda }</math> of cosmological constant in matter is constant and can be written as follows: : <math>~ -ck \stackrel{-}{\Lambda } = \frac {G \rho_0 c^2 \gamma_c}{\eta} \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - \frac {\rho^2_{0q} c^2 \gamma_c }{4 \pi \varepsilon_0 \eta \rho_0 }\cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) + \rho_0 \wp_c - \frac {\sigma\rho_0 c^2 \gamma_c }{\eta } . </math> This expression can be simplified by using scalar potential of gravitational field <math>~ \psi_a = - \frac {G m_g}{a}</math> and scalar potential of electric field <math>~ \varphi_a = \frac {q_b }{4 \pi \varepsilon_0 a}</math> on surface of body at <math>~ r=a </math> : : <math>~ -ck \stackrel{-}{\Lambda } \approx \rho_0\psi_a - \frac {G m \rho_0 \gamma_c }{2 a } + \rho_0 c^2 \gamma_c + \rho_{0q} \varphi_a + \frac {q \rho_{0q} \gamma_c }{8 \pi \varepsilon_0 a } + \rho_0 \wp_c . </math> == Field energy theorem == In a relativistic uniform system, the exact values of strengths and potentials of all active fields are known. This allows us to check the [[field energy theorem]] for such a system and verify the theorem.<ref> Fedosin S.G. [http://dergipark.org.tr/gujs/issue/45480/435567 The Integral Theorem of the Field Energy.] Gazi University Journal of Science. Vol. 32, No. 2, pp. 686-703 (2019). http://dx.doi.org/10.5281/zenodo.3252783. </ref> This theorem explains, in particular, why electrostatic energy can be calculated either through the field strength, included in the electromagnetic field tensor, or in another way, through the field potential. The kinetic energy and potential energy of electromagnetic field are defined as follows: :<math>~ E_{kf} = \int {A_\alpha j^\alpha \sqrt {-g} dx^1 dx^2 dx^3 }. </math> :<math>~ W_f = \frac {1}{4 \mu_0 } \int { F_{\mu \nu} F^{\mu \nu} \sqrt {-g} dx^1 dx^2 dx^3 }. </math> If we take entire infinite volume both inside and outside matter of the system, then in the framework of special theory of relativity and in the absence of magnetic fields, these expressions are simplified: : <math>~ E_{kf}= \int \rho_q \varphi_i dV \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fi}= \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fo}= \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> : <math>~ W_f = W_{fi} + W_{fo} \approx -\frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> By virtue of the field energy theorem, the following relation will be satisfied: : <math>~ E_{kf}+ 2 W_f = 0.</math> In general case, tensor invariant is expressed in terms of square of electric field strength and square of magnetic field induction: <math>~ F_{\mu \nu} F^{\mu \nu}= - \frac {2}{c^2} (E^2 - c^2 B^2) </math>. The field energy density is found through the time component of stress-energy tensor: <math>~ W^{00} = \frac {1}{2} (\varepsilon_0 E^2 + \frac {1}{\mu_ 0} B^2) </math>. In electrostatics, when there are no magnetic fields and <math>~ B = 0</math>, volume integral of tensor invariant becomes proportional to volume integral of the component <math>~W^{00} </math>. As a result, electrostatic energy can be calculated in different ways: : <math>~ U_e= E_{kf}+ W_f \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Besides: : <math>~ U_e= - W_f = \frac {1}{2} E_{kf} = \int W^{00} dV. </math> == Binding energy == With the help of covariant theory of gravitation total energy, binding energy, energy of fields, pressure energy and potential energy of a system consisting of particles and four fields is precisely calculated in the relativistic uniform model. <ref name="bi"> Fedosin S.G. The binding energy and the total energy of a macroscopic body in the relativistic uniform model. Middle East Journal of Science, Vol. 5, Issue 1, pp. 46-62 (2019). http://dx.doi.org/10.23884/mejs.2019.5.1.06. </ref> A noticeable difference is shown between the obtained results and relations for simple systems in classical mechanics, in which the acceleration field and pressure field are not taken into account or the pressure is considered to be a simple scalar quantity. In this case the inertial mass of a massive system is less than the total inertial mass of the system’s parts. == System mass == The article <ref> Fedosin S.G. [https://www.bpasjournals.com/physics/chapter-details.php?chap_id=2367&issue_type=177&volume=117&journal=7 The Mass Hierarchy in the Relativistic Uniform System]. Bulletin of Pure and Applied Sciences, Vol. 38 D (Physics), No. 2, pp. 73-80 (2019). http://dx.doi.org/10.5958/2320-3218.2019.00012.5. </ref> shows that relativistic uniform system with continuous matter distribution is characterized by five types of mass: the gauge mass <math>~m' </math> is related to cosmological constant and represents mass-energy of matter’s particles in four-potentials of the system’s fields; the inertial mass <math>~M </math>; the auxiliary mass <math>~m </math> is equal to product of the particles’ mass density by volume of the system; the mass <math>~m_b </math> is the sum of invariant masses (rest masses) of the system’s particles, which is equal in value to gravitational mass <math>~m_g </math>. The relation for these masses is as follows: :<math>~m' < M < m < m_b = m_g .</math> == Solution of 4/3 problem == For electromagnetic and gravitational fields, the 4/3 problem consists in inequality of mass-energy extracted from the energy of field of a body at rest, and mass-energy resulting from the field momentum of the moving body. If such a body is a relativistic uniform system of spherical shape, then mass-energy associated with electrostatic energy of the system is: :<math>~ m_f = \frac {E_e}{c^2} \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a c^2}. </math> The energy flux of electromagnetic field of a moving sphere is calculated using the Poynting vector. Let <math>~ \gamma </math> be Lorentz factor, and <math>~ v </math> be velocity of the sphere. Having calculated energy fluxes of the field inside and outside the sphere, as well as total energy flux, we can find corresponding quantities with dimension of momentum associated with these energy fluxes:<ref name="ge"/> :<math>~ g_{pi} \approx \frac { \gamma q^2 \gamma^2_c v}{30 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_{po} \approx \frac { \gamma q^2 \gamma^2_c v}{6 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_p = g_{pi} + g_{po} \approx \frac { \gamma q^2 \gamma^2_c v }{5 \pi \varepsilon_0 a c^2}. </math> From here we find the mass-energy associated with the field energy fluxes: :<math>~ m_p = \frac {g_p}{\gamma v} \approx \frac { q^2 \gamma^2_c }{5 \pi \varepsilon_0 a c^2}. </math> For mass-energies, a ratio describing the 4/3 problem is obtained: :<math>~ m_p =\frac {4}{3} m_f . </math> If we consider the energy and energy flux of electromagnetic field only inside the sphere, or only outside the sphere, similar correlations are obtained for corresponding mass-energies. As indicated in the article, <ref name="ge"/> the mass-energy mismatch is a consequence of the fact that time components of electromagnetic stress-energy tensor and their integrals over volume do not together form any four-vector. In contrast, four-momentum of a system is a four-vector, so that the same inertial mass enters both the energy and momentum of the system. On the other hand, energy and momentum of electromagnetic field are included only as components in energy and momentum of entire system under consideration, and therefore they themselves do not have to form a four-vector. To calculate a four-momentum of a system, it is necessary to add energy and momentum of other fields operating in the system to the energy and momentum of electromagnetic field. In addition to electromagnetic field, the minimum set of fields of the system includes acceleration field, pressure field and gravitational field, and therefore it is necessary to take into account their energy and momentum. In this case, inside the sphere, the sum of energies of all fields found through tensor invariants and through stress-energy tensors is zeroed out. The total energy flux and total momentum of fields inside the sphere are also zero, so that within the sphere, the 4/3 problem as applied to [[Physics/Essays/Fedosin/General field | general field]] disappears. The equality to zero of sum of energies and sum of momenta of fields inside the sphere with randomly moving particles is a consequence of the fact that particles and fields have the opportunity to exchange energy and momentum with each other. As a result, contribution to relativistic energy of the system is made only by particle energies in scalar potentials of fields, and energies of electromagnetic and gravitational fields outside the sphere. The 4/3 problem shows in particular why energy and momentum of an electron and any other body cannot be reduced only to action of its own electromagnetic field. Despite the fact that an electron has a maximum charge per unit mass and is extremely charged, there are other fields in the electron's matter, for example [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]]. These fields have their own energy and momentum, which contribute to four-momentum of the electron. == Relations between field potentials == In the article, <ref>Fedosin S.G. [https://rdcu.be/ccV9o The potentials of the acceleration field and pressure field in rotating relativistic uniform system]. Continuum Mechanics and Thermodynamics, Vol. 33, Issue 3, pp. 817-834 (2021). https://doi.org/10.1007/s00161-020-00960-7. </ref> a connection was found between scalar potentials of acceleration field and pressure field in relativistic uniform system: :<math>~ \wp = \frac {\sigma (\vartheta -c^2)}{ \eta } = \frac {2 (\vartheta -c^2)}{ 3 }. </math> In addition, a relativistic expression for pressure was found: <math> p = \frac{2\rho c^2 (\gamma - 1) }{3}= \frac {2 \rho c^2 }{3} \left( \frac {1}{\sqrt {1- v^2/ c^2 }}-1 \right) \approx \frac {\rho v^2}{3}, </math> where <math>\rho </math> is mass density of moving matter, <math> c </math> is speed of light, <math> \gamma =\frac {1}{\sqrt {1- v^2/ c^2 }} </math> is [[w:Lorentz factor |Lorentz factor]]. In the limit of low velocities, this relationship turns into standard formula of [[w:kinetic theory of gases |kinetic theory of gases]]. == Metric inside and outside system == Standard expression for square of interval between two close points in metric theories is the following: :<math> ds^2 \ = \ g_{\mu\nu}(x) \ dx^{\mu} \ dx^{\nu}.</math> For static metric with spherical coordinates <math> x^0 = ct, </math> <math> x^1 = r ,</math> <math> x^2 = \theta , </math> <math> x^3 = \phi , </math> there are four nonzero components of the metric tensor: <math> g_{00}, </math> <math> g_{11}, </math> <math> g_{22}, </math> and <math> g_{33}= g_{22} \sin^2 \theta .</math> As a result, there is :<math> ds^2 \ = g_{00} c^2 dt^2 + g_{11} dr^2 + g_{22} d\theta^2 + g_{22} \sin^2 \theta d\phi^2.</math> As it was found for components of metric inside a spherical body within the framework of relativistic uniform model, <ref>{{cite journal| last=Fedosin|first=S. G. |s2cid= 238253182 |url= https://physmath.spbstu.ru/en/article/2021.53.13/ |title= The relativistic uniform model: the metric of the covariant theory of gravitation inside a body |journal= St. Petersburg Polytechnical State University Journal. Physics and Mathematics (Научно-технические ведомости СПбГПУ. Физико-математические науки) | volume=14 |issue=3 |pages=168–184 |date=2021 |doi= 10.18721/JPM.14313 |arxiv=2110.00342 |bibcode=2021arXiv211000342F }} // [http://sergf.ru/ru.htm О метрике ковариантной теории гравитации внутри тела в релятивистской однородной модели].</ref> <math> g_{22}= - r^2, </math> and :<math> (g_{00})_i = -\frac {1}{ (g_{11})_i } = 1+ \frac{ 8 \pi G \beta r^2 } {3c^4 }\left( \rho_0 c^2 \gamma_c + \rho_0 \psi_a - \frac {G m \rho_0 \gamma_c }{2a} + \rho_{0q} \varphi_a + \frac {q \rho_{0q}\gamma_c }{8\pi \varepsilon_0 a}+ \rho_0 \wp_c \right), </math> where <math> G </math> is gravitational constant; <math> \beta </math> is a coefficient to be determined; <math> r </math> is radial coordinate; <math> c </math> is the speed of light; <math> \rho_0 </math> is invariant mass density of matter particles; <math> \gamma_c </math> is Lorentz factor of particles moving at the center of body; <math> \psi_a = - \frac {G m_g}{a} </math> is gravitational potential at the surface of sphere with radius <math> a </math> and gravitational mass <math> m_g </math>; quantities <math> m = \frac {4 \pi a^3 \rho_0}{3}</math> and <math> q = \frac {4 \pi a^3 \rho_{0q}}{3}</math> are auxiliary values; <math> \rho_{0q} </math> is invariant charge density of matter particles, moving inside the body; <math> \varphi_a = \frac {q_b}{4\pi \varepsilon_0 a} </math> is electric scalar potential at the surface of sphere with total charge <math> q_b </math>; <math> \wp_c </math> is potential of pressure field at the center of body. On surface of the body, with <math> r = a </math>, the component <math> (g_{00})_ i </math> of metric tensor inside the body must be equal to the component <math> (g_{00})_o </math> of metric tensor outside the body. This allows us to refine expression for metric tensor components outside the body: :<math> (g_{00})_o = -\frac {1}{ (g_{11})_o } = 1+ \frac {2G m \gamma_c \beta }{c^2 r} + \frac{ 2 G \beta } {c^4 r}\left( m \psi_a + \frac {1}{2} m_g (\psi - \psi_a ) - \frac {G m^2 \gamma_c }{2a} + q \varphi_a + \frac {1}{2} q_b (\varphi - \varphi_a ) + \frac {q^2 \gamma_c }{8\pi \varepsilon_0 a} + m \wp_c \right), </math> where <math> \psi = - \frac {G m_g}{r} </math> is gravitational potential outside the body; <math> \varphi = \frac {q_b}{4\pi \varepsilon_0 r} </math> is electric potential outside the body. == Generalized four-momentum and total four-momentum == In the paper, <ref> Fedosin S.G. Generalized Four-momentum for Continuously Distributed Materials. Gazi University Journal of Science, Vol. 37, Issue 3, pp. 1509-1538 (2024). https://doi.org/10.35378/gujs.1231793. // [http://sergf.ru/gfm.htm Обобщённый 4-импульс для непрерывно распределённого вещества].</ref> formulas were found for calculating generalized four-momentum of a physical system in curved space-time taking into account contribution from particles and fields of the system. A differential four-dimensional Euler-Lagrange equation for continuously distributed matter was also obtained. Both the formulas for generalized four-momentum and Euler-Lagrange equation are satisfied in relativistic uniform system. In the paper, <ref> Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45. // [http://sergf.ru/ws.htm Что мы должны понимать под 4-импульсом физической системы?] </ref> covariant formulas for relativistic four-momentum of a physical system were derived, which were also verified in a relativistic uniform system. It was shown that four-momentum is expressed by the sum of two four-vectors of integral type with covariant indices, one of these four-vectors is generalized four-momentum of the system, and the other four-vector describes four-momentum of fields of the system. Additionally, the 4/3 problem and interpretation of integral vector found by integrating over volume of time components of stress-energy tensor of the system were considered. The fact that integral vector cannot be four-momentum of the system, as is assumed in general theory of relativity, is confirmed by direct calculation and follows from the fact that a four-vector cannot be obtained from tensor components. Similarly, volume integral of time components of stress-energy tensor of electromagnetic field does not yield four-momentum of electromagnetic field, but an integral vector that is not a four-vector. As a consequence, the mass-energies contained in components of integral vector are not equal to each other and are related in the proportion 4/3. Covariant formulas for four-momentum were used to determine the components of angular momentum tensor of a physical system in the article. <ref>Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, Vol. 40, No. 02, 2450163 (2025). https://doi.org/10.1142/S0217751X2450163X. // [http://sergf.ru/la.htm Лагранжев формализм в теории релятивистских векторных полей]. </ref> == References == <references/> == See also == * [[Invariant energy]] * [[Physics/Essays/Fedosin/General field | General field]] * [[Acceleration field]] * [[Pressure field]] * [[w:Gravitational field | Gravitational field]] * [[w:Electromagnetic field | Electromagnetic field]] * [[Physics/Essays/Fedosin/Covariant theory of gravitation | Covariant theory of gravitation]] * [[Energy]] * [[Field energy theorem]] ==External links == * [http://www.wikiznanie.ru/wikipedia/index.php/%D0%A0%D0%B5%D0%BB%D1%8F%D1%82%D0%B8%D0%B2%D0%B8%D1%81%D1%82%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%B4%D0%BD%D0%BE%D1%80%D0%BE%D0%B4%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0 Relativistic uniform system in Russian] [[Category:Special relativity]] [[Category:Physical systems]] [[Category:Covariant theory of gravitation]] [[Category:Energy]] nlq6gunt2ufgd0uymq5xjw28zcwuemj 2834545 2834544 2026-09-26T10:28:00Z Fedosin 196292 /* Relativistic energy */ 2834545 wikitext text/x-wiki '''Relativistic uniform system''' is an ideal [[w:physical system |physical system]], in which mass density (or any other physical quantity) depends on the [[w:Lorentz factor |Lorentz factor]] of the system’s particles, but is constant in the reference frames associated with the moving particles. ==Difference from classical uniform system== In classical physics, the ideal uniform body model is widely used, in which mass density is constant throughout the volume of the body or is given as the volume-averaged quantity. This model simplifies solution of physical problems and allows us to quickly estimate different physical quantities. For example, the body mass is calculated by simply multiplying the mass density by the body volume, which is easier than integrating the density over the volume in case of dependence of the density on coordinates. The disadvantage of the classical model is that the majority of real physical systems are far from this ideal uniformity. The use of the concept of relativistic uniform system is based on the [[Theory of relativity/Special relativity|special theory of relativity]] (STR) and is the next step towards a more precise description of physical systems. In STR particular importance is given to invariant physical quantities, which can be calculated in each inertial reference frame and are equal to the values that these quantities have in the proper reference frame of the body. For example, multiplication of invariant mass by [[w:four-velocity |four-velocity]] gives the [[w:four-momentum |four-momentum]] of the body containing the [[invariant energy]], and multiplication of corresponding invariant quantities by four-velocity allows us in the case of motion of solid point particles to find the [[w:four-potential |four-potential]]s of any vector fields and to develop their complete theory. <ref name="pr"> [[user:Fedosin | Fedosin S.G.]] [http://vixra.org/abs/1406.0135 The procedure of finding the stress-energy tensor and vector field equations of any form]. Advanced Studies in Theoretical Physics, Vol. 8, no. 18, 771-779 (2014). http://dx.doi.org/10.12988/astp.2014.47101. </ref> Another example is that for determination of four-velocity or [[four-acceleration]] as a rule the [[operator of proper-time-derivative]] is used instead of time derivative. Therefore, the use of invariant mass density and charge density of moving particles that make up the system does not only conform to principles of STR but also significantly simplifies solution of relativistic equations of motion. ==Field functions for bodies of spherical shape== Field equations are most easily solved in case of spherical symmetry in the absence of general rotation of particles. In this case all the physical quantities depend only on current radius, which starts at the center of the sphere. Below are presented solutions of equations for various fields within the framework of STR, including solutions for scalar potentials, field strengths and solenoidal vectors. Due to random motion of particles in the system, the vector field potentials become equal to zero. This leads to zeroing of solenoidal vectors of fields, including [[w:magnetic field |magnetic field]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]]. === Acceleration field === The four-potential <math>~ U_\mu = \left(\frac {\vartheta }{c},- \mathbf U \right) </math> of [[acceleration field]] includes the scalar potential <math>~ \vartheta</math> and the vector potential <math>~ \mathbf U</math>. Applying four-curl to the four-potential gives [[acceleration tensor]] <math>~ u_{\mu \nu} = \nabla_\mu U_\nu - \nabla_\nu U_\mu </math>. In curved spacetime acceleration field equation with the field sources is derived from the principle of least action: <ref name="pr"/> : <math>~ \nabla^\nu u_{\mu \nu} = - \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation after expressing the acceleration tensor <math>~ u_{\mu \nu}</math> in terms of four-potential turns into the wave equation for finding the four-potential of acceleration field: : <math>~ \nabla^\nu \nabla_\mu U_\nu - \nabla^\nu \nabla_\nu U_\mu = - \frac {4 \pi \eta }{c^2} J_\mu , </math> which, taking into account the calibration condition of the four-potential <math>~\nabla^\mu U_\mu = 0 </math>, can be transformed as follows: :<math>~ \nabla^\nu \nabla_\nu U_\mu + R_{\mu \nu} U^\nu = \frac{4 \pi \eta }{c^2} J_\mu, </math> where <math>~ c </math> is the speed of light, <math>~ \eta </math> is acceleration field coefficient, <math>~ J_\mu = g_{\mu \nu } J^\nu = g_{\mu \nu } \rho_0 u^\nu </math> is mass four-current with the covariant index, <math>~ g_{\mu \nu } </math> is metric tensor, <math>~ R_{\mu \nu} </math> is Ricci tensor, <math>~ u^\nu </math> is four-velocity, <math>~ \rho_0 </math> is invariant mass density of particles in comoving reference frames, which is the same for all the particles. In Minkowski spacetime within the framework of STR, covariant derivatives of the form <math>~ \nabla_\mu </math> turn into partial derivatives of the form <math>~ \partial_\mu </math>, while the result of action of the partial derivatives does not depend on the order of their action. As a consequence of calibration of the 4-potential, the equality holds: <math>~ \partial^\nu \partial_\mu U_\nu = \partial_\mu \partial^\nu U_\nu = 0 </math>. As a result, the four-potential of acceleration field can be found from the wave equation: : <math>~ \partial^\nu \partial_\nu U_\mu = \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation can be divided into two equations – one for scalar potential and the other for vector potential of acceleration field. In the system under consideration the vector potential is equal to zero, and the scalar potential of acceleration field is given by: : <math>~\vartheta = c g_{0 \mu} u^\mu = \gamma' c^2 , </math> where <math>~ g_{0 \mu} </math> are time components of metric tensor, <math>~ \gamma' </math> is Lorentz factor of particles in the reference frame K' associated with the center of the sphere. Since scalar potential of stationary system does not depend on time, the wave equation for the scalar potential turns into [[Partial differential equations/Poisson Equation|Poisson equation]]: <ref name="ab"> Fedosin S.G. [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9, No. 1, pp. 1-30 (2016). http://dx.doi.org/10.5281/zenodo.889304. </ref> : <math>~\triangle \vartheta = - 4 \pi \eta \rho_0 \gamma' </math> and the following formula is obtained for the Lorentz factor of particles: <ref name="int"> Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12 . </ref> : <math>~ \gamma' = \frac {c \gamma_c }{r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \gamma_c - \frac {2 \pi \eta \rho_0 r^2 \gamma_c }{3 c^2 }, \qquad\qquad (1) </math> where <math>~ \gamma_c </math> is Lorentz factor of particles at the center of the sphere, <math>~ r </math> is current radius. The acceleration field strength and corresponding solenoidal vector are expressed by the formulas: : <math>~ \mathbf S = - \nabla \vartheta - \frac {\partial \mathbf U }{\partial t}= \frac { c^2 \gamma_c \mathbf r}{r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac {4 \pi \eta \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf N = \nabla \times \mathbf U = 0. </math> === Pressure field === The four-potential <math>~ \pi_\mu = \left(\frac {\wp }{c},- \mathbf \Pi \right) </math> of [[pressure field]] includes the scalar potential <math>~ \wp </math> and the vector potential <math>~ \mathbf \Pi </math>, and obeys the calibration condition: <math>~\nabla^\mu \pi_\mu =0</math>. The pressure field equation with the field sources, [[pressure field tensor]] <math>~ f_{\mu \nu}</math> and equation for finding the four-potential of pressure field have the form: <ref name="pr"/> : <math>~ \nabla^\nu f_{\mu \nu} = - \frac {4 \pi \sigma }{c^2} J_\mu , \quad f_{\mu \nu} = \nabla_\mu \pi_\nu - \nabla_\nu \pi_\mu , \quad \nabla^\nu \nabla_\nu \pi_\mu + R_{\mu \nu} \pi^\nu = \frac{4 \pi \sigma }{c^2} J_\mu, </math> where <math>~ \sigma </math> is pressure field coefficient. In STR the latter equation turns into the wave equation: : <math>~ \partial^\nu \partial_\nu \pi_\mu = \frac {4 \pi \sigma }{c^2} J_\mu . </math> In stationary case the potentials do not depend on time and time component of the wave equation turns into the Poisson equation for the scalar potential of pressure field: : <math>~\triangle \wp = - 4 \pi \sigma \rho_0 \gamma' .</math> Solution of this equation inside the sphere with particles is as follows: <ref name="int"/> : <math>~ \wp = \wp_c - \frac {\sigma c^2 \gamma_c }{\eta } + \frac {\sigma c^3 \gamma_c }{\eta r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \wp_c - \frac {2 \pi \sigma \rho_0 r^2 \gamma_c }{3 }. </math> where <math>~ \wp _c </math> is scalar potential at the center of the sphere. This potential is approximately equal to: <ref name="en"> Fedosin S.G. Energy and metric gauging in the covariant theory of gravitation. Aksaray University Journal of Science and Engineering, Vol. 2, Issue 2, pp. 127-143 (2018). http://dx.doi.org/10.29002/asujse.433947. </ref> :<math>~ \wp_c \approx \frac {3 \sigma m}{10 a} \left( 1+\frac {9}{2\sqrt {14}} \right) , </math> where acceleration field constant <math>~ \eta </math> and pressure field constant <math>~ \sigma </math> are expressed by the formulas: :<math>~ \eta = \frac {3}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) , \qquad \qquad \sigma = \frac {2}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) .</math> The strength of pressure field and corresponding solenoidal vector are found as follows: : <math>~ \mathbf C = - \nabla \wp - \frac {\partial \mathbf \Pi }{\partial t}= \frac { \sigma c^2 \gamma_c \mathbf r}{\eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx \frac {4 \pi \sigma \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf I = \nabla \times \mathbf \Pi = 0. </math> === Gravitational field === The [[gravitational four-potential]] <math>~ D_\mu = \left(\frac {\psi }{c},- \mathbf D \right) </math> of [[w:gravitational field |gravitational field]] is made up with the use of scalar <math>~ \psi </math> and vector <math>~ \mathbf D </math> potentials. Calibration condition of the four-potential is: <math>~\nabla^\mu D_\mu = 0</math>. The gravitational field equation with field sources, the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] <math>~ \Phi_{\mu \nu} </math> and equation for finding the four-potential of gravitational field in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation]] have the form: <ref>Fedosin S.G. [https://payhip.com/b/RZOb Fizicheskie teorii i beskonechnaia vlozhennost’ materii]. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289. {{ISBN|978-5-9901951-1-0}}. (in Russian). </ref> <ref> Fedosin S.G. [http://vixra.org/abs/1110.0069 The Principle of Least Action in Covariant Theory of Gravitation.] Hadronic Journal, Vol. 35, No. 1, pp. 35-70 (2012). http://dx.doi.org/10.5281/zenodo.889804. </ref> : <math>~ \nabla^\nu \Phi_{\mu \nu} = \frac {4 \pi G }{c^2} J_\mu , \quad \Phi_{\mu \nu} = \nabla_\mu D_\nu - \nabla_\nu D_\mu , \quad \nabla^\nu \nabla_\nu D_\mu + R_{\mu \nu} D^\nu = -\frac {4 \pi G }{c^2} J_\mu, </math> where <math>~ G </math> is [[Physics/Essays/Fedosin/Gravitational constant | gravitational constant]]. In STR the latter equation is simplified and becomes the wave equation: : <math>~ \partial^\nu \partial_\nu D_\mu = -\frac {4 \pi G }{c^2} J_\mu . </math> From the wave equation in stationary case, the Poisson equation follows for scalar potential inside the sphere with randomly moving particles in the framework of [[Physics/Essays/Fedosin/Lorentz-invariant theory of gravitation | Lorentz-invariant theory of gravitation]] (LITG): : <math>~\triangle \psi_i = 4 \pi G \rho_0 \gamma' .</math> The right-hand side of this equation contains Lorentz factor <math>~ \gamma' </math>, which depends on the radius according to (1). In addition, the internal scalar potential near the surface of the sphere must coincide with the scalar potential of external field of the system, in view of standard potential gauge, that is with equality of potential to zero at infinity. As a result, dependence of scalar potential on the current radius differs from dependence in classical case of uniform sphere with the radius <math>~ a </math> and is equal to it only approximately: <ref name="int"/> : <math>~ \psi_i = -\frac {G c^2 \gamma_c }{ \eta r} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx -\frac {2 \pi G \rho_0 \gamma_c (3a^2 - r^2)}{3 }. </math> For [[Physics/Essays/Fedosin/Gravitational field strength | gravitational field strength]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]] inside the sphere we obtain the following: <ref name="re"> Fedosin S.G. [http://vixra.org/abs/1405.0002 Relativistic Energy and Mass in the Weak Field Limit.] [http://journals.yu.edu.jo/jjp/Vol8No1Contents2015.html Jordan Journal of Physics.] Vol. 8, No. 1, pp. 1-16 (2015). http://dx.doi.org/10.5281/zenodo.889210. </ref> : <math>~ \mathbf \Gamma_i = - \nabla \psi_i - \frac {\partial \mathbf D_i }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { 4 \pi G \rho_0 \gamma_c \mathbf r }{3}\left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf \Omega_i = \nabla \times \mathbf D_i = 0. </math> Solutions for external gravitational field potential and for field strength <math>~ \Gamma_o </math> according to LITG are as follows: : <math>~ \psi_o = - \frac {G c^2 \gamma_c }{ \eta r } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx - \frac {G m \gamma_c }{r} \left( 1- \frac {3 \eta m }{10 a c^2} \right). </math> : <math>~ \mathbf \Gamma_o = - \nabla \psi_o - \frac {\partial \mathbf D_o }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx </math> : <math>~\approx - \frac {G m \gamma_c \mathbf r}{r^3} \left( 1- \frac {3 \eta m }{10 a c^2} \right).\qquad\qquad (2) </math> Here, the auxiliary mass <math>~ m </math> is equal to the product of mass density <math>~ \rho_0 </math> by volume of the sphere: <math>~ m = \frac {4 \pi \rho_0 a^3 }{3} </math>. From expressions for potential and strength of external gravitational field we can see that the role of gravitational mass is played by the mass <math>~ m_g \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) .</math> Since <math>~ \gamma_c > 1 </math> then the relation <math>~ m_g > m </math> is satisfied. To understand difference between these masses we should calculate total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. For motion of particles there should be some voids between them. Both the average accelerations and average velocities of particles inside the sphere are functions of current radius. Dividing the particles’ velocities by their acceleration, we can find dependence of average period of oscillatory motion of particles on the radius. Finally, multiplying the velocity by the average period of motion, we can obtain an estimate of the size of voids between the particles. In order to calculate volume of the sphere, it is necessary to sum up volumes of all typical particles moving inside the sphere, as well as volumes of the voids between them. Suppose now that the sizes of typical particles are much larger than the voids between the particles, and volume of the voids is substantially less than the total volume of particles. In this case, we can use approximation of continuous medium, so that unit of mass of matter inside the sphere will be given by approximate expression <math>~ dm \approx \rho_0 \gamma' dV </math>, where <math>~ \rho_0 </math> is mass density in reference frames associated with the particles, <math>~ \gamma' </math> is Lorentz factor of the moving particles, the product <math>~ \rho_0 \gamma' </math> gives mass density of the particles from viewpoint of an observer, who is stationary with respect to the sphere, and volume element <math>~ dV </math> inside the sphere corresponds to the volume of a particle from the viewpoint of this observer. This leads to the fact that total volume of particles moving inside the sphere becomes approximately equal to the volume of the sphere. For the mass, in view of Lorentz factor (1), the following relation is obtained: : <math>~ m_b = \int dm = \int \rho_0 \gamma' dV = \frac {c^2 \gamma_c }{\eta } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right). \qquad\qquad (3) </math> This implies equality of gravitational mass <math>~ m_g </math> and total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. The both masses are greater than the mass <math>~ m </math>. By the method of its calculation, the mass <math>~ m_b </math> is equal to the sum of invariant masses of particles that make up the system. The external gravitational torsion field is equal to zero: : <math>~ \mathbf \Omega_o = \nabla \times \mathbf D_o = 0. </math> === Electromagnetic field === The [[w:electromagnetic four-potential | electromagnetic four-potential]] <math>~ A_\mu = \left(\frac {\varphi }{c},- \mathbf A \right) </math> of [[w:electromagnetic field |electromagnetic field]] includes scalar potential <math>~ \varphi </math> and vector potential <math>~ \mathbf A </math>. The covariant Lorentz calibration for four-potential is: <math>~\nabla^\mu A_\mu = 0 </math>. For a fixed uniformly charged spherical body with random motion of charges total electromagnetic field on the average is purely electric and the vector potential is equal to zero. The electromagnetic field equation with the field sources, [[w:electromagnetic tensor |electromagnetic tensor]] <math>~ F_{\mu \nu}</math> and equation for finding four-potential are expressed as follows: : <math>~ \nabla^\nu F_{\mu \nu} = - \frac {1 }{\varepsilon_0 c^2} j_\mu , \quad F_{\mu \nu} = \nabla_\mu A_\nu - \nabla_\nu A_\mu , \quad \nabla^\nu \nabla_\nu A_\mu + R_{\mu \nu} A^\nu = \frac {1 }{\varepsilon_0 c^2} j_\mu, </math> where <math>~ \varepsilon_0 </math> is [[electric constant]], <math>~ j_\mu </math> is electromagnetic [[w:four-current | four-current]]. The latter equation in STR turns into the wave equation: : <math>~ \partial^\nu \partial_\nu A_\mu = \frac {1 }{\varepsilon_0 c^2} j_\mu . </math> Due to the absence of time-dependence in the case under consideration, the wave equation becomes the Poisson equation for scalar potential <math>~ \varphi_i </math> inside the sphere: : <math>~\triangle \varphi_i = - \frac {\rho_{0q} \gamma'}{\varepsilon_0 } ,</math> where <math>~ \rho_{0q} </math> is charge density in the reference frames associated with the charges. Dependence of scalar potential on current radius in general case differs from dependence in classical case of potential of a uniformly charged sphere with the radius <math>~ a </math>, coinciding with it only in the first approximation: <ref name="el">Fedosin S.G. The electromagnetic field in the relativistic uniform model. International Journal of Pure and Applied Sciences, Vol. 4, Issue. 2, pp. 110-116 (2018). http://dx.doi.org/10.29132/ijpas.430614. </ref> : <math>~ \varphi_i = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[\frac {c }{ \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac {\rho_{0q} \gamma_c (3a^2 - r^2)}{6 \varepsilon_0 }. </math> Electric field strength and magnetic field inside the sphere have the form: : <math>~ \mathbf E_i = - \nabla \varphi_i - \frac {\partial \mathbf A_i }{\partial t}= \frac { \rho_{0q} c^2 \gamma_c \mathbf r}{4 \pi \varepsilon_0 \eta \rho_0 r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac { \rho_{0q} \gamma_c \mathbf r }{3 \varepsilon_0 } \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf B_i = \nabla \times \mathbf A_i = 0. </math> Outside the system under consideration charge density is equal to zero and Poisson equation for scalar potential turns into Laplace equation: : <math>~\triangle \varphi_o = 0 .</math> Solution for external electric field potential, corresponding to potential gauge and [[Maxwell's equations]] for electric field strength <math>~ E_o </math> is given by: : <math>~ \varphi_o = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[ \frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx \frac { q \gamma_c }{4\pi \varepsilon_0 r }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> : <math>~ \mathbf E_o = - \nabla \varphi_o - \frac {\partial \mathbf A_o }{\partial t}= \frac {\rho_{0q} c^2 \gamma_c \mathbf r}{ 4 \pi \varepsilon_0 \eta \rho_0 r^3} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx \frac { q \gamma_c \mathbf r}{4\pi \varepsilon_0 r^3 }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> External magnetic field is equal to zero: : <math>~ \mathbf B_o = \nabla \times \mathbf A_o = 0. </math> In these expressions, the charge <math>~ q </math> is an auxiliary quantity equal to the product of charge density <math>~ \rho_{0q} </math> by volume of the sphere: <math>~ q = \frac {4 \pi \rho_{0q} a^3 }{3} </math>. In this case, the following quantity serves as total charge of the system: :<math>~ q_b = \int \rho_{0q} \gamma' dV = \frac {\rho_{0q}c^2 \gamma_c }{\eta \rho_0 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> :<math>~\approx q \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) ,</math> while <math>~ q_b > q .</math> The charge <math>~ q_b </math> is calculated in the same way as the mass <math>~ m_b </math> and has the meaning of the sum of charges of all the system’s particles. == Tensor field invariants == The knowledge of field strengths and solenoidal components of fields allows us to find tensor components of corresponding fields with covariant indices. To pass on to the field tensors with contravariant indices we need to know metric tensor. In STR the metric tensor does not depend on coordinates and time, is uniquely defined, and in Cartesian coordinates consists of zeros and unities. As a result, it is easy to find the tensor field invariants <math>~ u_{\mu \nu} u^{\mu \nu}</math>, <math>~ f_{\mu \nu} f^{\mu \nu}</math>, <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu}</math> and <math>~ F_{\mu \nu} F^{\mu \nu}</math>, where <math>~ u_{\mu \nu}</math>, <math>~ f_{\mu \nu}</math>, <math>~ \Phi_{\mu \nu}</math> and <math>~ F_{\mu \nu}</math> are the [[acceleration tensor]], the [[pressure field tensor]], the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] and the [[w:electromagnetic tensor |electromagnetic tensor]], respectively. The tensor field invariants are included in Lagrangian, Hamiltonian. action function and relativistic energy of the system, and they are located there inside integrals over space volume. In addition, they are included in corresponding stress-energy tensors of the fields. <ref name="ab"/> Since in the system under consideration solenoidal vectors are zero, the tensor invariants depend only on the field strengths: : <math>~ u_{\mu \nu} u^{\mu \nu} = - \frac {2}{c^2}(S^2 - c^2 N^2) = - \frac {2}{c^2}S^2.</math> : <math>~ f_{\mu \nu} f^{\mu \nu} = - \frac {2}{c^2}(C^2 - c^2 I^2) = - \frac {2}{c^2}C^2.</math> : <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu} = - \frac {2}{c^2}(\Gamma^2 - c^2 \Omega^2) = - \frac {2}{c^2}\Gamma^2.</math> : <math>~ F_{\mu \nu} F^{\mu \nu} = - \frac {2}{c^2}(E^2 - c^2 B^2) = - \frac {2}{c^2}E^2.</math> The volume integrals of tensor invariants multiplied by corresponding factors were calculated in the article. <ref name="re"/> For acceleration field and pressure field the integrals are taken only over volume of the sphere: : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \eta } u_{\mu \nu} u^{\mu \nu} dV = - \frac {c^4 \gamma^2_c }{2 \eta } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \sigma } f_{\mu \nu} f^{\mu \nu} dV = - \frac {\sigma c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> The gravitational and electromagnetic fields of the system are present not only inside but also outside the sphere, where they extend to infinity, while field strengths of internal and external fields behave differently. The field strengths <math>~ \mathbf \Gamma_i </math> and <math>~ \mathbf E_i </math> are substituted respectively into integrals of tensor invariants of these fields taken over volume of the sphere, which gives the following: : <math>~ - \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{8 \pi \varepsilon_0 \eta^2 \rho^2_0} \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> Into volume integrals of tensor invariants of gravitational and electromagnetic fields of the system outside the sphere the field strengths <math>~ \mathbf \Gamma_o </math> and <math>~ \mathbf E_o </math> are substituted, respectively: : <math>~ - \int \limits^{\infty}_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 a} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right). </math> : <math>~ \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{ 8 \pi \varepsilon_0 \eta^2 \rho^2_0 a } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> == Energies of particles in field potentials == All the four fields act on particles inside the sphere, and therefore each particle of the system acquires corresponding energy in a particular field. The energy of a particle in a field is calculated as volume integral of product of effective mass density <math>~ \rho = \rho_0 \gamma' </math> by corresponding scalar potential, and for electric field the energy is determined as volume integral of product of effective charge density <math>~ \rho_q = \rho_{0q} \gamma' </math> by scalar potential <math>~ \varphi </math>, where Lorentz factor <math>~ \gamma' </math> from (1) is used. In STR the energies of particles in acceleration field, pressure field, gravitational and electric fields in uniform relativistic spherical system, in view of expressions for the field potentials <ref name="re"/> and corrections to calculations, <ref name="el"/> <ref name="ge">Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. </ref> <ref name="gf"> Fedosin S.G. [http://www.uiss2016.ru/files/uiss2016_res.pdf The gravitational field in the relativistic uniform model within the framework of the covariant theory of gravitation]. 5th Ulyanovsk International School-Seminar “Problems of Theoretical and Observational Cosmology” ([http://www.uiss2016.ru/ UISS 2016]), Ulyanovsk, Russia, September 19-30, 2016, Abstracts, p. 23, {{ISBN|978-5-86045-872-7}}. </ref> <ref name="gr">Fedosin S.G. The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation. International Letters of Chemistry, Physics and Astronomy, Vol. 78, pp. 39-50 (2018). http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39.</ref> are, respectively: : <math>~ \int \rho \vartheta dV = \rho_0 c^2 \int \gamma'^2 dV = \frac {c^4 \gamma^2_c }{\eta } \left[ \frac {a}{2}- \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx </math> : <math>~ \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho \wp dV = \rho_0 \int \gamma' \wp dV = \frac {c^2 \gamma_c } {\eta } \left( \wp_c - \frac { \sigma c^2 \gamma_c }{\eta }\right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac { \sigma c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }}\sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3 \sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) . </math> : <math>~ \int \rho \psi_i dV = \rho_0 \int \gamma' \psi_i dV = </math> : <math>~= \frac {G c^4 \gamma^2_c }{\eta^2 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] - </math> : <math>~ - \frac {G c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2 a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho_q \varphi_i dV = \rho_{0q} \int \gamma' \varphi_i dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Note that all fields in which particles are located are not fields from external sources, but are generated by the particles themselves. As a result, the particles’ energies calculated above in scalar potentials of the fields are twice as large as potential energy of one or another interaction. For example, in order to calculate electrostatic energy of a system of two charges, it is sufficient to take potential of first charge at location of second charge and to multiply it by the value of the second charge. But if we use formula for energy in the form of an integral, then electrostatic energy will be taken into account twice, because the term is added, which contains potential of second charge at location of first charge multiplied by the value of the first charge. On the other hand, the electrostatic energy must consist of two components that take into account both the energy of particles in each other’s fields and the energy of electric field itself. Instead, in electrostatics, the electrostatic energy is calculated either through the scalar potential or through the field strength by integrating time component of stress-energy tensor over volume. Both methods provide the same result, but the connection between field energy and energy of particles in field potential is lost in this case, and it is not clear why these energies should coincide. == Relation between field coefficients == For the four fields under consideration equation of motion of matter in the concept of general field is as follows: <ref> Fedosin S.G. [http://www.oalib.com/paper/5263035#.VuFYxn2LQsY The Concept of the General Force Vector Field]. OALib Journal, Vol. 3, pp. 1-15 (2016), e2459. http://dx.doi.org/10.4236/oalib.1102459. </ref> <ref name="eq"> Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. </ref> : <math>~ u_{\mu \nu } J^\nu + f_{\mu \nu } J^\nu + \Phi_{\mu \nu } J^\nu + F_{\mu \nu } j^\nu = 0, </math> where <math>~ J_\mu </math> is mass four-current, <math>~ j^\nu </math> is electromagnetic [[w:four-current | four-current]]. Components of field tensors are field strengths and corresponding solenoidal vectors, but in the physical system under consideration the latter are equal to zero. As a result, space component of the equation of motion is reduced to the relation: : <math>~ \mathbf S + \mathbf C + \mathbf \Gamma_i + \frac {\rho_{0q}}{\rho_0 }\mathbf E_i = 0 . </math> If we substitute here expression for field strengths inside the sphere, we obtain relation between field coefficients: <ref name="es">Fedosin S.G. [http://www.nrcresearchpress.com/doi/10.1139/cjp-2015-0593#.Vv3piZyLQsY Estimation of the physical parameters of planets and stars in the gravitational equilibrium model.] Canadian Journal of Physics, Vol. 94, No. 4, pp. 370-379 (2016). http://dx.doi.org/10.1139/cjp-2015-0593. </ref> : <math>~\eta + \sigma = G - \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 }= G - \frac {q^2 }{ 4 \pi \varepsilon_0 m^2 }. \qquad \qquad (4) </math> The same is obtained for time component of equation of motion, which leads to generalized Poynting theorem. <ref name="ge"/> == Relation between energies of internal and external fields == In article <ref>Fedosin S.G. [http://vixra.org/abs/1205.0086 The Hamiltonian in Covariant Theory of Gravitation.] Advances in Natural Science, Vol. 5, No. 4, pp. 55-75 (2012). http://dx.doi.org/10.3968%2Fj.ans.1715787020120504.2023. </ref> it was found that energy of particles in gravitational field inside stationary sphere is up to a sign two times greater than total energy associated with tensor invariants of gravitational field inside and outside the sphere. A similar situation takes place in the system under consideration with random motion of particles and zero solenoidal vectors both for gravitational <ref name="gf"/> and electromagnetic fields. <ref name="el"/> In particular, we can write the following: : <math>~ \int \limits^{a}_{r=0} \rho \psi_i dV = 2 \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV + 2 \int \limits^{ \infty }_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = 2 \int \limits^{\infty }_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV. </math> : <math>~ \int \limits^{a}_{r=0} \rho_q \varphi_i dV = -2 \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV - 2 \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = - 2 \int \limits^{\infty }_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV. </math> These expressions relate the energy of particles in scalar field potentials with the energy found with the help of field strengths. == Relativistic energy == In curved spacetime the system’s energy for continuously distributed matter is given by the formula: <ref name="ab"/> <ref name="en"/> : <math>~E_r = \frac {1}{c} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> : <math>~ +\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}. \qquad \qquad (5)</math> This formula is valid in the case where it can be assumed that potentials and field strengths at each point in space do not have a direct dependence on the speeds of motion of individual particles of the system. In STR the metric tensor determinant is <math>~ g = -1 </math>, the time component of four-velocity is <math>~ u^0 = c \gamma'</math>, and in order to calculate the energy of spherical system with particles, taking into account the fields’ energies, we can use the above-mentioned energies of particles in field potentials and energies in the form of tensor invariants of the fields: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The expression for energy is simplified if we use the relation between field coefficients (4): : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> Taking into account relations between energies of internal and external fields also simplifies expression for the system’s energy: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{10 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) . </math> == Relation between energy and cosmological constant== In the approach under consideration, relativistic energy of the system is not an absolute value and requires gauging. For this purpose the [[w:cosmological constant | cosmological constant]] <math>~ \Lambda</math> is used. The gauge condition for the four main fields is related to sum of products of the fields’ four-potentials by corresponding four-currents and has the following form: <ref name="ab"/> <ref name="en"/> : <math>~ -ck \Lambda = A_\mu j^\mu + (D_\mu + U_\mu + \pi_\mu) J^\mu, \qquad \qquad (6) </math> where for large cosmic systems <math>~ -ck = \frac {c^4}{16\pi G \beta }</math>, and <math>~\beta </math> is a constant of order of unity. Within the framework of STR gauge condition has the following form: : <math>~ -ck \Lambda = \gamma \rho_{0q} (\varphi - \mathbf A \cdot \mathbf v) + \gamma \rho_{0} (\psi - \mathbf D \cdot \mathbf v + \vartheta - \mathbf U \cdot \mathbf v + \wp - \mathbf \Pi \cdot \mathbf v ). </math> If we divide the system’s particles and remove them to infinity and leave there at rest, the terms with products of vector field potentials by velocity of particles <math>~\mathbf v </math> would vanish, and Lorentz factor of an arbitrary particle would be <math>~ \gamma=1 </math>. On the right-hand side we will have only the sum of terms specifying energy density of particles located in potentials of their proper fields. Since <math>~ \vartheta \approx \gamma_c c^2 </math>, we see that the cosmological constant for each system’s particle is up to the multiplier <math>~ -ck</math> equal to rest energy density of this particle with a certain addition from its proper fields. Then the integral over volume of all the particles gives a certain energy: : <math>~ -ck \int \Lambda dV = m' c^2 ,</math> where the gauge mass <math>~ m' </math> is related to gauge condition of the energy. In the process of gravitational clustering the particles that were initially far from each other are united into closely bound systems, in which the field potentials increase manyfold. In the system under consideration <math>~ \gamma = \gamma' </math>, solenoidal vectors of fields are considered equal to zero due to random motion of particles, which gives the following: : <math>~ m' c^2 = \int [\gamma' \rho_{0q} \varphi_i + \gamma' \rho_{0} (\psi_i + \vartheta + \wp)] dV. </math> Expression on the right-hand side is part of relativistic energy <math>~E_r </math> of the system, so that the energy can be written as follows: : <math>~E_r = M c^2 \approx m' c^2 - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The mass <math>~ M </math> is related to relativistic energy of generally stationary system and is the inertial mass of the system. In view of (2), the energy will be equal to: : <math>~E_r = M c^2 \approx m' c^2 + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> This shows that relativistic energy of this system is equal to gauge mass-energy <math>~ m' c^2 </math>, from which the gravitational and electromagnetic energy of fields outside the system should be subtracted. == Lagrange function and motion integrals == Lagrange function for a system of particles and four main vector fields has the following form:<ref name="pr"/> <ref name="ab"/> :<math>~L = - \int {( U_\mu J^\mu + \pi_\mu J^\mu + D_\mu J^\mu + A_\mu j^\mu ) \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ +\int { \left( ckR - 2ck \Lambda -\frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} - \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} + \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} - \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}.</math> Here <math>~ R </math> is [[w:scalar curvature |scalar curvature]]. With the help of such Lagrange function, one can calculate generalized momentum of the system:<ref name="co">Fedosin S.G. [http://www.bpasjournals.com/physics/chapter-details.php?chap_id=2121&issue_type=158&volume=110&journal=7 The covariant additive integrals of motion in the theory of relativistic vector fields]. Bulletin of Pure and Applied Sciences, Vol. 37 D (Physics), No. 2, pp. 64-87 (2018). http://dx.doi.org/10.5958/2320-3218.2018.00013.1. </ref> :<math>~ \mathbf p = \frac {1}{c} \int {( \rho_0 \mathbf U + \rho_0 \mathbf \Pi + \rho_0 \mathbf D + \rho_{0q} \mathbf A ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> This vector depends on vector potentials of all four fields and is preserved in a closed physical system, that is, it is an integral of motion. Another integral of motion is relativistic energy of the system <math>~E_r</math>, which is found by formula (5). Further, it is assumed that one can neglect the contributions from gravitational and electromagnetic fields outside the matter and take into account only the generalized momentum. Then we can assume that these values form a four-momentum of the system, written with a covariant index: :<math>~ p_\mu = \left( \frac { E_r }{c}, - \mathbf p \right).</math> The angular momentum of the system is also an integral of motion: :<math>~ \mathbf M = \frac {1}{c} \int {( \rho_0 [\mathbf r \times \mathbf U] + \rho_0 [\mathbf r \times \mathbf \Pi] + \rho_0 [\mathbf r \times \mathbf D] + \rho_{0q} [\mathbf r \times \mathbf A] ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> The antisymmetric angular momentum pseudotensor is determined through the four-radius <math>~ x_\mu </math>, taken with a covariant index, and through the four-momentum <math>~ p_\mu </math>: :<math>~M_{\mu \nu} = \int {( x_\mu dp_\nu - x_\nu dp_\mu )} .</math> The spatial components of the angular momentum pseudotensor <math>~ M_{\mu \nu} </math> are the components of the angular momentum <math>~ \mathbf M </math> of the system: :<math>~ M_{12} = -M_{21} = -M_z , \qquad M_{13} = -M_{31} = M_y , \qquad M_{23} = -M_{32} = -M_x .</math> The radius-vector of the center of momentum of a physical system is determined by the formula: :<math>~ \mathbf R_m = \frac {1}{c E_r} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) \mathbf r u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ + \frac {1}{E_r}\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \mathbf r \sqrt {-g} dx^1 dx^2 dx^3}.</math> The time components of the pseudotensor <math>~ M_{\mu \nu} </math> are the components of three-dimensional vector <math>~ \mathbf {\mathbb C} </math>, which is often called time-varying dynamic mass moment: :<math>~ M_{01} = -M_{10} = -\mathbb C_x , \qquad M_{02} = -M_{20} = -\mathbb C_y , \qquad M_{03} = -M_{30} = -\mathbb C_z .</math> If we take into account definition of radius-vector of center of momentum and relationship between the momentum and velocity of the center of momentum in the form <math>~ \mathbf p = \frac { E_r }{c^2} \mathbf V </math>, we get the relation: :<math>~ \mathbf {\mathbb C} = \frac { E_r }{c} ( \mathbf V t - \mathbf R_m ) .</math> In a closed system the pseudotensor <math>~ M_{\mu \nu} </math> must be conserved, and its components must be some constants. For space components of the pseudotensor this results in conservation of angular momentum: <math>~ \mathbf M = const </math>. From equality of the pseudotensor’s time components and components of the vector <math>~ \mathbf {\mathbb C} </math> it follows that it should be <math>~ \mathbf {\mathbb C} = const </math>. Given the expression for <math>~ \mathbf {\mathbb C} </math>, it can be written as <math>~ \mathbf R_m = \mathbf R_{m0} + \mathbf V t </math>, where the constant vector <math>~ \mathbf R_{m0} </math> specifies position of the system’s center of momentum at <math>~ t=0 </math>. Thus, in this reference frame we obtain equation of motion of the center of momentum at constant velocity <math>~ \mathbf V </math>, as a property of motion of a closed system. The component <math> ~ M_z </math> of angular momentum of a uniform ball, taking into account relativistic corrections, can be calculated by the formula: <ref>Fedosin S.G. On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation. International Frontier Science Letters, Vol. 15, pp. 9-14 (2020). https://doi.org/10.18052/www.scipress.com/IFSL.15.9. </ref> :<math>~ M_z = \frac {3 \pi \rho_0 c^4 a}{2 \omega^3} - \frac {\pi \rho_0 c^2 a^3}{2 \omega} - \frac {3 \pi \rho_0 c^5 \left( 1- \frac {\omega^2 a^2}{c^2} \right) \left( 1+ \frac {\omega^2 a^2}{3c^2} \right) }{4 \omega^4} \ln \frac {1+ \frac {\omega a}{c} }{1- \frac {\omega a}{c} } .</math> Here <math> ~ \rho_0 </math> is invariant mass density, <math> ~ \omega </math> is angular velocity of rotation of the ball having a radius <math> ~ a </math>. == Integral vector == The equation used to find metric tensor components in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation] for tensors with mixed indices has the following form:<ref name="ab"/> :<math>~ R_\alpha^{\ \beta} - \frac {1}{4} R \delta_\alpha^{\ \beta} = - \frac {1}{2c k} \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) . </math> here <math>~ R_\alpha^{\ \beta}</math> is [[w:Ricci tensor |Ricci tensor]] with mixed indices; <math>~ \delta_\alpha^{\ \beta}</math> is unit tensor or [[w:Kronecker delta |Kronecker delta]]; <math>~ B_\alpha^{\ \beta}</math>, <math>~ P_\alpha^{\ \beta}</math>, <math>~ U_\alpha^{\ \beta}</math> and <math>~ W_\alpha^{\ \beta}</math> are stress-energy tensors of acceleration field and pressure field, gravitational and electromagnetic fields, respectively. With the help of covariant derivative <math>~ \nabla_\beta</math> we can find four-divergence of both sides of the above equation for metric. The divergence of the left-hand side is zero due to equality to zero of divergence of [[w:Einstein tensor |Einstein tensor]], <math>~ \nabla_\beta \left( R_\alpha^{\ \beta} - \frac {1}{2} R \delta_\alpha^{\ \beta}\right) =0 </math>, and also as a consequence of the fact that outside the body the scalar curvature vanishes, <math>~ R =0</math>, and inside the body it is constant. The latter follows from the gauge condition of energy of closed system. The divergence of the right-hand side of equation for the metric is also zero: :<math>~ \nabla_\beta \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) = \nabla_\beta T_\alpha^{\ \beta} = 0 , </math> where the tensor <math>~ T_\alpha^{\ \beta}</math> with mixed indices represents the sum of stress-energy tensors of all fields acting in the system. The resulting expression for tensors’ space components is nothing but differential equation of matter’s motion under action of forces generated by fields, which is written in a covariant form. <ref name="eq"/> As for the tensors’ time components, for them the expression is expression of generalized Poynting theorem for all the fields. <ref name="ge"/> In a weak field and at low velocities of motion of particles, the equation <math>~ \nabla_\beta T_\alpha^{\ \beta} \approx \partial_\beta T_\alpha^{\ \beta} = 0 </math> can be integrated over four-volume, taking into account the [[w:divergence theorem |divergence theorem]]. As a result, at initial moment of time for the system under consideration, the following relation will be valid: :<math>~ J_\alpha = \int { T_\alpha^{\ 0} dx^1 dx^2 dx^3} = const . </math> In a closed system, the four-dimensional integral vector <math>~ J_\alpha </math> must be constant. <ref name="co"/> For a stationary sphere with randomly moving particles in continuous medium approximation, the energy fluxes of fields defining the components <math>~ T_j^{\ 0}</math>, where <math>~ j =1,2,3</math>, are missing , so that the spatial components are zero, <math>~ J_j =0</math>. As for the time component <math>~ J_0 </math> of integral vector, then for volume occupied by matter inside the sphere, it also vanishes due to relation (4) for field coefficients. However, outside the sphere, where there are only gravitational and electromagnetic fields, the time component of integral vector is not equal to zero. As a result, the contribution to this component is made by energies of external fields: :<math>~ J_0 = - \frac {G m^2_g}{2a} + \frac {q^2_b}{8\pi \varepsilon_0 a} . </math> It follows from the above that integral vector shows distribution of energy and energy fluxes in the system under consideration. For the nonzero space components <math>~ J_j</math> of integral vector to appear some stationary motion of matter and fields is required, for example, general rotation, volume pulsations or mixing of matter. In this case, solenoidal vectors and the fields’ energy fluxes appear in the system. Since the integral vector <math>~ J_\alpha </math> is associated with energies and energy fluxes of fields in stress-energy tensors, it differs from the four-momentum <math>~ p_\mu </math>, which includes invariant mass and proportional to its rest energy. It turns out that difference between <math>~ J_\alpha </math> and <math>~ p_\mu </math> is due to fundamental difference between particles and fields, they cannot be reduced to each other, although they are interrelated with each other. == Virial theorem and kinetic energy of particles == In article <ref> Fedosin S.G. [https://zenodo.org/record/1037246 The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept]. Continuum Mechanics and Thermodynamics, Vol. 29, Issue 2, pp. 361-371 (2017). https://dx.doi.org/10.1007/s00161-016-0536-8. </ref> kinetic energy of particles of the system under consideration is estimated by three methods: from [[w:virial theorem | virial theorem]], from relativistic definition of energy and using generalized momenta and proper fields of the particles. In the limit of low velocities, all these methods give for kinetic energy the following: : <math>~E_k \approx \frac {0.3608\eta m^2 \gamma_c }{a} . </math> The possibility to use generalized momenta to calculate the energy of particles’ motion is associated with the fact that despite zeroing of vector potentials and solenoidal vectors on the large scale, in volume of each randomly moving particle these potentials and vectors are not equal to zero. As a result, the energy of motion of the system’s particles can be found as the half-sum of scalar products of vector field potentials by the particles’ momentum, while for electromagnetic field we should take not the momentum, but the product of charge by velocity and Lorentz factor. If we square the equation for <math>~ \gamma' </math> in (1), we can obtain dependence of squared velocity of particles’ random motion on current radius: : <math>~{v'}^2 \approx v^2_c - \frac {4 \pi \eta \rho_0 r^2 }{3} . </math> On the other hand, we can assume that <math>~ \mathbf v' = \mathbf v_r + \mathbf v_\perp ,</math> where <math>~ \mathbf v_r </math> denotes averaged velocity component directed along the radius, and <math>~ \mathbf v_\perp </math> is averaged velocity component perpendicular to the current radius. In addition, from statistical considerations, it follows that : <math>~{v'}^2 = v^2_r + v^2_\perp = 3 v^2_r . </math> This implies dependence of radial velocity on the radius: : <math>~v_r \approx \frac {v_c}{ \sqrt 3} \left( 1- \frac {2 \pi \eta \rho_0 r^2 }{3 v^2_c} \right) . </math> Next, from the virial theorem we find squared velocity of particles at the center of the sphere: : <math>~v^2_c \approx \frac {3 \eta m }{5 a} \left( 1 + \frac {9}{\sqrt {56}}\right) \approx \frac {1.3216 \eta m }{a} . </math> This makes it possible to estimate the Lorentz factor at the center: : <math>~\gamma_c = \frac {1}{\sqrt {1- \frac { v^2_c }{c^2}}} \approx 1+ \frac { v^2_c }{2c^2} +\frac {3 v^4_c }{8c^4} \approx 1+ \frac {3 \eta m}{10 a c^2} \left( 1+\frac {9}{2\sqrt {14}} \right) + \frac {27 \eta^2 m^2}{200 a^2 c^4} \left( 1+\frac {9}{2\sqrt {14}} \right)^2 . </math> In the ordinary interpretation of virial theorem the time-averaged kinetic energy of a system of particles must be two times less than averaged energy associated with the forces <math>~ \mathbf F_i </math> holding the particles at the radius-vectors <math>~ \mathbf r_i </math> : : <math>~ \langle W_k \rangle_m = - 0.5 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle. </math> However, in relativistic uniform system this equation is changed: : <math>~ \langle W_k \rangle \approx - 0.6 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle, </math> while the quantity <math>~ W_k </math> exceeds the kinetic energy of particles, <math>~ W_k \approx \gamma_c E_k </math>, and it becomes equal to it only in the limit of low velocities. In contrast to classical case, total time derivative of virial in stationary system is other than zero due to the virial’s dependence on the radius: : <math>~ \frac {dG_V}{dt} \approx \mathbf v \cdot \nabla {G_V}\approx \frac {0.1216 \eta m^2 \gamma^2_c }{a} . </math> An analysis of integral theorem of generalized virial makes it possible to find, on the basis of field theory, a formula for the root-mean-square speed of typical particles of a system without using the notion of temperature: <ref> Fedosin S.G. [http://em.rdcu.be/wf/click?upn=lMZy1lernSJ7apc5DgYM8f7AyOIJlVFO4uFv7zUQtzk-3D_DUeisO4Ue44lkDmCnrWVhK-2BAxKrUexyqlYtsmkyhvEp5zr527MDdThwbadScvhwZehXbanab8i5hqRa42b-2FKYwacOeM4LKDJeJuGA15M9FWvYOfBgfon7Bqg2f55NFYGJfVGaGhl0ghU-2BkIJ9Hz4M6SMBYS-2Fr-2FWWaj9eTxv23CKo9d8nFmYAbMtBBskFuW9fupsvIvN5eyv-2Fk-2BUc7hiS15rRISs1jpNnRQpDtk2OE9Hr6mYYe5Y-2B8lunO9GwVRw07Y1mdAqqtEZ-2BQjk5xUwPnA-3D-3D The integral theorem of generalized virial in the relativistic uniform model]. Continuum Mechanics and Thermodynamics, Vol. 31, Issue 3, pp. 627-638 (2019). https://dx.doi.org/10.1007/s00161-018-0715-x.</ref> :<math> v_\mathrm{rms} = c \sqrt{1- \frac {4 \pi \eta \rho_0 r^2}{c^2 \gamma^2_c \sin^2 {\left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) } } } .</math> == Extreme objects == In formula (2) for gravitational field strength <math>~ \mathbf \Gamma_o </math> outside a body there is a quantity <math>~A = \sin \delta - \delta \cos \delta</math>, where <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} </math>. As was shown in article, <ref name="gr"/> at the value <math>~ \delta = \delta_0 = 4.494 </math> radians the gravitational field strength <math>~ \mathbf \Gamma_o </math> vanishes and gravitational acceleration disappears. Therefore, in real physical objects the following condition must hold: <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} < \delta_0 </math>. If the angle <math>~ \delta </math> is increased, then the quantity <math>~A </math> would first increase, and then would begin to decrease and even change its sign. So, at <math>~ \delta = \frac {\pi}{2}</math> we have <math>~A =1</math>, at <math>~ \delta = \pi </math> we have <math>~A =\pi </math>, at <math>~ \delta = \frac {3 \pi}{2}</math> we have <math>~A = -1 </math>. Let us now consider the observable Universe, which on a scale 100 Mpc or more can be considered as a relativistic uniform system. The total mass-energy density of the Universe is close to the critical value <math>~ \rho_c \approx 10^{-26}</math> kg/m³ and the size of the Universe can be estimated as the Hubble length <math>~ R_H =c/H_0 \approx 10^{26}</math> m, where <math>~ H_0 </math> is Hubble parameter. Using approximate equality <math>~\eta \approx \frac {3}{5} G </math> according to, <ref name="es"/> we find the value <math>~ \delta_U = \frac { R_H }{c} \sqrt {4 \pi \eta \rho_c} \approx 1.7 > \frac {\pi}{2}</math> radians. Since the angle <math>~ \delta_U </math> is sufficiently large, then for modeling of gravitational field of the Universe it is necessary to use refined formulas with sines and cosines. For example, if we take the size of observable Universe equal to <math>~ 2.64 R_H </math>, then we have <math>~ \delta_U = \delta_0 </math>, and gravitational field at boundaries of the Universe will tend to zero. This is what we observe in the form of a large-scale cellular structure consisting of clusters of galaxies. The reason for the gravitation action weakening is assumed to be graviton scattering by the particles of space medium. <ref> Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Vol. 23, Special Issues No. 1, pp. 3-13 (2012). http://dx.doi.org/10.5281/zenodo.890806. </ref> Another extreme object is a proton, in which mass density in entire volume changes approximately by 1.5 times. As a result, in the first approximation a proton is a relativistic uniform system. The proton radius <math>~ r_p </math> is of the order of 0.873 fm, <ref>Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, Vol. 35, No. 4, pp. 349-363 (2012). http://dx.doi.org/10.5281/zenodo.889451. </ref> and average density is of the order of <math>~ \rho_p = 6 \cdot 10^{17}</math> kg/m³. As a gravitational constant at the atomic level the [[Physics/Essays/Fedosin/Strong gravitational constant | strong gravitational constant]] <math>~ G_s </math> should be used. An estimate of the quantity <math>~ \delta </math> for a proton at <math>~\eta \approx \frac {3}{5} G_s </math> gives: <math>~ \delta_p = \frac { r_p }{c} \sqrt {4 \pi \eta \rho_p} \approx 2.4 < \delta_0 </math> radians. This shows that a proton is an extreme object from the point of view of weakening of its gravitational field. In article, <ref name="gr"/> a method is provided for estimating Lorentz factor of matter’s motion at the center of a proton, which gives <math>~ \gamma_c =1.9 </math>. In addition, radius of action of [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]] in matter with the critical mass density <math>~ \rho_c \approx 10^{-26}</math> kg/m³ in observable Universe is estimated: <math>~ r_G <1.3 \cdot 10^7 </math> m. On a large scale in the Universe not the strong gravitation, but ordinary gravitation is acting with the radius of action of the order of Hubble length. Let us suppose that <math>~ r_G </math> corresponds to radius of a certain [[black hole]] for strong gravitation, calculated by the Schwarzschild formula: <math>~ r_G = \frac {2 G_s m} {c^2} </math>. If the mass is <math>~ m = \frac {4 \pi \rho_c r^3_G} {3}</math>, then for radius of a black hole with such mass we obtain<math>~ r_G =c \sqrt {\frac {3}{8 \pi G_s \rho_c }} = 2.7 \cdot 10^6 </math> m, and mass is <math>~ m = 8 \cdot 10^{-7} </math> kg. The Schwarzschild formula admits a black hole for strong gravitation at small mass of the order of proton mass, large mass density and a radius smaller than the proton radius. In addition, substitution of the mass <math>~ m </math> and the radius <math>~ r_G </math> into Schwarzschild formula formally corresponds to a black hole with a large radius and low density <math>~ \rho_c </math>. However, for an external observer, such a black hole would rather correspond not to a black hole, but to an object, containing strongly rarefied hydrogen gas of cosmic space. Similarly, the [[w:Observable universe |Metagalaxy]] with the radius of order of <math>~ r_H </math> and mass density <math>~ \rho_c </math> is not a black hole, although it corresponds to the Schwarzschild formula for ordinary gravitation. Hence, in accordance with the theory of infinite nesting of matter, conclusion follows – at each level of matter corresponding gravitation forms only one type of the most compact and stable object. So, at the level of nucleons a proton appears under the action of strong gravitation, and at the level of stars the ordinary gravitation generates a neutron star. If we multiply the radius of a neutron star by coefficient of similarity in size <math>~ P = 1.4 \cdot 10^{19}</math>, which is equal to the ratio of stellar radius to the proton radius, we obtain radius of the order of <math>1.7 \cdot 10^{23} </math> m. This radius must correspond to a compact object of a neutron star-type at the level of metagalaxies, which can emerge under the action of gravitation at this matter level. In the first approximation, the gravitational constant for metagalaxies is determined with the help of the similarity theory: <math>~ G_M =\frac {G P S^2} {\Phi} = 3 \cdot 10^{-50} </math> m³•s^–2•kg^–1, where <math>~ S=0.23 </math> is coefficient of similarity in velocities, <math>~ \Phi = 1.62 \cdot 10^{57} </math> is coefficient of similarity in mass. By analogy with the case of a proton, a neutron star is also considered as a relativistic uniform system. For a star with the mass of 1.35 Solar masses, the radius <math>~ R_s = 12 </math> km and average density <math>~ \rho_s \approx 3.7 \cdot 10^{17}</math> kg/m³, at <math>~\eta \approx \frac {3}{5} G </math> we obtain the angle <math>~ \delta_s = \frac { R_s }{c} \sqrt {4 \pi \eta \rho_s} \approx 0.546 </math> radians. With this in mind, if we substitute into (3) the stellar mass instead of <math>~ m_b </math> and the stellar radius instead of <math>~ a </math>, we can estimate Lorentz factor at the center of the star: <math>~ \gamma_{cs} =1.04 </math>. This allows us to estimate temperature at the center of the star: <math>~ T_s \approx 2.8 \cdot 10^{11} </math> K, which is close enough to calculation of temperature at the center of a newly formed star. <ref name="es"/> Thus, dependences of gravitational field inside and outside bodies in article <ref name="gr"/> are in good agreement with conclusions of [[w:Le Sage’s theory of gravitation |Le Sage’s theory of gravitation]] and the theory of [[Physics/Essays/Fedosin/Infinite Hierarchical Nesting of Matter|Infinite Hierarchical Nesting of Matter]], with strong gravitation at the level of nucleons and with the concept of a dynamic force vacuum field in [[Physics/Essays/Fedosin/Electrogravitational vacuum | electrogravitational vacuum]]. == Cosmological constant and scalar curvature == According to (6), outside a body, where the four-currents are equal to zero, cosmological constant <math>~ \Lambda</math> becomes equal to zero. In addition, scalar curvature <math>~ R</math> also becomes equal to zero. <ref name="en"/> Inside the body the relation <math>~ R= 2\Lambda </math> holds true, so that in matter with higher density both the scalar curvature and the cosmological constant increase. These quantities can be calculated using (6) as averaged values for typical particles of physical system. For cosmic space we obtain approximately the following: <math>~ \Lambda_0 \approx \frac {16 \pi G \rho_0}{c^2} \approx 10^{-52} </math> m^-2, where the average mass density is <math>~ \rho_0 \approx 2.7 \cdot 10^{-27}</math> kg/m³. A similar formula for a proton gives the following: <math>~ \Lambda \approx \frac {16 \pi G \rho_p}{c^2} \approx 2.2 \cdot 10^{-8} </math> m^-2. However, for a proton in the calculations we should use the strong gravitational constant <math>~ G_s </math>. In this case, we find: <math>~ \Lambda_p \approx \frac {16 \pi G_s \rho_p}{c^2} \approx 5.1 \cdot 10^{31} </math> m^-2. The obtained value is almost 84 orders of magnitude greater than the value of cosmological constant for cosmic space. The difference between cosmological constants for cosmic space and for a proton is associated with averaging procedure: the cosmological constant inside a proton is large, but in cosmic space matter containing protons, neutrons and electrons is very rarefied, the main place is occupied by void, so that cosmological constant averaged over entire space becomes a small value. Thus one of the paradoxes of general theory of relativity is solved, in which the cosmological constant is associated with zero vacuum energy and therefore it must be very large, but in fact the cosmological constant turns out to be a small value. For relativistic uniform system with four fields acting in it, average value <math>~ \stackrel{-}{\Lambda }</math> of cosmological constant in matter is constant and can be written as follows: : <math>~ -ck \stackrel{-}{\Lambda } = \frac {G \rho_0 c^2 \gamma_c}{\eta} \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - \frac {\rho^2_{0q} c^2 \gamma_c }{4 \pi \varepsilon_0 \eta \rho_0 }\cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) + \rho_0 \wp_c - \frac {\sigma\rho_0 c^2 \gamma_c }{\eta } . </math> This expression can be simplified by using scalar potential of gravitational field <math>~ \psi_a = - \frac {G m_g}{a}</math> and scalar potential of electric field <math>~ \varphi_a = \frac {q_b }{4 \pi \varepsilon_0 a}</math> on surface of body at <math>~ r=a </math> : : <math>~ -ck \stackrel{-}{\Lambda } \approx \rho_0\psi_a - \frac {G m \rho_0 \gamma_c }{2 a } + \rho_0 c^2 \gamma_c + \rho_{0q} \varphi_a + \frac {q \rho_{0q} \gamma_c }{8 \pi \varepsilon_0 a } + \rho_0 \wp_c . </math> == Field energy theorem == In a relativistic uniform system, the exact values of strengths and potentials of all active fields are known. This allows us to check the [[field energy theorem]] for such a system and verify the theorem.<ref> Fedosin S.G. [http://dergipark.org.tr/gujs/issue/45480/435567 The Integral Theorem of the Field Energy.] Gazi University Journal of Science. Vol. 32, No. 2, pp. 686-703 (2019). http://dx.doi.org/10.5281/zenodo.3252783. </ref> This theorem explains, in particular, why electrostatic energy can be calculated either through the field strength, included in the electromagnetic field tensor, or in another way, through the field potential. The kinetic energy and potential energy of electromagnetic field are defined as follows: :<math>~ E_{kf} = \int {A_\alpha j^\alpha \sqrt {-g} dx^1 dx^2 dx^3 }. </math> :<math>~ W_f = \frac {1}{4 \mu_0 } \int { F_{\mu \nu} F^{\mu \nu} \sqrt {-g} dx^1 dx^2 dx^3 }. </math> If we take entire infinite volume both inside and outside matter of the system, then in the framework of special theory of relativity and in the absence of magnetic fields, these expressions are simplified: : <math>~ E_{kf}= \int \rho_q \varphi_i dV \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fi}= \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fo}= \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> : <math>~ W_f = W_{fi} + W_{fo} \approx -\frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> By virtue of the field energy theorem, the following relation will be satisfied: : <math>~ E_{kf}+ 2 W_f = 0.</math> In general case, tensor invariant is expressed in terms of square of electric field strength and square of magnetic field induction: <math>~ F_{\mu \nu} F^{\mu \nu}= - \frac {2}{c^2} (E^2 - c^2 B^2) </math>. The field energy density is found through the time component of stress-energy tensor: <math>~ W^{00} = \frac {1}{2} (\varepsilon_0 E^2 + \frac {1}{\mu_ 0} B^2) </math>. In electrostatics, when there are no magnetic fields and <math>~ B = 0</math>, volume integral of tensor invariant becomes proportional to volume integral of the component <math>~W^{00} </math>. As a result, electrostatic energy can be calculated in different ways: : <math>~ U_e= E_{kf}+ W_f \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Besides: : <math>~ U_e= - W_f = \frac {1}{2} E_{kf} = \int W^{00} dV. </math> == Binding energy == With the help of covariant theory of gravitation total energy, binding energy, energy of fields, pressure energy and potential energy of a system consisting of particles and four fields is precisely calculated in the relativistic uniform model. <ref name="bi"> Fedosin S.G. The binding energy and the total energy of a macroscopic body in the relativistic uniform model. Middle East Journal of Science, Vol. 5, Issue 1, pp. 46-62 (2019). http://dx.doi.org/10.23884/mejs.2019.5.1.06. </ref> A noticeable difference is shown between the obtained results and relations for simple systems in classical mechanics, in which the acceleration field and pressure field are not taken into account or the pressure is considered to be a simple scalar quantity. In this case the inertial mass of a massive system is less than the total inertial mass of the system’s parts. == System mass == The article <ref> Fedosin S.G. [https://www.bpasjournals.com/physics/chapter-details.php?chap_id=2367&issue_type=177&volume=117&journal=7 The Mass Hierarchy in the Relativistic Uniform System]. Bulletin of Pure and Applied Sciences, Vol. 38 D (Physics), No. 2, pp. 73-80 (2019). http://dx.doi.org/10.5958/2320-3218.2019.00012.5. </ref> shows that relativistic uniform system with continuous matter distribution is characterized by five types of mass: the gauge mass <math>~m' </math> is related to cosmological constant and represents mass-energy of matter’s particles in four-potentials of the system’s fields; the inertial mass <math>~M </math>; the auxiliary mass <math>~m </math> is equal to product of the particles’ mass density by volume of the system; the mass <math>~m_b </math> is the sum of invariant masses (rest masses) of the system’s particles, which is equal in value to gravitational mass <math>~m_g </math>. The relation for these masses is as follows: :<math>~m' < M < m < m_b = m_g .</math> == Solution of 4/3 problem == For electromagnetic and gravitational fields, the 4/3 problem consists in inequality of mass-energy extracted from the energy of field of a body at rest, and mass-energy resulting from the field momentum of the moving body. If such a body is a relativistic uniform system of spherical shape, then mass-energy associated with electrostatic energy of the system is: :<math>~ m_f = \frac {E_e}{c^2} \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a c^2}. </math> The energy flux of electromagnetic field of a moving sphere is calculated using the Poynting vector. Let <math>~ \gamma </math> be Lorentz factor, and <math>~ v </math> be velocity of the sphere. Having calculated energy fluxes of the field inside and outside the sphere, as well as total energy flux, we can find corresponding quantities with dimension of momentum associated with these energy fluxes:<ref name="ge"/> :<math>~ g_{pi} \approx \frac { \gamma q^2 \gamma^2_c v}{30 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_{po} \approx \frac { \gamma q^2 \gamma^2_c v}{6 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_p = g_{pi} + g_{po} \approx \frac { \gamma q^2 \gamma^2_c v }{5 \pi \varepsilon_0 a c^2}. </math> From here we find the mass-energy associated with the field energy fluxes: :<math>~ m_p = \frac {g_p}{\gamma v} \approx \frac { q^2 \gamma^2_c }{5 \pi \varepsilon_0 a c^2}. </math> For mass-energies, a ratio describing the 4/3 problem is obtained: :<math>~ m_p =\frac {4}{3} m_f . </math> If we consider the energy and energy flux of electromagnetic field only inside the sphere, or only outside the sphere, similar correlations are obtained for corresponding mass-energies. As indicated in the article, <ref name="ge"/> the mass-energy mismatch is a consequence of the fact that time components of electromagnetic stress-energy tensor and their integrals over volume do not together form any four-vector. In contrast, four-momentum of a system is a four-vector, so that the same inertial mass enters both the energy and momentum of the system. On the other hand, energy and momentum of electromagnetic field are included only as components in energy and momentum of entire system under consideration, and therefore they themselves do not have to form a four-vector. To calculate a four-momentum of a system, it is necessary to add energy and momentum of other fields operating in the system to the energy and momentum of electromagnetic field. In addition to electromagnetic field, the minimum set of fields of the system includes acceleration field, pressure field and gravitational field, and therefore it is necessary to take into account their energy and momentum. In this case, inside the sphere, the sum of energies of all fields found through tensor invariants and through stress-energy tensors is zeroed out. The total energy flux and total momentum of fields inside the sphere are also zero, so that within the sphere, the 4/3 problem as applied to [[Physics/Essays/Fedosin/General field | general field]] disappears. The equality to zero of sum of energies and sum of momenta of fields inside the sphere with randomly moving particles is a consequence of the fact that particles and fields have the opportunity to exchange energy and momentum with each other. As a result, contribution to relativistic energy of the system is made only by particle energies in scalar potentials of fields, and energies of electromagnetic and gravitational fields outside the sphere. The 4/3 problem shows in particular why energy and momentum of an electron and any other body cannot be reduced only to action of its own electromagnetic field. Despite the fact that an electron has a maximum charge per unit mass and is extremely charged, there are other fields in the electron's matter, for example [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]]. These fields have their own energy and momentum, which contribute to four-momentum of the electron. == Relations between field potentials == In the article, <ref>Fedosin S.G. [https://rdcu.be/ccV9o The potentials of the acceleration field and pressure field in rotating relativistic uniform system]. Continuum Mechanics and Thermodynamics, Vol. 33, Issue 3, pp. 817-834 (2021). https://doi.org/10.1007/s00161-020-00960-7. </ref> a connection was found between scalar potentials of acceleration field and pressure field in relativistic uniform system: :<math>~ \wp = \frac {\sigma (\vartheta -c^2)}{ \eta } = \frac {2 (\vartheta -c^2)}{ 3 }. </math> In addition, a relativistic expression for pressure was found: <math> p = \frac{2\rho c^2 (\gamma - 1) }{3}= \frac {2 \rho c^2 }{3} \left( \frac {1}{\sqrt {1- v^2/ c^2 }}-1 \right) \approx \frac {\rho v^2}{3}, </math> where <math>\rho </math> is mass density of moving matter, <math> c </math> is speed of light, <math> \gamma =\frac {1}{\sqrt {1- v^2/ c^2 }} </math> is [[w:Lorentz factor |Lorentz factor]]. In the limit of low velocities, this relationship turns into standard formula of [[w:kinetic theory of gases |kinetic theory of gases]]. == Metric inside and outside system == Standard expression for square of interval between two close points in metric theories is the following: :<math> ds^2 \ = \ g_{\mu\nu}(x) \ dx^{\mu} \ dx^{\nu}.</math> For static metric with spherical coordinates <math> x^0 = ct, </math> <math> x^1 = r ,</math> <math> x^2 = \theta , </math> <math> x^3 = \phi , </math> there are four nonzero components of the metric tensor: <math> g_{00}, </math> <math> g_{11}, </math> <math> g_{22}, </math> and <math> g_{33}= g_{22} \sin^2 \theta .</math> As a result, there is :<math> ds^2 \ = g_{00} c^2 dt^2 + g_{11} dr^2 + g_{22} d\theta^2 + g_{22} \sin^2 \theta d\phi^2.</math> As it was found for components of metric inside a spherical body within the framework of relativistic uniform model, <ref>{{cite journal| last=Fedosin|first=S. G. |s2cid= 238253182 |url= https://physmath.spbstu.ru/en/article/2021.53.13/ |title= The relativistic uniform model: the metric of the covariant theory of gravitation inside a body |journal= St. Petersburg Polytechnical State University Journal. Physics and Mathematics (Научно-технические ведомости СПбГПУ. Физико-математические науки) | volume=14 |issue=3 |pages=168–184 |date=2021 |doi= 10.18721/JPM.14313 |arxiv=2110.00342 |bibcode=2021arXiv211000342F }} // [http://sergf.ru/ru.htm О метрике ковариантной теории гравитации внутри тела в релятивистской однородной модели].</ref> <math> g_{22}= - r^2, </math> and :<math> (g_{00})_i = -\frac {1}{ (g_{11})_i } = 1+ \frac{ 8 \pi G \beta r^2 } {3c^4 }\left( \rho_0 c^2 \gamma_c + \rho_0 \psi_a - \frac {G m \rho_0 \gamma_c }{2a} + \rho_{0q} \varphi_a + \frac {q \rho_{0q}\gamma_c }{8\pi \varepsilon_0 a}+ \rho_0 \wp_c \right), </math> where <math> G </math> is gravitational constant; <math> \beta </math> is a coefficient to be determined; <math> r </math> is radial coordinate; <math> c </math> is the speed of light; <math> \rho_0 </math> is invariant mass density of matter particles; <math> \gamma_c </math> is Lorentz factor of particles moving at the center of body; <math> \psi_a = - \frac {G m_g}{a} </math> is gravitational potential at the surface of sphere with radius <math> a </math> and gravitational mass <math> m_g </math>; quantities <math> m = \frac {4 \pi a^3 \rho_0}{3}</math> and <math> q = \frac {4 \pi a^3 \rho_{0q}}{3}</math> are auxiliary values; <math> \rho_{0q} </math> is invariant charge density of matter particles, moving inside the body; <math> \varphi_a = \frac {q_b}{4\pi \varepsilon_0 a} </math> is electric scalar potential at the surface of sphere with total charge <math> q_b </math>; <math> \wp_c </math> is potential of pressure field at the center of body. On surface of the body, with <math> r = a </math>, the component <math> (g_{00})_ i </math> of metric tensor inside the body must be equal to the component <math> (g_{00})_o </math> of metric tensor outside the body. This allows us to refine expression for metric tensor components outside the body: :<math> (g_{00})_o = -\frac {1}{ (g_{11})_o } = 1+ \frac {2G m \gamma_c \beta }{c^2 r} + \frac{ 2 G \beta } {c^4 r}\left( m \psi_a + \frac {1}{2} m_g (\psi - \psi_a ) - \frac {G m^2 \gamma_c }{2a} + q \varphi_a + \frac {1}{2} q_b (\varphi - \varphi_a ) + \frac {q^2 \gamma_c }{8\pi \varepsilon_0 a} + m \wp_c \right), </math> where <math> \psi = - \frac {G m_g}{r} </math> is gravitational potential outside the body; <math> \varphi = \frac {q_b}{4\pi \varepsilon_0 r} </math> is electric potential outside the body. == Generalized four-momentum and total four-momentum == In the paper, <ref> Fedosin S.G. Generalized Four-momentum for Continuously Distributed Materials. Gazi University Journal of Science, Vol. 37, Issue 3, pp. 1509-1538 (2024). https://doi.org/10.35378/gujs.1231793. // [http://sergf.ru/gfm.htm Обобщённый 4-импульс для непрерывно распределённого вещества].</ref> formulas were found for calculating generalized four-momentum of a physical system in curved space-time taking into account contribution from particles and fields of the system. A differential four-dimensional Euler-Lagrange equation for continuously distributed matter was also obtained. Both the formulas for generalized four-momentum and Euler-Lagrange equation are satisfied in relativistic uniform system. In the paper, <ref> Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45. // [http://sergf.ru/ws.htm Что мы должны понимать под 4-импульсом физической системы?] </ref> covariant formulas for relativistic four-momentum of a physical system were derived, which were also verified in a relativistic uniform system. It was shown that four-momentum is expressed by the sum of two four-vectors of integral type with covariant indices, one of these four-vectors is generalized four-momentum of the system, and the other four-vector describes four-momentum of fields of the system. Additionally, the 4/3 problem and interpretation of integral vector found by integrating over volume of time components of stress-energy tensor of the system were considered. The fact that integral vector cannot be four-momentum of the system, as is assumed in general theory of relativity, is confirmed by direct calculation and follows from the fact that a four-vector cannot be obtained from tensor components. Similarly, volume integral of time components of stress-energy tensor of electromagnetic field does not yield four-momentum of electromagnetic field, but an integral vector that is not a four-vector. As a consequence, the mass-energies contained in components of integral vector are not equal to each other and are related in the proportion 4/3. Covariant formulas for four-momentum were used to determine the components of angular momentum tensor of a physical system in the article. <ref>Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, Vol. 40, No. 02, 2450163 (2025). https://doi.org/10.1142/S0217751X2450163X. // [http://sergf.ru/la.htm Лагранжев формализм в теории релятивистских векторных полей]. </ref> == References == <references/> == See also == * [[Invariant energy]] * [[Physics/Essays/Fedosin/General field | General field]] * [[Acceleration field]] * [[Pressure field]] * [[w:Gravitational field | Gravitational field]] * [[w:Electromagnetic field | Electromagnetic field]] * [[Physics/Essays/Fedosin/Covariant theory of gravitation | Covariant theory of gravitation]] * [[Energy]] * [[Field energy theorem]] ==External links == * [http://www.wikiznanie.ru/wikipedia/index.php/%D0%A0%D0%B5%D0%BB%D1%8F%D1%82%D0%B8%D0%B2%D0%B8%D1%81%D1%82%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%B4%D0%BD%D0%BE%D1%80%D0%BE%D0%B4%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0 Relativistic uniform system in Russian] [[Category:Special relativity]] [[Category:Physical systems]] [[Category:Covariant theory of gravitation]] [[Category:Energy]] m5ji67jka3bjfsytt3d40pma96rjv00 2834548 2834545 2026-09-26T10:29:28Z Fedosin 196292 /* Relation between energy and cosmological constant */ 2834548 wikitext text/x-wiki '''Relativistic uniform system''' is an ideal [[w:physical system |physical system]], in which mass density (or any other physical quantity) depends on the [[w:Lorentz factor |Lorentz factor]] of the system’s particles, but is constant in the reference frames associated with the moving particles. ==Difference from classical uniform system== In classical physics, the ideal uniform body model is widely used, in which mass density is constant throughout the volume of the body or is given as the volume-averaged quantity. This model simplifies solution of physical problems and allows us to quickly estimate different physical quantities. For example, the body mass is calculated by simply multiplying the mass density by the body volume, which is easier than integrating the density over the volume in case of dependence of the density on coordinates. The disadvantage of the classical model is that the majority of real physical systems are far from this ideal uniformity. The use of the concept of relativistic uniform system is based on the [[Theory of relativity/Special relativity|special theory of relativity]] (STR) and is the next step towards a more precise description of physical systems. In STR particular importance is given to invariant physical quantities, which can be calculated in each inertial reference frame and are equal to the values that these quantities have in the proper reference frame of the body. For example, multiplication of invariant mass by [[w:four-velocity |four-velocity]] gives the [[w:four-momentum |four-momentum]] of the body containing the [[invariant energy]], and multiplication of corresponding invariant quantities by four-velocity allows us in the case of motion of solid point particles to find the [[w:four-potential |four-potential]]s of any vector fields and to develop their complete theory. <ref name="pr"> [[user:Fedosin | Fedosin S.G.]] [http://vixra.org/abs/1406.0135 The procedure of finding the stress-energy tensor and vector field equations of any form]. Advanced Studies in Theoretical Physics, Vol. 8, no. 18, 771-779 (2014). http://dx.doi.org/10.12988/astp.2014.47101. </ref> Another example is that for determination of four-velocity or [[four-acceleration]] as a rule the [[operator of proper-time-derivative]] is used instead of time derivative. Therefore, the use of invariant mass density and charge density of moving particles that make up the system does not only conform to principles of STR but also significantly simplifies solution of relativistic equations of motion. ==Field functions for bodies of spherical shape== Field equations are most easily solved in case of spherical symmetry in the absence of general rotation of particles. In this case all the physical quantities depend only on current radius, which starts at the center of the sphere. Below are presented solutions of equations for various fields within the framework of STR, including solutions for scalar potentials, field strengths and solenoidal vectors. Due to random motion of particles in the system, the vector field potentials become equal to zero. This leads to zeroing of solenoidal vectors of fields, including [[w:magnetic field |magnetic field]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]]. === Acceleration field === The four-potential <math>~ U_\mu = \left(\frac {\vartheta }{c},- \mathbf U \right) </math> of [[acceleration field]] includes the scalar potential <math>~ \vartheta</math> and the vector potential <math>~ \mathbf U</math>. Applying four-curl to the four-potential gives [[acceleration tensor]] <math>~ u_{\mu \nu} = \nabla_\mu U_\nu - \nabla_\nu U_\mu </math>. In curved spacetime acceleration field equation with the field sources is derived from the principle of least action: <ref name="pr"/> : <math>~ \nabla^\nu u_{\mu \nu} = - \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation after expressing the acceleration tensor <math>~ u_{\mu \nu}</math> in terms of four-potential turns into the wave equation for finding the four-potential of acceleration field: : <math>~ \nabla^\nu \nabla_\mu U_\nu - \nabla^\nu \nabla_\nu U_\mu = - \frac {4 \pi \eta }{c^2} J_\mu , </math> which, taking into account the calibration condition of the four-potential <math>~\nabla^\mu U_\mu = 0 </math>, can be transformed as follows: :<math>~ \nabla^\nu \nabla_\nu U_\mu + R_{\mu \nu} U^\nu = \frac{4 \pi \eta }{c^2} J_\mu, </math> where <math>~ c </math> is the speed of light, <math>~ \eta </math> is acceleration field coefficient, <math>~ J_\mu = g_{\mu \nu } J^\nu = g_{\mu \nu } \rho_0 u^\nu </math> is mass four-current with the covariant index, <math>~ g_{\mu \nu } </math> is metric tensor, <math>~ R_{\mu \nu} </math> is Ricci tensor, <math>~ u^\nu </math> is four-velocity, <math>~ \rho_0 </math> is invariant mass density of particles in comoving reference frames, which is the same for all the particles. In Minkowski spacetime within the framework of STR, covariant derivatives of the form <math>~ \nabla_\mu </math> turn into partial derivatives of the form <math>~ \partial_\mu </math>, while the result of action of the partial derivatives does not depend on the order of their action. As a consequence of calibration of the 4-potential, the equality holds: <math>~ \partial^\nu \partial_\mu U_\nu = \partial_\mu \partial^\nu U_\nu = 0 </math>. As a result, the four-potential of acceleration field can be found from the wave equation: : <math>~ \partial^\nu \partial_\nu U_\mu = \frac {4 \pi \eta }{c^2} J_\mu . </math> This equation can be divided into two equations – one for scalar potential and the other for vector potential of acceleration field. In the system under consideration the vector potential is equal to zero, and the scalar potential of acceleration field is given by: : <math>~\vartheta = c g_{0 \mu} u^\mu = \gamma' c^2 , </math> where <math>~ g_{0 \mu} </math> are time components of metric tensor, <math>~ \gamma' </math> is Lorentz factor of particles in the reference frame K' associated with the center of the sphere. Since scalar potential of stationary system does not depend on time, the wave equation for the scalar potential turns into [[Partial differential equations/Poisson Equation|Poisson equation]]: <ref name="ab"> Fedosin S.G. [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9, No. 1, pp. 1-30 (2016). http://dx.doi.org/10.5281/zenodo.889304. </ref> : <math>~\triangle \vartheta = - 4 \pi \eta \rho_0 \gamma' </math> and the following formula is obtained for the Lorentz factor of particles: <ref name="int"> Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12 . </ref> : <math>~ \gamma' = \frac {c \gamma_c }{r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \gamma_c - \frac {2 \pi \eta \rho_0 r^2 \gamma_c }{3 c^2 }, \qquad\qquad (1) </math> where <math>~ \gamma_c </math> is Lorentz factor of particles at the center of the sphere, <math>~ r </math> is current radius. The acceleration field strength and corresponding solenoidal vector are expressed by the formulas: : <math>~ \mathbf S = - \nabla \vartheta - \frac {\partial \mathbf U }{\partial t}= \frac { c^2 \gamma_c \mathbf r}{r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac {4 \pi \eta \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf N = \nabla \times \mathbf U = 0. </math> === Pressure field === The four-potential <math>~ \pi_\mu = \left(\frac {\wp }{c},- \mathbf \Pi \right) </math> of [[pressure field]] includes the scalar potential <math>~ \wp </math> and the vector potential <math>~ \mathbf \Pi </math>, and obeys the calibration condition: <math>~\nabla^\mu \pi_\mu =0</math>. The pressure field equation with the field sources, [[pressure field tensor]] <math>~ f_{\mu \nu}</math> and equation for finding the four-potential of pressure field have the form: <ref name="pr"/> : <math>~ \nabla^\nu f_{\mu \nu} = - \frac {4 \pi \sigma }{c^2} J_\mu , \quad f_{\mu \nu} = \nabla_\mu \pi_\nu - \nabla_\nu \pi_\mu , \quad \nabla^\nu \nabla_\nu \pi_\mu + R_{\mu \nu} \pi^\nu = \frac{4 \pi \sigma }{c^2} J_\mu, </math> where <math>~ \sigma </math> is pressure field coefficient. In STR the latter equation turns into the wave equation: : <math>~ \partial^\nu \partial_\nu \pi_\mu = \frac {4 \pi \sigma }{c^2} J_\mu . </math> In stationary case the potentials do not depend on time and time component of the wave equation turns into the Poisson equation for the scalar potential of pressure field: : <math>~\triangle \wp = - 4 \pi \sigma \rho_0 \gamma' .</math> Solution of this equation inside the sphere with particles is as follows: <ref name="int"/> : <math>~ \wp = \wp_c - \frac {\sigma c^2 \gamma_c }{\eta } + \frac {\sigma c^3 \gamma_c }{\eta r \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \approx \wp_c - \frac {2 \pi \sigma \rho_0 r^2 \gamma_c }{3 }. </math> where <math>~ \wp _c </math> is scalar potential at the center of the sphere. This potential is approximately equal to: <ref name="en"> Fedosin S.G. Energy and metric gauging in the covariant theory of gravitation. Aksaray University Journal of Science and Engineering, Vol. 2, Issue 2, pp. 127-143 (2018). http://dx.doi.org/10.29002/asujse.433947. </ref> :<math>~ \wp_c \approx \frac {3 \sigma m}{10 a} \left( 1+\frac {9}{2\sqrt {14}} \right) , </math> where acceleration field constant <math>~ \eta </math> and pressure field constant <math>~ \sigma </math> are expressed by the formulas: :<math>~ \eta = \frac {3}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) , \qquad \qquad \sigma = \frac {2}{5} \left( G- \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 } \right) .</math> The strength of pressure field and corresponding solenoidal vector are found as follows: : <math>~ \mathbf C = - \nabla \wp - \frac {\partial \mathbf \Pi }{\partial t}= \frac { \sigma c^2 \gamma_c \mathbf r}{\eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx \frac {4 \pi \sigma \rho_0 \gamma_c \mathbf r }{3} \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right). </math> : <math>~ \mathbf I = \nabla \times \mathbf \Pi = 0. </math> === Gravitational field === The [[gravitational four-potential]] <math>~ D_\mu = \left(\frac {\psi }{c},- \mathbf D \right) </math> of [[w:gravitational field |gravitational field]] is made up with the use of scalar <math>~ \psi </math> and vector <math>~ \mathbf D </math> potentials. Calibration condition of the four-potential is: <math>~\nabla^\mu D_\mu = 0</math>. The gravitational field equation with field sources, the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] <math>~ \Phi_{\mu \nu} </math> and equation for finding the four-potential of gravitational field in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation]] have the form: <ref>Fedosin S.G. [https://payhip.com/b/RZOb Fizicheskie teorii i beskonechnaia vlozhennost’ materii]. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289. {{ISBN|978-5-9901951-1-0}}. (in Russian). </ref> <ref> Fedosin S.G. [http://vixra.org/abs/1110.0069 The Principle of Least Action in Covariant Theory of Gravitation.] Hadronic Journal, Vol. 35, No. 1, pp. 35-70 (2012). http://dx.doi.org/10.5281/zenodo.889804. </ref> : <math>~ \nabla^\nu \Phi_{\mu \nu} = \frac {4 \pi G }{c^2} J_\mu , \quad \Phi_{\mu \nu} = \nabla_\mu D_\nu - \nabla_\nu D_\mu , \quad \nabla^\nu \nabla_\nu D_\mu + R_{\mu \nu} D^\nu = -\frac {4 \pi G }{c^2} J_\mu, </math> where <math>~ G </math> is [[Physics/Essays/Fedosin/Gravitational constant | gravitational constant]]. In STR the latter equation is simplified and becomes the wave equation: : <math>~ \partial^\nu \partial_\nu D_\mu = -\frac {4 \pi G }{c^2} J_\mu . </math> From the wave equation in stationary case, the Poisson equation follows for scalar potential inside the sphere with randomly moving particles in the framework of [[Physics/Essays/Fedosin/Lorentz-invariant theory of gravitation | Lorentz-invariant theory of gravitation]] (LITG): : <math>~\triangle \psi_i = 4 \pi G \rho_0 \gamma' .</math> The right-hand side of this equation contains Lorentz factor <math>~ \gamma' </math>, which depends on the radius according to (1). In addition, the internal scalar potential near the surface of the sphere must coincide with the scalar potential of external field of the system, in view of standard potential gauge, that is with equality of potential to zero at infinity. As a result, dependence of scalar potential on the current radius differs from dependence in classical case of uniform sphere with the radius <math>~ a </math> and is equal to it only approximately: <ref name="int"/> : <math>~ \psi_i = -\frac {G c^2 \gamma_c }{ \eta r} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx -\frac {2 \pi G \rho_0 \gamma_c (3a^2 - r^2)}{3 }. </math> For [[Physics/Essays/Fedosin/Gravitational field strength | gravitational field strength]] and [[Physics/Essays/Fedosin/Gravitational torsion field |gravitational torsion field]] inside the sphere we obtain the following: <ref name="re"> Fedosin S.G. [http://vixra.org/abs/1405.0002 Relativistic Energy and Mass in the Weak Field Limit.] [http://journals.yu.edu.jo/jjp/Vol8No1Contents2015.html Jordan Journal of Physics.] Vol. 8, No. 1, pp. 1-16 (2015). http://dx.doi.org/10.5281/zenodo.889210. </ref> : <math>~ \mathbf \Gamma_i = - \nabla \psi_i - \frac {\partial \mathbf D_i }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3} \left[ \frac {c }{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { 4 \pi G \rho_0 \gamma_c \mathbf r }{3}\left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf \Omega_i = \nabla \times \mathbf D_i = 0. </math> Solutions for external gravitational field potential and for field strength <math>~ \Gamma_o </math> according to LITG are as follows: : <math>~ \psi_o = - \frac {G c^2 \gamma_c }{ \eta r } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx - \frac {G m \gamma_c }{r} \left( 1- \frac {3 \eta m }{10 a c^2} \right). </math> : <math>~ \mathbf \Gamma_o = - \nabla \psi_o - \frac {\partial \mathbf D_o }{\partial t}= - \frac {G c^2 \gamma_c \mathbf r}{ \eta r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}}\sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx </math> : <math>~\approx - \frac {G m \gamma_c \mathbf r}{r^3} \left( 1- \frac {3 \eta m }{10 a c^2} \right).\qquad\qquad (2) </math> Here, the auxiliary mass <math>~ m </math> is equal to the product of mass density <math>~ \rho_0 </math> by volume of the sphere: <math>~ m = \frac {4 \pi \rho_0 a^3 }{3} </math>. From expressions for potential and strength of external gravitational field we can see that the role of gravitational mass is played by the mass <math>~ m_g \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) .</math> Since <math>~ \gamma_c > 1 </math> then the relation <math>~ m_g > m </math> is satisfied. To understand difference between these masses we should calculate total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. For motion of particles there should be some voids between them. Both the average accelerations and average velocities of particles inside the sphere are functions of current radius. Dividing the particles’ velocities by their acceleration, we can find dependence of average period of oscillatory motion of particles on the radius. Finally, multiplying the velocity by the average period of motion, we can obtain an estimate of the size of voids between the particles. In order to calculate volume of the sphere, it is necessary to sum up volumes of all typical particles moving inside the sphere, as well as volumes of the voids between them. Suppose now that the sizes of typical particles are much larger than the voids between the particles, and volume of the voids is substantially less than the total volume of particles. In this case, we can use approximation of continuous medium, so that unit of mass of matter inside the sphere will be given by approximate expression <math>~ dm \approx \rho_0 \gamma' dV </math>, where <math>~ \rho_0 </math> is mass density in reference frames associated with the particles, <math>~ \gamma' </math> is Lorentz factor of the moving particles, the product <math>~ \rho_0 \gamma' </math> gives mass density of the particles from viewpoint of an observer, who is stationary with respect to the sphere, and volume element <math>~ dV </math> inside the sphere corresponds to the volume of a particle from the viewpoint of this observer. This leads to the fact that total volume of particles moving inside the sphere becomes approximately equal to the volume of the sphere. For the mass, in view of Lorentz factor (1), the following relation is obtained: : <math>~ m_b = \int dm = \int \rho_0 \gamma' dV = \frac {c^2 \gamma_c }{\eta } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx m \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right). \qquad\qquad (3) </math> This implies equality of gravitational mass <math>~ m_g </math> and total relativistic mass <math>~ m_b </math> of particles moving inside the sphere. The both masses are greater than the mass <math>~ m </math>. By the method of its calculation, the mass <math>~ m_b </math> is equal to the sum of invariant masses of particles that make up the system. The external gravitational torsion field is equal to zero: : <math>~ \mathbf \Omega_o = \nabla \times \mathbf D_o = 0. </math> === Electromagnetic field === The [[w:electromagnetic four-potential | electromagnetic four-potential]] <math>~ A_\mu = \left(\frac {\varphi }{c},- \mathbf A \right) </math> of [[w:electromagnetic field |electromagnetic field]] includes scalar potential <math>~ \varphi </math> and vector potential <math>~ \mathbf A </math>. The covariant Lorentz calibration for four-potential is: <math>~\nabla^\mu A_\mu = 0 </math>. For a fixed uniformly charged spherical body with random motion of charges total electromagnetic field on the average is purely electric and the vector potential is equal to zero. The electromagnetic field equation with the field sources, [[w:electromagnetic tensor |electromagnetic tensor]] <math>~ F_{\mu \nu}</math> and equation for finding four-potential are expressed as follows: : <math>~ \nabla^\nu F_{\mu \nu} = - \frac {1 }{\varepsilon_0 c^2} j_\mu , \quad F_{\mu \nu} = \nabla_\mu A_\nu - \nabla_\nu A_\mu , \quad \nabla^\nu \nabla_\nu A_\mu + R_{\mu \nu} A^\nu = \frac {1 }{\varepsilon_0 c^2} j_\mu, </math> where <math>~ \varepsilon_0 </math> is [[electric constant]], <math>~ j_\mu </math> is electromagnetic [[w:four-current | four-current]]. The latter equation in STR turns into the wave equation: : <math>~ \partial^\nu \partial_\nu A_\mu = \frac {1 }{\varepsilon_0 c^2} j_\mu . </math> Due to the absence of time-dependence in the case under consideration, the wave equation becomes the Poisson equation for scalar potential <math>~ \varphi_i </math> inside the sphere: : <math>~\triangle \varphi_i = - \frac {\rho_{0q} \gamma'}{\varepsilon_0 } ,</math> where <math>~ \rho_{0q} </math> is charge density in the reference frames associated with the charges. Dependence of scalar potential on current radius in general case differs from dependence in classical case of potential of a uniformly charged sphere with the radius <math>~ a </math>, coinciding with it only in the first approximation: <ref name="el">Fedosin S.G. The electromagnetic field in the relativistic uniform model. International Journal of Pure and Applied Sciences, Vol. 4, Issue. 2, pp. 110-116 (2018). http://dx.doi.org/10.29132/ijpas.430614. </ref> : <math>~ \varphi_i = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[\frac {c }{ \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac {\rho_{0q} \gamma_c (3a^2 - r^2)}{6 \varepsilon_0 }. </math> Electric field strength and magnetic field inside the sphere have the form: : <math>~ \mathbf E_i = - \nabla \varphi_i - \frac {\partial \mathbf A_i }{\partial t}= \frac { \rho_{0q} c^2 \gamma_c \mathbf r}{4 \pi \varepsilon_0 \eta \rho_0 r^3 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) - r \cos \left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~ \approx \frac { \rho_{0q} \gamma_c \mathbf r }{3 \varepsilon_0 } \left( 1- \frac {4 \pi \eta \rho_0 r^2}{10 c^2}\right) . </math> : <math>~ \mathbf B_i = \nabla \times \mathbf A_i = 0. </math> Outside the system under consideration charge density is equal to zero and Poisson equation for scalar potential turns into Laplace equation: : <math>~\triangle \varphi_o = 0 .</math> Solution for external electric field potential, corresponding to potential gauge and [[Maxwell's equations]] for electric field strength <math>~ E_o </math> is given by: : <math>~ \varphi_o = \frac {\rho_{0q} c^2 \gamma_c }{ 4 \pi \varepsilon_0 \eta \rho_0 r } \left[ \frac {c}{\sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0}\right) \right] \approx \frac { q \gamma_c }{4\pi \varepsilon_0 r }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> : <math>~ \mathbf E_o = - \nabla \varphi_o - \frac {\partial \mathbf A_o }{\partial t}= \frac {\rho_{0q} c^2 \gamma_c \mathbf r}{ 4 \pi \varepsilon_0 \eta \rho_0 r^3} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> : <math>~ \approx \frac { q \gamma_c \mathbf r}{4\pi \varepsilon_0 r^3 }\left( 1- \frac {3 \eta m}{10 a c^2}\right) . </math> External magnetic field is equal to zero: : <math>~ \mathbf B_o = \nabla \times \mathbf A_o = 0. </math> In these expressions, the charge <math>~ q </math> is an auxiliary quantity equal to the product of charge density <math>~ \rho_{0q} </math> by volume of the sphere: <math>~ q = \frac {4 \pi \rho_{0q} a^3 }{3} </math>. In this case, the following quantity serves as total charge of the system: :<math>~ q_b = \int \rho_{0q} \gamma' dV = \frac {\rho_{0q}c^2 \gamma_c }{\eta \rho_0 } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right] \approx </math> :<math>~\approx q \gamma_c \left( 1- \frac {3 \eta m }{10 a c^2} \right) ,</math> while <math>~ q_b > q .</math> The charge <math>~ q_b </math> is calculated in the same way as the mass <math>~ m_b </math> and has the meaning of the sum of charges of all the system’s particles. == Tensor field invariants == The knowledge of field strengths and solenoidal components of fields allows us to find tensor components of corresponding fields with covariant indices. To pass on to the field tensors with contravariant indices we need to know metric tensor. In STR the metric tensor does not depend on coordinates and time, is uniquely defined, and in Cartesian coordinates consists of zeros and unities. As a result, it is easy to find the tensor field invariants <math>~ u_{\mu \nu} u^{\mu \nu}</math>, <math>~ f_{\mu \nu} f^{\mu \nu}</math>, <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu}</math> and <math>~ F_{\mu \nu} F^{\mu \nu}</math>, where <math>~ u_{\mu \nu}</math>, <math>~ f_{\mu \nu}</math>, <math>~ \Phi_{\mu \nu}</math> and <math>~ F_{\mu \nu}</math> are the [[acceleration tensor]], the [[pressure field tensor]], the [[Physics/Essays/Fedosin/Gravitational tensor | gravitational tensor]] and the [[w:electromagnetic tensor |electromagnetic tensor]], respectively. The tensor field invariants are included in Lagrangian, Hamiltonian. action function and relativistic energy of the system, and they are located there inside integrals over space volume. In addition, they are included in corresponding stress-energy tensors of the fields. <ref name="ab"/> Since in the system under consideration solenoidal vectors are zero, the tensor invariants depend only on the field strengths: : <math>~ u_{\mu \nu} u^{\mu \nu} = - \frac {2}{c^2}(S^2 - c^2 N^2) = - \frac {2}{c^2}S^2.</math> : <math>~ f_{\mu \nu} f^{\mu \nu} = - \frac {2}{c^2}(C^2 - c^2 I^2) = - \frac {2}{c^2}C^2.</math> : <math>~ \Phi_{\mu \nu} \Phi^{\mu \nu} = - \frac {2}{c^2}(\Gamma^2 - c^2 \Omega^2) = - \frac {2}{c^2}\Gamma^2.</math> : <math>~ F_{\mu \nu} F^{\mu \nu} = - \frac {2}{c^2}(E^2 - c^2 B^2) = - \frac {2}{c^2}E^2.</math> The volume integrals of tensor invariants multiplied by corresponding factors were calculated in the article. <ref name="re"/> For acceleration field and pressure field the integrals are taken only over volume of the sphere: : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \eta } u_{\mu \nu} u^{\mu \nu} dV = - \frac {c^4 \gamma^2_c }{2 \eta } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2}{16 \pi \sigma } f_{\mu \nu} f^{\mu \nu} dV = - \frac {\sigma c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> The gravitational and electromagnetic fields of the system are present not only inside but also outside the sphere, where they extend to infinity, while field strengths of internal and external fields behave differently. The field strengths <math>~ \mathbf \Gamma_i </math> and <math>~ \mathbf E_i </math> are substituted respectively into integrals of tensor invariants of these fields taken over volume of the sphere, which gives the following: : <math>~ - \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 } \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{8 \pi \varepsilon_0 \eta^2 \rho^2_0} \left[\frac {a}{2} + \frac {c}{4 \sqrt {4 \pi \eta \rho_0}} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0} \right) - \frac {c^2}{4 \pi \eta \rho_0 a} \sin^2 \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0} \right) \right] \approx </math> : <math>~\approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> Into volume integrals of tensor invariants of gravitational and electromagnetic fields of the system outside the sphere the field strengths <math>~ \mathbf \Gamma_o </math> and <math>~ \mathbf E_o </math> are substituted, respectively: : <math>~ - \int \limits^{\infty}_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = </math> : <math>~ = \frac {G c^4 \gamma^2_c }{2 \eta^2 a} \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right). </math> : <math>~ \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{ 8 \pi \varepsilon_0 \eta^2 \rho^2_0 a } \left[\frac {c}{\sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 }\right) \right]^2 \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> == Energies of particles in field potentials == All the four fields act on particles inside the sphere, and therefore each particle of the system acquires corresponding energy in a particular field. The energy of a particle in a field is calculated as volume integral of product of effective mass density <math>~ \rho = \rho_0 \gamma' </math> by corresponding scalar potential, and for electric field the energy is determined as volume integral of product of effective charge density <math>~ \rho_q = \rho_{0q} \gamma' </math> by scalar potential <math>~ \varphi </math>, where Lorentz factor <math>~ \gamma' </math> from (1) is used. In STR the energies of particles in acceleration field, pressure field, gravitational and electric fields in uniform relativistic spherical system, in view of expressions for the field potentials <ref name="re"/> and corrections to calculations, <ref name="el"/> <ref name="ge">Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. </ref> <ref name="gf"> Fedosin S.G. [http://www.uiss2016.ru/files/uiss2016_res.pdf The gravitational field in the relativistic uniform model within the framework of the covariant theory of gravitation]. 5th Ulyanovsk International School-Seminar “Problems of Theoretical and Observational Cosmology” ([http://www.uiss2016.ru/ UISS 2016]), Ulyanovsk, Russia, September 19-30, 2016, Abstracts, p. 23, {{ISBN|978-5-86045-872-7}}. </ref> <ref name="gr">Fedosin S.G. The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation. International Letters of Chemistry, Physics and Astronomy, Vol. 78, pp. 39-50 (2018). http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39.</ref> are, respectively: : <math>~ \int \rho \vartheta dV = \rho_0 c^2 \int \gamma'^2 dV = \frac {c^4 \gamma^2_c }{\eta } \left[ \frac {a}{2}- \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx </math> : <math>~ \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho \wp dV = \rho_0 \int \gamma' \wp dV = \frac {c^2 \gamma_c } {\eta } \left( \wp_c - \frac { \sigma c^2 \gamma_c }{\eta }\right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac { \sigma c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }}\sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3 \sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) . </math> : <math>~ \int \rho \psi_i dV = \rho_0 \int \gamma' \psi_i dV = </math> : <math>~= \frac {G c^4 \gamma^2_c }{\eta^2 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] - </math> : <math>~ - \frac {G c^4 \gamma^2_c }{\eta^2 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2 a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ \int \rho_q \varphi_i dV = \rho_{0q} \int \gamma' \varphi_i dV = </math> : <math>~ = -\frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \left[ \frac {c}{ \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - a \cos \left(\frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] + </math> : <math>~ + \frac {\rho^2_{0q} c^4 \gamma^2_c }{4 \pi \varepsilon_0 \eta^2 \rho^2_0 } \left[ \frac {a}{2} - \frac {c}{4 \sqrt {4 \pi \eta \rho_0 }} \sin \left(\frac {2a}{c} \sqrt {4 \pi \eta \rho_0 } \right) \right] \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Note that all fields in which particles are located are not fields from external sources, but are generated by the particles themselves. As a result, the particles’ energies calculated above in scalar potentials of the fields are twice as large as potential energy of one or another interaction. For example, in order to calculate electrostatic energy of a system of two charges, it is sufficient to take potential of first charge at location of second charge and to multiply it by the value of the second charge. But if we use formula for energy in the form of an integral, then electrostatic energy will be taken into account twice, because the term is added, which contains potential of second charge at location of first charge multiplied by the value of the first charge. On the other hand, the electrostatic energy must consist of two components that take into account both the energy of particles in each other’s fields and the energy of electric field itself. Instead, in electrostatics, the electrostatic energy is calculated either through the scalar potential or through the field strength by integrating time component of stress-energy tensor over volume. Both methods provide the same result, but the connection between field energy and energy of particles in field potential is lost in this case, and it is not clear why these energies should coincide. == Relation between field coefficients == For the four fields under consideration equation of motion of matter in the concept of general field is as follows: <ref> Fedosin S.G. [http://www.oalib.com/paper/5263035#.VuFYxn2LQsY The Concept of the General Force Vector Field]. OALib Journal, Vol. 3, pp. 1-15 (2016), e2459. http://dx.doi.org/10.4236/oalib.1102459. </ref> <ref name="eq"> Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. </ref> : <math>~ u_{\mu \nu } J^\nu + f_{\mu \nu } J^\nu + \Phi_{\mu \nu } J^\nu + F_{\mu \nu } j^\nu = 0, </math> where <math>~ J_\mu </math> is mass four-current, <math>~ j^\nu </math> is electromagnetic [[w:four-current | four-current]]. Components of field tensors are field strengths and corresponding solenoidal vectors, but in the physical system under consideration the latter are equal to zero. As a result, space component of the equation of motion is reduced to the relation: : <math>~ \mathbf S + \mathbf C + \mathbf \Gamma_i + \frac {\rho_{0q}}{\rho_0 }\mathbf E_i = 0 . </math> If we substitute here expression for field strengths inside the sphere, we obtain relation between field coefficients: <ref name="es">Fedosin S.G. [http://www.nrcresearchpress.com/doi/10.1139/cjp-2015-0593#.Vv3piZyLQsY Estimation of the physical parameters of planets and stars in the gravitational equilibrium model.] Canadian Journal of Physics, Vol. 94, No. 4, pp. 370-379 (2016). http://dx.doi.org/10.1139/cjp-2015-0593. </ref> : <math>~\eta + \sigma = G - \frac {\rho^2_{0q}}{ 4 \pi \varepsilon_0 \rho^2_0 }= G - \frac {q^2 }{ 4 \pi \varepsilon_0 m^2 }. \qquad \qquad (4) </math> The same is obtained for time component of equation of motion, which leads to generalized Poynting theorem. <ref name="ge"/> == Relation between energies of internal and external fields == In article <ref>Fedosin S.G. [http://vixra.org/abs/1205.0086 The Hamiltonian in Covariant Theory of Gravitation.] Advances in Natural Science, Vol. 5, No. 4, pp. 55-75 (2012). http://dx.doi.org/10.3968%2Fj.ans.1715787020120504.2023. </ref> it was found that energy of particles in gravitational field inside stationary sphere is up to a sign two times greater than total energy associated with tensor invariants of gravitational field inside and outside the sphere. A similar situation takes place in the system under consideration with random motion of particles and zero solenoidal vectors both for gravitational <ref name="gf"/> and electromagnetic fields. <ref name="el"/> In particular, we can write the following: : <math>~ \int \limits^{a}_{r=0} \rho \psi_i dV = 2 \int \limits^{a}_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV + 2 \int \limits^{ \infty }_{r=a} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV = 2 \int \limits^{\infty }_{r=0} \frac {c^2}{16 \pi G } \Phi_{\mu \nu} \Phi^{\mu \nu} dV. </math> : <math>~ \int \limits^{a}_{r=0} \rho_q \varphi_i dV = -2 \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV - 2 \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV = - 2 \int \limits^{\infty }_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV. </math> These expressions relate the energy of particles in scalar field potentials with the energy found with the help of field strengths. == Relativistic energy == In curved spacetime the system’s energy for continuously distributed matter is given by the formula: <ref name="ab"/> <ref name="en"/> : <math>~E_r = \frac {1}{c} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> : <math>~ +\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}. \qquad \qquad (5)</math> This formula is valid in the case where it can be assumed that potentials and field strengths at each point in space do not have a direct dependence on the speeds of motion of individual particles of the system. In STR the metric tensor determinant is <math>~ g = -1 </math>, the time component of four-velocity is <math>~ u^0 = c \gamma'</math>, and in order to calculate the energy of spherical system with particles, taking into account the fields’ energies, we can use the above-mentioned energies of particles in field potentials and energies in the form of tensor invariants of the fields: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The expression for energy is simplified if we use the relation between field coefficients (4): : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{5 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> Taking into account relations between energies of internal and external fields also simplifies expression for the system’s energy: : <math>~E_r \approx m c^2 \gamma^2_c - \frac {3 \eta m^2 \gamma^2_c }{5a} \left( 1- \frac {2 \eta m }{7 a c^2} \right) + m \wp_c \gamma_c \left( 1 - \frac {3 \eta m }{10 a c^2} \right) - \frac {3\sigma m^2 \gamma^2_c }{10 a} \left( 1 - \frac {13 \eta m }{28 a c^2} \right) - </math> : <math>~ - \frac {6 G m^2 \gamma^2_c }{10 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) + \frac {3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right) - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) . </math> == Relation between energy and cosmological constant== In the approach under consideration, relativistic energy of the system is not an absolute value and requires gauging. For this purpose the [[w:cosmological constant | cosmological constant]] <math>~ \Lambda</math> is used. The gauge condition for the four main fields is related to sum of products of the fields’ four-potentials by corresponding four-currents and has the following form: <ref name="ab"/> <ref name="en"/> : <math>~ -ck \Lambda = A_\mu j^\mu + (D_\mu + U_\mu + \pi_\mu) J^\mu, \qquad \qquad (6) </math> where for large cosmic systems <math>~ -ck = \frac {c^4}{16\pi G \beta }</math>, and <math>~\beta </math> is a constant of order of unity. Within the framework of STR gauge condition has the following form: : <math>~ -ck \Lambda = \gamma \rho_{0q} (\varphi - \mathbf A \cdot \mathbf v) + \gamma \rho_{0} (\psi - \mathbf D \cdot \mathbf v + \vartheta - \mathbf U \cdot \mathbf v + \wp - \mathbf \Pi \cdot \mathbf v ). </math> If we divide the system’s particles and remove them to infinity and leave there at rest, the terms with products of vector field potentials by velocity of particles <math>~\mathbf v </math> would vanish, and Lorentz factor of an arbitrary particle would be <math>~ \gamma=1 </math>. On the right-hand side we will have only the sum of terms specifying energy density of particles located in potentials of their proper fields. Since <math>~ \vartheta \approx \gamma_c c^2 </math>, we see that the cosmological constant for each system’s particle is up to the multiplier <math>~ -ck</math> equal to rest energy density of this particle with a certain addition from its proper fields. Then the integral over volume of all the particles gives a certain energy: : <math>~ -ck \int \Lambda dV = m' c^2 ,</math> where the gauge mass <math>~ m' </math> is related to gauge condition of the energy. In the process of gravitational clustering the particles that were initially far from each other are united into closely bound systems, in which the field potentials increase manyfold. In the system under consideration <math>~ \gamma = \gamma' </math>, solenoidal vectors of fields are considered equal to zero due to random motion of particles, which gives the following: : <math>~ m' c^2 = \int [\gamma' \rho_{0q} \varphi_i + \gamma' \rho_{0} (\psi_i + \vartheta + \wp)] dV. </math> Expression on the right-hand side is part of relativistic energy <math>~E_r </math> of the system, so that the energy can be written as follows: : <math>~E_r = M c^2 \approx m' c^2 - \frac { \eta m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { \sigma m^2 \gamma^2_c }{10 a}\left( 1- \frac {3 \eta m }{7 a c^2} \right) + </math> : <math>~ + \frac { G m^2 \gamma^2_c }{10 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right) + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> The mass <math>~ M </math> is related to relativistic energy of generally stationary system and is the inertial mass of the system. In view of (4), the energy will be equal to: : <math>~E_r = M c^2 \approx m' c^2 + \frac { G m^2 \gamma^2_c }{2 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> This shows that relativistic energy of this system is equal to gauge mass-energy <math>~ m' c^2 </math>, from which the gravitational and electromagnetic energy of fields outside the system should be subtracted. == Lagrange function and motion integrals == Lagrange function for a system of particles and four main vector fields has the following form:<ref name="pr"/> <ref name="ab"/> :<math>~L = - \int {( U_\mu J^\mu + \pi_\mu J^\mu + D_\mu J^\mu + A_\mu j^\mu ) \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ +\int { \left( ckR - 2ck \Lambda -\frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} - \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} + \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} - \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \sqrt {-g} dx^1 dx^2 dx^3}.</math> Here <math>~ R </math> is [[w:scalar curvature |scalar curvature]]. With the help of such Lagrange function, one can calculate generalized momentum of the system:<ref name="co">Fedosin S.G. [http://www.bpasjournals.com/physics/chapter-details.php?chap_id=2121&issue_type=158&volume=110&journal=7 The covariant additive integrals of motion in the theory of relativistic vector fields]. Bulletin of Pure and Applied Sciences, Vol. 37 D (Physics), No. 2, pp. 64-87 (2018). http://dx.doi.org/10.5958/2320-3218.2018.00013.1. </ref> :<math>~ \mathbf p = \frac {1}{c} \int {( \rho_0 \mathbf U + \rho_0 \mathbf \Pi + \rho_0 \mathbf D + \rho_{0q} \mathbf A ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> This vector depends on vector potentials of all four fields and is preserved in a closed physical system, that is, it is an integral of motion. Another integral of motion is relativistic energy of the system <math>~E_r</math>, which is found by formula (5). Further, it is assumed that one can neglect the contributions from gravitational and electromagnetic fields outside the matter and take into account only the generalized momentum. Then we can assume that these values form a four-momentum of the system, written with a covariant index: :<math>~ p_\mu = \left( \frac { E_r }{c}, - \mathbf p \right).</math> The angular momentum of the system is also an integral of motion: :<math>~ \mathbf M = \frac {1}{c} \int {( \rho_0 [\mathbf r \times \mathbf U] + \rho_0 [\mathbf r \times \mathbf \Pi] + \rho_0 [\mathbf r \times \mathbf D] + \rho_{0q} [\mathbf r \times \mathbf A] ) u^0 \sqrt {-g} dx^1 dx^2 dx^3 }.</math> The antisymmetric angular momentum pseudotensor is determined through the four-radius <math>~ x_\mu </math>, taken with a covariant index, and through the four-momentum <math>~ p_\mu </math>: :<math>~M_{\mu \nu} = \int {( x_\mu dp_\nu - x_\nu dp_\mu )} .</math> The spatial components of the angular momentum pseudotensor <math>~ M_{\mu \nu} </math> are the components of the angular momentum <math>~ \mathbf M </math> of the system: :<math>~ M_{12} = -M_{21} = -M_z , \qquad M_{13} = -M_{31} = M_y , \qquad M_{23} = -M_{32} = -M_x .</math> The radius-vector of the center of momentum of a physical system is determined by the formula: :<math>~ \mathbf R_m = \frac {1}{c E_r} \int {( \rho_0 \vartheta + \rho_0 \wp + \rho_0 \psi+ \rho_{0q} \varphi ) \mathbf r u^0 \sqrt {-g} dx^1 dx^2 dx^3 +}</math> :<math>~ + \frac {1}{E_r}\int { \left( \frac {c^2}{16 \pi \eta} u_{ \mu\nu} u^{ \mu\nu} + \frac {c^2}{16 \pi \sigma} f_{ \mu\nu} f^{ \mu\nu} - \frac {c^2}{16 \pi G} \Phi_{ \mu\nu}\Phi^{ \mu\nu} + \frac {c^2 \varepsilon_0}{4} F_{ \mu\nu}F^{ \mu\nu} \right) \mathbf r \sqrt {-g} dx^1 dx^2 dx^3}.</math> The time components of the pseudotensor <math>~ M_{\mu \nu} </math> are the components of three-dimensional vector <math>~ \mathbf {\mathbb C} </math>, which is often called time-varying dynamic mass moment: :<math>~ M_{01} = -M_{10} = -\mathbb C_x , \qquad M_{02} = -M_{20} = -\mathbb C_y , \qquad M_{03} = -M_{30} = -\mathbb C_z .</math> If we take into account definition of radius-vector of center of momentum and relationship between the momentum and velocity of the center of momentum in the form <math>~ \mathbf p = \frac { E_r }{c^2} \mathbf V </math>, we get the relation: :<math>~ \mathbf {\mathbb C} = \frac { E_r }{c} ( \mathbf V t - \mathbf R_m ) .</math> In a closed system the pseudotensor <math>~ M_{\mu \nu} </math> must be conserved, and its components must be some constants. For space components of the pseudotensor this results in conservation of angular momentum: <math>~ \mathbf M = const </math>. From equality of the pseudotensor’s time components and components of the vector <math>~ \mathbf {\mathbb C} </math> it follows that it should be <math>~ \mathbf {\mathbb C} = const </math>. Given the expression for <math>~ \mathbf {\mathbb C} </math>, it can be written as <math>~ \mathbf R_m = \mathbf R_{m0} + \mathbf V t </math>, where the constant vector <math>~ \mathbf R_{m0} </math> specifies position of the system’s center of momentum at <math>~ t=0 </math>. Thus, in this reference frame we obtain equation of motion of the center of momentum at constant velocity <math>~ \mathbf V </math>, as a property of motion of a closed system. The component <math> ~ M_z </math> of angular momentum of a uniform ball, taking into account relativistic corrections, can be calculated by the formula: <ref>Fedosin S.G. On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation. International Frontier Science Letters, Vol. 15, pp. 9-14 (2020). https://doi.org/10.18052/www.scipress.com/IFSL.15.9. </ref> :<math>~ M_z = \frac {3 \pi \rho_0 c^4 a}{2 \omega^3} - \frac {\pi \rho_0 c^2 a^3}{2 \omega} - \frac {3 \pi \rho_0 c^5 \left( 1- \frac {\omega^2 a^2}{c^2} \right) \left( 1+ \frac {\omega^2 a^2}{3c^2} \right) }{4 \omega^4} \ln \frac {1+ \frac {\omega a}{c} }{1- \frac {\omega a}{c} } .</math> Here <math> ~ \rho_0 </math> is invariant mass density, <math> ~ \omega </math> is angular velocity of rotation of the ball having a radius <math> ~ a </math>. == Integral vector == The equation used to find metric tensor components in [[Physics/Essays/Fedosin/Covariant theory of gravitation | covariant theory of gravitation] for tensors with mixed indices has the following form:<ref name="ab"/> :<math>~ R_\alpha^{\ \beta} - \frac {1}{4} R \delta_\alpha^{\ \beta} = - \frac {1}{2c k} \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) . </math> here <math>~ R_\alpha^{\ \beta}</math> is [[w:Ricci tensor |Ricci tensor]] with mixed indices; <math>~ \delta_\alpha^{\ \beta}</math> is unit tensor or [[w:Kronecker delta |Kronecker delta]]; <math>~ B_\alpha^{\ \beta}</math>, <math>~ P_\alpha^{\ \beta}</math>, <math>~ U_\alpha^{\ \beta}</math> and <math>~ W_\alpha^{\ \beta}</math> are stress-energy tensors of acceleration field and pressure field, gravitational and electromagnetic fields, respectively. With the help of covariant derivative <math>~ \nabla_\beta</math> we can find four-divergence of both sides of the above equation for metric. The divergence of the left-hand side is zero due to equality to zero of divergence of [[w:Einstein tensor |Einstein tensor]], <math>~ \nabla_\beta \left( R_\alpha^{\ \beta} - \frac {1}{2} R \delta_\alpha^{\ \beta}\right) =0 </math>, and also as a consequence of the fact that outside the body the scalar curvature vanishes, <math>~ R =0</math>, and inside the body it is constant. The latter follows from the gauge condition of energy of closed system. The divergence of the right-hand side of equation for the metric is also zero: :<math>~ \nabla_\beta \left( B_\alpha^{\ \beta}+ P_\alpha^{\ \beta} + U_\alpha^{\ \beta} + W_\alpha^{\ \beta} \right) = \nabla_\beta T_\alpha^{\ \beta} = 0 , </math> where the tensor <math>~ T_\alpha^{\ \beta}</math> with mixed indices represents the sum of stress-energy tensors of all fields acting in the system. The resulting expression for tensors’ space components is nothing but differential equation of matter’s motion under action of forces generated by fields, which is written in a covariant form. <ref name="eq"/> As for the tensors’ time components, for them the expression is expression of generalized Poynting theorem for all the fields. <ref name="ge"/> In a weak field and at low velocities of motion of particles, the equation <math>~ \nabla_\beta T_\alpha^{\ \beta} \approx \partial_\beta T_\alpha^{\ \beta} = 0 </math> can be integrated over four-volume, taking into account the [[w:divergence theorem |divergence theorem]]. As a result, at initial moment of time for the system under consideration, the following relation will be valid: :<math>~ J_\alpha = \int { T_\alpha^{\ 0} dx^1 dx^2 dx^3} = const . </math> In a closed system, the four-dimensional integral vector <math>~ J_\alpha </math> must be constant. <ref name="co"/> For a stationary sphere with randomly moving particles in continuous medium approximation, the energy fluxes of fields defining the components <math>~ T_j^{\ 0}</math>, where <math>~ j =1,2,3</math>, are missing , so that the spatial components are zero, <math>~ J_j =0</math>. As for the time component <math>~ J_0 </math> of integral vector, then for volume occupied by matter inside the sphere, it also vanishes due to relation (4) for field coefficients. However, outside the sphere, where there are only gravitational and electromagnetic fields, the time component of integral vector is not equal to zero. As a result, the contribution to this component is made by energies of external fields: :<math>~ J_0 = - \frac {G m^2_g}{2a} + \frac {q^2_b}{8\pi \varepsilon_0 a} . </math> It follows from the above that integral vector shows distribution of energy and energy fluxes in the system under consideration. For the nonzero space components <math>~ J_j</math> of integral vector to appear some stationary motion of matter and fields is required, for example, general rotation, volume pulsations or mixing of matter. In this case, solenoidal vectors and the fields’ energy fluxes appear in the system. Since the integral vector <math>~ J_\alpha </math> is associated with energies and energy fluxes of fields in stress-energy tensors, it differs from the four-momentum <math>~ p_\mu </math>, which includes invariant mass and proportional to its rest energy. It turns out that difference between <math>~ J_\alpha </math> and <math>~ p_\mu </math> is due to fundamental difference between particles and fields, they cannot be reduced to each other, although they are interrelated with each other. == Virial theorem and kinetic energy of particles == In article <ref> Fedosin S.G. [https://zenodo.org/record/1037246 The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept]. Continuum Mechanics and Thermodynamics, Vol. 29, Issue 2, pp. 361-371 (2017). https://dx.doi.org/10.1007/s00161-016-0536-8. </ref> kinetic energy of particles of the system under consideration is estimated by three methods: from [[w:virial theorem | virial theorem]], from relativistic definition of energy and using generalized momenta and proper fields of the particles. In the limit of low velocities, all these methods give for kinetic energy the following: : <math>~E_k \approx \frac {0.3608\eta m^2 \gamma_c }{a} . </math> The possibility to use generalized momenta to calculate the energy of particles’ motion is associated with the fact that despite zeroing of vector potentials and solenoidal vectors on the large scale, in volume of each randomly moving particle these potentials and vectors are not equal to zero. As a result, the energy of motion of the system’s particles can be found as the half-sum of scalar products of vector field potentials by the particles’ momentum, while for electromagnetic field we should take not the momentum, but the product of charge by velocity and Lorentz factor. If we square the equation for <math>~ \gamma' </math> in (1), we can obtain dependence of squared velocity of particles’ random motion on current radius: : <math>~{v'}^2 \approx v^2_c - \frac {4 \pi \eta \rho_0 r^2 }{3} . </math> On the other hand, we can assume that <math>~ \mathbf v' = \mathbf v_r + \mathbf v_\perp ,</math> where <math>~ \mathbf v_r </math> denotes averaged velocity component directed along the radius, and <math>~ \mathbf v_\perp </math> is averaged velocity component perpendicular to the current radius. In addition, from statistical considerations, it follows that : <math>~{v'}^2 = v^2_r + v^2_\perp = 3 v^2_r . </math> This implies dependence of radial velocity on the radius: : <math>~v_r \approx \frac {v_c}{ \sqrt 3} \left( 1- \frac {2 \pi \eta \rho_0 r^2 }{3 v^2_c} \right) . </math> Next, from the virial theorem we find squared velocity of particles at the center of the sphere: : <math>~v^2_c \approx \frac {3 \eta m }{5 a} \left( 1 + \frac {9}{\sqrt {56}}\right) \approx \frac {1.3216 \eta m }{a} . </math> This makes it possible to estimate the Lorentz factor at the center: : <math>~\gamma_c = \frac {1}{\sqrt {1- \frac { v^2_c }{c^2}}} \approx 1+ \frac { v^2_c }{2c^2} +\frac {3 v^4_c }{8c^4} \approx 1+ \frac {3 \eta m}{10 a c^2} \left( 1+\frac {9}{2\sqrt {14}} \right) + \frac {27 \eta^2 m^2}{200 a^2 c^4} \left( 1+\frac {9}{2\sqrt {14}} \right)^2 . </math> In the ordinary interpretation of virial theorem the time-averaged kinetic energy of a system of particles must be two times less than averaged energy associated with the forces <math>~ \mathbf F_i </math> holding the particles at the radius-vectors <math>~ \mathbf r_i </math> : : <math>~ \langle W_k \rangle_m = - 0.5 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle. </math> However, in relativistic uniform system this equation is changed: : <math>~ \langle W_k \rangle \approx - 0.6 \langle \sum^{N}_{i=1} \mathbf F_i \cdot \mathbf r_i \rangle, </math> while the quantity <math>~ W_k </math> exceeds the kinetic energy of particles, <math>~ W_k \approx \gamma_c E_k </math>, and it becomes equal to it only in the limit of low velocities. In contrast to classical case, total time derivative of virial in stationary system is other than zero due to the virial’s dependence on the radius: : <math>~ \frac {dG_V}{dt} \approx \mathbf v \cdot \nabla {G_V}\approx \frac {0.1216 \eta m^2 \gamma^2_c }{a} . </math> An analysis of integral theorem of generalized virial makes it possible to find, on the basis of field theory, a formula for the root-mean-square speed of typical particles of a system without using the notion of temperature: <ref> Fedosin S.G. [http://em.rdcu.be/wf/click?upn=lMZy1lernSJ7apc5DgYM8f7AyOIJlVFO4uFv7zUQtzk-3D_DUeisO4Ue44lkDmCnrWVhK-2BAxKrUexyqlYtsmkyhvEp5zr527MDdThwbadScvhwZehXbanab8i5hqRa42b-2FKYwacOeM4LKDJeJuGA15M9FWvYOfBgfon7Bqg2f55NFYGJfVGaGhl0ghU-2BkIJ9Hz4M6SMBYS-2Fr-2FWWaj9eTxv23CKo9d8nFmYAbMtBBskFuW9fupsvIvN5eyv-2Fk-2BUc7hiS15rRISs1jpNnRQpDtk2OE9Hr6mYYe5Y-2B8lunO9GwVRw07Y1mdAqqtEZ-2BQjk5xUwPnA-3D-3D The integral theorem of generalized virial in the relativistic uniform model]. Continuum Mechanics and Thermodynamics, Vol. 31, Issue 3, pp. 627-638 (2019). https://dx.doi.org/10.1007/s00161-018-0715-x.</ref> :<math> v_\mathrm{rms} = c \sqrt{1- \frac {4 \pi \eta \rho_0 r^2}{c^2 \gamma^2_c \sin^2 {\left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right) } } } .</math> == Extreme objects == In formula (2) for gravitational field strength <math>~ \mathbf \Gamma_o </math> outside a body there is a quantity <math>~A = \sin \delta - \delta \cos \delta</math>, where <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} </math>. As was shown in article, <ref name="gr"/> at the value <math>~ \delta = \delta_0 = 4.494 </math> radians the gravitational field strength <math>~ \mathbf \Gamma_o </math> vanishes and gravitational acceleration disappears. Therefore, in real physical objects the following condition must hold: <math>~ \delta = \frac {a}{c} \sqrt {4 \pi \eta \rho_0} < \delta_0 </math>. If the angle <math>~ \delta </math> is increased, then the quantity <math>~A </math> would first increase, and then would begin to decrease and even change its sign. So, at <math>~ \delta = \frac {\pi}{2}</math> we have <math>~A =1</math>, at <math>~ \delta = \pi </math> we have <math>~A =\pi </math>, at <math>~ \delta = \frac {3 \pi}{2}</math> we have <math>~A = -1 </math>. Let us now consider the observable Universe, which on a scale 100 Mpc or more can be considered as a relativistic uniform system. The total mass-energy density of the Universe is close to the critical value <math>~ \rho_c \approx 10^{-26}</math> kg/m³ and the size of the Universe can be estimated as the Hubble length <math>~ R_H =c/H_0 \approx 10^{26}</math> m, where <math>~ H_0 </math> is Hubble parameter. Using approximate equality <math>~\eta \approx \frac {3}{5} G </math> according to, <ref name="es"/> we find the value <math>~ \delta_U = \frac { R_H }{c} \sqrt {4 \pi \eta \rho_c} \approx 1.7 > \frac {\pi}{2}</math> radians. Since the angle <math>~ \delta_U </math> is sufficiently large, then for modeling of gravitational field of the Universe it is necessary to use refined formulas with sines and cosines. For example, if we take the size of observable Universe equal to <math>~ 2.64 R_H </math>, then we have <math>~ \delta_U = \delta_0 </math>, and gravitational field at boundaries of the Universe will tend to zero. This is what we observe in the form of a large-scale cellular structure consisting of clusters of galaxies. The reason for the gravitation action weakening is assumed to be graviton scattering by the particles of space medium. <ref> Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Vol. 23, Special Issues No. 1, pp. 3-13 (2012). http://dx.doi.org/10.5281/zenodo.890806. </ref> Another extreme object is a proton, in which mass density in entire volume changes approximately by 1.5 times. As a result, in the first approximation a proton is a relativistic uniform system. The proton radius <math>~ r_p </math> is of the order of 0.873 fm, <ref>Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, Vol. 35, No. 4, pp. 349-363 (2012). http://dx.doi.org/10.5281/zenodo.889451. </ref> and average density is of the order of <math>~ \rho_p = 6 \cdot 10^{17}</math> kg/m³. As a gravitational constant at the atomic level the [[Physics/Essays/Fedosin/Strong gravitational constant | strong gravitational constant]] <math>~ G_s </math> should be used. An estimate of the quantity <math>~ \delta </math> for a proton at <math>~\eta \approx \frac {3}{5} G_s </math> gives: <math>~ \delta_p = \frac { r_p }{c} \sqrt {4 \pi \eta \rho_p} \approx 2.4 < \delta_0 </math> radians. This shows that a proton is an extreme object from the point of view of weakening of its gravitational field. In article, <ref name="gr"/> a method is provided for estimating Lorentz factor of matter’s motion at the center of a proton, which gives <math>~ \gamma_c =1.9 </math>. In addition, radius of action of [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]] in matter with the critical mass density <math>~ \rho_c \approx 10^{-26}</math> kg/m³ in observable Universe is estimated: <math>~ r_G <1.3 \cdot 10^7 </math> m. On a large scale in the Universe not the strong gravitation, but ordinary gravitation is acting with the radius of action of the order of Hubble length. Let us suppose that <math>~ r_G </math> corresponds to radius of a certain [[black hole]] for strong gravitation, calculated by the Schwarzschild formula: <math>~ r_G = \frac {2 G_s m} {c^2} </math>. If the mass is <math>~ m = \frac {4 \pi \rho_c r^3_G} {3}</math>, then for radius of a black hole with such mass we obtain<math>~ r_G =c \sqrt {\frac {3}{8 \pi G_s \rho_c }} = 2.7 \cdot 10^6 </math> m, and mass is <math>~ m = 8 \cdot 10^{-7} </math> kg. The Schwarzschild formula admits a black hole for strong gravitation at small mass of the order of proton mass, large mass density and a radius smaller than the proton radius. In addition, substitution of the mass <math>~ m </math> and the radius <math>~ r_G </math> into Schwarzschild formula formally corresponds to a black hole with a large radius and low density <math>~ \rho_c </math>. However, for an external observer, such a black hole would rather correspond not to a black hole, but to an object, containing strongly rarefied hydrogen gas of cosmic space. Similarly, the [[w:Observable universe |Metagalaxy]] with the radius of order of <math>~ r_H </math> and mass density <math>~ \rho_c </math> is not a black hole, although it corresponds to the Schwarzschild formula for ordinary gravitation. Hence, in accordance with the theory of infinite nesting of matter, conclusion follows – at each level of matter corresponding gravitation forms only one type of the most compact and stable object. So, at the level of nucleons a proton appears under the action of strong gravitation, and at the level of stars the ordinary gravitation generates a neutron star. If we multiply the radius of a neutron star by coefficient of similarity in size <math>~ P = 1.4 \cdot 10^{19}</math>, which is equal to the ratio of stellar radius to the proton radius, we obtain radius of the order of <math>1.7 \cdot 10^{23} </math> m. This radius must correspond to a compact object of a neutron star-type at the level of metagalaxies, which can emerge under the action of gravitation at this matter level. In the first approximation, the gravitational constant for metagalaxies is determined with the help of the similarity theory: <math>~ G_M =\frac {G P S^2} {\Phi} = 3 \cdot 10^{-50} </math> m³•s^–2•kg^–1, where <math>~ S=0.23 </math> is coefficient of similarity in velocities, <math>~ \Phi = 1.62 \cdot 10^{57} </math> is coefficient of similarity in mass. By analogy with the case of a proton, a neutron star is also considered as a relativistic uniform system. For a star with the mass of 1.35 Solar masses, the radius <math>~ R_s = 12 </math> km and average density <math>~ \rho_s \approx 3.7 \cdot 10^{17}</math> kg/m³, at <math>~\eta \approx \frac {3}{5} G </math> we obtain the angle <math>~ \delta_s = \frac { R_s }{c} \sqrt {4 \pi \eta \rho_s} \approx 0.546 </math> radians. With this in mind, if we substitute into (3) the stellar mass instead of <math>~ m_b </math> and the stellar radius instead of <math>~ a </math>, we can estimate Lorentz factor at the center of the star: <math>~ \gamma_{cs} =1.04 </math>. This allows us to estimate temperature at the center of the star: <math>~ T_s \approx 2.8 \cdot 10^{11} </math> K, which is close enough to calculation of temperature at the center of a newly formed star. <ref name="es"/> Thus, dependences of gravitational field inside and outside bodies in article <ref name="gr"/> are in good agreement with conclusions of [[w:Le Sage’s theory of gravitation |Le Sage’s theory of gravitation]] and the theory of [[Physics/Essays/Fedosin/Infinite Hierarchical Nesting of Matter|Infinite Hierarchical Nesting of Matter]], with strong gravitation at the level of nucleons and with the concept of a dynamic force vacuum field in [[Physics/Essays/Fedosin/Electrogravitational vacuum | electrogravitational vacuum]]. == Cosmological constant and scalar curvature == According to (6), outside a body, where the four-currents are equal to zero, cosmological constant <math>~ \Lambda</math> becomes equal to zero. In addition, scalar curvature <math>~ R</math> also becomes equal to zero. <ref name="en"/> Inside the body the relation <math>~ R= 2\Lambda </math> holds true, so that in matter with higher density both the scalar curvature and the cosmological constant increase. These quantities can be calculated using (6) as averaged values for typical particles of physical system. For cosmic space we obtain approximately the following: <math>~ \Lambda_0 \approx \frac {16 \pi G \rho_0}{c^2} \approx 10^{-52} </math> m^-2, where the average mass density is <math>~ \rho_0 \approx 2.7 \cdot 10^{-27}</math> kg/m³. A similar formula for a proton gives the following: <math>~ \Lambda \approx \frac {16 \pi G \rho_p}{c^2} \approx 2.2 \cdot 10^{-8} </math> m^-2. However, for a proton in the calculations we should use the strong gravitational constant <math>~ G_s </math>. In this case, we find: <math>~ \Lambda_p \approx \frac {16 \pi G_s \rho_p}{c^2} \approx 5.1 \cdot 10^{31} </math> m^-2. The obtained value is almost 84 orders of magnitude greater than the value of cosmological constant for cosmic space. The difference between cosmological constants for cosmic space and for a proton is associated with averaging procedure: the cosmological constant inside a proton is large, but in cosmic space matter containing protons, neutrons and electrons is very rarefied, the main place is occupied by void, so that cosmological constant averaged over entire space becomes a small value. Thus one of the paradoxes of general theory of relativity is solved, in which the cosmological constant is associated with zero vacuum energy and therefore it must be very large, but in fact the cosmological constant turns out to be a small value. For relativistic uniform system with four fields acting in it, average value <math>~ \stackrel{-}{\Lambda }</math> of cosmological constant in matter is constant and can be written as follows: : <math>~ -ck \stackrel{-}{\Lambda } = \frac {G \rho_0 c^2 \gamma_c}{\eta} \cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) - \frac {\rho^2_{0q} c^2 \gamma_c }{4 \pi \varepsilon_0 \eta \rho_0 }\cos \left( \frac {a}{c} \sqrt {4 \pi \eta \rho_0 } \right) + \rho_0 \wp_c - \frac {\sigma\rho_0 c^2 \gamma_c }{\eta } . </math> This expression can be simplified by using scalar potential of gravitational field <math>~ \psi_a = - \frac {G m_g}{a}</math> and scalar potential of electric field <math>~ \varphi_a = \frac {q_b }{4 \pi \varepsilon_0 a}</math> on surface of body at <math>~ r=a </math> : : <math>~ -ck \stackrel{-}{\Lambda } \approx \rho_0\psi_a - \frac {G m \rho_0 \gamma_c }{2 a } + \rho_0 c^2 \gamma_c + \rho_{0q} \varphi_a + \frac {q \rho_{0q} \gamma_c }{8 \pi \varepsilon_0 a } + \rho_0 \wp_c . </math> == Field energy theorem == In a relativistic uniform system, the exact values of strengths and potentials of all active fields are known. This allows us to check the [[field energy theorem]] for such a system and verify the theorem.<ref> Fedosin S.G. [http://dergipark.org.tr/gujs/issue/45480/435567 The Integral Theorem of the Field Energy.] Gazi University Journal of Science. Vol. 32, No. 2, pp. 686-703 (2019). http://dx.doi.org/10.5281/zenodo.3252783. </ref> This theorem explains, in particular, why electrostatic energy can be calculated either through the field strength, included in the electromagnetic field tensor, or in another way, through the field potential. The kinetic energy and potential energy of electromagnetic field are defined as follows: :<math>~ E_{kf} = \int {A_\alpha j^\alpha \sqrt {-g} dx^1 dx^2 dx^3 }. </math> :<math>~ W_f = \frac {1}{4 \mu_0 } \int { F_{\mu \nu} F^{\mu \nu} \sqrt {-g} dx^1 dx^2 dx^3 }. </math> If we take entire infinite volume both inside and outside matter of the system, then in the framework of special theory of relativity and in the absence of magnetic fields, these expressions are simplified: : <math>~ E_{kf}= \int \rho_q \varphi_i dV \approx \frac {3 q^2 \gamma^2_c }{10 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fi}= \int \limits^{a}_{r=0} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{40 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{7 a c^2} \right). </math> : <math>~ W_{fo}= \int \limits^{\infty}_{r=a} \frac {c^2 \varepsilon_0}{4 } F_{\mu \nu} F^{\mu \nu} dV \approx -\frac { q^2 \gamma^2_c }{8 \pi \varepsilon_0 a} \left( 1- \frac {3 \eta m }{5 a c^2} \right) . </math> : <math>~ W_f = W_{fi} + W_{fo} \approx -\frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> By virtue of the field energy theorem, the following relation will be satisfied: : <math>~ E_{kf}+ 2 W_f = 0.</math> In general case, tensor invariant is expressed in terms of square of electric field strength and square of magnetic field induction: <math>~ F_{\mu \nu} F^{\mu \nu}= - \frac {2}{c^2} (E^2 - c^2 B^2) </math>. The field energy density is found through the time component of stress-energy tensor: <math>~ W^{00} = \frac {1}{2} (\varepsilon_0 E^2 + \frac {1}{\mu_ 0} B^2) </math>. In electrostatics, when there are no magnetic fields and <math>~ B = 0</math>, volume integral of tensor invariant becomes proportional to volume integral of the component <math>~W^{00} </math>. As a result, electrostatic energy can be calculated in different ways: : <math>~ U_e= E_{kf}+ W_f \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a} \left( 1- \frac {4 \eta m }{7 a c^2} \right). </math> Besides: : <math>~ U_e= - W_f = \frac {1}{2} E_{kf} = \int W^{00} dV. </math> == Binding energy == With the help of covariant theory of gravitation total energy, binding energy, energy of fields, pressure energy and potential energy of a system consisting of particles and four fields is precisely calculated in the relativistic uniform model. <ref name="bi"> Fedosin S.G. The binding energy and the total energy of a macroscopic body in the relativistic uniform model. Middle East Journal of Science, Vol. 5, Issue 1, pp. 46-62 (2019). http://dx.doi.org/10.23884/mejs.2019.5.1.06. </ref> A noticeable difference is shown between the obtained results and relations for simple systems in classical mechanics, in which the acceleration field and pressure field are not taken into account or the pressure is considered to be a simple scalar quantity. In this case the inertial mass of a massive system is less than the total inertial mass of the system’s parts. == System mass == The article <ref> Fedosin S.G. [https://www.bpasjournals.com/physics/chapter-details.php?chap_id=2367&issue_type=177&volume=117&journal=7 The Mass Hierarchy in the Relativistic Uniform System]. Bulletin of Pure and Applied Sciences, Vol. 38 D (Physics), No. 2, pp. 73-80 (2019). http://dx.doi.org/10.5958/2320-3218.2019.00012.5. </ref> shows that relativistic uniform system with continuous matter distribution is characterized by five types of mass: the gauge mass <math>~m' </math> is related to cosmological constant and represents mass-energy of matter’s particles in four-potentials of the system’s fields; the inertial mass <math>~M </math>; the auxiliary mass <math>~m </math> is equal to product of the particles’ mass density by volume of the system; the mass <math>~m_b </math> is the sum of invariant masses (rest masses) of the system’s particles, which is equal in value to gravitational mass <math>~m_g </math>. The relation for these masses is as follows: :<math>~m' < M < m < m_b = m_g .</math> == Solution of 4/3 problem == For electromagnetic and gravitational fields, the 4/3 problem consists in inequality of mass-energy extracted from the energy of field of a body at rest, and mass-energy resulting from the field momentum of the moving body. If such a body is a relativistic uniform system of spherical shape, then mass-energy associated with electrostatic energy of the system is: :<math>~ m_f = \frac {E_e}{c^2} \approx \frac { 3 q^2 \gamma^2_c }{20 \pi \varepsilon_0 a c^2}. </math> The energy flux of electromagnetic field of a moving sphere is calculated using the Poynting vector. Let <math>~ \gamma </math> be Lorentz factor, and <math>~ v </math> be velocity of the sphere. Having calculated energy fluxes of the field inside and outside the sphere, as well as total energy flux, we can find corresponding quantities with dimension of momentum associated with these energy fluxes:<ref name="ge"/> :<math>~ g_{pi} \approx \frac { \gamma q^2 \gamma^2_c v}{30 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_{po} \approx \frac { \gamma q^2 \gamma^2_c v}{6 \pi \varepsilon_0 a c^2}. </math> :<math>~ g_p = g_{pi} + g_{po} \approx \frac { \gamma q^2 \gamma^2_c v }{5 \pi \varepsilon_0 a c^2}. </math> From here we find the mass-energy associated with the field energy fluxes: :<math>~ m_p = \frac {g_p}{\gamma v} \approx \frac { q^2 \gamma^2_c }{5 \pi \varepsilon_0 a c^2}. </math> For mass-energies, a ratio describing the 4/3 problem is obtained: :<math>~ m_p =\frac {4}{3} m_f . </math> If we consider the energy and energy flux of electromagnetic field only inside the sphere, or only outside the sphere, similar correlations are obtained for corresponding mass-energies. As indicated in the article, <ref name="ge"/> the mass-energy mismatch is a consequence of the fact that time components of electromagnetic stress-energy tensor and their integrals over volume do not together form any four-vector. In contrast, four-momentum of a system is a four-vector, so that the same inertial mass enters both the energy and momentum of the system. On the other hand, energy and momentum of electromagnetic field are included only as components in energy and momentum of entire system under consideration, and therefore they themselves do not have to form a four-vector. To calculate a four-momentum of a system, it is necessary to add energy and momentum of other fields operating in the system to the energy and momentum of electromagnetic field. In addition to electromagnetic field, the minimum set of fields of the system includes acceleration field, pressure field and gravitational field, and therefore it is necessary to take into account their energy and momentum. In this case, inside the sphere, the sum of energies of all fields found through tensor invariants and through stress-energy tensors is zeroed out. The total energy flux and total momentum of fields inside the sphere are also zero, so that within the sphere, the 4/3 problem as applied to [[Physics/Essays/Fedosin/General field | general field]] disappears. The equality to zero of sum of energies and sum of momenta of fields inside the sphere with randomly moving particles is a consequence of the fact that particles and fields have the opportunity to exchange energy and momentum with each other. As a result, contribution to relativistic energy of the system is made only by particle energies in scalar potentials of fields, and energies of electromagnetic and gravitational fields outside the sphere. The 4/3 problem shows in particular why energy and momentum of an electron and any other body cannot be reduced only to action of its own electromagnetic field. Despite the fact that an electron has a maximum charge per unit mass and is extremely charged, there are other fields in the electron's matter, for example [[Physics/Essays/Fedosin/Strong gravitation | strong gravitation]]. These fields have their own energy and momentum, which contribute to four-momentum of the electron. == Relations between field potentials == In the article, <ref>Fedosin S.G. [https://rdcu.be/ccV9o The potentials of the acceleration field and pressure field in rotating relativistic uniform system]. Continuum Mechanics and Thermodynamics, Vol. 33, Issue 3, pp. 817-834 (2021). https://doi.org/10.1007/s00161-020-00960-7. </ref> a connection was found between scalar potentials of acceleration field and pressure field in relativistic uniform system: :<math>~ \wp = \frac {\sigma (\vartheta -c^2)}{ \eta } = \frac {2 (\vartheta -c^2)}{ 3 }. </math> In addition, a relativistic expression for pressure was found: <math> p = \frac{2\rho c^2 (\gamma - 1) }{3}= \frac {2 \rho c^2 }{3} \left( \frac {1}{\sqrt {1- v^2/ c^2 }}-1 \right) \approx \frac {\rho v^2}{3}, </math> where <math>\rho </math> is mass density of moving matter, <math> c </math> is speed of light, <math> \gamma =\frac {1}{\sqrt {1- v^2/ c^2 }} </math> is [[w:Lorentz factor |Lorentz factor]]. In the limit of low velocities, this relationship turns into standard formula of [[w:kinetic theory of gases |kinetic theory of gases]]. == Metric inside and outside system == Standard expression for square of interval between two close points in metric theories is the following: :<math> ds^2 \ = \ g_{\mu\nu}(x) \ dx^{\mu} \ dx^{\nu}.</math> For static metric with spherical coordinates <math> x^0 = ct, </math> <math> x^1 = r ,</math> <math> x^2 = \theta , </math> <math> x^3 = \phi , </math> there are four nonzero components of the metric tensor: <math> g_{00}, </math> <math> g_{11}, </math> <math> g_{22}, </math> and <math> g_{33}= g_{22} \sin^2 \theta .</math> As a result, there is :<math> ds^2 \ = g_{00} c^2 dt^2 + g_{11} dr^2 + g_{22} d\theta^2 + g_{22} \sin^2 \theta d\phi^2.</math> As it was found for components of metric inside a spherical body within the framework of relativistic uniform model, <ref>{{cite journal| last=Fedosin|first=S. G. |s2cid= 238253182 |url= https://physmath.spbstu.ru/en/article/2021.53.13/ |title= The relativistic uniform model: the metric of the covariant theory of gravitation inside a body |journal= St. Petersburg Polytechnical State University Journal. Physics and Mathematics (Научно-технические ведомости СПбГПУ. Физико-математические науки) | volume=14 |issue=3 |pages=168–184 |date=2021 |doi= 10.18721/JPM.14313 |arxiv=2110.00342 |bibcode=2021arXiv211000342F }} // [http://sergf.ru/ru.htm О метрике ковариантной теории гравитации внутри тела в релятивистской однородной модели].</ref> <math> g_{22}= - r^2, </math> and :<math> (g_{00})_i = -\frac {1}{ (g_{11})_i } = 1+ \frac{ 8 \pi G \beta r^2 } {3c^4 }\left( \rho_0 c^2 \gamma_c + \rho_0 \psi_a - \frac {G m \rho_0 \gamma_c }{2a} + \rho_{0q} \varphi_a + \frac {q \rho_{0q}\gamma_c }{8\pi \varepsilon_0 a}+ \rho_0 \wp_c \right), </math> where <math> G </math> is gravitational constant; <math> \beta </math> is a coefficient to be determined; <math> r </math> is radial coordinate; <math> c </math> is the speed of light; <math> \rho_0 </math> is invariant mass density of matter particles; <math> \gamma_c </math> is Lorentz factor of particles moving at the center of body; <math> \psi_a = - \frac {G m_g}{a} </math> is gravitational potential at the surface of sphere with radius <math> a </math> and gravitational mass <math> m_g </math>; quantities <math> m = \frac {4 \pi a^3 \rho_0}{3}</math> and <math> q = \frac {4 \pi a^3 \rho_{0q}}{3}</math> are auxiliary values; <math> \rho_{0q} </math> is invariant charge density of matter particles, moving inside the body; <math> \varphi_a = \frac {q_b}{4\pi \varepsilon_0 a} </math> is electric scalar potential at the surface of sphere with total charge <math> q_b </math>; <math> \wp_c </math> is potential of pressure field at the center of body. On surface of the body, with <math> r = a </math>, the component <math> (g_{00})_ i </math> of metric tensor inside the body must be equal to the component <math> (g_{00})_o </math> of metric tensor outside the body. This allows us to refine expression for metric tensor components outside the body: :<math> (g_{00})_o = -\frac {1}{ (g_{11})_o } = 1+ \frac {2G m \gamma_c \beta }{c^2 r} + \frac{ 2 G \beta } {c^4 r}\left( m \psi_a + \frac {1}{2} m_g (\psi - \psi_a ) - \frac {G m^2 \gamma_c }{2a} + q \varphi_a + \frac {1}{2} q_b (\varphi - \varphi_a ) + \frac {q^2 \gamma_c }{8\pi \varepsilon_0 a} + m \wp_c \right), </math> where <math> \psi = - \frac {G m_g}{r} </math> is gravitational potential outside the body; <math> \varphi = \frac {q_b}{4\pi \varepsilon_0 r} </math> is electric potential outside the body. == Generalized four-momentum and total four-momentum == In the paper, <ref> Fedosin S.G. Generalized Four-momentum for Continuously Distributed Materials. Gazi University Journal of Science, Vol. 37, Issue 3, pp. 1509-1538 (2024). https://doi.org/10.35378/gujs.1231793. // [http://sergf.ru/gfm.htm Обобщённый 4-импульс для непрерывно распределённого вещества].</ref> formulas were found for calculating generalized four-momentum of a physical system in curved space-time taking into account contribution from particles and fields of the system. A differential four-dimensional Euler-Lagrange equation for continuously distributed matter was also obtained. Both the formulas for generalized four-momentum and Euler-Lagrange equation are satisfied in relativistic uniform system. In the paper, <ref> Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45. // [http://sergf.ru/ws.htm Что мы должны понимать под 4-импульсом физической системы?] </ref> covariant formulas for relativistic four-momentum of a physical system were derived, which were also verified in a relativistic uniform system. It was shown that four-momentum is expressed by the sum of two four-vectors of integral type with covariant indices, one of these four-vectors is generalized four-momentum of the system, and the other four-vector describes four-momentum of fields of the system. Additionally, the 4/3 problem and interpretation of integral vector found by integrating over volume of time components of stress-energy tensor of the system were considered. The fact that integral vector cannot be four-momentum of the system, as is assumed in general theory of relativity, is confirmed by direct calculation and follows from the fact that a four-vector cannot be obtained from tensor components. Similarly, volume integral of time components of stress-energy tensor of electromagnetic field does not yield four-momentum of electromagnetic field, but an integral vector that is not a four-vector. As a consequence, the mass-energies contained in components of integral vector are not equal to each other and are related in the proportion 4/3. Covariant formulas for four-momentum were used to determine the components of angular momentum tensor of a physical system in the article. <ref>Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, Vol. 40, No. 02, 2450163 (2025). https://doi.org/10.1142/S0217751X2450163X. // [http://sergf.ru/la.htm Лагранжев формализм в теории релятивистских векторных полей]. </ref> == References == <references/> == See also == * [[Invariant energy]] * [[Physics/Essays/Fedosin/General field | General field]] * [[Acceleration field]] * [[Pressure field]] * [[w:Gravitational field | Gravitational field]] * [[w:Electromagnetic field | Electromagnetic field]] * [[Physics/Essays/Fedosin/Covariant theory of gravitation | Covariant theory of gravitation]] * [[Energy]] * [[Field energy theorem]] ==External links == * [http://www.wikiznanie.ru/wikipedia/index.php/%D0%A0%D0%B5%D0%BB%D1%8F%D1%82%D0%B8%D0%B2%D0%B8%D1%81%D1%82%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%B4%D0%BD%D0%BE%D1%80%D0%BE%D0%B4%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0 Relativistic uniform system in Russian] [[Category:Special relativity]] [[Category:Physical systems]] [[Category:Covariant theory of gravitation]] [[Category:Energy]] dfbb0z08o58eoe8hu0347233deqj51t 2 283170 2834496 2834405 2026-09-25T23:30:11Z Elominius 2911372 blktrace 2834496 wikitext text/x-wiki ; Possibly useful packages for Linux users: 7z mediainfo ffmpeg mplayer mkvtoolnix sdparm udftools qpxtool dvd+rw-tools cdrkit cdrtools xorriso hwinfo lsscsi gameconqueror xdotool autokey blender inkscape iotop htop filezilla k3b lmms pavucontrol virtualbox sqlite3 tlp bluez blueberry kdenlive picard easytag libimage-exiftool-perl vsftpd proftpd-basic nemo file-roller searchmonkey catfish lzip lziprecover xed kate hexedit ghex ddrescue foremost sleuthkit testdisk gparted git perf-tools xvattr imap-tools android-tools-adb sg3-utils libimage-exiftool-perl ucommon-utils smartmontools blktrace l4dsjahhfqq03x4zzkj9q10nweda53p 2834497 2834496 2026-09-25T23:31:24Z Elominius 2911372 mpv - modernized mplayer 2834497 wikitext text/x-wiki ; Possibly useful packages for Linux users: 7z mediainfo ffmpeg mplayer mpv mkvtoolnix sdparm udftools qpxtool dvd+rw-tools cdrkit cdrtools xorriso hwinfo lsscsi gameconqueror xdotool autokey blender inkscape iotop htop filezilla k3b lmms pavucontrol virtualbox sqlite3 tlp bluez blueberry kdenlive picard easytag libimage-exiftool-perl vsftpd proftpd-basic nemo file-roller searchmonkey catfish lzip lziprecover xed kate hexedit ghex ddrescue foremost sleuthkit testdisk gparted git perf-tools xvattr imap-tools android-tools-adb sg3-utils libimage-exiftool-perl ucommon-utils smartmontools blktrace rizuwf1wv94qj2d9onaze9n06oknwiq 0 301040 2834524 2834343 2026-09-26T07:45:29Z D.H 52339 + 2834524 wikitext text/x-wiki {| style="width:20%; font-size:13px;" align=right |{{../Other Topics (header)}} |} ==Early history of the twin paradox== {{Lorentzbox|Text={{center|Date of article creation: 9 November 2023; Last major revision: 26 September 2026}}}} a) When was the [[:w:twin paradox]] applied to life forms and human beings? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /><ref group=S name=during /> report that {{slink||Einstein 1911-HU}} discussed the aging of living organisms, and that {{slink||Langevin 1911-HU}} and {{slink||Wiechert 1911-HU}} explicitly discussed the aging of human beings. :*More details in sections {{slink||Human beings in 1911|Twins from 1911 to 1920}}, including newspaper articles from 1911 written by {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}} that clearly show that Einstein was the first to explicitly discuss the aging of human beings as well. b) Who was the first to formulate the principle of maximal proper time along straight worldlines, upon which differential aging in the standard twin paradox is based? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> mention Langevin (1911), Laue (1911). :*More details in section {{slink||Maximal proper time}} with the contributions of Langevin (1911), Wiechert (1911), Study (1911), Laue (1911-13). c) Who was the first to formulate [[w:Triangle inequality#Reversal in Minkowski space|inverse triangle inequality]] in Minkowski space, which represents the simplest version of the twin paradox? :*See details in section {{slink||Triangle inequality}} with the contributions of Robb (1914-20), Eddington (1922), Rogers (1922). d) Who was the first to show that any influence of proper acceleration on clocks can be neglected in the computation of the twin paradox from the viewpoint of the stay-at-home twin? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Einstein (1911), Laue (1913). :*More details in section {{slink||Negligibility of proper acceleration}} with the contributions of Einstein (1911), Wiechert (1911), Laue (1913), Lorentz (1913). e) Who was the first to introduce the three clock/brother example that completely removes acceleration from the clock/twin paradox? :*Historical accounts<ref group=S name=debs /><ref group=S name=alizzi /> date it back to Lange (1927) and Lord Halsbury (1957). :*More details in section {{slink||Relay (three brothers) experiment}} with the contributions of Grünbaum (1911) and Wiechert (1920-22). f) Who was the first to use acceleration as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref name=cuvaj group=S /><ref group=S name=pes /> mention Langevin (1911), Einstein (1918). :*More details in section {{slink||Acceleration as asymmetry indicator}} with the contributions of Langevin (1911), Sommerfeld (1913), Lorentz (1913), Einstein (1914-20). g) Who was the first to use different frame distribution as asymmetry indicator as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Laue (1911-13). :*More details in section {{slink||Frame distribution as asymmetry indicator}} with the contributions of Laue (1911-13), Bloch (1918). h) Who was the first to describe the perspective of the traveler? :*Historical accounts<ref group=S name=miller /><ref group=S name=beng /> mention Langevin (1911), Lorentz (1914), Einstein (1918). :*More details in section {{slink||Perspective of the traveler}} with the contributions of Langevin (1911), Lorentz (1913-14), Einstein (1918), Thirring (1921). i) Who was the first to describe a round-trip experiment in curved spacetime? :*See section {{slink||Curved spacetime}} with the contribution of Becquerel (1922). j) Who was the first to interprete the twin paradox in terms of an aether or absolute space? :*See section {{slink||Aether interpretations}} with the contribution of Langevin (1911), Wiechert (1911), Lechalas (1912). k) Who was the first to denote the round-trip experiment as paradoxical? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> point to Laue (1911). :*See section {{slink||Paradoxical?}} for details. l) Who was the first to misunderstand the twin paradox? :*See section {{slink||Misunderstandings}} with the contributions of Berg (1910), Wiechert (1911), Campbell (1911/12), Gruner (1912). m) What were Einstein's contributions? :*See section {{slink||Einstein's contributions}}. ==Human beings in 1911== {| class="wikitable" style="background-color:white;{{text default color}};" ![[w:Albert Einstein|Einstein]] |- |{{anchor|Einstein 1905}}In 1905<ref name=einstein05 /> he showed that a clock moving on a round-trip away from A and back along a polygonal or curved path, is retarded with respect to a clock stationary at A by approximately <math>\tfrac{1}{2}t(v/V)^{2}</math> at reunion. For example, a clock on the equator is retarded with respect to a clock on the pole. He described this consequence as being "peculiar" (German: eigentümlich). {{anchor|Einstein 1911-HU}}In a lecture given on January 1911<ref name=einstein11a /> (published in November), he extended this "funny" (German: drollig) experiment to living organisms: {| ! width=55% | Einstein wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Wenn wir z. B. einen lebenden Organismus in eine Schachtel hineinbrächten und ihn dieselbe Hin- und Herbewegung ausführen lassen wie vorher die Uhr, so könnte man es erreichen, dass dieser Organismus nach einem beliebig langen Fluge beliebig wenig geändert wieder an seinen ursprünglichen Ort zurückkehrt, während ganz entsprechend beschaffene Organismen, welche an den ursprünglichen Orten ruhend geblieben sind, bereits längst neuen Generationen Platz gemacht haben. Für den bewegten Organismus war die lange Zeit der Reise nur ein Augenblick, falls die Bewegung annähernd mit Lichtgeschwindigkeit erfolgte! | style="padding: 0px 20px 0px 20px;" |For example, if we put a living organism in a box and make it undergo the same back and forth movement as the clock before, we could achieve that this organism returns to its original location with arbitrary little change after a flight of arbitrary length, whereas completely identical organisms that remained at rest in the original location have long since made room for new generations. To the moving organism, the long journey was only a moment if the movement happened close to the speed of light! |} {{Lorentzbox|Text=Two participants of that lecture, {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}}, report that Einstein also talked about the aging of ''human beings''.}} |- !{{anchor|Lämmel 1911-HU}}[[w:Rudolf Lämmel|Lämmel]] |- |He attended Einstein's 1911 lecture and gave a popular report about it in the Swiss newspaper "[[w:Neue Zürcher Zeitung|Neue Zürcher Zeitung]]" published on 28 April 1911,<ref name=lammel /> including additional details. Regarding the round-trip clock experiment he wrote: {| ! width=50% | Lämmel wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bewegt sich eine Uhr mit Lichtgeschwindigkeit längs einer Geraden, auf der gerichtete Uhren stehen, so scheint die bewegte Uhr, beurteilt vom Standpunkt der ruhenden aus, im oben stizzierten Sinn, stillzustehen. Kehrt die Uhr, nach einem Ruck, mit Lichtgeschwindigkeit wieder zurück zur Zentral-Uhr, so ist, nach Einstein, für den Beobachter bei der Zentral-Uhr die Sache so, als ob ein mit der bewegten Uhr mitgeführter Beobachter (samt dessen Uhr) nicht gealtert hätte. Hinge also des letzteren Alter von den Angaben des ruhenden Beobachters ab, so könnte der von einer großen Reise ins Weltall zurückkehrende Beobachter bei der Zentral-Uhr spätere Generationen antreffen – er selber hätte nicht gealtert. Welche Bedeutung diese ''ad absurdum'' geführte Gedankenspielerei etwa hat, läßt sich heute nicht absehen – vielleicht, ja wahrscheinlich ist sie ohne jeden Einfluß auf die tatsächlichen Verhältnisse. Aber man sieht dabei immerhin, daß die Physik imstande ist, die kühnsten Träume der Phantasie noch – zu überbieten. | style="padding: 0px 20px 0px 20px;" |Let a clock be moving at speed of light along a line on which regulated clocks are standing, then the moving clock's hand appears to be standing still (in the sense described above) as judged from the standpoint of the resting one. If the clock, after one jolt, comes back with light speed to the central clock, then according to Einstein the matter presents itself to the observer at the central clock, as if the observer comoving with the clock (together with his clock itself) hasn't been grown older. Thus if the age of the latter would depend on the indications of the resting observer, the observer returning from a great journey into space could meet later generations at the central-clock – he himself hasn't been grown older. The importance of this play of thought led ''ad absurdum'' cannot be seen today – maybe, or even probably, it is without any influence on the actual situations. Though at least one can see that physics is able to – surpass – even the boldest dreams and fantasies. |} Lämmel in December 1920 (published 1921)<ref name=lammel2 /> again alluded to Einstein's lectures in Zürich (possibly the one from 1911, and maybe also later ones), describing a discussion between himself and Einstein. After Einstein concluded that the travelers who came back after their journey will probably meet their former contemporaries as old men while they themselves could have been away for only a few years, Lämmel objected that this conclusion is only drawn with respect to rods and clocks, but not with respect to living beings. Einstein responded though, that all processes in the blood, in the nerves etc. are eventually periodical oscillations, i.e. motions. Yet to any such motion the relativity principle applies, thus the conclusion regarding the unevenly rapid aging it permissive. {{Lorentzbox|Text=While the official publication of Einstein's January lecture ({{slink||Einstein 1911-HU}}) mentions the aging of organisms, Lämmel recalls the reference to the aging of a human space traveler ("observer returning from a great journey into space"). This means that Einstein was the first to use human beings in the clock/twin paradox on January 16 which was first published by Lämmel on April 28, 1911. In comparison, {{slink||Langevin 1911-HU}} used space travelers in a lecture on April 10 with publication in July, and {{slink||Wiechert 1911-HU}} used space travelers in lectures held between March 25 and May 23 with publication in July/September. It seems very unlikely that before April 28, Lämmel became somehow aware of the content of Langevin's or Wiechert's lectures held a few weeks earlier, in order to use them in his description of Einstein's lecture.}} |- !{{anchor|Langevin 1911-HU}}[[w:Paul Langevin|Langevin]] |- |On 10 April 1911, published July 1911,<ref name=langevin1 /> he held a now famous lecture popularizing the clock/twin paradox which he derived from the proper time integral as described in {{slink||Langevin 1911-PT}}. He demonstrated that a moving radioactive sample of radium is less evolved and less aged and therefore more active at return then the ones that remained in the laboratory. He also used light signals and the Doppler effect to visualize the effect. The most famous part concerned his description of the aging of human space travelers: {| ! width=50% | Langevin wrote ! [[:s:Translation:The Evolution of Space and Time|English Wikisource translation]] |- | style="padding: 0px 20px 0px 20px;" |Cette remarque fournit le moyen, à celui d’entre nous qui voudrait y consacrer deux années de sa vie, de savoir ce que sera la Terre dans deux cents ans, d’explorer l’avenir de la Terre en faisant dans la vie de celle-ci un saut en avant qui pour elle durera deux siècles et pour lui durera deux ans, mais ceci sans espoir de retour, sans possibilité de venir nous informer du résultat de son voyage puisque toute tentative du même genre ne pourrait que le transporter de plus en plus avant. Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse. Revenu à la Terre ayant vieilli de deux ans, il sortira de son arche et trouvera notre globe vieilli de deux cents ans si sa vitesse est restée dans l’intervalle inférieure d’un vingt-millième seulement à la vitesse de la lumière. Les faits expérimentaux les plus sûrement établis de la physique nous permettent d’affirmer qu’il en serait bien ainsi. | style="padding: 0px 20px 0px 20px;" |This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. |} {{Lorentzbox|Text=Reading his lecture in full, one finds the word "paradoxical" only in relation to the constancy of light speed, not on relation to the round-trip clock experiment.}} |- !{{anchor|Wiechert 1911-HU}}[[w:Emil Wiechert|Wiechert]] |- |In lectures on 25 March and 23 May 1911, submitted July and published September 1911,<ref name=wiechert11 /> he described the round-trip clock experiment with two equal clocks regulated to the same rate and brought to the same pointer position, or by introducing the same chemical process two times, or by introducing ''two life forms that began their life at the same time''. At the end of his paper he applied this to human travelers: {| ! width=50% | Wiechert wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Nehmen wir aber wieder eine Relativgeschwindigkeit an, die bis auf 3 Proz. der Lichtgeschwindigkeit nahekommt, dann wird das Verhältnis der empfundenen Zeitlängen wie 4:1. Das Bild mag etwas weiter noch ausgemalt werden. Denken wir uns, daß ein Beobachter durch den Raum unseres Sternhimmels mit dieser Geschwindigkeit in einer Kreisbahn mit einem Radius von 16 Lichtjahren fährt, dann wird er nach unserer Zeitrechnung nach je 100 Jahren wieder an unserem Sonnensystem vorüberkommen. In seinem Gefährt wird dabei die Zentrifugalkraft so auf ihn einwirken, daß sie gemäß den Relativitätsgesetzen der Einwirkung der Schwerkraft auf uns Erdenbewohner gleich erscheint. Es sind also die wirkenden Kräfte nur so groß, daß der Phantasie die Möglichkeit geboten wird, den Reisenden als menschliches Wesen zu denken. Da hier dauernd <math>\sqrt{1-v^{2}/c^{2}}</math> ist, fließt die Eigenzeit für den Reisenden viermal langsamer dahin, als für die Bewohner der Gestirne. Wenn er also nach 100 unserer Jahre wieder zu unserem Sonnensystem zurückkehrt, wird er sich selbst nur um 25 Jahre gealtert fühlen. Erreicht er nach der Entwicklung seines Körpers und nach seiner Zeitempfindung ein Alter von 75 Jahren, so entspricht dies doch einer dreimaligen Wiederkehr zu unserem Sonnensystem, also 300 unserer Erdenjahre. | style="padding: 0px 20px 0px 20px;" |Yet if we again assume a relative velocity approximating the speed of light by 3 percent, then the ratio of the experienced duration of time becomes 4:1. This image can be further extended. Let's imagine that an observer travels with that velocity on a circular path at a radius of 16 light years through the space of our galaxy, then according to our time calculation he passes by our solar system every 100 years. In his vehicle the centrifugal force will act on him in such a way, that in accordance with the relativity laws it will appear to be equal to the force of gravity acting upon the inhabitants of Earth. Thus the acting forces are only thus big, in order to give our fantasy the possibility to imagine the traveler as a human being. Since we have <math>\sqrt{1-v^{2}/c^{2}}</math> throughout, proper time flows four times slower for the traveler than for the inhabitants of the stars. Thus when he comes back to our solar system after 100 of our years, he will feel to have aged only by about 25 years. If he reaches an age of 75 years according to the development of his body and his own time experience, then this corresponds to a threefold return to our solar system, i.e. 300 of our Earth years. |} {{Lorentzbox|Text=a) Wiechert (1915)<ref name=wiechert15 /> later provided a short historical survey of the clock/twin paradox. He referred to the fact that already {{slink||Einstein 1905}} considered the case of two clocks ("Einstein's clock experiment"), and even though [[w:Hermann Minkowski|Minkowski]] himself didn't consider the case, his proper time formula provides the result in a straight forward manner. The latter was done by himself in lectures on 25 March and 23 May 1911, as well as by Langevin published in July 1911. Wiechert pointed out that he himself and Langevin used "humorist" examples in order to clarify the situation: While Wiechert argued that one has to make a journey in order to stay young, Langevin argued that one has to romp about in a laboratory in order to stay young. Both of them used human beings, arguing that their physical and mental life should have been influenced in the same way as any other process in nature. b) The dates given by Wiechert (1915) are not complete. The correct ones are: *Langevin's lecture on 10 April 1911, published in July. *Wiechert's lectures on 25 March and 23 May 1911, submitted on July 26, published in September. *He was still unaware of Einstein's lecture from January 1911, published in November 1911.}} |- !{{anchor|Müller 1911-HU}}[[w:Fritz Müller-Partenkirchen|Müller]] |- |The freelance writer and law student Fritz Müller (who was later known as [[w:Fritz Müller-Partenkirchen|Müller-Partenkirchen]]) attended Einstein's lecture and wrote a popular report about it in the German newspaper "[[w:Berliner Tageblatt|Berliner Tageblatt]]" on 16th and 23rd October 1911,<ref name=muller /> in which he gave further details (compare with {{slink||Lämmel 1911-HU}}). Regarding the clock/twin paradox he wrote: {| ! width=50% | Müller wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Zwei gleichgehende Uhren sollen je einen Beobachter haben und nebeneinander ruhen. Nun soll die eine mit ihrem Beobachter plötzlich mit Lichtgeschwindigkeit in den Weltenraum hinausreisen. Vorher haben die beiden vereinbart, sich alle Sekunden mit einem Lichtsignal die Zeit zu telegraphieren. [...] In unserem Grenzfall, wo die Reise mit Lichtgeschwindigkeit vor sich geht, müßte der ruhende Beobachter erklären, jene andere Uhr käme in der Zeit überhaupt nicht voran. Die Zeit stünde dort still. Tatsächlich kommen die Einsteinschen Gleichungen zu diesem Resultat. Für den mit der Uhr reisenden Beobachter, sagt Einstein, gelte dasselbe. Das heißt, im Urteil des Zurückbleibenden würde jener niemals alt. „Und wenn er auf einer gebrochenen Reiselinie wieder an seinen Ausgangspunkt zurückkehrte?" fragt man den Vortragenden in der Diskussion. – „So bliebe er in unserem Urteil so jung wie bei der Ausreise," erwidert Einstein mit vollem Ernst, „selbst wenn wir Zurückgebliebenen inzwischen Männer mit weißen Bärten geworden sind – die Gleichungen liefern für jede Richtung der Bewegung, auch für eine gebrochene Bewegung, unerschütterlich die selben Resultate." – Wir sehen einander an. Das klingt märchenhaft. Märchenhaft? Gewiß, die alten Märchen vom Mönch von Heisterbach, vom Rip van Winkle, von Urashima Taro steigen auf. Merkwürdig, wie die Volksphantasie bei den Deutschen, bei den Amerikanern, bei den Japanern in der gleichen Richtung gearbeitet hat – alle drei Märchen erzählen ja von Leuten, deren Leben still steht, viele hundert Jahre lang, während die andern altern. So fanden sie bei ihrer Rückkehr ein anderes Land und eine andere Generation. | style="padding: 0px 20px 0px 20px;" |Two synchronous clocks at rest next to each other, shall each be accompanied by an observer. Now one of them, together with its observer, suddenly travels into space at the speed of light. Previously, both have arranged that every second they telegraph their time to each other using light signals. [...] In our limiting case where the journey happens at light speed, the resting observer would have to declare that the other clock would not proceed in time at all. Time would stand still at this place. Einstein's equations indeed produce this result. As to the observer traveling with the clock, says Einstein, the same is true. That means in the judgment of the remaining one, the other one would never become old. Then the lecturer [i.e. Einstein] was asked in the discussion: "And if he comes back to his starting point on a curved travel path?", to which Einstein replied in full earnest: "Then in our judgment he would remain as young as he was at departure, even if we remaining ones became men with white beards in the meantime, the equations unshakably give the same result in every direction of motion, also for curved motion". We look at each other. That sounds fabulous. Fabulous? Of course, the old fairy tales of [[w:Heisterbach Abbey|w:The monk of Heisterbach]] or [[w:Rip Van Winkle]] or [[w:Urashima Tarō]] come forward. Strange, how the folk fantasy of the Germans, the Americans, the Japanese worked in the same direction, all three fairy tales indeed tell about people whose life stands still, many hundred years long, while the other ones grow old. Thus they found another country and another generation when they returned. |} {{Lorentzbox|Text=Müller's account confirms {{slink||Lämmel 1911-HU}} that Einstein indeed mentioned human beings, but his description also suggests that Einstein was the first to use mutually sent light signals. However, as this was published in October, it cannot be excluded that Müller's description of light signals was influenced by {{slink||Langevin 1911-HU}}, published in July, in which light signals were used as well.}} |} ==Twins from 1911 to 1920== We now provide a list of authors who employed ''twins'', i.e. ''two'' life forms or humans that initially were of ''same age'' when the round-trip began: {| class="wikitable" style="background-color:white;" |- ! Author !! Date !! Description |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> |1911 |Two life forms that begin their life at the ''same time'' (German: "Zwei Lebewesen [..] die ihr Leben gleichzeitig beginnen"), of which the moving one returns retarded in its progression with respect to the stationary one. |- |[[w:Paul Gruner|Gruner]]<ref name=gruner /> |1912 |Two persons of ''same age'' (French: "deux personnes du même âge"), of which the moving one returns less developed than stationary one. |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> |1913 |The moving life form returns younger than its ''former agemates'' (German: "ehemaligen Altersgenossen"). |- |[[w:Hermann Weyl|Weyl]]<ref name=weyl /> |Easter 1918 | {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Von zwei Zwillingsbrüdern, die sich in einem Weltpunkt A trennen, bleibe der eine in der Heimat (d. h. ruhe dauernd in einem tauglichen Bezugsraum), der andere aber unternehme Reisen, bei denen er Geschwindigkeiten (relativ zur »Heimat«) entwickelt, die der Lichtgeschwindigkeit nahekommen; dann wird sich der Reisende, wenn er dereinst in die Heimat zurückkehrt, als merklich jünger herausstellen denn der Seßhafte. |Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. |} {{Lorentzbox|Text=Weyl was the first to ''explicitly use twins'' in relation to the round-trip experiment. The fourth edition (1920) of that book was translated from German into English and French in 1922.}} |- |[[w:Albert Einstein|Einstein]]<ref name=einstein20 /> |1920/21 |{{Anchor|Einstein 1921-TW}} {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Trifft A wieder bei B ein, so kann es sich ereignen, daß der beharrende Zwilling inzwischen 60 Erdjahre alt geworden ist, während der zurückkehrende nur 15 Jahre zählt, oder sich gar noch im Säuglingsstadium befindet. [..] Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls -Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. |If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still. [..] In the case of these two twins, Einstein declared, we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures. |} {{Lorentzbox|Text=This was based on an interview of Einstein by Moszkowski. While the expression "clock paradox" was used since 1911/12 (see section {{slink||Paradoxical?}}), this seems to be the first time that it was rebranded as "twin paradox". The copyright mark indicates 1920, while the title page indicates 1921. The translation from German into English also appeared in 1921.}} |} ==Maximal proper time== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]] 1911 |{{anchor|Langevin 1911-PT}}In April 1911 (published July),<ref name=langevin1 /> he described the round-trip experiment without formulas using two portions of matter present at two events happening at the same place. The ''integration of proper time'' along the entire wordlines shows that the portion of matter that starts a closed cycle by receding and finally coming back, will have a ''smaller proper time'' than the one that stayed behind. In October 1911 (published 1912),<ref name=langevin2 /> Langevin again showed that the portion of matter that described a closed cycle will have a ''smaller proper time'' <math>R</math> than the one that stayed in an inertial frame, which is defined by the equation: :<math>\begin{matrix}V^{2}\left(t-t_{0}\right)^{2}=d^{2}-R\\ \left[d^{2}=\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}\right] \end{matrix}</math> |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> Lectures March-May 1911 submitted July published September |{{anchor|Wiechert 1911-PT}}Let two equal processes be observed in two equal material systems colocated in two moments (1) and (2), and let there velocities have been changed in arbitrarily different ways in the meantime. It follows that the ratio of advancement of those processes is given by the two intervals <math>\Delta\tau </math> of their respective ''proper times''. He concluded that any round-trip clock experiment can be easily comprehended from that theorem by computation. The corresponding integral is: :<math>\Delta\tau=\int_{1}^{2}d\tau=\int_{1}^{2}dt\sqrt{1-\frac{\mathfrak{v}^{2}}{c^{2}}}</math> |- |[[w:Eduard Study|Study]]<ref name=study /> June 1911 |Minkowski's concept of worldlines implies that the straight path between two points of the same worldline is the ''longest'' among all paths between those points, if the path length on a worldline is defined by the related proper time. {{Lorentzbox|Text=Study's book was purely mathematical without mentioning clocks or the round-trip experiment, alluding to his result only in a footnote.}} |- |[[w:Max von Laue|Laue]] 1911-13 |{{anchor|Laue 1911/12-PT}}In December 1911 (published 1912),<ref name=laue1 /> Laue showed without formulas that the round-trip experiment is represented by a curved worldline, which at worldpoint A decomposes into a row of curves, after which all of them will be re-united at worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the ''longest proper time.'' {{anchor|Laue 1912/13-PT}}In December 1912 (published 1913) in the second edition of this relativity book,<ref name=laue1 /> Laue described the proper time integral between events 1 and 2 of a slowly accelerated clock covering a broken line and a stationary clock covering a straight worldline. Of all worldlines covering 1 and 2, the straight line has the ''longest proper time''. Therefore the traveling clock in the round-trip experiment is retarded at reunion, because its curved worldline corresponds to a shorter proper time. This result he presented in terms of the following inequality, of which the right-hand side refers to the straight curve of the stationary clock, while all others possible curves are represented on left-hand side: :<math>\tfrac{1}{c}\int_{1}^{2}\sqrt{du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}<\tfrac{1}{c}\int_{1}^{2}du</math> {{Lorentzbox|Text={{anchor|Sommerfeld 1913-PT}}Similar treatments can be found in the textbooks of [[w:Arnold Sommerfeld|Sommerfeld]] (1913),<ref name=sommerfeld /> [[w:Hermann Weyl|Weyl]] (1918),<ref name=weyl /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Jean Becquerel|Becquerel]] (1922).<ref name=becqu1 />}} |} ==Triangle inequality== {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Alfred Robb|Robb]] 1914-1920 |{{anchor|Robb 1914-TR}}In 1914<ref name=robb1 /> he showed that there are three types of triangles formed by intervals in Minkowski space, depending on whether one deals with "separation lines" (spacelike intervals), "optical lines" (lightlike intervals), or "inertia lines" (timelike intervals representing the path of nonaccelerated particles defined by <math>{\scriptstyle \left(x_{1}-x_{0}\right)^{2}+\left(y_{1}-y_{0}\right)^{2}+\left(z_{1}-z_{0}\right)^{2}-c^{2}\left(t_{1}-t_{0}\right)^{2}<0}</math>). As to a triangle formed by inertia lines, he showed that the sum of a certain two sides is ''less'' than that of the third one. {{Lorentzbox|Text=So the triangle inequality derived from time-like intervals in Minkowski space is ''[[w:Triangle inequality#Reversal in Minkowski space|inverse]]'' to the inequality in Euclidean space. This inverse inequality directly represents the most simple variant of the twin paradox: the traveler follows two sides of the time-triangle, while the stay-at-home observer follows the third side indicating maximal proper time.}} [[File:RobbTriangle.svg|right|150px]] In 1920<ref name=robb2 /> Robb gave a numerical example of the triangle ABC with time-like intervals ("inertia lines") defined by coordinates :<math>\begin{matrix} & x & y & z & t\\ A\ & 0 & 0 & 0 & 0\\ B\ & 0 & 0 & 0 & 10\\ C\ & 4 & 0 & 0 & 5 \end{matrix}</math> which he plugged into :<math>\bar{s}^{2}=\left(t_{1}-t_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}-\left(y_{1}-y_{0}\right)^{2}-\left(z_{1}-z_{0}\right)^{2}</math> from which he obtained the sides AB=10, AC=3, CB=3 and the inequality <math>AC+CB<AB</math>. |- |[[w:Arthur Eddington|Eddington]]<ref name=edding2 /> 1922 |He distinguished between the "space-triangle" for spacelike intervals, and the "time-triangle" for time-like intervals. The latter is measured with a clock from A to B and from B to C, with the sum of those readings ''is always less'' than the reading of a clock measuring directly from A to C. In the ordinary space-triangle any two sides are together greater than the third side; in the time-triangle two sides are together ''less'' than the third side. |- |Rogers<ref name=rogers /> 1922 |He showed that the "pure time-triangle" C, A, B (in their proper time order) satisfies the relation <math>\cosh C=\tfrac{\alpha^{2}+\beta^{2}-\gamma^{2}}{2\alpha\beta}</math>, where <math>\cosh C</math> denotes the unit-scalar product of the vectors CA, CB, and <math>\alpha,\beta,\gamma </math> the real and positive intervals BC, CA, AB. Since <math>\alpha>\beta </math> and <math>\cosh C>1</math>, it follows that <math>\alpha>\beta+\gamma </math>. That is, "the greatest side of pure time-triangle is greater than the sum of the other two sides". It follows at once that the stationary value of the proper time integral is an "absolute maximum". |} ==Negligibility of proper acceleration== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |style="vertical-align:top" |[[w:Albert Einstein|Einstein]] 1905-1918 |In 1905,<ref name=einstein05 /> Einstein used velocity time dilation <math>\tau=t\sqrt{1-\left(\frac{v}{V}\right)^{2}}</math> to derive the retardation of a clock performing a round-trip with constant speed <math>v</math> along a polygonal path or a continuously curved line, without mentioning any influence of acceleration at turnaround. {{anchor|Einstein 1911-VA}} In 1911 (published 1912),<ref name=einstein3 /> Einstein said that special relativity doesn't say anything about what happened to the clock's pointer position during the acceleration that changes the clock's direction along the round-trip, yet the influence of this change must be getting smaller the longer the clock ''is moving uniformly'', i.e. the longer one chooses the dimensions of the path. {{anchor|Einstein 1912-VA}}In an unpublished manuscript on special relativity from 1912,<ref name=einst12manu /> he pointed out that any influence of acceleration during the round-trip experiment, can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygonal path. {{anchor|Einstein 1914a-VA}}In a letter from April 1914,<ref name=einstpetz /> Einstein showed that any ''finite'' acceleration at turnaround during the round-trip experiment can only influence the clock in a ''finite'' way, thus it can be neglected by minimizing the time of acceleration with respect to the time of uniform translation. So it ''must be concluded'' that the clock is retarded at reunion after traveling on a polygonal path. {{anchor|Einstein 1914b-VA}}During a conversation in May 1914,<ref name=rowe group=S /> Einstein is reported to have replied that the accelerations during the round-trip are "irrelevant for the amount of the time difference". (Compare with {{slink||Einstein 1914b-AC}}) {{anchor|Einstein 1918-VA}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918,<ref name=einstein18 /> Einstein pointed out that any effect of velocity changes at turnaround must be limited, thus the traveling clock must be retarded at reunion due to time dilation if one makes the path AB and back along the round-trip long enough. (Compare with {{slink||Einstein 1918-AC}}) |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> 1911 |{{Anchor|Wiechert 1911-VA}}[[File:WiechertTwin.svg|110px|right]] He demonstrated that differential aging along the round-trip cannot be caused during the passage from one velocity to another (i.e. acceleration) at turnaround, because the same result also follows when ''both'' A and B experience the ''same velocity changes'' with respect to another frame, only with the difference that B has relative velocities <math>+u</math> and <math>-u</math> for a long time, while A is brought after a short time from relative velocity <math>+u</math> to relative rest at which it remains a long time, and then it is brought to relative velocity <math>-u</math> for a short time. {{Lorentzbox|Text=He was probably the first to use an example in which both accelerate with same magnitude.}} |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> 1913 |{{anchor|Laue 1913-VA}}He showed that the problem of the influence of acceleration at turnaround in the round-trip experiment, can be eliminated by ''arbitrarily'' enlarging the time in inertial motion. {{Lorentzbox|Text=This is the same argument as given in {{slink||Einstein 1911-VA}}. The Einstein-Laue argument was also used by others such as [[w:Hans Thirring|Thirring]] (1921)<ref name=thirring /> or [[w:Max Born|Born]] (1921).<ref name=born />}} |- |[[w:Hendrik Lorentz|Lorentz]]<ref name=lorentz1 /> 1913 |He pointed out that any effect of acceleration on the traveling clock at turnaround, can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip. {{Lorentzbox|Text=Similarly, [[w:Wolfgang Pauli|Pauli]] (1921) stated that the arising infinitesimal accelerations at turnaround are certainly independent of the total travel time and ''therefore easy to eliminate''.<ref name=pauli />}} |} ==Relay (three brothers) experiment== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:de:Fritz Grünbaum (Physiker)|Grünbaum]]<ref name=gbaum /> 1911 |He discussed a one-way time dilation experiment in which the first clock is set into motion from the origin and then moving to the second clock. He argued that one can avoid the problem of acceleration experienced by the first clock when set into motion, by replacing it with a ''third'' clock that is already in motion with constant velocity and is synchronized at the origin with the first clock. {{Lorentzbox|Text=While Grünbaum didn't discuss round-trip experiments, his introduction of a third clock in order to avoid acceleration is the basis of the three-brother experiment.}} |- |style="vertical-align:top"|[[w:Emil Wiechert|Wiechert]] 1920-1922 |In 1920 (published 1921),<ref name=wiechert20 /> Wiechert explained how to completely remove acceleration from the round-trip experiment: Bodies A, B, C move undisturbed and non-accelerated in different directions. A and B pass each other at time (1), B and C pass each other at a later time (2), and C and A finally pass each other at an even later time (3). So in this setup, the condition of C is the continuation of the condition of B. On any of the three bodies one can count the oscillations of light of a certain spectral-line, in which case relativity predicts that the ''combined sum of all oscillations'' on B+C is smaller than the number of oscillations on A alone. Wiechert also held that one can replace the light oscillations by the life functions of human-like beings which live on A, B and C. For instance, while the inhabitants of B+C only had time for one meal, there were arbitrarily many generations on A who follow after each other by death and birth. [[File:Wiechert1922a.png|180px|right]] In 1921 (published 1922),<ref name=wiechert21 /> Wiechert extended his previous acceleration-free round-trip experiment to an arbitrary number of non-accelerated bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., which constitutes a "relay" (German: Stafette) starting from body A and back again. The first B passes A and moves away, and after some time the last B comes back to A. Since any B body continues the fate of the previous one, all bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., combined have emitted fewer oscillations than A alone during the relay race. Wiechert pointed out that instead of light oscillations one can also choose the aging of life forms. {{Lorentzbox|Text=Such relay experiments were later independently rediscovered in English language papers<ref name=debs group=S /> such as by Lange (1927)<ref group=S name=lange /> in which the brothers synchronize their times when they pass each other (“three brother experiment”).}} |} ==Acceleration as asymmetry indicator== While it was known that any direct influence of [[w:proper acceleration]] on clocks can be neglected in the computation of the inertial frame of the stay-at-home twin (see previous section {{slink||Negligibility of proper acceleration}}), the very fact that only one of them is accelerating is still useful as an asymmetry argument in order to show that there is no contradiction to the relativity principle. {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{Anchor|Langevin 1911-AC}}He derived differential aging in the round-trip experiment using the proper time integral along worldlines (see {{slink||Langevin 1911-PT}}) and used acceleration as an asymmetry indicator: The result of the round-trip experiment is "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". |- |[[w:Arnold Sommerfeld|Sommerfeld]]<ref name=sommerfeld /> 1913 |After he showed (see {{slink||Sommerfeld 1913-PT}}) that retardation of time in the round-trip experiment derived from the proper time integral rests on the assumption that the clock's rate ''only depends on its momentary velocity'' (now called "clock hypothesis"), he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle since one of the clocks has to be accelerated in order to come back, thus the retardation in the round-trip experiment does not demonstrate "motion", but "accelerated motion". |- |[[w:Hendrik Lorentz|Lorentz]] 1913<ref name=lorentz1 /> |After he derived differential aging in the round-trip experiment from velocity time dilation and pointed out the negligibility of proper acceleration for the computation, he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle, since one of them changes velocity and accelerates; the relativity principle does not require symmetry between inertial and non-inertial observers. |- |style="vertical-align:top"|[[w:Albert Einstein|Einstein]] 1914-1920 |{{anchor|Einstein 1914b-AC}} During a conversation in 1914,<ref name=rowe group=S /> Einstein is reported to have said that moving clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are ''irrelevant'' for the ''amount'' of the time difference, their ''presence'' nevertheless cause B to fall behind ("accelerated motions are absolute"). {{anchor|Einstein 1918-AC}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918<ref name=einstein18 />, Einstein pointed out the negligibility of velocity changes from the viewpoint of an inertial frame (see {{slink||Einstein 1918-VA}}). Then he used ''acceleration as an asymmetry indicator'' in order to show, that there is no contradiction to the relativity principle, because relativity only predicts the equivalence of non-accelerated inertial frames: "only K is such a frame while K' is temporarily accelerated, thus the retardation of U2 with respect to U1 cannot be used to construe a contradiction against the theory." {{anchor|Einstein 1920-AC}}Einstein is reported to have said in an interview from 1920:<ref name=einstein20 /> {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls-Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. Dieser Grund für das Jüngerbleiben des A ergibt sich vom Gesichtspunkt der speziellen Relativitätstheorie aus der Tatsache, daß das betreffende Geschöpf — und nur dieses — Beschleunigungen erlitten hat. | style="padding: 0px 20px 0px 20px;" |In the case of these two twins," Einstein declared, "we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures . This ground, which counts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations." |} In a discussion from 1922,<ref name=morand /> Einstein is reported to have said that there is no contradiction in the round-trip experiment (in terms of a train leaving the station and returning later): The relativity principle is not applicable to this case, because the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two frames having velocities in opposite direction is not an inertial frame. There is no reciprocity between a frame that changes direction and one that doesn't. |} ==Frame distribution as asymmetry indicator== Because any direct influence of proper acceleration on the traveling clock at turnaround can be neglected (see {{slink||Negligibility of proper acceleration}}), the importance of {{slink||Acceleration as asymmetry indicator}} is limited to the mere fact that it reveals that only the traveler was in a non-inertial frame as only he changed his inertial frames, thus instead of emphasizing the occurrence of proper acceleration at turnaround, it's possible to describe the asymmetry more geometrically by emphasizing the different distribution of inertial frames of the twins along their worldlines. {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Max von Laue|Laue]] 1911-1913 |{{Anchor|Laue 1911/12-VA}} In 1911/12,<ref name=laue1 /> he pointed out that during the time of separation, that clock is most advanced which was at rest in an inertial frame all the time; namely there is ''always one, and only one inertial frame'', in which the locations of separation and re-encounter lie in the same geometric point. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1911/12-PT}}). In 1912/13,<ref name=laue2 /> he argued that in the round-trip experiment, we indeed can decide, which one of the clocks was steadily at rest in one and the same reference system, and which one was in the meantime at rest in two or more such systems. Among them there is of course a real physical difference. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1912/13-PT}}). In 1913<ref name=laue3 /> Laue pointed out: {| !style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Aber nach unseren Voraussetzungen ruht während der Zeit der Trennung die erste Uhr in ''einem'' berechtigten Bezugssystem, die zweite hingegen ruht zwar sowohl bei der Hin- wie bei der Rückbewegung in berechtigten Bezugssystemen, aber notwendig in ''zwei verschiedenen. Deshalb'' unterscheiden sich beider Schicksale physikalisch. Ließe man die zweite Uhr in der ihr anfangs erteilten Bewegung und schickte man ihr dafür die erste Uhr nach einiger Zeit mit größerer Geschwindigkeit nach, so würde beim Zusammentreffen die erste gegen die zweite zurückgeblieben sein; denn jetzt hat die erste während der Trennung in zwei verschiedenen Systemen geruht. (Footnote: Dem naheliegenden Einwand, daß wir über den Gang einer Uhr während eines Geschwindigkeits''wechsels'' nichts aussagen können, begegnet man am einfachsten mit dem Hinweis, daß man die Zeiten der gleichförmigen Bewegung ''beliebig'' groß gegen die der Beschleunigung machen kann.) | style="padding: 0px 20px 0px 20px;" | However, by our presuppositions, one clock is at rest in ''one'' valid reference system during the time of separation, while the second one is at rest in valid reference systems both during the forward- and the backward motion, but necessarily in ''two different ones. Therefore'' the two fates differ physically. If the second clock remains in the motion which was given to it at the start, and if after some time it is followed by the first clock with greater velocity, then the first one would be retarded with respect to the second one at the encounter; since now it was the first one that was at rest in two different systems during the separation. (Footnote: The objection which is near at hand, that we cannot say anything about the rate of a clock during a velocity ''change'', can be met most simply by the allusion, that we can render the times of uniform motion ''arbitrarily'' great with respect to acceleration..) |} |- |[[w:Werner Bloch|Bloch]]<ref name=bloch /> September 1918 |{{anchor|Bloch 1918-VA}} He represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. |} ==Perspective of the traveler== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{anchor|Langevin 1911-LI}}[[Image:rstd4.gif|170px|right]] After deriving differential aging from the proper time integral in {{slink||Langevin 1911-PT}} and using human beings in {{slink||Langevin 1911-HU}}, he described the perspectives of both observers using light signals and the Doppler effect. When they separate they see each other live 200 times slower, while at return they see each other live 200 times faster. So ''from the explorer's viewpoint'', in the first year he sees the Earth perform the actions of two days, while in the second year he sees the Earth perform the actions of two centuries. The asymmetry can be seen by noticing, that the observer on Earth in 200 years sees the explorer performs the actions of 1 year. Then the explorer turns around, after which the observer on Earth in 2 days sees the projectile perform the actions of another year. {{Lorentzbox|Text=Langevin used <math>v=c\left(1-\tfrac{1}{20000}\right)</math>, producing Lorentz factor <math>\gamma\approx100</math> and Doppler factor <math>\sqrt{\tfrac{c+v}{c-v}}\approx200</math>.}} |- |[[w:Hendrik Lorentz|Lorentz]] Lectures published in 1913<ref name=lorentz1 /> Similar treatment in 1914<ref name=lorentz3 /> |{{anchor|Lorentz 1913/14-LI}}Described the round-trip experiment in terms of inertial observer A (equipped with clock K) and traveling observer B (equipped with clock K'). In the frame of A, clock K' is retarded with respect to K at reunion due to time dilation. He then described the perspective of the traveling observer B by using two-way propagation of light from K' to K and back to K', leading to three periods defined by the moment of B's turnaround: In the first period the light signals return to K' before turnaround; in the second period the signals are emitted before turnaround and return after turnaround; in the third period emission and return of the signals are both happening after turnaround. Lorentz showed that K is time dilated by a factor of <math>\sqrt{1-v^{2}/c^{2}}</math> with respect to K' in the first and third period, but in the second period K is ticking ''faster'' than K' by a factor of <math>\sqrt{\tfrac{c+v}{c-v}}</math> which overcompensates the dilation in the other periods and explains, even from the perspective of B, why K' is retarded with respect to K at reunion. {{Lorentzbox|Text=In a review of the German translation of Lorentz's book, Einstein (1914) didn't directly mention Lorentz's treatment of the twin paradox, but he wrote that nobody who is seriously interested in relativity should neglect to read that book.<ref name=einstlor /> [[w:Wolfgang Pauli|Pauli]] (1921) refers to Lorentz's book as one of three papers that analyze the twin paradox more closely.<ref name=pauli />}} |- |style="vertical-align:top"| [[w:Albert Einstein|Einstein]] 1916-1920 |{{anchor|Einstein 1916-EP}}In a lecture from 1916,<ref name=einstein16 /> of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of [[w:general relativity]]." {{anchor|Einstein 1918a-EP}}In a letter from September 1918,<ref name=einadl /> Einstein showed that general relativity makes the inertial frame K and and the accelerated frame K' of the clocks in the round-trip experiment "equally justified", explaining the time difference in K' by combining the influence of velocity and gravitational potential on clocks. {{anchor|Einstein 1918-EP}}In his famous "Dialog about Objections against the Theory of Relativity" from November 1918,<ref name=einstein18 /> aimed at clarifying misconceptions of the clock paradox, he explained that there is no paradox in special relativity because there is no symmetry between clock U1 at rest in inertial frame K and clock U2 at rest in accelerated frame K' (see {{slink||Einstein 1918-AC}}). Yet [[w:general relativity]] and the [[w:equivalence principle]] allow the treatment of this problem also from the standpoint of frame K', where clock U2 remains at rest all of the time while U1 makes the following movements: (1) It is accelerated by a homogeneous gravitational field in the negative direction, (2) it moves with constant velocity <math>-v</math>, (3) it is accelerated in the positive direction until it turns around and comes by with constant velocity <math>+v</math>, (4) it moves with velocity <math>+v</math>, (5) it is accelerated in the negative direction until it stops. Clock U1 is retarded with respect to U2 in periods 2) and 4) due to velocity time dilation, but this retardation is overcompensated by the faster rate of U1 during period 3), because U1 is at a higher gravitational potential. He argued that the computation (which he didn't provide) shows that the advance of U1 in period 3) is double its retardation during periods 2) and 4). Einstein concluded that by this consideration "the paradox is completely resolved". Using [[w:Mach's principle]], he pointed out that the gravitational field in K' might be induced by the masses of the universe that are accelerated in this frame. {{anchor|Einstein 1918b-EP}}In a letter to Einstein from December 1918, [[w:Max Jakob|Jakob]] doubted the result that the advance in period 3) is double the retardation during periods 2) and 4). Einstein responded by letter,<ref name=einstein18b /> in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). {{anchor|Einstein 1921-EP}}Einstein is reported to have said in an interview from 1920,<ref name=einstein20 /> that while acceleration explains the age difference between the stationary twin B and the traveling twin A in terms of special relativity (see {{slink||Einstein 1920-AC}}), the "proper" description in terms of general relativity is as follows: {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Eine tiefere Erfassung des Grundes ist indeß nur auf dem Boden der „Allgemeinen Relativitätstheorie" zu erlangen, die uns erkennen läßt, daß von A aus beurteilt ein Zentrifugalfeld existiert, von B aus betrachtet aber nicht; und dieses Feld hat einen Einfluß auf den relativen Ablauf und die Raschheit der Lebensvorgänge. | style="padding: 0px 20px 0px 20px;" | A proper grasp of the reason is furnished only when we adopt the general theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life." |} {{Lorentzbox|Text=a) Einstein's explanation was quickly adopted in the textbooks of [[w:Werner Bloch|Bloch]] (1920),<ref name=bloch2 /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Karl Bollert|Bollert]] (1921),<ref name=bollert1 /> [[w:Max Born|Born]] (1921),<ref name=born /> expressing the view that general relativity is "necessary" to provide the "complete" solution of the twin paradox. b) From a modern standpoint, however, Einstein's explanation has nothing to do with general relativity, but is rather an application of accelerated frames and "pseudo"-gravitational fields to flat Minkowski space of ''special'' relativity.<ref name=weiss group=S />}} |- |[[w:Hans Thirring|Thirring]]<ref name=thirring /> April 1921 |{{anchor|Thirring 1921-DS}}[[Image:Twin Paradox Minkowski Diagram.svg|right|200px]] He described the round-trip experiment by using two platforms K (clock A) and K' (clock B) each equipped with rows of clocks. He first demonstrated the symmetry of time dilation and the mutual relativity of simultaneity on the platforms and its effect on clock synchronization. The K clocks that B passes are all advanced because of <math>t'=\gamma\left(t-vx/c^{2}\right)</math>, and the same is true after turnaround since only the direction of velocity has to be changed in the Lorentz transformation <math>t'-t'_{0}=\gamma\left(t+vx/c^{2}\right)</math> leading to the effect of clock desynchronization, where <math>t'_{0}</math> is a constant depending on which clock one uses as standard for the new synchronization. He graphically showed using Minkowski diagrams, that this simultaneity jump due to desynchronization amounts to double the velocity time dilation during the inertial phases, explaining why A is more advanced than B at reunion. {{Lorentzbox|Text=Using clock B as synchronization standard, Thirring's constant is given by <math>t'_{0}=2l\gamma v/c^{2}=2t\gamma v^{2}/c^{2}</math> with <math>l=vt</math> as position of turnaround. A similar explanation was subsequently given by Langevin (1922).<ref name=morand />}} |} ==Curved spacetime== While the previous examples are defined in flat Minkowski spacetime and therefore can be fully discussed in terms of special relativity, [[general relativity]] is required when [[:w:spacetime curvature]] in the presence of mass and energy cannot be neglected any more.<ref name=koks group=S /> {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |[[w:Jean Becquerel|Becquerel]]<ref name=becqu1 /> 1922 |After defining gravitational time dilation <math>d\tau=\sqrt{1-\tfrac{2GM}{c^{2}r}}dt</math> in terms of the [[w:Schwarzschild metric]] around a material center, he discussed the following round-trip experiment: There are two identical clocks A and B placed next to each other, at a point very far from the material center, initially marking the same time <math>t</math>. Let us transport clock A to a point where the field is more intense, at a distance <math>r</math> from the center; this clock will measure time <math>\int d\tau</math> which is shorter than <math>\int dt</math>, thus it will run more slowly. If we bring clock A back to clock B, we will have to note that it is retarded with respect to B. |} ==Aether interpretations== [[w:Lorentz ether theory]] (LET) is empirically equivalent to special relativity since both models use the Lorentz transformation, thus the description of the twin paradox gives the same result as well. However, special relativity is preferred by the scientific community, because of the validity of the relativity principle in LET is only apparent due to a conspiracy of effects which makes the aether undetecable, and because the measured times and lengths in the aether are supposedly be giving the "true" values even though it is empirically impossible to determine which ones are true or apparent. {| class=wikitable style="background-color:white;{{text default color}};" |- ! style="width:150px" | Author !! Description |- |Langevin (1911)<ref name=langevin1 /> |He argued that it's true that uniform translation with respect to the aether has no experimental meaning in special relativity, though one can still speak of "absolute acceleration" with respect to an aether which he defined as the light carrying medium, so it was "premature to abandon the aether". The absolute nature of acceleration can be seen in the radiation of accelerated charges, as well as in the twin paradox in which the traveler that is more agitated or accelerated is younger at reunion. {{Lorentzbox|Text=Langevin didn't mention this aether interpretation in his later discussions of the twin paradox in 1911/12<ref name=langevin2 /> and 1919.<ref name=langevin3 />}} |- |{{Anchor|Wiechert 1911b}}Wiechert (1911)<ref name=wiechert11 /> |Contrary to Langevin, he emphasized the fact that the influence of acceleration can be minimized so that differential aging can be attributed to constant velocity alone. From that he concluded that the clock's "strides" (German: Schreitungen, denoting the "absolute meaning" of non-accelerated motions) are not equivalent or anisotropic, in contradiction to the "unconditional" relativity principle Einstein's. Instead he proposed a "conditional" relativity principle in which an aether (in the sense of Lorentz) determines all processes in nature. This should explain the non-equivalence of the "strides" because they can be seen as absolute motions with respect to this aether, thus the progression rate of processes is ''really'' altered when passing from one stride to another. {{Lorentzbox|Text=a) This aether interpretation was maintained by Wiechert also in subsequent publications in 1915-1922.<ref name=wiechert15 /><ref name=wiechert20 /><ref name=wiechert21 /> b) Wiechert's interpretation in terms of of absolute non-accelerated motions was also independently given by others: [[s:fr:Georges Lechalas]] (1912/13)<ref name=lech /> argued that time dilation and asymmetric aging are the result of absolute speeds with respect to an aether, while criticizing Langevin's (1911) argument that only accelerations can indicate the aether and are responsible for the asymmetric aging; [[w:Edward Vermilye Huntington]] (1912)<ref name=hunt /> argued that the "famous paradoxes of the theory of relativity" represented by the reciprocal nature of length contraction and time dilation, appear as necessary consequences of perfectly natural and reasonable conventions for setting clocks and laying out coordinates, when the Lorentz transformation is derived and interpreted on the basis of a stationary aether in the sense of Lorentz. c) Laue (1911/12)<ref name=laue1 /> applauded Wiechert for the "particularly striking way" in which he demonstrated that asymmetric aging indeed follows from the relativity laws. However, he rejected Wiechert's claim that this contradicts the "unconditional" relativity principle: The straight worldline connecting two events A and B is only preferred insofar as it indicates the maximal proper time between them, yet this preference is ''not'' the result of the natural laws employed, but is rather due to the choice of points A and B. By analogy, the geometric result that two points determine a straight line and thus a direction as well, doesn't refute the physical equivalence of all directions in space. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.}} |} ==Paradoxical?== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" | German original of [[w:Max von Laue|Laue]] (1911/12):<ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> ! English translation |- |Unter all den paradox erscheinenden Folgerungen aus der Zeittransformation der Relativitätstheorie gibt es wohl keine, gegen welche sich der natürliche Menschenverstand bei jedem, der der Sache noch ungewohnt ist, so sehr sträubt, wie gegen die, daß die Zeitangabe einer Uhr von ihrem Bewegungszustand abhängen soll. Schon in seiner grundlegenden Arbeit hat Einstein diese Paradoxie auf die Spitze getrieben in einem Gedankenexperiment, welches neuerdings von Langevin in einem auch sonst sehr lesenswerten Vortrage besonders hübsch erläutert worden ist. |Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. |- |colspan=2|{{Lorentzbox|Text=Laue was probably the first to denote the round-trip experiment as paradoxical (even though he pointed out that there are no real contradictions). Subsequently, [[:w:Paul Gruner|Gruner]] (1912)<ref name=gruner /> and others including Einstein (1918)<ref name=einstein18 /> explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas [[w:Rudolf Seeliger|Seeliger]] (1913)<ref name=seel /> spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon").}} |} ==Misunderstandings== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" padding=10 | German original by [[w:Otto Berg (scientist)|Berg]] (1910):<ref name=berg /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |Im Punkte <math>x = 0</math> des Systems S befinde sich eine Uhr, eine andere im Punkte <math>x'=0</math> von S'. Diese zweite bewege sich mit S' bis zum Punkte <math>x = a</math>, kehre dort um und bewege sich nun mit der Geschwindigkeit <math>v</math> zurück bis zum Punkte <math>x= 0</math>. Welche Zeit müssen beide Uhren in dem Moment angeben, wo sie sich wieder treffen? Wir beantworten diese Frage zunächst vom Standpunkt des Beobachters in S. Die Uhr in <math>x' = 0</math> hat sich mit der Geschwindigkeit <math>v</math> bis zum Punkte <math>x = a</math> bewegt; dazu brauchte sie die Zeit <math>\tau=\tfrac{a}{v}</math>. Zum Rückweg ist dieselbe Zeit nötig. Nach der Zeit <math>2\tau=2\tfrac{a}{v}</math> ist die Uhr also wieder im Punkte <math>x = 0</math> angelangt. Wir stellen uns nun auf den Standpunkt des Beobachters in S'. Für diesen führt nach dem Relativitätsprinzip das System S genau dieselben Bewegungen aus wie das System S' für den Beobachter in S, nur in entgegengesetzter Richtung. Die Zeit bis zum Zusammentreffen beider Uhren ist also im System S' ebenfalls gegeben durch <math>2\tau=2\tfrac{a}{v}</math>. Betrachtungen, die auf anschauliche Vorstellungen, wie Nachgehen von Uhren, gestützt sind, führen hier leicht zu Irrtümern, von denen auch die Fachlitteratur nicht frei ist. | style="padding: 0px 20px 0px 20px;" |There is a clock at point <math>x=0</math> of system S, and another one at point <math>x'=0</math> of S'. The second one moves together with S' until point <math>x=a</math>, turns around and now moves back with speed <math>v</math> to point <math>x=0</math>. Which time must both clocks indicate at the moment at which they encounter again? We answer this question at first from the standpoint of the observer in S. The clock at <math>x=0</math> has been moving with speed <math>v</math> until point <math>x=a</math>, for which it required time <math>\tau=\tfrac{a}{v}</math>. The same time is required for the way back. After time <math>2\tau=2\tfrac{a}{v}</math> the clock has thus arrived again at point <math>x=0</math>. Let's now take the standpoint of the observer in S'. In his view in accordance with the relativity principle, system S is conducting exactly the same motions as those of system S' with respect to the observer in S, only in opposite direction. Thus the time until the meeting of both clocks is given by <math>2\tau=2\tfrac{a}{v}</math> in system S' as well. Considerations based on illustrative notions, such as the retardation of clocks, easily lead to mistakes at this place, of which also the professional literature isn't free. |- |colspan=2|{{Lorentzbox|Text=a) Berg was probably the first to turn the relativity principle against asymmetric aging in the round-trip experiment, claiming that both clocks must indicate the same time at reunion. See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem. b) Berg's mistake also seems to be based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" padding=10 | German original by [[w:Otto Lehmann (physicist)|Lehmann]] (1910/11):<ref name=lehm /> ! English translation |- | style="padding: 0px 20px 0px 20px;" | Hat man zwei genau gleich gehende Uhren nebeneinander und bewegt nun die eine auf einer beliebigen Kurve bis wieder zur anderen zurück, welche Bewegung <math>t</math> Sekunden gedauert haben möge, so geht sie gegen diese um <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> oder annähernd <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> Sekunden zu spät, weil sie während der Bewegung auf langsameren Gang reguliert werden mußte, um mit der ruhenden Uhr in Übereinstimmung zu bleiben. | style="padding: 0px 20px 0px 20px;" | If there are two exactly identical clocks next to each other, and if one of them will be moved on an arbitrary curve until it comes back, which may have lasted <math>t</math> seconds, it [the moving clock] will lag behind the other one by <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> or approximately <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> seconds, because it [the moving clock] had to be regulated to a slower rate during motion in order to remain synchronous with the resting clock. |- |colspan=2|{{Lorentzbox|Text=a) So Lehmann erroneously thinks that the time difference at reunion is only the result of "regulating" the moving clock. This implies that he (like Berg) believed that special relativity predicts ''equal'' clock times at reunion if the moving clock would have been left ''unregulated'' during the round-trip. b) Lehmann's mistake (similar to Berg) seems to based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" | German original by [[w:Emil Wiechert|Wiechert]] (1911)<ref name=wiechert11 /> ! English translation |- |colspan=2| Even though he correctly derived differential clock aging in the round-trip experiment, he (like Berg and Lehmann) claimed that effects like time dilation are "apparent" if one admits Einstein's "unconditional" relativity principle in which there is no aether and all "strides" (i.e. non-accelerated motions) are physically equivalent, but they are "real" if one admits the existence of an aether in the framework of a "conditional" relativity principle in which all strides are physically non-equivalent or anisotropic. This led him to the following interpretation of the clock paradox: |- | style="padding: 0px 20px 0px 20px;" |[...] so muß am Schluß des Versuches B in seinem Fortschritt gegenüber A im Verhältnis <math>1:\sqrt{1-u^{2}/c^{2}}</math> zurückgeblieben sein. Und dieses Zurückbleiben ist unbedingt reell, denn die beiden Gebilde A und B können ja unter gleichen Umständen unmittelbar beieinander verglichen werden. Hier ist es ganz sicher ausgeschlossen, an einen Schein zu glauben, der durch unsere Auffassung der Zeit bewirkt wird. So ist denn also auch die Folgerung unabwendbar, daß für den Verlauf der Weltvorgänge die Schreitungen nicht gleichwertig sind, ''und damit sind wir von neuem zu einem Schluß gekommen, welcher der Unbedingtheit des Relativitätsprinzipes durchaus widerspricht.'' [...] Man kann den Versuch noch mannigfach variieren, z. B. so, daß A ebenso wie B zwei verschiedene Schreitungen, <math>+u</math> und <math>-u</math>, nacheinander inne hat. Wird dann zu A der Wert <math>u_{1}</math>, zu B der Wert <math>u_{2}</math>, zugeordnet, so muß der Vergleich von A und B am Schluß des Versuches ergeben, daß B oder A in seinem Fortschritt zurückgeblieben erscheint, je nachdem die Schreitungen <math>+u_{1}</math>, <math>-u_{1}</math>, oder <math>+u_{2}</math>, <math>-u_{2}</math> weiter auseinanderliegen. ''Vielleicht ist gerade diese Formulierung des Satzes besonders geeignet, um die Ungleichwertigkeit der verschiedenen Schreitungen klar und deutlich zu zeigen.'' | style="padding: 0px 20px 0px 20px;" | [...] thus B's progress must be retarded with respect to A's in the ratio <math>1:\sqrt{1-u^{2}/c^{2}}</math> at the end of the experiment. And this retardation is definitely real, since both bodies A and B indeed can be immediately compared side by side under the same conditions. Here it is certainly excluded to believe that this is an appearance due to our conception of time. Thus the consequence is unavoidable too, that the strides are not equivalent in the course of the world processes, ''and therefore we again came to a conclusion that completely contradicts the unconditionality of the relativity principle.'' [...] One can vary this experiment in many ways, for instance, so that A in the same way as B successively undergoes two different strides <math>+u</math> and <math>-u</math>. If we apply the value <math>u_{1}</math> to A and <math>u_{2}</math> to B, then the comparison of A and B at the end of the experiment must give the result, that B or A is retarded in its progress depending on whether the strides <math>+u_{2},-u_{2}</math> or <math>+u_{1},-u_{1}</math> are further apart. ''Probably it is precisely this formulation of the theorem that is particularly suitable to demonstrate the non-equivalence of the different strides clearly and explicitly.'' |- |colspan=2|{{Lorentzbox|Text=This interpretation was directly rebutted by Laue (1911/12) who demonstrated the geometrical meaning of differential aging in Minkowski space, see sections {{slink||Laue 1911/12-PT|Laue 1911/12-VA}}, showing that there is no need to assume non-equivalance or anisotropy of motions. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.<ref name=laue1 />}} |- ! style="width:50%" | German original by [[w:Norman Robert Campbell|Campbell]] (November 1911, published 1912)<ref name=camp /> ! English translation |- |colspan=2|After describing the round-trip experiment (as given by Wiechert) according to which the traveling clock B is retarded when it returns with respect to stationary clock A, he abandoned differential clock aging as follows: |- | style="padding: 0px 20px 0px 20px;" |Dieser Schluß ist nicht richtig. Die Beziehung zwischen <math>t</math>, der Ablesung an der Uhr auf A seitens des Beobachters auf A und <math>t'</math>, der Ablesung an der Uhr auf B seitens des Beobachters auf A, ist (unter der Annahme, daß zu Beginn des Versuchs <math>t=t'</math> ist) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. Der Unterschied zwischen <math>t'</math> and <math>t</math> ist eine Funktion von <math>z</math> und <math>v</math> allein. Wenn man diesen Größen ihre früheren Werte wiedergibt, indem man die beiden Uhren wieder zur Koinzidenz bringt, während sie relativ zueinander ruhen, so geht der Unterschied zwischen <math>t'</math> and <math>t</math> wieder auf null zurück, gleichviel, welche Werte <math>z</math> und <math>v</math> während der Zwischenzeit gehabt haben mögen. Wenn an irgendeinem Punkte der Bahn die Geschwindigkeit von B relativ zu A eine endliche plötzliche Änderung erfährt, so erfährt auch der Wert von <math>v</math> eine endliche plötzliche Änderung. | style="padding: 0px 20px 0px 20px;" |This conclusion is not correct. The relationship between <math>t</math> as the reading on the clock on A by the observer on A, and <math>t'</math> as the reading on the clock on B by the observer on A, is given by (assuming that <math>t=t'</math> at the beginning of the experiment) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. The difference between <math>t'</math> and <math>t</math> is a function of <math>z</math> and <math>v</math> alone. If these quantities are given their previous values by bringing the two clocks back to coincidence during which they are at rest relative to one another, the difference between <math>t'</math> and <math>t</math> goes back to zero, no matter what values <math>z</math> and <math>v</math> may have had in the meantime. If at any point on the path the speed of B experiences a finite sudden change relative to A, then the value of <math>t'</math> also undergoes a finite sudden change. |- |colspan=2|{{Lorentzbox|Text=a) So Campbell claims that any time difference during the outbound path is wiped out during the inbound path. His mistake is obvious: He is confusing coordinate differences stemming from the Lorentz transformation of ''events'' (which indeed depend on position and direction) with differences in ''clock aging'' derived from the proper time integral (which is ''accumulative'' and independent of position and direction.) b) As Campbell's paper was a reply to Wiechert, it's interesting to compare them: Campbell was correct in dismissing the aether but wrong in denying asymmetric aging, while Wiechert was correct in deriving asymmetric aging but wrong in requiring the aether. }} |- ! style="width:50%" | French original by [[w:Paul Gruner|Gruner]] (March 1912):<ref name=gruner /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |[...] deux personnes du même âge, se séparant dans des systèmes de « marche » très différents et retournant après un laps de temps assez long, constateront une différence d'âge très sensible. [...] le principe de relativité exige toujours la ''réciprocité parfaite'' des phénomènes entre deux systèmes qui possèdent un mouvement relatif. Si, dans l'exemple cité, les deux personnes du même âge se séparent avec une vitesse relative pour se retrouver plus tard, la constatation d'une différence d'âge sera parfaitement mutuelle : A dira positivement que B est resté en arrière dans son développement, et B affirmera avec le même droit que c'est A qui ne s'est pas développé assez vite. Ainsi le principe absolu de la relativité montre ses conséquences les plus extrèmes et il est clair que l'introduction de l’éther n'est plus en état de résoudre cette contradiction irréductible et inconcevable. | style="padding: 0px 20px 0px 20px;" | [...] two people of same age, separating into very different systems of motion and returning after a quite long period of time, will notice a very significant age difference. [...] the principle of relativity always requires the ''perfect reciprocity'' of the phenomenons between two systems that possess relative motion. When, in the cited example, the two persons of same age are separated by some relative velocity only to meet again later, the finding of an age difference will be perfectly mutual: A will positively say that B stayed behind in its development, and B will assert with same right that it was A who has not developed fast enough. By that, the absolute relativity principle shows its most extreme consequences and it is clear, that the introduction of the aether is no longer able to resolve this irreducible and inconceivable contradiction. |- |colspan=2|{{Lorentzbox|Text=Gruner was probably the first to claim that combining the round-trip experiment with the symmetry of time dilation leads to the contradictory situation, that both must attribute younger age to one another at reunion. At the end of his paper, we also find the expression "clock paradox" (French: paradoxe des horloges). See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem.}} |} ==Einstein's contributions== 1905:<ref name=einstein05 /> Introduction of the "peculiar" (German: eigentümlich) round-trip experiment with clocks in terms of a polygonal path as well as a continuously curved path, and an experiment comparing a clock at the pole with one at the equator. January 1911 (published November):<ref name=einstein11a /> In a lecture from January, Einstein extended the "funny" (German: drollig) round-trip experiment to living organisms. According to [[w:Rudolf Lämmel]] in April 1911<ref name=lammel /> and [[w:Fritz Müller-Partenkirchen|Fritz Müller]] in October 1911,<ref name=muller /> Einstein spoke of human beings as well. January 1911 (published January 1912):<ref name=einstein3 /> During a discussion with Einstein directly after the previous lecture, [[w:Fritz Müller-Partenkirchen|Fritz Müller]] claimed that any time difference during the round-trip should vanish at reunion, in analogy to the fact that the Lorentz contraction of a moving rod vanishes when it is at rest again. Einstein showed that the analogy is incorrect: While the clock rates are indeed the same again when they are mutually at rest, the clocks do not indicate the same time at reunion because "clocks are carriers of the time differential"; he went on to show that any possible influence of acceleration during the turnaround can be made negligible by elongating the constant velocity periods. 1912:<ref name=einst12manu /> In an unpublished manuscript on special relativity, Einstein showed that if system <math>\Sigma'</math> makes a round-trip along a polygon, then its inner processes will be retarded with respect to resting system <math>\Sigma </math> at reunion. He pointed out that any influence of acceleration can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygon. April 1914:<ref name=einstpetz /> [[w:Joseph Petzoldt]] criticized asymmetric clock aging in the round-trip experiment as a "fallback into absolutist way of thinking", claiming that special relativity requires that any difference between the clocks vanishes when their relative velocity is zero again, even though he added that any treatment of the clock paradox in special relativity is unrealistic anyway, since the theory only concerns uniform motions and therefore cannot handle velocity changes, so one has to modify the theory. Einstein responded by letter in which he praised Petzoldt's philosophical take on relativity, yet he rejected Petzoldt's conclusions concerning the clock paradox by showing that any finite acceleration at turnaround during the round-trip can only influence the clock in a finite way and therefore can be neglected by minimizing the time of acceleration with respect to the time of uniform translation, so it "must be concluded" that the clock traveling on a polygonal path is retarded at reunion. May 1914:<ref name=rowe group=S /> During a conversation with [[w:Ernst Gehrcke]] who claimed that the clock paradox contradicts the relativity principle, Einstein replied that clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are irrelevant for the amount of the time difference, their presence nevertheless cause B to fall behind ("accelerated motions are absolute in the theory of relativity"). 1916:<ref name=einstein16 /> In a lecture of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of general relativity." September 1918:<ref name=einadl /> In a letter to Einstein, [[w:Friedrich Adler (politician)|Friedrich Adler]] (while in prison for the [[w:Assassination of Karl von Stürgkh]]) claimed that the clock paradox which he described on a circular round-trip contradicts the special relativity principle, and also referred to the similar opinions of Berg and Petzoldt. Einstein responded by letter and explained that there is no contradiction as one of them accelerates; he then showed that general relativity makes both inertial frame K and accelerated frame K' equally justified, explaining the time difference in K' by combining the influence of velocity and gravitational potential, concluding that "Berg and Petzoldt were wrong". November 1918:<ref name=einstein18 /> In a fictitious dialogue between a relativity critic and a relativity apologist written by Einstein, the "critic" said that special relativity must predict differential clock aging in round-trip experiments, which was confirmed by the "relativist" who regretfully noted that even some pro-relativity authors tried to "circumvent this unavoidable result". Yet the critic claimed that this leads to a contradiction: From the viewpoint of K, clock U1 is at rest while the clock U2 was in motion and therefore returns being retarded with respect to U1, but from the viewpoint of K', clock U2 is at rest while clock U1 was in motion and therefore returns being retarded with respect to U2, which was rebutted by the relativist by pointing out the acceleration of U2. Then the critic claimed that this problem "rises again from the dead" in general relativity which allows to symmetrically treat both K and K', which was rebutted by the relativist using the equivalence principle: In K', the rate increase of U1 during turnaround period 3) is "the double" of its velocity time dilation in the inertial periods 2) and 4). December 1918:<ref name=einstein18b /> In a letter to Einstein, [[w:Max Jakob]] doubted the result from Einstein's dialogue, according to which the advance of U1 in period 3) is the double of its retardation during periods 2) and 4). Einstein responded by letter, in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). 1920:<ref name=einstein20 /> In conversations with [[w:Alexander Moszkowski]] between 1919 and 1920, Einstein argued that differential aging of the twins is rather a paradox of feeling, not a paradox of thought, because the latter would only arise if there were no reason for the asymmetric aging. The reason in special relativity lies in the fact that one of them suffered accelerations, while a deeper understanding of that question is obtained by using general relativity. Einstein argued that our "common sense" is located in the realm of feeling and analogy drawn from our ordinary experience; since there is no analogy to the example of the twins in our experience, it might appear paradoxical to the common sense, while it appears logical and necessary in light of intensified abstraction of the trained scientific mind. August 1920:<ref name=rowe group=S /> At an anti-relativity event organized by the right-wing agitator [[w:Paul Weyland]] during which [[w:antisemitic]] leaflets were distributed and [[w:swastika]]s offered at the entrance, a lecture was given by Gehrcke re-iterating his criticism of the twin paradox, claiming that the stationary first organism is old or even dead at reunion while the second organism was in motion and therefore stayed young, but from the standpoint of the second organism he himself is old or even dead while the first organism was in motion and stayed young, thus relativity is either contradictory or it leads to different realities and physical [[w:solipsism]]. Einstein who was present at that event, directly responded in a newspaper article;<ref name=einst20 /> after suspecting antisemitic motives of his critics, he specifically addressed Gehrcke's objections regarding the "well known example of the clocks (or twins)", remarking that the charge of solipsism will be "greeted by the experts as a joke", and characterized the claim that relativity requires mutual retardation of two co-located clocks as a "deliberate attempt to misinform the lay public". 1922:<ref name=morand /><ref name=nord /> [[w:Paul Painlevé]], Einstein and Langevin discussed the clock paradox at a meeting in Paris. Painlevé imagined a clock on a train that performs a round-trip with constant speed and returns being retarded with respect to the station clock, yet he claimed that the relativity principle also allows to say that the station clock performed the round-trip and returned being retarded with respect to the train clock, in contradiction to the previous result. Einstein replied that the relativity principle cannot be applied since the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two systems having velocities in opposite direction is not an inertial frame; there is no reciprocity between a frame that changes direction and one that doesn't. Langevin consequently gave a detailed analysis in terms of the Lorentz transformation. 1954:<ref name=einstein54 /> In a letter, Einstein explained the "well known clock paradoxon" using two clocks <math>B_{1}</math> and <math>B_{2}</math>; clock <math>B_{2}</math> has to reverse its speed in order to come back, thus it was initially at rest in inertial frame <math>S_{2}</math> and then at rest in <math>S_{2}^{+}</math>, whereas <math>B_{1}</math> constantly remains at rest in <math>S_{1}</math>, which explains the asymmetry between them. ==Historical references== <references> <ref name=einstein05>See p. 904f in: {{Citation |author=Einstein, A. |date=1905 |title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik |volume=322 |issue=10 |pages=891–921 |doi=10.1002/andp.19053221004|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 2, Document 23}}. See also: [https://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation at fourmilab].</ref> <ref name=einstein11a>See p. 10. in: {{Citation |author=Einstein, A. |title=Die Relativitäts-Theorie|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |issue=1-2|pages=1–14 |date=27 November 1911|orig-date=Lecture 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n11/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 17}}.<br /> The publication date 27 November 1911 can be seen on the [https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n5/mode/2up Title page and TOC of issue 1-2].</ref> <ref name=einstein3>Discussion between Einstien, Müller, Lämmel and others after the Zürich lecture: {{Citation |author=Einstein, A.; Müller, F., Lämmel, R.|title=Diskussion zu "Die Relativitäts-Theorie"|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |pages=II-IX |date=January 1912|orig-date=Lecture on 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n587/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 18, and in the corresponding English translation volume}}<br /> While the discussion already happened on January 1911, the publication followed one year later in January 1912 in the session proceedings (Sitzungsberichte) of the third issue, see [https://www.ngzh.ch/publikationen/vjs/56/3 Full issue Nr. 3] with [http://www.ngzh.ch/archiv/1911_56/56_1-2/56_3.pdf Title page and TOC] and the [http://www.ngzh.ch/archiv/1911_56/56_3/56_30.pdf Sitzungsberichte including Einstein's discussion on pp. II-IX]. </ref> <ref name=einst12manu>See p. 46 in: {{Citation |author=Einstein, A. |date=1912 |chapter=Document 1: Einstein's manuscript on the special theory of relativity|title=The collected papers of Albert Einstein|volume=4|pages=3-108|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstlor>{{Citation|author=Einstein, A.|date=1914|title=Review of "Lorentz, H. A. – Das Relativitätsprinzip" |journal=Die Naturwissenschaften|volume=2|pages=1018|url=https://archive.org/details/CAT31421305002/page/1018/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 6, Document 11}}</ref> <ref name=einstpetz>{{Citation |author=Einstein, A. |date=1914 |chapter=Document 5: Letter from Einstein to Petzoldt|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein16>See p. 423f in: {{Citation |author=Einstein, A. |date=1916 |title=Announcement of Einstein's lecture "Über einige anschauliche Überlegungen aus dem Gebiete der Relativitätstheorie"|journal=Berliner Sitzungsberichte|pages=423|volume=1916 (part 1)|url=https://archive.org/details/sitzungsberichte1916deutsch/page/423/mode/2up}}</ref> <ref name=einadl>Letter exchange between Einstein and Adler in which the critique on the clock paradox by Berg (1910) and Petzoldt (1914) was mentioned, together with the general relativity solution in terms of the gravitational potential, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Adler's letter in Document 620 and Einstein's reply in Document 628|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein18>Einstein discussed in terms of inertial frames (special relativity) on pp. 697f; accelerated frames (general relativity) on pp. 698f.; distant masses (Mach's principle) on pp. 700f. in: {{citation |author=Einstein, A.|title=[[s:de:Dialog über Einwände gegen die Relativitätstheorie|Dialog über Einwände gegen die Relativitätstheorie]]|date=November 1918|volume=6|issue=48|journal=Die Naturwissenschaften|pages=697-702|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 7, Document 13}}; See also English translation [[:s:Translation:Dialog about Objections against the Theory of Relativity|Dialog about Objections against the Theory of Relativity]] on Wikisource.</ref> <ref name=einstein18b>Letter exchange between Max Jakob and Einstein from December 1918, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Jakob's letter in Document 661c and Einstein's reply in Document 663a|title=The collected papers of Albert Einstein|volume=10|pages=189-190}}</ref> <ref name=einstein20>Interview of Einstein by Moszkowski, see p. 204f. in: {{citation |author=Moszkowski, A.|title=Einstein. Einblicke in seine Gedankenwelt|orig-date=Copyright date 1920 |date=1921|place=Hamburg|url=https://www.archive.org/details/einsteineinblick00moszuoft}}; See also English translation by H. L. Brose (1921): [https://archive.org/details/einsteinsearch00moszrich Einstein, the searcher], p. 206</ref> <ref name=einst20>{{Citation|author=Einstein, A.|date=27 August 1920|journal=Berliner Tageblatt|title=Meine Antwort - Ueber die anti-relativitätstheoretische G. m. b. H.|issue=402|pages=1-2|url=https://www.deutsche-digitale-bibliothek.de/newspaper/item/YH65KFT53MOG4SMXDXK4IVUPTR3QRY7Q?issuepage=1|quote=Reprinted in "The Collected Papers of Albert Einstein", Vol. 7, Document 45}}</ref> <ref name=einstein54>Letter from Einstein to N. V. Pope from March 1954; [[w:Albert Einstein Archives]], Object number 27-88 ([https://ein-web.adlibhosting.com/aea/Details/archive/110021626 Online dataset]); Scanned version as [https://groups.google.com/group/npachat/attach/d3121322d37764f2/Einstein%20letter.doc?part=0.1 Word document on Usenet] published by [https://groups.google.com/g/npachat/c/Haoib97d6OA/m/8mR30yITEtMJ Pope himself])</ref> <ref name=morand>Discussion between Painlevé, Einstein, and Langevin on p. 316ff in: {{citation |author=Morand, M.|title=Einstein au collège de france|date=April 1922|journal=La Nature|volume=50|issue=2511|pages=315-320|url=http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.102/319/100/620/5/613}}</ref> <ref name=lammel>{{Citation|author=Lämmel, R.|date=28 April 1911|title=Die Relativitäts-Lehre|journal=Neue Zürcher Zeitung|volume=117|pages=1|url=https://www.e-newspaperarchives.ch/?a=d&d=NZZ19110428-01.2.4.1}}; English translation of the part concering the twin pardox at [[:v:History of Topics in Special Relativity/Twin paradox#Lämmel 1911-Hum|Wikiversity:Early history of the twin paradox - Lämmel]]</ref> <ref name=lammel2>See p. 84ff in: {{Citation|author=Lämmel, R.|date=1921|orig-date=Preface December 1920|title=Die Grundlagen der Relativitätstheorie|place=Berlin|publisher=Springer|url=https://archive.org/details/diegrundlagende00lmgoog}}</ref> <ref name=langevin1>He derived differential aging from the proper time integral; pointed out that this demonstrates the "absolute nature of acceleration" with respect to an aether, see: {{citation |author=Langevin, P.|title=[[:s:fr:L’Évolution de l’espace et du temps|L’Évolution de l’espace et du temps]]|journal=Scientia |volume=X |pages=31–54 |date=July 1911|orig-date=Lecture 10 April 1911}}; English translation [[:s:en:Translation:The Evolution of Space and Time|The Evolution of Space and Time]] on Wikisource</ref> <ref name=langevin2>See p. 329 in: {{citation |author=Langevin, P. |title=Le temps, l'espace et la causalité dans la physique moderne |journal=Bulletin de la Société française de philosophie |volume=12 |orig-date=Lecture October 1911|date=1912|pages=1-28|url=http://ahp.li/1f7fc22d283fdf0deeca.pdf}}</ref> <ref name=langevin3>See p. 622f in: {{citation |author=Langevin, P. |title=Le Principe de relativité |journal=Bulletin de la société française des électriciens |volume=9 |date=1919 |pages=601-639|url=https://archive.org/details/bulletin-de-la-societe-francaise-des-electriciens-ser.-3-vol-9/page/600}}; Republished in 1922 as separate booklet: [[:s:fr:Le Principe de relativité|Le Principe de relativité]], Éditions Étienne Chiron</ref> <ref name=wiechert11>See p. 745f. general description and proper time; 757f. space travel; in: {{Citation |author=Wiechert, E. |date=September 1911|orig-date=Lectures March-May 1911, submitted 26 July|title=[[:s:de:Relativitätsprinzip und Äther|Relativitätsprinzip und Äther]]|journal=Physikalische Zeitschrift |volume=12 |issue=17-18 |pages=[https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/741 689-707] published September 1; [https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/789 737–758] published September 15}}</ref> <ref name=wiechert15>See p. 46 (Einstein, Langevin, Wiechert) and pp. 51f (Laue versus Wiechert) in: {{citation |author=Wiechert, E.|contribution=Die Mechanik im Rahmen der allgemeinen Physik| title=Die Kultur der Gegenwart: Physik|volume=3.3.1|date=1915 |orig-date=Submitted July 1914|pages=1–78|contribution-url=https://www.archive.org/details/physikunterredak00warbuoft}}</ref> <ref name=wiechert20>See p. 46f in: {{citation |author=Wiechert, E.|title=Der Äther im Weltbild der Physik|orig-date=Presented December 1920|date=1921|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse|pages=29-70|url=http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN00250586X}}</ref> <ref name=wiechert21>See p. 25ff in: {{citation |author=Wiechert, E.|title=[[:s:de:Prinzipielles über Äther und Relativität|Prinzipielles über Äther und Relativität]]|date=1922|orig-date=Lecture September 1921|journal=Physikalische Zeitschrift|volume=23|pages=25-28}}</ref> <ref name=muller>See p. 9 in: {{Citation|author=Müller, F.|date=October 1911|journal=Berliner Tageblatt|title=[[:s:de:Das Zeitproblem (1911)|Das Zeitproblem]]|pages=[https://www.deutsche-digitale-bibliothek.de/newspaper/item/2QKOIOLGNVQILTCEZQOGQPLTRVLPM5PZ?query=zeit&issuepage=9 Part 1 published 16 October 1911] and [https://www.deutsche-digitale-bibliothek.de/newspaper/item/IO44I6QBC4SVV5YUKUDSGXYIPQUXXBN5?query=zeit&issuepage=11 Part 2 published 23 October 1911]}}</ref> <ref name=gruner>See p. 253f in: {{Citation |author=Gruner, P. |title=[[:s:fr:Rapport sur la dernière discussion concernant le principe de la relativité et l’éther|Rapport sur la dernière discussion concernant le principe de la relativité et l’éther]] |journal=Archives des sciences physiques et naturelles |volume=33|issue=4 |pages=252-254 |date=March 1912}}</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=weyl>See p. 147f. in: {{Citation |author=Weyl, H. |date=March 1918|title=Raum-Zeit-Materie (first edition)|publisher=Berlin: Springer|url=https://archive.org/details/RaumZeitMaterieVolIMeinerFrauGewidmet}}; English translation of the 4th edition by H. Brose (1921): [https://www.gutenberg.org/ebooks/43006 Space—Time—Matter], pp. 278f.</ref> <ref name=gbaum>See footnote on p. 507 in: {{Citation|author=Grünbaum, F. |title=Über einige ideelle Versuche zum Relativitätsprinzip|journal=Physikalische Zeitschrift|volume=12|pages=500–509|date=1911|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/540}}</ref> <ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> <ref name=laue2>See p. 42f. for general description; p. 58f. in terms of proper time; in: {{Citation |author=Laue, M. v. |orig-date=Preface December 1912|date=1913 |title=Das Relativitätsprinzip (Second Edition) |publisher=Vieweg |place=Braunschweig|url=https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE4597082}}; See also English translation [[:s:Translation:The Principle of Relativity (Laue 1913)|The Principle of Relativity, Second edition, Part III]] on Wikisource</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=berg>See p. 369f in: {{Citation |author=Berg, O. |date=1910 |title=Das Relativitätsprinzip der Elektrodynamik |journal=Abhandlungen der Fries'schen Schule |volume=3 |issue=2|pages=333-382 |url=http://hdl.handle.net/2027/hvd.hnuynk?urlappend=%3Bseq=351}}</ref> <ref name=camp>See p. 123f in: {{Citation |author=Campbell, N. |title=Relativitätsprinzip und Äther: Eine Entgegnung an Herrn Wiechert |journal=Physikalische Zeitschrift |volume=13 |pages=120-128 |issue=3|orig-date=Submitted December 1911|date=February 1912|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/150}}. The is based on an English manuscript translated by Max Iklé, and Campbell's first name was Germanised as "Normann".</ref> <ref name=seel>{{Citation|author=Seeliger, R.|title=Review of "P. Gruner – Rapport sur la dernière discussion concernant le principe de la relativité et l'éther"|journal=Die Fortschritte der Physik|volume=68|issue=2|pages=336|date=1913|url=https://books.google.com/books?id=fSJGAQAAMAAJ&pg=PA336}}</ref> <ref name=study>See footnote on p. 111 in: {{citation |author=Study, E. |title=Vorlesungen über ausgewählte Gegenstände der Geometrie |date=June 1911|url=https://archive.org/details/vorlesungenber00studuoft|publisher=B.G. Teubner|place=Leipzig}} </ref> <ref name=robb1>See pp. 356ff. in: {{Citation|author=Robb, A.|date=1914|title=A theory of time and space|place=Cambridge|publisher=University Press|url=https://archive.org/details/theoryoftimespac00robbrich}} </ref> <ref name=robb2>See §12 in: {{citation |author=Robb, A. A.|title=The Straight Path|date=1920 |journal=Nature|pages=599|volume=104|issue=2623|url=https://archive.org/details/sim_nature-uk_1920-02-05_104_2623/page/598/mode/2up}}</ref> <ref name=edding2>See p. 22 in: {{Citation |author=Eddington, A. S. |date=1922 |title=The theory of relativity, and its influence on scientific thought |publisher=Oxford Clarendon Press |url=https://archive.org/details/cu31924005748573}}</ref> <ref name=rogers>{{citation |author=Rogers, R. A. P.|title=The Time-Triangle and Time-Triad in Special Relativity|date=November 1922|journal=Nature|volume=110|issue=2769|pages=698–699|url=https://archive.org/details/sim_nature-uk_1922-11-25_110_2769/page/698/mode/2up}}</ref> <ref name=lorentz1>See pp. 37f, 55ff in: {{citation |author=Lorentz, H. A.|date=1913|title=Het relativiteitsbeginsel : drie voordrachten gehouden in Teyler's stichting|publisher=De Erven Loosjes |place=Haarlem|url=https://resolver.kb.nl/resolve?urn=MMKB24:063387000:00005}}; German translation on pp. 31f, 47f in: {{citation |author=Lorentz, H. A.|date=1914| title=Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem|publisher=B.G. Teubner |place=Leipzig and Berlin|url=https://archive.org/details/bub_gb_89PPAAAAMAAJ}}; See also the transcription [[:s:de:Das Relativitätsprinzip (Lorentz)|Das Relativitätsprinzip]] on German Wikisource and the English translation [[:s:Translation:The Principle of Relativity (Lorentz)|The Principle of Relativity]] on English Wikisource</ref> <ref name=lorentz3>See §12 in: {{citation |author=Lorentz, H. A.|title=Considérations élémentaires sur le principe de relativité|date=1914 |journal=Revue générale des sciences pures et appliquées|pages=179-186|url=https://archive.org/details/revuegnraled25pari/page/178/mode/2up}}</ref> <ref name=bloch>See pp. 67 ff. in: {{Citation | author=Bloch, W.| date=September 1918|title=Einführung in die Relativitätstheorie| publisher=B. G. Teubner |url=https://hdl.handle.net/2027/njp.32101040276907}}</ref> <ref name=bloch2>See pp. 69ff. (special relativity) and 102ff. (general relativity) in: {{Citation | author=Bloch, W.| date=1920 |title=Einführung in die Relativitätstheorie (second edition)| publisher=B. G. Teubner |url=https://www.archive.org/details/einfhrungindier00blocgoog}}</ref> <ref name=bollert1>See p. 6 (special relativity), pp. 24-26 (EP) in: {{citation |author=Bollert, K.|title=Einstein’s Relativitätstheorie und ihre Stellung im System der Gesamterfahrung |date=April 1921|publisher=Steinkopff|url=https://archive.org/details/dbc.wroc.pl.001504}}</ref> <ref name=born>See pp. 190f. (special relativity), 250f (EP) in: {{Citation | author=Born, M.| date=1921 |title=Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Second edition)| publisher=Springer | place=Berlin|url=https://hdl.handle.net/2027/mdp.39015017387310}}; The [https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE5426498 first edition (1920)] of Born's book didn't include the twin paradox. English translation of the third edition by H. Brose (1924): [https://archive.org/details/einsteinstheoryo00born Einstein's theory of relativity]</ref> <ref name=pauli>See p. 558f (general description); p. 624f (proper time); p. 713f (accelerated frames); in: {{Citation |author=Pauli, W. |date=1921 |journal=Encyclopädie der Mathematischen Wissenschaften|title=Die Relativitätstheorie|pages=539–776|volume=5|issue=2 |url=http://resolver.sub.uni-goettingen.de/purl?PPN360709672}}; English translation by G. Field (1958): [https://books.google.com/books?id=rc3DAgAAQBAJ Theory of Relativity]</ref> <ref name=thirring>See p. 209ff in: {{citation |author=Thirring, H.|title=Über das Uhrenparadoxon in der Relativitätstheorie|date=April 1921|journal=Naturwissenschaften|volume=9|issue=18|pages=209-212|url=https://archive.org/details/sim_naturwissenschaften_1921-04-01_9_13/mode/2up}}</ref> <ref name=sommerfeld>See p. 71 in: {{citation |author=Sommerfeld, A. |date=May 1913|chapter=Remarks on Minkowski's "Space and Time"|title=Das Relativitätsprinzip|editor=Otto Blumenthal|pages=69-73|url=https://www.archive.org/details/dasrelativittsp00minkgoog}}</ref> <ref name=kopff>See pp. 45ff (special relativity and proper time); pp. 117ff (EP); pp. 189ff (Mach's principle), in: {{citation |author=Kopff, A.|title=Grundzüge der Einsteinschen Relativitätstheorie |date=February 1921|publisher=S. Hirzel|place=Leipzig|url=https://www.archive.org/details/grundzgedereins00kopfgoog}}; English translation by H. Levy (1923): [https://hdl.handle.net/2027/mdp.39015017188817 The mathematical theory of relativity].</ref> <ref name=becqu1>See p. 48ff (proper time), p. 240f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Le Principe de relativité et la théorie de la gravitation|Le Principe de relativité et la théorie de la gravitation]] |date=1922 |publisher=Gauthier-Villars|place=Paris}}; See also p. 57ff (proper time), p. 177f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Exposé élémentaire de la théorie d’Einstein et de sa généralisation|Exposé élémentaire de la théorie d’Einstein et de sa généralisation]]|date=1922 |publisher=Payot|place=Paris}}</ref> <ref name=nord>Discussion between Painlevé, Einstein, and Langevin on pp. 146ff in: {{citation |author=Nordmann, C.|title=[[s:fr:Einstein expose et discute sa théorie|Einstein expose et discute sa théorie]]|date=May 1922|journal=Revue des deux mondes|volume=IX|pages=129-166}}</ref> <ref name=lehm>{{Citation |author=Lehmann, Otto |orig-date=September 1910 |date=1911|title=Das Relativitätsprinzip der neue Fundamentalsatz der Physik |title-link=s:de:Das Relativitätsprinzip der neue Fundamentalsatz der Physik|journal=Verhandlungen des naturwissenschaften Vereins in Karlsruhe |volume=23 |pages=49-74}}</ref> <ref name=lech>See p. 19ff in: {{citation |author=Lechalas, G. |orig-date=Submitted December 1912|date=1913 |title=Le nouveau temps |journal=L’Année philosophique|volume=XXIII|pages=19-44|url=https://gallica.bnf.fr/ark:/12148/bpt6k255882z/f22.item}}</ref> <ref name=hunt>See pp. 494ff in: <br>{{Citation|author=Huntington, E. V. |year=1912 |title=A new approach to the theory of relativity|journal=Philosophical Magazine |volume=23|pages=494-512|url=https://archive.org/details/londonedinburg6231912lond/page/494/mode/2up}}</ref> </references> ==Secondary sources== <references group=S> <ref name=miller>{{Citation |author=Miller, A. I. |date=1981 |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |place=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}; See section 7.4.13 (Langevin, Wiechert, Laue, Einstein), footnotes 29-34 of chapter 7 (Petzoldt, Sommerfeld, Bergson, Einstein)</ref> <ref name=lange>{{Citation|author=Lange, L.|date=1927|title=The clock paradox of the theory of relativity|journal=The American Mathematical Monthly|volume=34|issue=1|pages=22-30|jstor=2299914}}</ref> <ref name=pes>{{Citation |author=Pesic, P. |date=2003 |title=Einstein and the twin paradox |journal=European Journal of Physics |volume=24 |issue=6 |pages=585–590 |doi=10.1088/0143-0807/24/6/004}}</ref> <ref name=during>{{Citation |author=During, É. |date=2014 |title=Langevin ou le paradoxe introuvable |journal=Revue de métaphysique et de morale |volume=84 |pages=513-527 |doi=10.3917/rmm.144.0513|doi-access=free}}; See pp. 515f (Langevin), 520f. (Einstein, Laue, Weyl, Painlevé).</ref> <ref name=debs>{{Citation |author=Debs, T. A., & Redhead, M. L. |title=The twin paradox and the conventionality of simultaneity |date=1996 |journal=American Journal of Physics |volume=64|issue=1| pages=384-392 |doi=10.1119/1.18252}}</ref> <ref name=alizzi>{{Citation |author=Alizzi, A., Sen, A., & Silagadze, Z. K.|title=Do moving clocks slow down? |year=2022 |journal=European Journal of Physics |volume=43|issue=6|pages=065601 |doi=10.1088/1361-6404/ac93ca|arxiv=2209.12654}}; Appendix B with reference to Lange and Halsbury</ref> <ref name=beng>{{Citation |author=Benguigui, L. G. |date=2020 |title=A Tale Of Two Twins: The Langevin Experiment Of A Traveler To A Star |publisher=World Scientific|isbn=9789811219115}}; See early solutions (Einstein, Langevin, Lorentz, Born/Kopff) and the Bergson controversy. A shorter version appeared in {{arxiv|1212.4414}}.</ref> <ref name=rowe>{{Citation|author=Rowe, D. E.|date=2006|title=Einstein's allies and enemies: Debating relativity in Germany 1916–1920|journal=Interactions: Mathematics, Physics and Philosophy|pages=231-280|publisher=Springer|doi=10.1007/978-1-4020-5195-1_8}}; Covering the criticism of Gehrcke starting with 1912; discussion between Einstein and Gehrcke in 1914; Einstein's dialogue (1918) as response to antirelativists; the Weyland event in 1920 and Einstein's response.</ref> <ref name=weiss>Weiss, W. (Physics FAQ): [https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html The Twin Paradox: The Equivalence Principle Analysis]</ref> <ref name=cuvaj>{{Citation |author=Cuvaj, C. |date=1971 |title=Paul Langevin and the theory of relativity|journal=Japanese studies in the history of science|volume=10| pages=113-142|url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf}}</ref> <ref name=koks>Koks, D. (2018): [https://math.ucr.edu/home/baez/physics/Relativity/SR/sr-gr.html Physics FAQ: Where is the Boundary between Special and General Relativity?]</ref> </references> [[Category:History of special relativity]] [[Category:Paradoxes]] j0c6f7hkodvfi2by6azdzetvpy5u8gu 2834525 2834524 2026-09-26T07:51:55Z D.H 52339 Wording 2834525 wikitext text/x-wiki {| style="width:20%; font-size:13px;" align=right |{{../Other Topics (header)}} |} ==Early history of the twin paradox== {{Lorentzbox|Text={{center|Date of article creation: 9 November 2023; Last major revision: 26 September 2026}}}} a) When was the [[:w:twin paradox]] applied to life forms and human beings? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /><ref group=S name=during /> report that {{slink||Einstein 1911-HU}} discussed the aging of living organisms, and that {{slink||Langevin 1911-HU}} and {{slink||Wiechert 1911-HU}} explicitly discussed the aging of human beings. :*More details in sections {{slink||Human beings in 1911|Twins from 1911 to 1920}}, including newspaper articles from 1911 written by {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}} that clearly show that Einstein was the first to explicitly discuss the aging of human beings as well. b) Who was the first to formulate the principle of maximal proper time along straight worldlines, upon which differential aging in the standard twin paradox is based? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> mention Langevin (1911), Laue (1911). :*More details in section {{slink||Maximal proper time}} with the contributions of Langevin (1911), Wiechert (1911), Study (1911), Laue (1911-13). c) Who was the first to formulate [[w:Triangle inequality#Reversal in Minkowski space|inverse triangle inequality]] in Minkowski space, which represents the simplest version of the twin paradox? :*See details in section {{slink||Triangle inequality}} with the contributions of Robb (1914-20), Eddington (1922), Rogers (1922). d) Who was the first to show that any influence of proper acceleration on clocks can be neglected in the computation of the twin paradox from the viewpoint of the stay-at-home twin? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Einstein (1911), Laue (1913). :*More details in section {{slink||Negligibility of proper acceleration}} with the contributions of Einstein (1911), Wiechert (1911), Laue (1913), Lorentz (1913). e) Who was the first to introduce the three clock/brother example that completely removes acceleration from the clock/twin paradox? :*Historical accounts<ref group=S name=debs /><ref group=S name=alizzi /> date it back to Lange (1927) and Lord Halsbury (1957). :*More details in section {{slink||Relay (three brothers) experiment}} with the contributions of Grünbaum (1911) and Wiechert (1920-22). f) Who was the first to use acceleration as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref name=cuvaj group=S /><ref group=S name=pes /> mention Langevin (1911), Einstein (1918). :*More details in section {{slink||Acceleration as asymmetry indicator}} with the contributions of Langevin (1911), Sommerfeld (1913), Lorentz (1913), Einstein (1914-20). g) Who was the first to use different frame distribution as asymmetry indicator as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Laue (1911-13). :*More details in section {{slink||Frame distribution as asymmetry indicator}} with the contributions of Laue (1911-13), Bloch (1918). h) Who was the first to describe the perspective of the traveler? :*Historical accounts<ref group=S name=miller /><ref group=S name=beng /> mention Langevin (1911), Lorentz (1914), Einstein (1918). :*More details in section {{slink||Perspective of the traveler}} with the contributions of Langevin (1911), Lorentz (1913-14), Einstein (1918), Thirring (1921). i) Who was the first to describe a round-trip experiment in curved spacetime? :*See section {{slink||Curved spacetime}} with the contribution of Becquerel (1922). j) Who was the first to interprete the twin paradox in terms of an aether or absolute space? :*See section {{slink||Aether interpretations}} with the contribution of Langevin (1911), Wiechert (1911), Lechalas (1912). k) Who was the first to denote the round-trip experiment as paradoxical? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> point to Laue (1911). :*See section {{slink||Paradoxical?}} for details. l) Who was the first to misunderstand the twin paradox? :*See section {{slink||Misunderstandings}} with the contributions of Berg (1910), Wiechert (1911), Campbell (1911/12), Gruner (1912). m) What were Einstein's contributions? :*See section {{slink||Einstein's contributions}}. ==Human beings in 1911== {| class="wikitable" style="background-color:white;{{text default color}};" ![[w:Albert Einstein|Einstein]] |- |{{anchor|Einstein 1905}}In 1905<ref name=einstein05 /> he showed that a clock moving on a round-trip away from A and back along a polygonal or curved path, is retarded with respect to a clock stationary at A by approximately <math>\tfrac{1}{2}t(v/V)^{2}</math> at reunion. For example, a clock on the equator is retarded with respect to a clock on the pole. He described this consequence as being "peculiar" (German: eigentümlich). {{anchor|Einstein 1911-HU}}In a lecture given on January 1911<ref name=einstein11a /> (published in November), he extended this "funny" (German: drollig) experiment to living organisms: {| ! width=55% | Einstein wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Wenn wir z. B. einen lebenden Organismus in eine Schachtel hineinbrächten und ihn dieselbe Hin- und Herbewegung ausführen lassen wie vorher die Uhr, so könnte man es erreichen, dass dieser Organismus nach einem beliebig langen Fluge beliebig wenig geändert wieder an seinen ursprünglichen Ort zurückkehrt, während ganz entsprechend beschaffene Organismen, welche an den ursprünglichen Orten ruhend geblieben sind, bereits längst neuen Generationen Platz gemacht haben. Für den bewegten Organismus war die lange Zeit der Reise nur ein Augenblick, falls die Bewegung annähernd mit Lichtgeschwindigkeit erfolgte! | style="padding: 0px 20px 0px 20px;" |For example, if we put a living organism in a box and make it undergo the same back and forth movement as the clock before, we could achieve that this organism returns to its original location with arbitrary little change after a flight of arbitrary length, whereas completely identical organisms that remained at rest in the original location have long since made room for new generations. To the moving organism, the long journey was only a moment if the movement happened close to the speed of light! |} {{Lorentzbox|Text=Two participants of that lecture, {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}}, report that Einstein also talked about the aging of ''human beings''.}} |- !{{anchor|Lämmel 1911-HU}}[[w:Rudolf Lämmel|Lämmel]] |- |He attended Einstein's 1911 lecture and gave a popular report about it in the Swiss newspaper "[[w:Neue Zürcher Zeitung|Neue Zürcher Zeitung]]" published on 28 April 1911,<ref name=lammel /> including additional details. Regarding the round-trip clock experiment he wrote: {| ! width=50% | Lämmel wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bewegt sich eine Uhr mit Lichtgeschwindigkeit längs einer Geraden, auf der gerichtete Uhren stehen, so scheint die bewegte Uhr, beurteilt vom Standpunkt der ruhenden aus, im oben stizzierten Sinn, stillzustehen. Kehrt die Uhr, nach einem Ruck, mit Lichtgeschwindigkeit wieder zurück zur Zentral-Uhr, so ist, nach Einstein, für den Beobachter bei der Zentral-Uhr die Sache so, als ob ein mit der bewegten Uhr mitgeführter Beobachter (samt dessen Uhr) nicht gealtert hätte. Hinge also des letzteren Alter von den Angaben des ruhenden Beobachters ab, so könnte der von einer großen Reise ins Weltall zurückkehrende Beobachter bei der Zentral-Uhr spätere Generationen antreffen – er selber hätte nicht gealtert. Welche Bedeutung diese ''ad absurdum'' geführte Gedankenspielerei etwa hat, läßt sich heute nicht absehen – vielleicht, ja wahrscheinlich ist sie ohne jeden Einfluß auf die tatsächlichen Verhältnisse. Aber man sieht dabei immerhin, daß die Physik imstande ist, die kühnsten Träume der Phantasie noch – zu überbieten. | style="padding: 0px 20px 0px 20px;" |Let a clock be moving at speed of light along a line on which regulated clocks are standing, then the moving clock's hand appears to be standing still (in the sense described above) as judged from the standpoint of the resting one. If the clock, after one jolt, comes back with light speed to the central clock, then according to Einstein the matter presents itself to the observer at the central clock, as if the observer comoving with the clock (together with his clock itself) hasn't been grown older. Thus if the age of the latter would depend on the indications of the resting observer, the observer returning from a great journey into space could meet later generations at the central-clock – he himself hasn't been grown older. The importance of this play of thought led ''ad absurdum'' cannot be seen today – maybe, or even probably, it is without any influence on the actual situations. Though at least one can see that physics is able to – surpass – even the boldest dreams and fantasies. |} Lämmel in December 1920 (published 1921)<ref name=lammel2 /> again alluded to Einstein's lectures in Zürich (possibly the one from 1911, and maybe also later ones), describing a discussion between himself and Einstein. After Einstein concluded that the travelers who came back after their journey will probably meet their former contemporaries as old men while they themselves could have been away for only a few years, Lämmel objected that this conclusion is only drawn with respect to rods and clocks, but not with respect to living beings. Einstein responded though, that all processes in the blood, in the nerves etc. are eventually periodical oscillations, i.e. motions. Yet to any such motion the relativity principle applies, thus the conclusion regarding the unevenly rapid aging it permissive. {{Lorentzbox|Text=While the official publication of Einstein's January lecture ({{slink||Einstein 1911-HU}}) mentions the aging of organisms, Lämmel recalls the reference to the aging of a human space traveler ("observer returning from a great journey into space"). This means that Einstein was the first to use human beings in the clock/twin paradox on January 16 which was first published by Lämmel on April 28, 1911. In comparison, {{slink||Langevin 1911-HU}} used space travelers in a lecture on April 10 with publication in July, and {{slink||Wiechert 1911-HU}} used space travelers in lectures held between March 25 and May 23 with publication in July/September. It seems very unlikely that before April 28, Lämmel became somehow aware of the content of Langevin's or Wiechert's lectures held a few weeks earlier, in order to use them in his description of Einstein's lecture.}} |- !{{anchor|Langevin 1911-HU}}[[w:Paul Langevin|Langevin]] |- |On 10 April 1911, published July 1911,<ref name=langevin1 /> he held a now famous lecture popularizing the clock/twin paradox which he derived from the proper time integral as described in {{slink||Langevin 1911-PT}}. He demonstrated that a moving radioactive sample of radium is less evolved and less aged and therefore more active at return then the ones that remained in the laboratory. He also used light signals and the Doppler effect to visualize the effect. The most famous part concerned his description of the aging of human space travelers: {| ! width=50% | Langevin wrote ! [[:s:Translation:The Evolution of Space and Time|English Wikisource translation]] |- | style="padding: 0px 20px 0px 20px;" |Cette remarque fournit le moyen, à celui d’entre nous qui voudrait y consacrer deux années de sa vie, de savoir ce que sera la Terre dans deux cents ans, d’explorer l’avenir de la Terre en faisant dans la vie de celle-ci un saut en avant qui pour elle durera deux siècles et pour lui durera deux ans, mais ceci sans espoir de retour, sans possibilité de venir nous informer du résultat de son voyage puisque toute tentative du même genre ne pourrait que le transporter de plus en plus avant. Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse. Revenu à la Terre ayant vieilli de deux ans, il sortira de son arche et trouvera notre globe vieilli de deux cents ans si sa vitesse est restée dans l’intervalle inférieure d’un vingt-millième seulement à la vitesse de la lumière. Les faits expérimentaux les plus sûrement établis de la physique nous permettent d’affirmer qu’il en serait bien ainsi. | style="padding: 0px 20px 0px 20px;" |This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. |} {{Lorentzbox|Text=Reading his lecture in full, one finds the word "paradoxical" only in relation to the constancy of light speed, not on relation to the round-trip clock experiment.}} |- !{{anchor|Wiechert 1911-HU}}[[w:Emil Wiechert|Wiechert]] |- |In lectures on 25 March and 23 May 1911, submitted July and published September 1911,<ref name=wiechert11 /> he described the round-trip clock experiment with two equal clocks regulated to the same rate and brought to the same pointer position, or by introducing the same chemical process two times, or by introducing ''two life forms that began their life at the same time''. At the end of his paper he applied this to human travelers: {| ! width=50% | Wiechert wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Nehmen wir aber wieder eine Relativgeschwindigkeit an, die bis auf 3 Proz. der Lichtgeschwindigkeit nahekommt, dann wird das Verhältnis der empfundenen Zeitlängen wie 4:1. Das Bild mag etwas weiter noch ausgemalt werden. Denken wir uns, daß ein Beobachter durch den Raum unseres Sternhimmels mit dieser Geschwindigkeit in einer Kreisbahn mit einem Radius von 16 Lichtjahren fährt, dann wird er nach unserer Zeitrechnung nach je 100 Jahren wieder an unserem Sonnensystem vorüberkommen. In seinem Gefährt wird dabei die Zentrifugalkraft so auf ihn einwirken, daß sie gemäß den Relativitätsgesetzen der Einwirkung der Schwerkraft auf uns Erdenbewohner gleich erscheint. Es sind also die wirkenden Kräfte nur so groß, daß der Phantasie die Möglichkeit geboten wird, den Reisenden als menschliches Wesen zu denken. Da hier dauernd <math>\sqrt{1-v^{2}/c^{2}}</math> ist, fließt die Eigenzeit für den Reisenden viermal langsamer dahin, als für die Bewohner der Gestirne. Wenn er also nach 100 unserer Jahre wieder zu unserem Sonnensystem zurückkehrt, wird er sich selbst nur um 25 Jahre gealtert fühlen. Erreicht er nach der Entwicklung seines Körpers und nach seiner Zeitempfindung ein Alter von 75 Jahren, so entspricht dies doch einer dreimaligen Wiederkehr zu unserem Sonnensystem, also 300 unserer Erdenjahre. | style="padding: 0px 20px 0px 20px;" |Yet if we again assume a relative velocity approximating the speed of light by 3 percent, then the ratio of the experienced duration of time becomes 4:1. This image can be further extended. Let's imagine that an observer travels with that velocity on a circular path at a radius of 16 light years through the space of our galaxy, then according to our time calculation he passes by our solar system every 100 years. In his vehicle the centrifugal force will act on him in such a way, that in accordance with the relativity laws it will appear to be equal to the force of gravity acting upon the inhabitants of Earth. Thus the acting forces are only thus big, in order to give our fantasy the possibility to imagine the traveler as a human being. Since we have <math>\sqrt{1-v^{2}/c^{2}}</math> throughout, proper time flows four times slower for the traveler than for the inhabitants of the stars. Thus when he comes back to our solar system after 100 of our years, he will feel to have aged only by about 25 years. If he reaches an age of 75 years according to the development of his body and his own time experience, then this corresponds to a threefold return to our solar system, i.e. 300 of our Earth years. |} {{Lorentzbox|Text=a) Wiechert (1915)<ref name=wiechert15 /> later provided a short historical survey of the clock/twin paradox. He referred to the fact that already {{slink||Einstein 1905}} considered the case of two clocks ("Einstein's clock experiment"), and even though [[w:Hermann Minkowski|Minkowski]] himself didn't consider the case, his proper time formula provides the result in a straight forward manner. The latter was done by himself in lectures on 25 March and 23 May 1911, as well as by Langevin published in July 1911. Wiechert pointed out that he himself and Langevin used "humorist" examples in order to clarify the situation: While Wiechert argued that one has to make a journey in order to stay young, Langevin argued that one has to romp about in a laboratory in order to stay young. Both of them used human beings, arguing that their physical and mental life should have been influenced in the same way as any other process in nature. b) The dates given by Wiechert (1915) are not complete. The correct ones are: *Langevin's lecture on 10 April 1911, published in July. *Wiechert's lectures on 25 March and 23 May 1911, submitted on July 26, published in September. *He was still unaware of Einstein's lecture from January 1911, published in November 1911.}} |- !{{anchor|Müller 1911-HU}}[[w:Fritz Müller-Partenkirchen|Müller]] |- |The freelance writer and law student Fritz Müller (who was later known as [[w:Fritz Müller-Partenkirchen|Müller-Partenkirchen]]) attended Einstein's lecture and wrote a popular report about it in the German newspaper "[[w:Berliner Tageblatt|Berliner Tageblatt]]" on 16th and 23rd October 1911,<ref name=muller /> in which he gave further details (compare with {{slink||Lämmel 1911-HU}}). Regarding the clock/twin paradox he wrote: {| ! width=50% | Müller wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Zwei gleichgehende Uhren sollen je einen Beobachter haben und nebeneinander ruhen. Nun soll die eine mit ihrem Beobachter plötzlich mit Lichtgeschwindigkeit in den Weltenraum hinausreisen. Vorher haben die beiden vereinbart, sich alle Sekunden mit einem Lichtsignal die Zeit zu telegraphieren. [...] In unserem Grenzfall, wo die Reise mit Lichtgeschwindigkeit vor sich geht, müßte der ruhende Beobachter erklären, jene andere Uhr käme in der Zeit überhaupt nicht voran. Die Zeit stünde dort still. Tatsächlich kommen die Einsteinschen Gleichungen zu diesem Resultat. Für den mit der Uhr reisenden Beobachter, sagt Einstein, gelte dasselbe. Das heißt, im Urteil des Zurückbleibenden würde jener niemals alt. „Und wenn er auf einer gebrochenen Reiselinie wieder an seinen Ausgangspunkt zurückkehrte?" fragt man den Vortragenden in der Diskussion. – „So bliebe er in unserem Urteil so jung wie bei der Ausreise," erwidert Einstein mit vollem Ernst, „selbst wenn wir Zurückgebliebenen inzwischen Männer mit weißen Bärten geworden sind – die Gleichungen liefern für jede Richtung der Bewegung, auch für eine gebrochene Bewegung, unerschütterlich die selben Resultate." – Wir sehen einander an. Das klingt märchenhaft. Märchenhaft? Gewiß, die alten Märchen vom Mönch von Heisterbach, vom Rip van Winkle, von Urashima Taro steigen auf. Merkwürdig, wie die Volksphantasie bei den Deutschen, bei den Amerikanern, bei den Japanern in der gleichen Richtung gearbeitet hat – alle drei Märchen erzählen ja von Leuten, deren Leben still steht, viele hundert Jahre lang, während die andern altern. So fanden sie bei ihrer Rückkehr ein anderes Land und eine andere Generation. | style="padding: 0px 20px 0px 20px;" |Two synchronous clocks at rest next to each other, shall each be accompanied by an observer. Now one of them, together with its observer, suddenly travels into space at the speed of light. Previously, both have arranged that every second they telegraph their time to each other using light signals. [...] In our limiting case where the journey happens at light speed, the resting observer would have to declare that the other clock would not proceed in time at all. Time would stand still at this place. Einstein's equations indeed produce this result. As to the observer traveling with the clock, says Einstein, the same is true. That means in the judgment of the remaining one, the other one would never become old. Then the lecturer [i.e. Einstein] was asked in the discussion: "And if he comes back to his starting point on a curved travel path?", to which Einstein replied in full earnest: "Then in our judgment he would remain as young as he was at departure, even if we remaining ones became men with white beards in the meantime, the equations unshakably give the same result in every direction of motion, also for curved motion". We look at each other. That sounds fabulous. Fabulous? Of course, the old fairy tales of [[w:Heisterbach Abbey|w:The monk of Heisterbach]] or [[w:Rip Van Winkle]] or [[w:Urashima Tarō]] come forward. Strange, how the folk fantasy of the Germans, the Americans, the Japanese worked in the same direction, all three fairy tales indeed tell about people whose life stands still, many hundred years long, while the other ones grow old. Thus they found another country and another generation when they returned. |} {{Lorentzbox|Text=Müller's account confirms {{slink||Lämmel 1911-HU}} that Einstein indeed mentioned human beings, but his description also suggests that Einstein was the first to use mutually sent light signals. However, as this was published in October, it cannot be excluded that Müller's description of light signals was influenced by {{slink||Langevin 1911-HU}}, published in July, in which light signals were used as well.}} |} ==Twins from 1911 to 1920== We now provide a list of authors who employed ''twins'', i.e. ''two'' life forms or humans that initially were of ''same age'' when the round-trip began: {| class="wikitable" style="background-color:white;" |- ! Author !! Date !! Description |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> |1911 |Two life forms that begin their life at the ''same time'' (German: "Zwei Lebewesen [..] die ihr Leben gleichzeitig beginnen"), of which the moving one returns retarded in its progression with respect to the stationary one. |- |[[w:Paul Gruner|Gruner]]<ref name=gruner /> |1912 |Two persons of ''same age'' (French: "deux personnes du même âge"), of which the moving one returns less developed than stationary one. |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> |1913 |The moving life form returns younger than its ''former agemates'' (German: "ehemaligen Altersgenossen"). |- |[[w:Hermann Weyl|Weyl]]<ref name=weyl /> |Easter 1918 | {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Von zwei Zwillingsbrüdern, die sich in einem Weltpunkt A trennen, bleibe der eine in der Heimat (d. h. ruhe dauernd in einem tauglichen Bezugsraum), der andere aber unternehme Reisen, bei denen er Geschwindigkeiten (relativ zur »Heimat«) entwickelt, die der Lichtgeschwindigkeit nahekommen; dann wird sich der Reisende, wenn er dereinst in die Heimat zurückkehrt, als merklich jünger herausstellen denn der Seßhafte. |Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. |} {{Lorentzbox|Text=Weyl was the first to ''explicitly use twins'' in relation to the round-trip experiment. The fourth edition (1920) of that book was translated from German into English and French in 1922.}} |- |[[w:Albert Einstein|Einstein]]<ref name=einstein20 /> |1920/21 |{{Anchor|Einstein 1921-TW}} {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Trifft A wieder bei B ein, so kann es sich ereignen, daß der beharrende Zwilling inzwischen 60 Erdjahre alt geworden ist, während der zurückkehrende nur 15 Jahre zählt, oder sich gar noch im Säuglingsstadium befindet. [..] Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls -Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. |If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still. [..] In the case of these two twins, Einstein declared, we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures. |} {{Lorentzbox|Text=This was based on an interview of Einstein by Moszkowski. While the expression "clock paradox" was used since 1911/12 (see section {{slink||Paradoxical?}}), this seems to be the first time that it was rebranded as "twin paradox". The copyright mark indicates 1920, while the title page indicates 1921. The translation from German into English also appeared in 1921.}} |} ==Maximal proper time== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]] 1911 |{{anchor|Langevin 1911-PT}}In April 1911 (published July),<ref name=langevin1 /> he described the round-trip experiment without formulas using two portions of matter present at two events happening at the same place. The ''integration of proper time'' along the entire wordlines shows that the portion of matter that starts a closed cycle by receding and finally coming back, will have a ''smaller proper time'' than the one that stayed behind. In October 1911 (published 1912),<ref name=langevin2 /> Langevin again showed that the portion of matter that described a closed cycle will have a ''smaller proper time'' <math>R</math> than the one that stayed in an inertial frame, which is defined by the equation: :<math>\begin{matrix}V^{2}\left(t-t_{0}\right)^{2}=d^{2}-R\\ \left[d^{2}=\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}\right] \end{matrix}</math> |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> Lectures March-May 1911 submitted July published September |{{anchor|Wiechert 1911-PT}}Let two equal processes be observed in two equal material systems colocated in two moments (1) and (2), and let there velocities have been changed in arbitrarily different ways in the meantime. It follows that the ratio of advancement of those processes is given by the two intervals <math>\Delta\tau </math> of their respective ''proper times''. He concluded that any round-trip clock experiment can be easily comprehended from that theorem by computation. The corresponding integral is: :<math>\Delta\tau=\int_{1}^{2}d\tau=\int_{1}^{2}dt\sqrt{1-\frac{\mathfrak{v}^{2}}{c^{2}}}</math> |- |[[w:Eduard Study|Study]]<ref name=study /> June 1911 |Minkowski's concept of worldlines implies that the straight path between two points of the same worldline is the ''longest'' among all paths between those points, if the path length on a worldline is defined by the related proper time. {{Lorentzbox|Text=Study's book was purely mathematical without mentioning clocks or the round-trip experiment, alluding to his result only in a footnote.}} |- |[[w:Max von Laue|Laue]] 1911-13 |{{anchor|Laue 1911/12-PT}}In December 1911 (published 1912),<ref name=laue1 /> Laue showed without formulas that the round-trip experiment is represented by a curved worldline, which at worldpoint A decomposes into a row of curves, after which all of them will be re-united at worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the ''longest proper time.'' {{anchor|Laue 1912/13-PT}}In December 1912 (published 1913) in the second edition of this relativity book,<ref name=laue1 /> Laue described the proper time integral between events 1 and 2 of a slowly accelerated clock covering a broken line and a stationary clock covering a straight worldline. Of all worldlines covering 1 and 2, the straight line has the ''longest proper time''. Therefore the traveling clock in the round-trip experiment is retarded at reunion, because its curved worldline corresponds to a shorter proper time. This result he presented in terms of the following inequality, of which the right-hand side refers to the straight curve of the stationary clock, while all others possible curves are represented on left-hand side: :<math>\tfrac{1}{c}\int_{1}^{2}\sqrt{du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}<\tfrac{1}{c}\int_{1}^{2}du</math> {{Lorentzbox|Text={{anchor|Sommerfeld 1913-PT}}Similar treatments can be found in the textbooks of [[w:Arnold Sommerfeld|Sommerfeld]] (1913),<ref name=sommerfeld /> [[w:Hermann Weyl|Weyl]] (1918),<ref name=weyl /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Jean Becquerel|Becquerel]] (1922).<ref name=becqu1 />}} |} ==Triangle inequality== {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Alfred Robb|Robb]] 1914-1920 |{{anchor|Robb 1914-TR}}In 1914<ref name=robb1 /> he showed that there are three types of triangles formed by intervals in Minkowski space, depending on whether one deals with "separation lines" (spacelike intervals), "optical lines" (lightlike intervals), or "inertia lines" (timelike intervals representing the path of nonaccelerated particles defined by <math>{\scriptstyle \left(x_{1}-x_{0}\right)^{2}+\left(y_{1}-y_{0}\right)^{2}+\left(z_{1}-z_{0}\right)^{2}-c^{2}\left(t_{1}-t_{0}\right)^{2}<0}</math>). As to a triangle formed by inertia lines, he showed that the sum of a certain two sides is ''less'' than that of the third one. {{Lorentzbox|Text=So the triangle inequality derived from time-like intervals in Minkowski space is ''[[w:Triangle inequality#Reversal in Minkowski space|inverse]]'' to the inequality in Euclidean space. This inverse inequality directly represents the most simple variant of the twin paradox: the traveler follows two sides of the time-triangle, while the stay-at-home observer follows the third side indicating maximal proper time.}} [[File:RobbTriangle.svg|right|150px]] In 1920<ref name=robb2 /> Robb gave a numerical example of the triangle ABC with time-like intervals ("inertia lines") defined by coordinates :<math>\begin{matrix} & x & y & z & t\\ A\ & 0 & 0 & 0 & 0\\ B\ & 0 & 0 & 0 & 10\\ C\ & 4 & 0 & 0 & 5 \end{matrix}</math> which he plugged into :<math>\bar{s}^{2}=\left(t_{1}-t_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}-\left(y_{1}-y_{0}\right)^{2}-\left(z_{1}-z_{0}\right)^{2}</math> from which he obtained the sides AB=10, AC=3, CB=3 and the inequality <math>AC+CB<AB</math>. |- |[[w:Arthur Eddington|Eddington]]<ref name=edding2 /> 1922 |He distinguished between the "space-triangle" for spacelike intervals, and the "time-triangle" for time-like intervals. The latter is measured with a clock from A to B and from B to C, with the sum of those readings ''is always less'' than the reading of a clock measuring directly from A to C. In the ordinary space-triangle any two sides are together greater than the third side; in the time-triangle two sides are together ''less'' than the third side. |- |Rogers<ref name=rogers /> 1922 |He showed that the "pure time-triangle" C, A, B (in their proper time order) satisfies the relation <math>\cosh C=\tfrac{\alpha^{2}+\beta^{2}-\gamma^{2}}{2\alpha\beta}</math>, where <math>\cosh C</math> denotes the unit-scalar product of the vectors CA, CB, and <math>\alpha,\beta,\gamma </math> the real and positive intervals BC, CA, AB. Since <math>\alpha>\beta </math> and <math>\cosh C>1</math>, it follows that <math>\alpha>\beta+\gamma </math>. That is, "the greatest side of pure time-triangle is greater than the sum of the other two sides". It follows at once that the stationary value of the proper time integral is an "absolute maximum". |} ==Negligibility of proper acceleration== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |style="vertical-align:top" |[[w:Albert Einstein|Einstein]] 1905-1918 |In 1905,<ref name=einstein05 /> Einstein used velocity time dilation <math>\tau=t\sqrt{1-\left(\frac{v}{V}\right)^{2}}</math> to derive the retardation of a clock performing a round-trip with constant speed <math>v</math> along a polygonal path or a continuously curved line, without mentioning any influence of acceleration at turnaround. {{anchor|Einstein 1911-VA}} In 1911 (published 1912),<ref name=einstein3 /> Einstein said that special relativity doesn't say anything about what happened to the clock's pointer position during the acceleration that changes the clock's direction along the round-trip, yet the influence of this change must be getting smaller the longer the clock ''is moving uniformly'', i.e. the longer one chooses the dimensions of the path. {{anchor|Einstein 1912-VA}}In an unpublished manuscript on special relativity from 1912,<ref name=einst12manu /> he pointed out that any influence of acceleration during the round-trip experiment, can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygonal path. {{anchor|Einstein 1914a-VA}}In a letter from April 1914,<ref name=einstpetz /> Einstein showed that any ''finite'' acceleration at turnaround during the round-trip experiment can only influence the clock in a ''finite'' way, thus it can be neglected by minimizing the time of acceleration with respect to the time of uniform translation. So it ''must be concluded'' that the clock is retarded at reunion after traveling on a polygonal path. {{anchor|Einstein 1914b-VA}}During a conversation in May 1914,<ref name=rowe group=S /> Einstein is reported to have replied that the accelerations during the round-trip are "irrelevant for the amount of the time difference". (Compare with {{slink||Einstein 1914b-AC}}) {{anchor|Einstein 1918-VA}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918,<ref name=einstein18 /> Einstein pointed out that any effect of velocity changes at turnaround must be limited, thus the traveling clock must be retarded at reunion due to time dilation if one makes the path AB and back along the round-trip long enough. (Compare with {{slink||Einstein 1918-AC}}) |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> 1911 |{{Anchor|Wiechert 1911-VA}}[[File:WiechertTwin.svg|110px|right]] He demonstrated that differential aging along the round-trip cannot be caused during the passage from one velocity to another (i.e. acceleration) at turnaround, because the same result also follows when ''both'' A and B experience the ''same velocity changes'' with respect to another frame, only with the difference that B has relative velocities <math>+u</math> and <math>-u</math> for a long time, while A is brought after a short time from relative velocity <math>+u</math> to relative rest at which it remains a long time, and then it is brought to relative velocity <math>-u</math> for a short time. {{Lorentzbox|Text=He was probably the first to use an example in which both accelerate with same magnitude.}} |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> 1913 |{{anchor|Laue 1913-VA}}He showed that the problem of the influence of acceleration at turnaround in the round-trip experiment, can be eliminated by ''arbitrarily'' enlarging the time in inertial motion. {{Lorentzbox|Text=This is the same argument as given in {{slink||Einstein 1911-VA}}. The Einstein-Laue argument was also used by others such as [[w:Hans Thirring|Thirring]] (1921)<ref name=thirring /> or [[w:Max Born|Born]] (1921).<ref name=born />}} |- |[[w:Hendrik Lorentz|Lorentz]]<ref name=lorentz1 /> 1913 |He pointed out that any effect of acceleration on the traveling clock at turnaround, can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip. {{Lorentzbox|Text=Similarly, [[w:Wolfgang Pauli|Pauli]] (1921) stated that the arising infinitesimal accelerations at turnaround are certainly independent of the total travel time and ''therefore easy to eliminate''.<ref name=pauli />}} |} ==Relay (three brothers) experiment== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:de:Fritz Grünbaum (Physiker)|Grünbaum]]<ref name=gbaum /> 1911 |He discussed a one-way time dilation experiment in which the first clock is set into motion from the origin and then moving to the second clock. He argued that one can avoid the problem of acceleration experienced by the first clock when set into motion, by replacing it with a ''third'' clock that is already in motion with constant velocity and is synchronized at the origin with the first clock. {{Lorentzbox|Text=While Grünbaum didn't discuss round-trip experiments, his introduction of a third clock in order to avoid acceleration is the basis of the three-brother experiment.}} |- |style="vertical-align:top"|[[w:Emil Wiechert|Wiechert]] 1920-1922 |In 1920 (published 1921),<ref name=wiechert20 /> Wiechert explained how to completely remove acceleration from the round-trip experiment: Bodies A, B, C move undisturbed and non-accelerated in different directions. A and B pass each other at time (1), B and C pass each other at a later time (2), and C and A finally pass each other at an even later time (3). So in this setup, the condition of C is the continuation of the condition of B. On any of the three bodies one can count the oscillations of light of a certain spectral-line, in which case relativity predicts that the ''combined sum of all oscillations'' on B+C is smaller than the number of oscillations on A alone. Wiechert also held that one can replace the light oscillations by the life functions of human-like beings which live on A, B and C. For instance, while the inhabitants of B+C only had time for one meal, there were arbitrarily many generations on A who follow after each other by death and birth. [[File:Wiechert1922a.png|180px|right]] In 1921 (published 1922),<ref name=wiechert21 /> Wiechert extended his previous acceleration-free round-trip experiment to an arbitrary number of non-accelerated bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., which constitutes a "relay" (German: Stafette) starting from body A and back again. The first B passes A and moves away, and after some time the last B comes back to A. Since any B body continues the fate of the previous one, all bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., combined have emitted fewer oscillations than A alone during the relay race. Wiechert pointed out that instead of light oscillations one can also choose the aging of life forms. {{Lorentzbox|Text=Such relay experiments were later independently rediscovered in English language papers<ref name=debs group=S /> such as by Lange (1927)<ref group=S name=lange /> in which the brothers synchronize their times when they pass each other (“three brother experiment”).}} |} ==Acceleration as asymmetry indicator== While it was known that any direct influence of [[w:proper acceleration]] on clocks can be neglected in the computation of the inertial frame of the stay-at-home twin (see previous section {{slink||Negligibility of proper acceleration}}), the very fact that only one of them is accelerating is still useful as an asymmetry argument in order to show that there is no contradiction to the relativity principle. {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{Anchor|Langevin 1911-AC}}He derived differential aging in the round-trip experiment using the proper time integral along worldlines (see {{slink||Langevin 1911-PT}}) and used acceleration as an asymmetry indicator: The result of the round-trip experiment is "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". |- |[[w:Arnold Sommerfeld|Sommerfeld]]<ref name=sommerfeld /> 1913 |After he showed (see {{slink||Sommerfeld 1913-PT}}) that retardation of time in the round-trip experiment derived from the proper time integral rests on the assumption that the clock's rate ''only depends on its momentary velocity'' (now called "clock hypothesis"), he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle since one of the clocks has to be accelerated in order to come back, thus the retardation in the round-trip experiment does not demonstrate "motion", but "accelerated motion". |- |[[w:Hendrik Lorentz|Lorentz]] 1913<ref name=lorentz1 /> |After he derived differential aging in the round-trip experiment from velocity time dilation and pointed out the negligibility of proper acceleration for the computation, he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle, since one of them changes velocity and accelerates; the relativity principle does not require symmetry between inertial and non-inertial observers. |- |style="vertical-align:top"|[[w:Albert Einstein|Einstein]] 1914-1920 |{{anchor|Einstein 1914b-AC}} During a conversation in 1914,<ref name=rowe group=S /> Einstein is reported to have said that moving clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are ''irrelevant'' for the ''amount'' of the time difference, their ''presence'' nevertheless cause B to fall behind ("accelerated motions are absolute"). {{anchor|Einstein 1918-AC}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918<ref name=einstein18 />, Einstein pointed out the negligibility of velocity changes from the viewpoint of an inertial frame (see {{slink||Einstein 1918-VA}}). Then he used ''acceleration as an asymmetry indicator'' in order to show, that there is no contradiction to the relativity principle, because relativity only predicts the equivalence of non-accelerated inertial frames: "only K is such a frame while K' is temporarily accelerated, thus the retardation of U2 with respect to U1 cannot be used to construe a contradiction against the theory." {{anchor|Einstein 1920-AC}}Einstein is reported to have said in an interview from 1920:<ref name=einstein20 /> {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls-Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. Dieser Grund für das Jüngerbleiben des A ergibt sich vom Gesichtspunkt der speziellen Relativitätstheorie aus der Tatsache, daß das betreffende Geschöpf — und nur dieses — Beschleunigungen erlitten hat. | style="padding: 0px 20px 0px 20px;" |In the case of these two twins," Einstein declared, "we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures . This ground, which counts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations." |} In a discussion from 1922,<ref name=morand /> Einstein is reported to have said that there is no contradiction in the round-trip experiment (in terms of a train leaving the station and returning later): The relativity principle is not applicable to this case, because the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two frames having velocities in opposite direction is not an inertial frame. There is no reciprocity between a frame that changes direction and one that doesn't. |} ==Frame distribution as asymmetry indicator== Because any direct influence of proper acceleration on the traveling clock at turnaround can be neglected (see {{slink||Negligibility of proper acceleration}}), the importance of {{slink||Acceleration as asymmetry indicator}} is limited to the mere fact that it reveals that only the traveler was in a non-inertial frame as only he changed his inertial frames, thus instead of emphasizing the occurrence of proper acceleration at turnaround, it's possible to describe the asymmetry more geometrically by emphasizing the different distribution of inertial frames of the twins along their worldlines. {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Max von Laue|Laue]] 1911-1913 |{{Anchor|Laue 1911/12-VA}} In 1911/12,<ref name=laue1 /> he pointed out that during the time of separation, that clock is most advanced which was at rest in an inertial frame all the time; namely there is ''always one, and only one inertial frame'', in which the locations of separation and re-encounter lie in the same geometric point. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1911/12-PT}}). In 1912/13,<ref name=laue2 /> he argued that in the round-trip experiment, we indeed can decide, which one of the clocks was steadily at rest in one and the same reference system, and which one was in the meantime at rest in two or more such systems. Among them there is of course a real physical difference. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1912/13-PT}}). In 1913<ref name=laue3 /> Laue pointed out: {| !style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Aber nach unseren Voraussetzungen ruht während der Zeit der Trennung die erste Uhr in ''einem'' berechtigten Bezugssystem, die zweite hingegen ruht zwar sowohl bei der Hin- wie bei der Rückbewegung in berechtigten Bezugssystemen, aber notwendig in ''zwei verschiedenen. Deshalb'' unterscheiden sich beider Schicksale physikalisch. Ließe man die zweite Uhr in der ihr anfangs erteilten Bewegung und schickte man ihr dafür die erste Uhr nach einiger Zeit mit größerer Geschwindigkeit nach, so würde beim Zusammentreffen die erste gegen die zweite zurückgeblieben sein; denn jetzt hat die erste während der Trennung in zwei verschiedenen Systemen geruht. (Footnote: Dem naheliegenden Einwand, daß wir über den Gang einer Uhr während eines Geschwindigkeits''wechsels'' nichts aussagen können, begegnet man am einfachsten mit dem Hinweis, daß man die Zeiten der gleichförmigen Bewegung ''beliebig'' groß gegen die der Beschleunigung machen kann.) | style="padding: 0px 20px 0px 20px;" | However, by our presuppositions, one clock is at rest in ''one'' valid reference system during the time of separation, while the second one is at rest in valid reference systems both during the forward- and the backward motion, but necessarily in ''two different ones. Therefore'' the two fates differ physically. If the second clock remains in the motion which was given to it at the start, and if after some time it is followed by the first clock with greater velocity, then the first one would be retarded with respect to the second one at the encounter; since now it was the first one that was at rest in two different systems during the separation. (Footnote: The objection which is near at hand, that we cannot say anything about the rate of a clock during a velocity ''change'', can be met most simply by the allusion, that we can render the times of uniform motion ''arbitrarily'' great with respect to acceleration..) |} |- |[[w:Werner Bloch|Bloch]]<ref name=bloch /> September 1918 |{{anchor|Bloch 1918-VA}} He represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. |} ==Perspective of the traveler== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{anchor|Langevin 1911-LI}}[[Image:rstd4.gif|170px|right]] After deriving differential aging from the proper time integral in {{slink||Langevin 1911-PT}} and using human beings in {{slink||Langevin 1911-HU}}, he described the perspectives of both observers using light signals and the Doppler effect. When they separate they see each other live 200 times slower, while at return they see each other live 200 times faster. So ''from the explorer's viewpoint'', in the first year he sees the Earth perform the actions of two days, while in the second year he sees the Earth perform the actions of two centuries. The asymmetry can be seen by noticing, that the observer on Earth in 200 years sees the explorer performs the actions of 1 year. Then the explorer turns around, after which the observer on Earth in 2 days sees the projectile perform the actions of another year. {{Lorentzbox|Text=Langevin used <math>v=c\left(1-\tfrac{1}{20000}\right)</math>, producing Lorentz factor <math>\gamma\approx100</math> and Doppler factor <math>\sqrt{\tfrac{c+v}{c-v}}\approx200</math>.}} |- |[[w:Hendrik Lorentz|Lorentz]] Lectures published in 1913<ref name=lorentz1 /> Similar treatment in 1914<ref name=lorentz3 /> |{{anchor|Lorentz 1913/14-LI}}Described the round-trip experiment in terms of inertial observer A (equipped with clock K) and traveling observer B (equipped with clock K'). In the frame of A, clock K' is retarded with respect to K at reunion due to time dilation. He then described the perspective of the traveling observer B by using two-way propagation of light from K' to K and back to K', leading to three periods defined by the moment of B's turnaround: In the first period the light signals return to K' before turnaround; in the second period the signals are emitted before turnaround and return after turnaround; in the third period emission and return of the signals are both happening after turnaround. Lorentz showed that K is time dilated by a factor of <math>\sqrt{1-v^{2}/c^{2}}</math> with respect to K' in the first and third period, but in the second period K is ticking ''faster'' than K' by a factor of <math>\sqrt{\tfrac{c+v}{c-v}}</math> which overcompensates the dilation in the other periods and explains, even from the perspective of B, why K' is retarded with respect to K at reunion. {{Lorentzbox|Text=In a review of the German translation of Lorentz's book, Einstein (1914) didn't directly mention Lorentz's treatment of the twin paradox, but he wrote that nobody who is seriously interested in relativity should neglect to read that book.<ref name=einstlor /> [[w:Wolfgang Pauli|Pauli]] (1921) refers to Lorentz's book as one of three papers that analyze the twin paradox more closely.<ref name=pauli />}} |- |style="vertical-align:top"| [[w:Albert Einstein|Einstein]] 1916-1920 |{{anchor|Einstein 1916-EP}}In a lecture from 1916,<ref name=einstein16 /> of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of [[w:general relativity]]." {{anchor|Einstein 1918a-EP}}In a letter from September 1918,<ref name=einadl /> Einstein showed that general relativity makes the inertial frame K and and the accelerated frame K' of the clocks in the round-trip experiment "equally justified", explaining the time difference in K' by combining the influence of velocity and gravitational potential on clocks. {{anchor|Einstein 1918-EP}}In his famous "Dialog about Objections against the Theory of Relativity" from November 1918,<ref name=einstein18 /> aimed at clarifying misconceptions of the clock paradox, he explained that there is no paradox in special relativity because there is no symmetry between clock U1 at rest in inertial frame K and clock U2 at rest in accelerated frame K' (see {{slink||Einstein 1918-AC}}). Yet [[w:general relativity]] and the [[w:equivalence principle]] allow the treatment of this problem also from the standpoint of frame K', where clock U2 remains at rest all of the time while U1 makes the following movements: (1) It is accelerated by a homogeneous gravitational field in the negative direction, (2) it moves with constant velocity <math>-v</math>, (3) it is accelerated in the positive direction until it turns around and comes by with constant velocity <math>+v</math>, (4) it moves with velocity <math>+v</math>, (5) it is accelerated in the negative direction until it stops. Clock U1 is retarded with respect to U2 in periods 2) and 4) due to velocity time dilation, but this retardation is overcompensated by the faster rate of U1 during period 3), because U1 is at a higher gravitational potential. He argued that the computation (which he didn't provide) shows that the advance of U1 in period 3) is double its retardation during periods 2) and 4). Einstein concluded that by this consideration "the paradox is completely resolved". Using [[w:Mach's principle]], he pointed out that the gravitational field in K' might be induced by the masses of the universe that are accelerated in this frame. {{anchor|Einstein 1918b-EP}}In a letter to Einstein from December 1918, [[w:Max Jakob|Jakob]] doubted the result that the advance in period 3) is double the retardation during periods 2) and 4). Einstein responded by letter,<ref name=einstein18b /> in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). {{anchor|Einstein 1921-EP}}Einstein is reported to have said in an interview from 1920,<ref name=einstein20 /> that while acceleration explains the age difference between the stationary twin B and the traveling twin A in terms of special relativity (see {{slink||Einstein 1920-AC}}), the "proper" description in terms of general relativity is as follows: {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Eine tiefere Erfassung des Grundes ist indeß nur auf dem Boden der „Allgemeinen Relativitätstheorie" zu erlangen, die uns erkennen läßt, daß von A aus beurteilt ein Zentrifugalfeld existiert, von B aus betrachtet aber nicht; und dieses Feld hat einen Einfluß auf den relativen Ablauf und die Raschheit der Lebensvorgänge. | style="padding: 0px 20px 0px 20px;" | A proper grasp of the reason is furnished only when we adopt the general theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life." |} {{Lorentzbox|Text=a) Einstein's explanation was quickly adopted in the textbooks of [[w:Werner Bloch|Bloch]] (1920),<ref name=bloch2 /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Karl Bollert|Bollert]] (1921),<ref name=bollert1 /> [[w:Max Born|Born]] (1921),<ref name=born /> expressing the view that general relativity is "necessary" to provide the "complete" solution of the twin paradox. b) From a modern standpoint, however, Einstein's explanation has nothing to do with general relativity, but is rather an application of accelerated frames and "pseudo"-gravitational fields to flat Minkowski space of ''special'' relativity.<ref name=weiss group=S />}} |- |[[w:Hans Thirring|Thirring]]<ref name=thirring /> April 1921 |{{anchor|Thirring 1921-DS}}[[Image:Twin Paradox Minkowski Diagram.svg|right|200px]] He described the round-trip experiment by using two platforms K (clock A) and K' (clock B) each equipped with rows of clocks. He first demonstrated the symmetry of time dilation and the mutual relativity of simultaneity on the platforms and its effect on clock synchronization. The K clocks that B passes are all advanced because of <math>t'=\gamma\left(t-vx/c^{2}\right)</math>, and the same is true after turnaround since only the direction of velocity has to be changed in the Lorentz transformation <math>t'-t'_{0}=\gamma\left(t+vx/c^{2}\right)</math> leading to the effect of clock desynchronization, where <math>t'_{0}</math> is a constant depending on which clock one uses as standard for the new synchronization. He graphically showed using Minkowski diagrams, that this simultaneity jump due to desynchronization amounts to double the velocity time dilation during the inertial phases, explaining why A is more advanced than B at reunion. {{Lorentzbox|Text=Using clock B as synchronization standard, Thirring's constant is given by <math>t'_{0}=2l\gamma v/c^{2}=2t\gamma v^{2}/c^{2}</math> with <math>l=vt</math> as position of turnaround. A similar explanation was subsequently given by Langevin (1922).<ref name=morand />}} |} ==Curved spacetime== While the previous examples are defined in flat Minkowski spacetime and therefore can be fully discussed in terms of special relativity, [[general relativity]] is required when [[:w:spacetime curvature]] in the presence of mass and energy cannot be neglected any more.<ref name=koks group=S /> {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |[[w:Jean Becquerel|Becquerel]]<ref name=becqu1 /> 1922 |After defining gravitational time dilation <math>d\tau=\sqrt{1-\tfrac{2GM}{c^{2}r}}dt</math> in terms of the [[w:Schwarzschild metric]] around a material center, he discussed the following round-trip experiment: There are two identical clocks A and B placed next to each other, at a point very far from the material center, initially marking the same time <math>t</math>. Let us transport clock A to a point where the field is more intense, at a distance <math>r</math> from the center; this clock will measure time <math>\int d\tau</math> which is shorter than <math>\int dt</math>, thus it will run more slowly. If we bring clock A back to clock B, we will have to note that it is retarded with respect to B. |} ==Aether interpretations== [[w:Lorentz ether theory]] (LET) is empirically equivalent to special relativity since both models use the Lorentz transformation, thus the description of the twin paradox gives the same result as well. However, special relativity is preferred by the scientific community, because of the validity of the relativity principle in LET is only apparent due to a conspiracy of effects which makes the aether undetecable, and because the measured times and lengths in the aether are supposedly be giving the "true" values even though it is empirically impossible to determine which ones are true or apparent. {| class=wikitable style="background-color:white;{{text default color}};" |- ! style="width:150px" | Author !! Description |- |Langevin (1911)<ref name=langevin1 /> |He argued that it's true that uniform translation with respect to the aether has no experimental meaning in special relativity, though one can still speak of "absolute acceleration" with respect to an aether which he defined as the light carrying medium, so it was "premature to abandon the aether". The absolute nature of acceleration can be seen in the radiation of accelerated charges, as well as in the twin paradox in which the traveler that is more agitated or accelerated is younger at reunion. {{Lorentzbox|Text=Langevin didn't mention this aether interpretation in his later discussions of the twin paradox in 1911/12<ref name=langevin2 /> and 1919.<ref name=langevin3 />}} |- |style="vertical-align:top" |{{Anchor|Wiechert 1911b}}Wiechert (1911)<ref name=wiechert11 /> |Contrary to Langevin, he emphasized the fact that the influence of acceleration can be minimized so that differential aging can be attributed to constant velocity alone. From that he concluded that the clock's "strides" (German: Schreitungen, denoting the "absolute meaning" of non-accelerated motions) are not equivalent or anisotropic, in contradiction to the "unconditional" relativity principle Einstein's. Instead he proposed a "conditional" relativity principle in which an aether (in the sense of Lorentz) determines all processes in nature. This should explain the non-equivalence of the "strides" because they can be seen as absolute motions with respect to this aether, thus the progression rate of processes is ''really'' altered when passing from one stride to another. {{Lorentzbox|Text=a) This aether interpretation was maintained by Wiechert also in subsequent publications in 1915-1922.<ref name=wiechert15 /><ref name=wiechert20 /><ref name=wiechert21 /> b) Wiechert's interpretation in terms of absolute non-accelerated motions was also independently given by others: [[s:fr:Georges Lechalas]] (1912/13)<ref name=lech /> argued that time dilation and asymmetric aging are the result of absolute speeds with respect to an aether, while criticizing Langevin's (1911) argument that only accelerations can indicate the aether and are responsible for the asymmetric aging; [[w:Edward Vermilye Huntington]] (1912)<ref name=hunt /> argued that the "famous paradoxes of the theory of relativity" represented by the reciprocal nature of length contraction and time dilation, appear as necessary consequences of perfectly natural and reasonable conventions for setting clocks and laying out coordinates, when the Lorentz transformation is derived and interpreted on the basis of a stationary aether in the sense of Lorentz. c) Laue (1911/12)<ref name=laue1 /> applauded Wiechert for the "particularly striking way" in which he demonstrated that asymmetric aging indeed follows from the relativity laws, yet he rejected Wiechert's aether interpretation and Wiechert's claim that asymmetric aging contradicts the "unconditional" relativity principle: Laue pointed out that the straight worldline connecting two events A and B is only "preferred" insofar as it indicates the maximal proper time between them, yet this preference is ''not'' the result of the natural laws employed, but is rather due to the choice of points A and B; by analogy, the geometric result that two points determine a straight line and thus a direction as well, doesn't refute the physical equivalence of all directions in space; finally, as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.}} |} ==Paradoxical?== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" | German original of [[w:Max von Laue|Laue]] (1911/12):<ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> ! English translation |- |Unter all den paradox erscheinenden Folgerungen aus der Zeittransformation der Relativitätstheorie gibt es wohl keine, gegen welche sich der natürliche Menschenverstand bei jedem, der der Sache noch ungewohnt ist, so sehr sträubt, wie gegen die, daß die Zeitangabe einer Uhr von ihrem Bewegungszustand abhängen soll. Schon in seiner grundlegenden Arbeit hat Einstein diese Paradoxie auf die Spitze getrieben in einem Gedankenexperiment, welches neuerdings von Langevin in einem auch sonst sehr lesenswerten Vortrage besonders hübsch erläutert worden ist. |Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. |- |colspan=2|{{Lorentzbox|Text=Laue was probably the first to denote the round-trip experiment as paradoxical (even though he pointed out that there are no real contradictions). Subsequently, [[:w:Paul Gruner|Gruner]] (1912)<ref name=gruner /> and others including Einstein (1918)<ref name=einstein18 /> explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas [[w:Rudolf Seeliger|Seeliger]] (1913)<ref name=seel /> spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon").}} |} ==Misunderstandings== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" padding=10 | German original by [[w:Otto Berg (scientist)|Berg]] (1910):<ref name=berg /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |Im Punkte <math>x = 0</math> des Systems S befinde sich eine Uhr, eine andere im Punkte <math>x'=0</math> von S'. Diese zweite bewege sich mit S' bis zum Punkte <math>x = a</math>, kehre dort um und bewege sich nun mit der Geschwindigkeit <math>v</math> zurück bis zum Punkte <math>x= 0</math>. Welche Zeit müssen beide Uhren in dem Moment angeben, wo sie sich wieder treffen? Wir beantworten diese Frage zunächst vom Standpunkt des Beobachters in S. Die Uhr in <math>x' = 0</math> hat sich mit der Geschwindigkeit <math>v</math> bis zum Punkte <math>x = a</math> bewegt; dazu brauchte sie die Zeit <math>\tau=\tfrac{a}{v}</math>. Zum Rückweg ist dieselbe Zeit nötig. Nach der Zeit <math>2\tau=2\tfrac{a}{v}</math> ist die Uhr also wieder im Punkte <math>x = 0</math> angelangt. Wir stellen uns nun auf den Standpunkt des Beobachters in S'. Für diesen führt nach dem Relativitätsprinzip das System S genau dieselben Bewegungen aus wie das System S' für den Beobachter in S, nur in entgegengesetzter Richtung. Die Zeit bis zum Zusammentreffen beider Uhren ist also im System S' ebenfalls gegeben durch <math>2\tau=2\tfrac{a}{v}</math>. Betrachtungen, die auf anschauliche Vorstellungen, wie Nachgehen von Uhren, gestützt sind, führen hier leicht zu Irrtümern, von denen auch die Fachlitteratur nicht frei ist. | style="padding: 0px 20px 0px 20px;" |There is a clock at point <math>x=0</math> of system S, and another one at point <math>x'=0</math> of S'. The second one moves together with S' until point <math>x=a</math>, turns around and now moves back with speed <math>v</math> to point <math>x=0</math>. Which time must both clocks indicate at the moment at which they encounter again? We answer this question at first from the standpoint of the observer in S. The clock at <math>x=0</math> has been moving with speed <math>v</math> until point <math>x=a</math>, for which it required time <math>\tau=\tfrac{a}{v}</math>. The same time is required for the way back. After time <math>2\tau=2\tfrac{a}{v}</math> the clock has thus arrived again at point <math>x=0</math>. Let's now take the standpoint of the observer in S'. In his view in accordance with the relativity principle, system S is conducting exactly the same motions as those of system S' with respect to the observer in S, only in opposite direction. Thus the time until the meeting of both clocks is given by <math>2\tau=2\tfrac{a}{v}</math> in system S' as well. Considerations based on illustrative notions, such as the retardation of clocks, easily lead to mistakes at this place, of which also the professional literature isn't free. |- |colspan=2|{{Lorentzbox|Text=a) Berg was probably the first to turn the relativity principle against asymmetric aging in the round-trip experiment, claiming that both clocks must indicate the same time at reunion. See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem. b) Berg's mistake also seems to be based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" padding=10 | German original by [[w:Otto Lehmann (physicist)|Lehmann]] (1910/11):<ref name=lehm /> ! English translation |- | style="padding: 0px 20px 0px 20px;" | Hat man zwei genau gleich gehende Uhren nebeneinander und bewegt nun die eine auf einer beliebigen Kurve bis wieder zur anderen zurück, welche Bewegung <math>t</math> Sekunden gedauert haben möge, so geht sie gegen diese um <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> oder annähernd <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> Sekunden zu spät, weil sie während der Bewegung auf langsameren Gang reguliert werden mußte, um mit der ruhenden Uhr in Übereinstimmung zu bleiben. | style="padding: 0px 20px 0px 20px;" | If there are two exactly identical clocks next to each other, and if one of them will be moved on an arbitrary curve until it comes back, which may have lasted <math>t</math> seconds, it [the moving clock] will lag behind the other one by <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> or approximately <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> seconds, because it [the moving clock] had to be regulated to a slower rate during motion in order to remain synchronous with the resting clock. |- |colspan=2|{{Lorentzbox|Text=a) So Lehmann erroneously thinks that the time difference at reunion is only the result of "regulating" the moving clock. This implies that he (like Berg) believed that special relativity predicts ''equal'' clock times at reunion if the moving clock would have been left ''unregulated'' during the round-trip. b) Lehmann's mistake (similar to Berg) seems to based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" | German original by [[w:Emil Wiechert|Wiechert]] (1911)<ref name=wiechert11 /> ! English translation |- |colspan=2| Even though he correctly derived differential clock aging in the round-trip experiment, he (like Berg and Lehmann) claimed that effects like time dilation are "apparent" if one admits Einstein's "unconditional" relativity principle in which there is no aether and all "strides" (i.e. non-accelerated motions) are physically equivalent, but they are "real" if one admits the existence of an aether in the framework of a "conditional" relativity principle in which all strides are physically non-equivalent or anisotropic. This led him to the following interpretation of the clock paradox: |- | style="padding: 0px 20px 0px 20px;" |[...] so muß am Schluß des Versuches B in seinem Fortschritt gegenüber A im Verhältnis <math>1:\sqrt{1-u^{2}/c^{2}}</math> zurückgeblieben sein. Und dieses Zurückbleiben ist unbedingt reell, denn die beiden Gebilde A und B können ja unter gleichen Umständen unmittelbar beieinander verglichen werden. Hier ist es ganz sicher ausgeschlossen, an einen Schein zu glauben, der durch unsere Auffassung der Zeit bewirkt wird. So ist denn also auch die Folgerung unabwendbar, daß für den Verlauf der Weltvorgänge die Schreitungen nicht gleichwertig sind, ''und damit sind wir von neuem zu einem Schluß gekommen, welcher der Unbedingtheit des Relativitätsprinzipes durchaus widerspricht.'' [...] Man kann den Versuch noch mannigfach variieren, z. B. so, daß A ebenso wie B zwei verschiedene Schreitungen, <math>+u</math> und <math>-u</math>, nacheinander inne hat. Wird dann zu A der Wert <math>u_{1}</math>, zu B der Wert <math>u_{2}</math>, zugeordnet, so muß der Vergleich von A und B am Schluß des Versuches ergeben, daß B oder A in seinem Fortschritt zurückgeblieben erscheint, je nachdem die Schreitungen <math>+u_{1}</math>, <math>-u_{1}</math>, oder <math>+u_{2}</math>, <math>-u_{2}</math> weiter auseinanderliegen. ''Vielleicht ist gerade diese Formulierung des Satzes besonders geeignet, um die Ungleichwertigkeit der verschiedenen Schreitungen klar und deutlich zu zeigen.'' | style="padding: 0px 20px 0px 20px;" | [...] thus B's progress must be retarded with respect to A's in the ratio <math>1:\sqrt{1-u^{2}/c^{2}}</math> at the end of the experiment. And this retardation is definitely real, since both bodies A and B indeed can be immediately compared side by side under the same conditions. Here it is certainly excluded to believe that this is an appearance due to our conception of time. Thus the consequence is unavoidable too, that the strides are not equivalent in the course of the world processes, ''and therefore we again came to a conclusion that completely contradicts the unconditionality of the relativity principle.'' [...] One can vary this experiment in many ways, for instance, so that A in the same way as B successively undergoes two different strides <math>+u</math> and <math>-u</math>. If we apply the value <math>u_{1}</math> to A and <math>u_{2}</math> to B, then the comparison of A and B at the end of the experiment must give the result, that B or A is retarded in its progress depending on whether the strides <math>+u_{2},-u_{2}</math> or <math>+u_{1},-u_{1}</math> are further apart. ''Probably it is precisely this formulation of the theorem that is particularly suitable to demonstrate the non-equivalence of the different strides clearly and explicitly.'' |- |colspan=2|{{Lorentzbox|Text=This interpretation was directly rebutted by Laue (1911/12) who demonstrated the geometrical meaning of differential aging in Minkowski space, see sections {{slink||Laue 1911/12-PT|Laue 1911/12-VA}}, showing that there is no need to assume non-equivalance or anisotropy of motions. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.<ref name=laue1 />}} |- ! style="width:50%" | German original by [[w:Norman Robert Campbell|Campbell]] (November 1911, published 1912)<ref name=camp /> ! English translation |- |colspan=2|After describing the round-trip experiment (as given by Wiechert) according to which the traveling clock B is retarded when it returns with respect to stationary clock A, he abandoned differential clock aging as follows: |- | style="padding: 0px 20px 0px 20px;" |Dieser Schluß ist nicht richtig. Die Beziehung zwischen <math>t</math>, der Ablesung an der Uhr auf A seitens des Beobachters auf A und <math>t'</math>, der Ablesung an der Uhr auf B seitens des Beobachters auf A, ist (unter der Annahme, daß zu Beginn des Versuchs <math>t=t'</math> ist) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. Der Unterschied zwischen <math>t'</math> and <math>t</math> ist eine Funktion von <math>z</math> und <math>v</math> allein. Wenn man diesen Größen ihre früheren Werte wiedergibt, indem man die beiden Uhren wieder zur Koinzidenz bringt, während sie relativ zueinander ruhen, so geht der Unterschied zwischen <math>t'</math> and <math>t</math> wieder auf null zurück, gleichviel, welche Werte <math>z</math> und <math>v</math> während der Zwischenzeit gehabt haben mögen. Wenn an irgendeinem Punkte der Bahn die Geschwindigkeit von B relativ zu A eine endliche plötzliche Änderung erfährt, so erfährt auch der Wert von <math>v</math> eine endliche plötzliche Änderung. | style="padding: 0px 20px 0px 20px;" |This conclusion is not correct. The relationship between <math>t</math> as the reading on the clock on A by the observer on A, and <math>t'</math> as the reading on the clock on B by the observer on A, is given by (assuming that <math>t=t'</math> at the beginning of the experiment) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. The difference between <math>t'</math> and <math>t</math> is a function of <math>z</math> and <math>v</math> alone. If these quantities are given their previous values by bringing the two clocks back to coincidence during which they are at rest relative to one another, the difference between <math>t'</math> and <math>t</math> goes back to zero, no matter what values <math>z</math> and <math>v</math> may have had in the meantime. If at any point on the path the speed of B experiences a finite sudden change relative to A, then the value of <math>t'</math> also undergoes a finite sudden change. |- |colspan=2|{{Lorentzbox|Text=a) So Campbell claims that any time difference during the outbound path is wiped out during the inbound path. His mistake is obvious: He is confusing coordinate differences stemming from the Lorentz transformation of ''events'' (which indeed depend on position and direction) with differences in ''clock aging'' derived from the proper time integral (which is ''accumulative'' and independent of position and direction.) b) As Campbell's paper was a reply to Wiechert, it's interesting to compare them: Campbell was correct in dismissing the aether but wrong in denying asymmetric aging, while Wiechert was correct in deriving asymmetric aging but wrong in requiring the aether. }} |- ! style="width:50%" | French original by [[w:Paul Gruner|Gruner]] (March 1912):<ref name=gruner /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |[...] deux personnes du même âge, se séparant dans des systèmes de « marche » très différents et retournant après un laps de temps assez long, constateront une différence d'âge très sensible. [...] le principe de relativité exige toujours la ''réciprocité parfaite'' des phénomènes entre deux systèmes qui possèdent un mouvement relatif. Si, dans l'exemple cité, les deux personnes du même âge se séparent avec une vitesse relative pour se retrouver plus tard, la constatation d'une différence d'âge sera parfaitement mutuelle : A dira positivement que B est resté en arrière dans son développement, et B affirmera avec le même droit que c'est A qui ne s'est pas développé assez vite. Ainsi le principe absolu de la relativité montre ses conséquences les plus extrèmes et il est clair que l'introduction de l’éther n'est plus en état de résoudre cette contradiction irréductible et inconcevable. | style="padding: 0px 20px 0px 20px;" | [...] two people of same age, separating into very different systems of motion and returning after a quite long period of time, will notice a very significant age difference. [...] the principle of relativity always requires the ''perfect reciprocity'' of the phenomenons between two systems that possess relative motion. When, in the cited example, the two persons of same age are separated by some relative velocity only to meet again later, the finding of an age difference will be perfectly mutual: A will positively say that B stayed behind in its development, and B will assert with same right that it was A who has not developed fast enough. By that, the absolute relativity principle shows its most extreme consequences and it is clear, that the introduction of the aether is no longer able to resolve this irreducible and inconceivable contradiction. |- |colspan=2|{{Lorentzbox|Text=Gruner was probably the first to claim that combining the round-trip experiment with the symmetry of time dilation leads to the contradictory situation, that both must attribute younger age to one another at reunion. At the end of his paper, we also find the expression "clock paradox" (French: paradoxe des horloges). See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem.}} |} ==Einstein's contributions== 1905:<ref name=einstein05 /> Introduction of the "peculiar" (German: eigentümlich) round-trip experiment with clocks in terms of a polygonal path as well as a continuously curved path, and an experiment comparing a clock at the pole with one at the equator. January 1911 (published November):<ref name=einstein11a /> In a lecture from January, Einstein extended the "funny" (German: drollig) round-trip experiment to living organisms. According to [[w:Rudolf Lämmel]] in April 1911<ref name=lammel /> and [[w:Fritz Müller-Partenkirchen|Fritz Müller]] in October 1911,<ref name=muller /> Einstein spoke of human beings as well. January 1911 (published January 1912):<ref name=einstein3 /> During a discussion with Einstein directly after the previous lecture, [[w:Fritz Müller-Partenkirchen|Fritz Müller]] claimed that any time difference during the round-trip should vanish at reunion, in analogy to the fact that the Lorentz contraction of a moving rod vanishes when it is at rest again. Einstein showed that the analogy is incorrect: While the clock rates are indeed the same again when they are mutually at rest, the clocks do not indicate the same time at reunion because "clocks are carriers of the time differential"; he went on to show that any possible influence of acceleration during the turnaround can be made negligible by elongating the constant velocity periods. 1912:<ref name=einst12manu /> In an unpublished manuscript on special relativity, Einstein showed that if system <math>\Sigma'</math> makes a round-trip along a polygon, then its inner processes will be retarded with respect to resting system <math>\Sigma </math> at reunion. He pointed out that any influence of acceleration can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygon. April 1914:<ref name=einstpetz /> [[w:Joseph Petzoldt]] criticized asymmetric clock aging in the round-trip experiment as a "fallback into absolutist way of thinking", claiming that special relativity requires that any difference between the clocks vanishes when their relative velocity is zero again, even though he added that any treatment of the clock paradox in special relativity is unrealistic anyway, since the theory only concerns uniform motions and therefore cannot handle velocity changes, so one has to modify the theory. Einstein responded by letter in which he praised Petzoldt's philosophical take on relativity, yet he rejected Petzoldt's conclusions concerning the clock paradox by showing that any finite acceleration at turnaround during the round-trip can only influence the clock in a finite way and therefore can be neglected by minimizing the time of acceleration with respect to the time of uniform translation, so it "must be concluded" that the clock traveling on a polygonal path is retarded at reunion. May 1914:<ref name=rowe group=S /> During a conversation with [[w:Ernst Gehrcke]] who claimed that the clock paradox contradicts the relativity principle, Einstein replied that clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are irrelevant for the amount of the time difference, their presence nevertheless cause B to fall behind ("accelerated motions are absolute in the theory of relativity"). 1916:<ref name=einstein16 /> In a lecture of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of general relativity." September 1918:<ref name=einadl /> In a letter to Einstein, [[w:Friedrich Adler (politician)|Friedrich Adler]] (while in prison for the [[w:Assassination of Karl von Stürgkh]]) claimed that the clock paradox which he described on a circular round-trip contradicts the special relativity principle, and also referred to the similar opinions of Berg and Petzoldt. Einstein responded by letter and explained that there is no contradiction as one of them accelerates; he then showed that general relativity makes both inertial frame K and accelerated frame K' equally justified, explaining the time difference in K' by combining the influence of velocity and gravitational potential, concluding that "Berg and Petzoldt were wrong". November 1918:<ref name=einstein18 /> In a fictitious dialogue between a relativity critic and a relativity apologist written by Einstein, the "critic" said that special relativity must predict differential clock aging in round-trip experiments, which was confirmed by the "relativist" who regretfully noted that even some pro-relativity authors tried to "circumvent this unavoidable result". Yet the critic claimed that this leads to a contradiction: From the viewpoint of K, clock U1 is at rest while the clock U2 was in motion and therefore returns being retarded with respect to U1, but from the viewpoint of K', clock U2 is at rest while clock U1 was in motion and therefore returns being retarded with respect to U2, which was rebutted by the relativist by pointing out the acceleration of U2. Then the critic claimed that this problem "rises again from the dead" in general relativity which allows to symmetrically treat both K and K', which was rebutted by the relativist using the equivalence principle: In K', the rate increase of U1 during turnaround period 3) is "the double" of its velocity time dilation in the inertial periods 2) and 4). December 1918:<ref name=einstein18b /> In a letter to Einstein, [[w:Max Jakob]] doubted the result from Einstein's dialogue, according to which the advance of U1 in period 3) is the double of its retardation during periods 2) and 4). Einstein responded by letter, in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). 1920:<ref name=einstein20 /> In conversations with [[w:Alexander Moszkowski]] between 1919 and 1920, Einstein argued that differential aging of the twins is rather a paradox of feeling, not a paradox of thought, because the latter would only arise if there were no reason for the asymmetric aging. The reason in special relativity lies in the fact that one of them suffered accelerations, while a deeper understanding of that question is obtained by using general relativity. Einstein argued that our "common sense" is located in the realm of feeling and analogy drawn from our ordinary experience; since there is no analogy to the example of the twins in our experience, it might appear paradoxical to the common sense, while it appears logical and necessary in light of intensified abstraction of the trained scientific mind. August 1920:<ref name=rowe group=S /> At an anti-relativity event organized by the right-wing agitator [[w:Paul Weyland]] during which [[w:antisemitic]] leaflets were distributed and [[w:swastika]]s offered at the entrance, a lecture was given by Gehrcke re-iterating his criticism of the twin paradox, claiming that the stationary first organism is old or even dead at reunion while the second organism was in motion and therefore stayed young, but from the standpoint of the second organism he himself is old or even dead while the first organism was in motion and stayed young, thus relativity is either contradictory or it leads to different realities and physical [[w:solipsism]]. Einstein who was present at that event, directly responded in a newspaper article;<ref name=einst20 /> after suspecting antisemitic motives of his critics, he specifically addressed Gehrcke's objections regarding the "well known example of the clocks (or twins)", remarking that the charge of solipsism will be "greeted by the experts as a joke", and characterized the claim that relativity requires mutual retardation of two co-located clocks as a "deliberate attempt to misinform the lay public". 1922:<ref name=morand /><ref name=nord /> [[w:Paul Painlevé]], Einstein and Langevin discussed the clock paradox at a meeting in Paris. Painlevé imagined a clock on a train that performs a round-trip with constant speed and returns being retarded with respect to the station clock, yet he claimed that the relativity principle also allows to say that the station clock performed the round-trip and returned being retarded with respect to the train clock, in contradiction to the previous result. Einstein replied that the relativity principle cannot be applied since the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two systems having velocities in opposite direction is not an inertial frame; there is no reciprocity between a frame that changes direction and one that doesn't. Langevin consequently gave a detailed analysis in terms of the Lorentz transformation. 1954:<ref name=einstein54 /> In a letter, Einstein explained the "well known clock paradoxon" using two clocks <math>B_{1}</math> and <math>B_{2}</math>; clock <math>B_{2}</math> has to reverse its speed in order to come back, thus it was initially at rest in inertial frame <math>S_{2}</math> and then at rest in <math>S_{2}^{+}</math>, whereas <math>B_{1}</math> constantly remains at rest in <math>S_{1}</math>, which explains the asymmetry between them. ==Historical references== <references> <ref name=einstein05>See p. 904f in: {{Citation |author=Einstein, A. |date=1905 |title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik |volume=322 |issue=10 |pages=891–921 |doi=10.1002/andp.19053221004|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 2, Document 23}}. See also: [https://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation at fourmilab].</ref> <ref name=einstein11a>See p. 10. in: {{Citation |author=Einstein, A. |title=Die Relativitäts-Theorie|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |issue=1-2|pages=1–14 |date=27 November 1911|orig-date=Lecture 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n11/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 17}}.<br /> The publication date 27 November 1911 can be seen on the [https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n5/mode/2up Title page and TOC of issue 1-2].</ref> <ref name=einstein3>Discussion between Einstien, Müller, Lämmel and others after the Zürich lecture: {{Citation |author=Einstein, A.; Müller, F., Lämmel, R.|title=Diskussion zu "Die Relativitäts-Theorie"|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |pages=II-IX |date=January 1912|orig-date=Lecture on 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n587/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 18, and in the corresponding English translation volume}}<br /> While the discussion already happened on January 1911, the publication followed one year later in January 1912 in the session proceedings (Sitzungsberichte) of the third issue, see [https://www.ngzh.ch/publikationen/vjs/56/3 Full issue Nr. 3] with [http://www.ngzh.ch/archiv/1911_56/56_1-2/56_3.pdf Title page and TOC] and the [http://www.ngzh.ch/archiv/1911_56/56_3/56_30.pdf Sitzungsberichte including Einstein's discussion on pp. II-IX]. </ref> <ref name=einst12manu>See p. 46 in: {{Citation |author=Einstein, A. |date=1912 |chapter=Document 1: Einstein's manuscript on the special theory of relativity|title=The collected papers of Albert Einstein|volume=4|pages=3-108|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstlor>{{Citation|author=Einstein, A.|date=1914|title=Review of "Lorentz, H. A. – Das Relativitätsprinzip" |journal=Die Naturwissenschaften|volume=2|pages=1018|url=https://archive.org/details/CAT31421305002/page/1018/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 6, Document 11}}</ref> <ref name=einstpetz>{{Citation |author=Einstein, A. |date=1914 |chapter=Document 5: Letter from Einstein to Petzoldt|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein16>See p. 423f in: {{Citation |author=Einstein, A. |date=1916 |title=Announcement of Einstein's lecture "Über einige anschauliche Überlegungen aus dem Gebiete der Relativitätstheorie"|journal=Berliner Sitzungsberichte|pages=423|volume=1916 (part 1)|url=https://archive.org/details/sitzungsberichte1916deutsch/page/423/mode/2up}}</ref> <ref name=einadl>Letter exchange between Einstein and Adler in which the critique on the clock paradox by Berg (1910) and Petzoldt (1914) was mentioned, together with the general relativity solution in terms of the gravitational potential, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Adler's letter in Document 620 and Einstein's reply in Document 628|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein18>Einstein discussed in terms of inertial frames (special relativity) on pp. 697f; accelerated frames (general relativity) on pp. 698f.; distant masses (Mach's principle) on pp. 700f. in: {{citation |author=Einstein, A.|title=[[s:de:Dialog über Einwände gegen die Relativitätstheorie|Dialog über Einwände gegen die Relativitätstheorie]]|date=November 1918|volume=6|issue=48|journal=Die Naturwissenschaften|pages=697-702|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 7, Document 13}}; See also English translation [[:s:Translation:Dialog about Objections against the Theory of Relativity|Dialog about Objections against the Theory of Relativity]] on Wikisource.</ref> <ref name=einstein18b>Letter exchange between Max Jakob and Einstein from December 1918, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Jakob's letter in Document 661c and Einstein's reply in Document 663a|title=The collected papers of Albert Einstein|volume=10|pages=189-190}}</ref> <ref name=einstein20>Interview of Einstein by Moszkowski, see p. 204f. in: {{citation |author=Moszkowski, A.|title=Einstein. Einblicke in seine Gedankenwelt|orig-date=Copyright date 1920 |date=1921|place=Hamburg|url=https://www.archive.org/details/einsteineinblick00moszuoft}}; See also English translation by H. L. Brose (1921): [https://archive.org/details/einsteinsearch00moszrich Einstein, the searcher], p. 206</ref> <ref name=einst20>{{Citation|author=Einstein, A.|date=27 August 1920|journal=Berliner Tageblatt|title=Meine Antwort - Ueber die anti-relativitätstheoretische G. m. b. H.|issue=402|pages=1-2|url=https://www.deutsche-digitale-bibliothek.de/newspaper/item/YH65KFT53MOG4SMXDXK4IVUPTR3QRY7Q?issuepage=1|quote=Reprinted in "The Collected Papers of Albert Einstein", Vol. 7, Document 45}}</ref> <ref name=einstein54>Letter from Einstein to N. V. Pope from March 1954; [[w:Albert Einstein Archives]], Object number 27-88 ([https://ein-web.adlibhosting.com/aea/Details/archive/110021626 Online dataset]); Scanned version as [https://groups.google.com/group/npachat/attach/d3121322d37764f2/Einstein%20letter.doc?part=0.1 Word document on Usenet] published by [https://groups.google.com/g/npachat/c/Haoib97d6OA/m/8mR30yITEtMJ Pope himself])</ref> <ref name=morand>Discussion between Painlevé, Einstein, and Langevin on p. 316ff in: {{citation |author=Morand, M.|title=Einstein au collège de france|date=April 1922|journal=La Nature|volume=50|issue=2511|pages=315-320|url=http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.102/319/100/620/5/613}}</ref> <ref name=lammel>{{Citation|author=Lämmel, R.|date=28 April 1911|title=Die Relativitäts-Lehre|journal=Neue Zürcher Zeitung|volume=117|pages=1|url=https://www.e-newspaperarchives.ch/?a=d&d=NZZ19110428-01.2.4.1}}; English translation of the part concering the twin pardox at [[:v:History of Topics in Special Relativity/Twin paradox#Lämmel 1911-Hum|Wikiversity:Early history of the twin paradox - Lämmel]]</ref> <ref name=lammel2>See p. 84ff in: {{Citation|author=Lämmel, R.|date=1921|orig-date=Preface December 1920|title=Die Grundlagen der Relativitätstheorie|place=Berlin|publisher=Springer|url=https://archive.org/details/diegrundlagende00lmgoog}}</ref> <ref name=langevin1>He derived differential aging from the proper time integral; pointed out that this demonstrates the "absolute nature of acceleration" with respect to an aether, see: {{citation |author=Langevin, P.|title=[[:s:fr:L’Évolution de l’espace et du temps|L’Évolution de l’espace et du temps]]|journal=Scientia |volume=X |pages=31–54 |date=July 1911|orig-date=Lecture 10 April 1911}}; English translation [[:s:en:Translation:The Evolution of Space and Time|The Evolution of Space and Time]] on Wikisource</ref> <ref name=langevin2>See p. 329 in: {{citation |author=Langevin, P. |title=Le temps, l'espace et la causalité dans la physique moderne |journal=Bulletin de la Société française de philosophie |volume=12 |orig-date=Lecture October 1911|date=1912|pages=1-28|url=http://ahp.li/1f7fc22d283fdf0deeca.pdf}}</ref> <ref name=langevin3>See p. 622f in: {{citation |author=Langevin, P. |title=Le Principe de relativité |journal=Bulletin de la société française des électriciens |volume=9 |date=1919 |pages=601-639|url=https://archive.org/details/bulletin-de-la-societe-francaise-des-electriciens-ser.-3-vol-9/page/600}}; Republished in 1922 as separate booklet: [[:s:fr:Le Principe de relativité|Le Principe de relativité]], Éditions Étienne Chiron</ref> <ref name=wiechert11>See p. 745f. general description and proper time; 757f. space travel; in: {{Citation |author=Wiechert, E. |date=September 1911|orig-date=Lectures March-May 1911, submitted 26 July|title=[[:s:de:Relativitätsprinzip und Äther|Relativitätsprinzip und Äther]]|journal=Physikalische Zeitschrift |volume=12 |issue=17-18 |pages=[https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/741 689-707] published September 1; [https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/789 737–758] published September 15}}</ref> <ref name=wiechert15>See p. 46 (Einstein, Langevin, Wiechert) and pp. 51f (Laue versus Wiechert) in: {{citation |author=Wiechert, E.|contribution=Die Mechanik im Rahmen der allgemeinen Physik| title=Die Kultur der Gegenwart: Physik|volume=3.3.1|date=1915 |orig-date=Submitted July 1914|pages=1–78|contribution-url=https://www.archive.org/details/physikunterredak00warbuoft}}</ref> <ref name=wiechert20>See p. 46f in: {{citation |author=Wiechert, E.|title=Der Äther im Weltbild der Physik|orig-date=Presented December 1920|date=1921|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse|pages=29-70|url=http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN00250586X}}</ref> <ref name=wiechert21>See p. 25ff in: {{citation |author=Wiechert, E.|title=[[:s:de:Prinzipielles über Äther und Relativität|Prinzipielles über Äther und Relativität]]|date=1922|orig-date=Lecture September 1921|journal=Physikalische Zeitschrift|volume=23|pages=25-28}}</ref> <ref name=muller>See p. 9 in: {{Citation|author=Müller, F.|date=October 1911|journal=Berliner Tageblatt|title=[[:s:de:Das Zeitproblem (1911)|Das Zeitproblem]]|pages=[https://www.deutsche-digitale-bibliothek.de/newspaper/item/2QKOIOLGNVQILTCEZQOGQPLTRVLPM5PZ?query=zeit&issuepage=9 Part 1 published 16 October 1911] and [https://www.deutsche-digitale-bibliothek.de/newspaper/item/IO44I6QBC4SVV5YUKUDSGXYIPQUXXBN5?query=zeit&issuepage=11 Part 2 published 23 October 1911]}}</ref> <ref name=gruner>See p. 253f in: {{Citation |author=Gruner, P. |title=[[:s:fr:Rapport sur la dernière discussion concernant le principe de la relativité et l’éther|Rapport sur la dernière discussion concernant le principe de la relativité et l’éther]] |journal=Archives des sciences physiques et naturelles |volume=33|issue=4 |pages=252-254 |date=March 1912}}</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=weyl>See p. 147f. in: {{Citation |author=Weyl, H. |date=March 1918|title=Raum-Zeit-Materie (first edition)|publisher=Berlin: Springer|url=https://archive.org/details/RaumZeitMaterieVolIMeinerFrauGewidmet}}; English translation of the 4th edition by H. Brose (1921): [https://www.gutenberg.org/ebooks/43006 Space—Time—Matter], pp. 278f.</ref> <ref name=gbaum>See footnote on p. 507 in: {{Citation|author=Grünbaum, F. |title=Über einige ideelle Versuche zum Relativitätsprinzip|journal=Physikalische Zeitschrift|volume=12|pages=500–509|date=1911|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/540}}</ref> <ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> <ref name=laue2>See p. 42f. for general description; p. 58f. in terms of proper time; in: {{Citation |author=Laue, M. v. |orig-date=Preface December 1912|date=1913 |title=Das Relativitätsprinzip (Second Edition) |publisher=Vieweg |place=Braunschweig|url=https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE4597082}}; See also English translation [[:s:Translation:The Principle of Relativity (Laue 1913)|The Principle of Relativity, Second edition, Part III]] on Wikisource</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=berg>See p. 369f in: {{Citation |author=Berg, O. |date=1910 |title=Das Relativitätsprinzip der Elektrodynamik |journal=Abhandlungen der Fries'schen Schule |volume=3 |issue=2|pages=333-382 |url=http://hdl.handle.net/2027/hvd.hnuynk?urlappend=%3Bseq=351}}</ref> <ref name=camp>See p. 123f in: {{Citation |author=Campbell, N. |title=Relativitätsprinzip und Äther: Eine Entgegnung an Herrn Wiechert |journal=Physikalische Zeitschrift |volume=13 |pages=120-128 |issue=3|orig-date=Submitted December 1911|date=February 1912|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/150}}. The is based on an English manuscript translated by Max Iklé, and Campbell's first name was Germanised as "Normann".</ref> <ref name=seel>{{Citation|author=Seeliger, R.|title=Review of "P. Gruner – Rapport sur la dernière discussion concernant le principe de la relativité et l'éther"|journal=Die Fortschritte der Physik|volume=68|issue=2|pages=336|date=1913|url=https://books.google.com/books?id=fSJGAQAAMAAJ&pg=PA336}}</ref> <ref name=study>See footnote on p. 111 in: {{citation |author=Study, E. |title=Vorlesungen über ausgewählte Gegenstände der Geometrie |date=June 1911|url=https://archive.org/details/vorlesungenber00studuoft|publisher=B.G. Teubner|place=Leipzig}} </ref> <ref name=robb1>See pp. 356ff. in: {{Citation|author=Robb, A.|date=1914|title=A theory of time and space|place=Cambridge|publisher=University Press|url=https://archive.org/details/theoryoftimespac00robbrich}} </ref> <ref name=robb2>See §12 in: {{citation |author=Robb, A. A.|title=The Straight Path|date=1920 |journal=Nature|pages=599|volume=104|issue=2623|url=https://archive.org/details/sim_nature-uk_1920-02-05_104_2623/page/598/mode/2up}}</ref> <ref name=edding2>See p. 22 in: {{Citation |author=Eddington, A. S. |date=1922 |title=The theory of relativity, and its influence on scientific thought |publisher=Oxford Clarendon Press |url=https://archive.org/details/cu31924005748573}}</ref> <ref name=rogers>{{citation |author=Rogers, R. A. P.|title=The Time-Triangle and Time-Triad in Special Relativity|date=November 1922|journal=Nature|volume=110|issue=2769|pages=698–699|url=https://archive.org/details/sim_nature-uk_1922-11-25_110_2769/page/698/mode/2up}}</ref> <ref name=lorentz1>See pp. 37f, 55ff in: {{citation |author=Lorentz, H. A.|date=1913|title=Het relativiteitsbeginsel : drie voordrachten gehouden in Teyler's stichting|publisher=De Erven Loosjes |place=Haarlem|url=https://resolver.kb.nl/resolve?urn=MMKB24:063387000:00005}}; German translation on pp. 31f, 47f in: {{citation |author=Lorentz, H. A.|date=1914| title=Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem|publisher=B.G. Teubner |place=Leipzig and Berlin|url=https://archive.org/details/bub_gb_89PPAAAAMAAJ}}; See also the transcription [[:s:de:Das Relativitätsprinzip (Lorentz)|Das Relativitätsprinzip]] on German Wikisource and the English translation [[:s:Translation:The Principle of Relativity (Lorentz)|The Principle of Relativity]] on English Wikisource</ref> <ref name=lorentz3>See §12 in: {{citation |author=Lorentz, H. A.|title=Considérations élémentaires sur le principe de relativité|date=1914 |journal=Revue générale des sciences pures et appliquées|pages=179-186|url=https://archive.org/details/revuegnraled25pari/page/178/mode/2up}}</ref> <ref name=bloch>See pp. 67 ff. in: {{Citation | author=Bloch, W.| date=September 1918|title=Einführung in die Relativitätstheorie| publisher=B. G. Teubner |url=https://hdl.handle.net/2027/njp.32101040276907}}</ref> <ref name=bloch2>See pp. 69ff. (special relativity) and 102ff. (general relativity) in: {{Citation | author=Bloch, W.| date=1920 |title=Einführung in die Relativitätstheorie (second edition)| publisher=B. G. Teubner |url=https://www.archive.org/details/einfhrungindier00blocgoog}}</ref> <ref name=bollert1>See p. 6 (special relativity), pp. 24-26 (EP) in: {{citation |author=Bollert, K.|title=Einstein’s Relativitätstheorie und ihre Stellung im System der Gesamterfahrung |date=April 1921|publisher=Steinkopff|url=https://archive.org/details/dbc.wroc.pl.001504}}</ref> <ref name=born>See pp. 190f. (special relativity), 250f (EP) in: {{Citation | author=Born, M.| date=1921 |title=Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Second edition)| publisher=Springer | place=Berlin|url=https://hdl.handle.net/2027/mdp.39015017387310}}; The [https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE5426498 first edition (1920)] of Born's book didn't include the twin paradox. English translation of the third edition by H. Brose (1924): [https://archive.org/details/einsteinstheoryo00born Einstein's theory of relativity]</ref> <ref name=pauli>See p. 558f (general description); p. 624f (proper time); p. 713f (accelerated frames); in: {{Citation |author=Pauli, W. |date=1921 |journal=Encyclopädie der Mathematischen Wissenschaften|title=Die Relativitätstheorie|pages=539–776|volume=5|issue=2 |url=http://resolver.sub.uni-goettingen.de/purl?PPN360709672}}; English translation by G. Field (1958): [https://books.google.com/books?id=rc3DAgAAQBAJ Theory of Relativity]</ref> <ref name=thirring>See p. 209ff in: {{citation |author=Thirring, H.|title=Über das Uhrenparadoxon in der Relativitätstheorie|date=April 1921|journal=Naturwissenschaften|volume=9|issue=18|pages=209-212|url=https://archive.org/details/sim_naturwissenschaften_1921-04-01_9_13/mode/2up}}</ref> <ref name=sommerfeld>See p. 71 in: {{citation |author=Sommerfeld, A. |date=May 1913|chapter=Remarks on Minkowski's "Space and Time"|title=Das Relativitätsprinzip|editor=Otto Blumenthal|pages=69-73|url=https://www.archive.org/details/dasrelativittsp00minkgoog}}</ref> <ref name=kopff>See pp. 45ff (special relativity and proper time); pp. 117ff (EP); pp. 189ff (Mach's principle), in: {{citation |author=Kopff, A.|title=Grundzüge der Einsteinschen Relativitätstheorie |date=February 1921|publisher=S. Hirzel|place=Leipzig|url=https://www.archive.org/details/grundzgedereins00kopfgoog}}; English translation by H. Levy (1923): [https://hdl.handle.net/2027/mdp.39015017188817 The mathematical theory of relativity].</ref> <ref name=becqu1>See p. 48ff (proper time), p. 240f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Le Principe de relativité et la théorie de la gravitation|Le Principe de relativité et la théorie de la gravitation]] |date=1922 |publisher=Gauthier-Villars|place=Paris}}; See also p. 57ff (proper time), p. 177f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Exposé élémentaire de la théorie d’Einstein et de sa généralisation|Exposé élémentaire de la théorie d’Einstein et de sa généralisation]]|date=1922 |publisher=Payot|place=Paris}}</ref> <ref name=nord>Discussion between Painlevé, Einstein, and Langevin on pp. 146ff in: {{citation |author=Nordmann, C.|title=[[s:fr:Einstein expose et discute sa théorie|Einstein expose et discute sa théorie]]|date=May 1922|journal=Revue des deux mondes|volume=IX|pages=129-166}}</ref> <ref name=lehm>{{Citation |author=Lehmann, Otto |orig-date=September 1910 |date=1911|title=Das Relativitätsprinzip der neue Fundamentalsatz der Physik |title-link=s:de:Das Relativitätsprinzip der neue Fundamentalsatz der Physik|journal=Verhandlungen des naturwissenschaften Vereins in Karlsruhe |volume=23 |pages=49-74}}</ref> <ref name=lech>See p. 19ff in: {{citation |author=Lechalas, G. |orig-date=Submitted December 1912|date=1913 |title=Le nouveau temps |journal=L’Année philosophique|volume=XXIII|pages=19-44|url=https://gallica.bnf.fr/ark:/12148/bpt6k255882z/f22.item}}</ref> <ref name=hunt>See pp. 494ff in: <br>{{Citation|author=Huntington, E. V. |year=1912 |title=A new approach to the theory of relativity|journal=Philosophical Magazine |volume=23|pages=494-512|url=https://archive.org/details/londonedinburg6231912lond/page/494/mode/2up}}</ref> </references> ==Secondary sources== <references group=S> <ref name=miller>{{Citation |author=Miller, A. I. |date=1981 |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |place=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}; See section 7.4.13 (Langevin, Wiechert, Laue, Einstein), footnotes 29-34 of chapter 7 (Petzoldt, Sommerfeld, Bergson, Einstein)</ref> <ref name=lange>{{Citation|author=Lange, L.|date=1927|title=The clock paradox of the theory of relativity|journal=The American Mathematical Monthly|volume=34|issue=1|pages=22-30|jstor=2299914}}</ref> <ref name=pes>{{Citation |author=Pesic, P. |date=2003 |title=Einstein and the twin paradox |journal=European Journal of Physics |volume=24 |issue=6 |pages=585–590 |doi=10.1088/0143-0807/24/6/004}}</ref> <ref name=during>{{Citation |author=During, É. |date=2014 |title=Langevin ou le paradoxe introuvable |journal=Revue de métaphysique et de morale |volume=84 |pages=513-527 |doi=10.3917/rmm.144.0513|doi-access=free}}; See pp. 515f (Langevin), 520f. (Einstein, Laue, Weyl, Painlevé).</ref> <ref name=debs>{{Citation |author=Debs, T. A., & Redhead, M. L. |title=The twin paradox and the conventionality of simultaneity |date=1996 |journal=American Journal of Physics |volume=64|issue=1| pages=384-392 |doi=10.1119/1.18252}}</ref> <ref name=alizzi>{{Citation |author=Alizzi, A., Sen, A., & Silagadze, Z. K.|title=Do moving clocks slow down? |year=2022 |journal=European Journal of Physics |volume=43|issue=6|pages=065601 |doi=10.1088/1361-6404/ac93ca|arxiv=2209.12654}}; Appendix B with reference to Lange and Halsbury</ref> <ref name=beng>{{Citation |author=Benguigui, L. G. |date=2020 |title=A Tale Of Two Twins: The Langevin Experiment Of A Traveler To A Star |publisher=World Scientific|isbn=9789811219115}}; See early solutions (Einstein, Langevin, Lorentz, Born/Kopff) and the Bergson controversy. A shorter version appeared in {{arxiv|1212.4414}}.</ref> <ref name=rowe>{{Citation|author=Rowe, D. E.|date=2006|title=Einstein's allies and enemies: Debating relativity in Germany 1916–1920|journal=Interactions: Mathematics, Physics and Philosophy|pages=231-280|publisher=Springer|doi=10.1007/978-1-4020-5195-1_8}}; Covering the criticism of Gehrcke starting with 1912; discussion between Einstein and Gehrcke in 1914; Einstein's dialogue (1918) as response to antirelativists; the Weyland event in 1920 and Einstein's response.</ref> <ref name=weiss>Weiss, W. (Physics FAQ): [https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html The Twin Paradox: The Equivalence Principle Analysis]</ref> <ref name=cuvaj>{{Citation |author=Cuvaj, C. |date=1971 |title=Paul Langevin and the theory of relativity|journal=Japanese studies in the history of science|volume=10| pages=113-142|url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf}}</ref> <ref name=koks>Koks, D. (2018): [https://math.ucr.edu/home/baez/physics/Relativity/SR/sr-gr.html Physics FAQ: Where is the Boundary between Special and General Relativity?]</ref> </references> [[Category:History of special relativity]] [[Category:Paradoxes]] qpi905845t6b6s8w647dylknn0ivc27 2834526 2834525 2026-09-26T08:00:39Z D.H 52339 Wording 2834526 wikitext text/x-wiki {| style="width:20%; font-size:13px;" align=right |{{../Other Topics (header)}} |} ==Early history of the twin paradox== {{Lorentzbox|Text={{center|Date of article creation: 9 November 2023; Last major revision: 26 September 2026}}}} a) When was the [[:w:twin paradox]] applied to life forms and human beings? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /><ref group=S name=during /> report that {{slink||Einstein 1911-HU}} discussed the aging of living organisms, and that {{slink||Langevin 1911-HU}} and {{slink||Wiechert 1911-HU}} explicitly discussed the aging of human beings. :*More details in sections {{slink||Human beings in 1911|Twins from 1911 to 1920}}, including newspaper articles from 1911 written by {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}} that clearly show that Einstein was the first to explicitly discuss the aging of human beings as well. b) Who was the first to formulate the principle of maximal proper time along straight worldlines, upon which differential aging in the standard twin paradox is based? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> mention Langevin (1911), Laue (1911). :*More details in section {{slink||Maximal proper time}} with the contributions of Langevin (1911), Wiechert (1911), Study (1911), Laue (1911-13). c) Who was the first to formulate [[w:Triangle inequality#Reversal in Minkowski space|inverse triangle inequality]] in Minkowski space, which represents the simplest version of the twin paradox? :*See details in section {{slink||Triangle inequality}} with the contributions of Robb (1914-20), Eddington (1922), Rogers (1922). d) Who was the first to show that any influence of proper acceleration on clocks can be neglected in the computation of the twin paradox from the viewpoint of the stay-at-home twin? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Einstein (1911), Laue (1913). :*More details in section {{slink||Negligibility of proper acceleration}} with the contributions of Einstein (1911), Wiechert (1911), Laue (1913), Lorentz (1913). e) Who was the first to introduce the three clock/brother example that completely removes acceleration from the clock/twin paradox? :*Historical accounts<ref group=S name=debs /><ref group=S name=alizzi /> date it back to Lange (1927) and Lord Halsbury (1957). :*More details in section {{slink||Relay (three brothers) experiment}} with the contributions of Grünbaum (1911) and Wiechert (1920-22). f) Who was the first to use acceleration as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref name=cuvaj group=S /><ref group=S name=pes /> mention Langevin (1911), Einstein (1918). :*More details in section {{slink||Acceleration as asymmetry indicator}} with the contributions of Langevin (1911), Sommerfeld (1913), Lorentz (1913), Einstein (1914-20). g) Who was the first to use different frame distribution as asymmetry indicator as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Laue (1911-13). :*More details in section {{slink||Frame distribution as asymmetry indicator}} with the contributions of Laue (1911-13), Bloch (1918). h) Who was the first to describe the perspective of the traveler? :*Historical accounts<ref group=S name=miller /><ref group=S name=beng /> mention Langevin (1911), Lorentz (1914), Einstein (1918). :*More details in section {{slink||Perspective of the traveler}} with the contributions of Langevin (1911), Lorentz (1913-14), Einstein (1918), Thirring (1921). i) Who was the first to describe a round-trip experiment in curved spacetime? :*See section {{slink||Curved spacetime}} with the contribution of Becquerel (1922). j) Who was the first to interprete the twin paradox in terms of an aether or absolute space? :*See section {{slink||Aether interpretations}} with the contribution of Langevin (1911), Wiechert (1911), Lechalas (1912). k) Who was the first to denote the round-trip experiment as paradoxical? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> point to Laue (1911). :*See section {{slink||Paradoxical?}} for details. l) Who was the first to misunderstand the twin paradox? :*See section {{slink||Misunderstandings}} with the contributions of Berg (1910), Wiechert (1911), Campbell (1911/12), Gruner (1912). m) What were Einstein's contributions? :*See section {{slink||Einstein's contributions}}. ==Human beings in 1911== {| class="wikitable" style="background-color:white;{{text default color}};" ![[w:Albert Einstein|Einstein]] |- |{{anchor|Einstein 1905}}In 1905<ref name=einstein05 /> he showed that a clock moving on a round-trip away from A and back along a polygonal or curved path, is retarded with respect to a clock stationary at A by approximately <math>\tfrac{1}{2}t(v/V)^{2}</math> at reunion. For example, a clock on the equator is retarded with respect to a clock on the pole. He described this consequence as being "peculiar" (German: eigentümlich). {{anchor|Einstein 1911-HU}}In a lecture given on January 1911<ref name=einstein11a /> (published in November), he extended this "funny" (German: drollig) experiment to living organisms: {| ! width=55% | Einstein wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Wenn wir z. B. einen lebenden Organismus in eine Schachtel hineinbrächten und ihn dieselbe Hin- und Herbewegung ausführen lassen wie vorher die Uhr, so könnte man es erreichen, dass dieser Organismus nach einem beliebig langen Fluge beliebig wenig geändert wieder an seinen ursprünglichen Ort zurückkehrt, während ganz entsprechend beschaffene Organismen, welche an den ursprünglichen Orten ruhend geblieben sind, bereits längst neuen Generationen Platz gemacht haben. Für den bewegten Organismus war die lange Zeit der Reise nur ein Augenblick, falls die Bewegung annähernd mit Lichtgeschwindigkeit erfolgte! | style="padding: 0px 20px 0px 20px;" |For example, if we put a living organism in a box and make it undergo the same back and forth movement as the clock before, we could achieve that this organism returns to its original location with arbitrary little change after a flight of arbitrary length, whereas completely identical organisms that remained at rest in the original location have long since made room for new generations. To the moving organism, the long journey was only a moment if the movement happened close to the speed of light! |} {{Lorentzbox|Text=Two participants of that lecture, {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}}, report that Einstein also talked about the aging of ''human beings''.}} |- !{{anchor|Lämmel 1911-HU}}[[w:Rudolf Lämmel|Lämmel]] |- |He attended Einstein's 1911 lecture and gave a popular report about it in the Swiss newspaper "[[w:Neue Zürcher Zeitung|Neue Zürcher Zeitung]]" published on 28 April 1911,<ref name=lammel /> including additional details. Regarding the round-trip clock experiment he wrote: {| ! width=50% | Lämmel wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bewegt sich eine Uhr mit Lichtgeschwindigkeit längs einer Geraden, auf der gerichtete Uhren stehen, so scheint die bewegte Uhr, beurteilt vom Standpunkt der ruhenden aus, im oben stizzierten Sinn, stillzustehen. Kehrt die Uhr, nach einem Ruck, mit Lichtgeschwindigkeit wieder zurück zur Zentral-Uhr, so ist, nach Einstein, für den Beobachter bei der Zentral-Uhr die Sache so, als ob ein mit der bewegten Uhr mitgeführter Beobachter (samt dessen Uhr) nicht gealtert hätte. Hinge also des letzteren Alter von den Angaben des ruhenden Beobachters ab, so könnte der von einer großen Reise ins Weltall zurückkehrende Beobachter bei der Zentral-Uhr spätere Generationen antreffen – er selber hätte nicht gealtert. Welche Bedeutung diese ''ad absurdum'' geführte Gedankenspielerei etwa hat, läßt sich heute nicht absehen – vielleicht, ja wahrscheinlich ist sie ohne jeden Einfluß auf die tatsächlichen Verhältnisse. Aber man sieht dabei immerhin, daß die Physik imstande ist, die kühnsten Träume der Phantasie noch – zu überbieten. | style="padding: 0px 20px 0px 20px;" |Let a clock be moving at speed of light along a line on which regulated clocks are standing, then the moving clock's hand appears to be standing still (in the sense described above) as judged from the standpoint of the resting one. If the clock, after one jolt, comes back with light speed to the central clock, then according to Einstein the matter presents itself to the observer at the central clock, as if the observer comoving with the clock (together with his clock itself) hasn't been grown older. Thus if the age of the latter would depend on the indications of the resting observer, the observer returning from a great journey into space could meet later generations at the central-clock – he himself hasn't been grown older. The importance of this play of thought led ''ad absurdum'' cannot be seen today – maybe, or even probably, it is without any influence on the actual situations. Though at least one can see that physics is able to – surpass – even the boldest dreams and fantasies. |} Lämmel in December 1920 (published 1921)<ref name=lammel2 /> again alluded to Einstein's lectures in Zürich (possibly the one from 1911, and maybe also later ones), describing a discussion between himself and Einstein. After Einstein concluded that the travelers who came back after their journey will probably meet their former contemporaries as old men while they themselves could have been away for only a few years, Lämmel objected that this conclusion is only drawn with respect to rods and clocks, but not with respect to living beings. Einstein responded though, that all processes in the blood, in the nerves etc. are eventually periodical oscillations, i.e. motions. Yet to any such motion the relativity principle applies, thus the conclusion regarding the unevenly rapid aging it permissive. {{Lorentzbox|Text=While the official publication of Einstein's January lecture ({{slink||Einstein 1911-HU}}) mentions the aging of organisms, Lämmel recalls the reference to the aging of a human space traveler ("observer returning from a great journey into space"). This means that Einstein was the first to use human beings in the clock/twin paradox on January 16 which was first published by Lämmel on April 28, 1911. In comparison, {{slink||Langevin 1911-HU}} used space travelers in a lecture on April 10 with publication in July, and {{slink||Wiechert 1911-HU}} used space travelers in lectures held between March 25 and May 23 with publication in July/September. It seems very unlikely that before April 28, Lämmel became somehow aware of the content of Langevin's or Wiechert's lectures held a few weeks earlier, in order to use them in his description of Einstein's lecture.}} |- !{{anchor|Langevin 1911-HU}}[[w:Paul Langevin|Langevin]] |- |On 10 April 1911, published July 1911,<ref name=langevin1 /> he held a now famous lecture popularizing the clock/twin paradox which he derived from the proper time integral as described in {{slink||Langevin 1911-PT}}. He demonstrated that a moving radioactive sample of radium is less evolved and less aged and therefore more active at return then the ones that remained in the laboratory. He also used light signals and the Doppler effect to visualize the effect. The most famous part concerned his description of the aging of human space travelers: {| ! width=50% | Langevin wrote ! [[:s:Translation:The Evolution of Space and Time|English Wikisource translation]] |- | style="padding: 0px 20px 0px 20px;" |Cette remarque fournit le moyen, à celui d’entre nous qui voudrait y consacrer deux années de sa vie, de savoir ce que sera la Terre dans deux cents ans, d’explorer l’avenir de la Terre en faisant dans la vie de celle-ci un saut en avant qui pour elle durera deux siècles et pour lui durera deux ans, mais ceci sans espoir de retour, sans possibilité de venir nous informer du résultat de son voyage puisque toute tentative du même genre ne pourrait que le transporter de plus en plus avant. Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse. Revenu à la Terre ayant vieilli de deux ans, il sortira de son arche et trouvera notre globe vieilli de deux cents ans si sa vitesse est restée dans l’intervalle inférieure d’un vingt-millième seulement à la vitesse de la lumière. Les faits expérimentaux les plus sûrement établis de la physique nous permettent d’affirmer qu’il en serait bien ainsi. | style="padding: 0px 20px 0px 20px;" |This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. |} {{Lorentzbox|Text=Reading his lecture in full, one finds the word "paradoxical" only in relation to the constancy of light speed, not on relation to the round-trip clock experiment.}} |- !{{anchor|Wiechert 1911-HU}}[[w:Emil Wiechert|Wiechert]] |- |In lectures on 25 March and 23 May 1911, submitted July and published September 1911,<ref name=wiechert11 /> he described the round-trip clock experiment with two equal clocks regulated to the same rate and brought to the same pointer position, or by introducing the same chemical process two times, or by introducing ''two life forms that began their life at the same time''. At the end of his paper he applied this to human travelers: {| ! width=50% | Wiechert wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Nehmen wir aber wieder eine Relativgeschwindigkeit an, die bis auf 3 Proz. der Lichtgeschwindigkeit nahekommt, dann wird das Verhältnis der empfundenen Zeitlängen wie 4:1. Das Bild mag etwas weiter noch ausgemalt werden. Denken wir uns, daß ein Beobachter durch den Raum unseres Sternhimmels mit dieser Geschwindigkeit in einer Kreisbahn mit einem Radius von 16 Lichtjahren fährt, dann wird er nach unserer Zeitrechnung nach je 100 Jahren wieder an unserem Sonnensystem vorüberkommen. In seinem Gefährt wird dabei die Zentrifugalkraft so auf ihn einwirken, daß sie gemäß den Relativitätsgesetzen der Einwirkung der Schwerkraft auf uns Erdenbewohner gleich erscheint. Es sind also die wirkenden Kräfte nur so groß, daß der Phantasie die Möglichkeit geboten wird, den Reisenden als menschliches Wesen zu denken. Da hier dauernd <math>\sqrt{1-v^{2}/c^{2}}</math> ist, fließt die Eigenzeit für den Reisenden viermal langsamer dahin, als für die Bewohner der Gestirne. Wenn er also nach 100 unserer Jahre wieder zu unserem Sonnensystem zurückkehrt, wird er sich selbst nur um 25 Jahre gealtert fühlen. Erreicht er nach der Entwicklung seines Körpers und nach seiner Zeitempfindung ein Alter von 75 Jahren, so entspricht dies doch einer dreimaligen Wiederkehr zu unserem Sonnensystem, also 300 unserer Erdenjahre. | style="padding: 0px 20px 0px 20px;" |Yet if we again assume a relative velocity approximating the speed of light by 3 percent, then the ratio of the experienced duration of time becomes 4:1. This image can be further extended. Let's imagine that an observer travels with that velocity on a circular path at a radius of 16 light years through the space of our galaxy, then according to our time calculation he passes by our solar system every 100 years. In his vehicle the centrifugal force will act on him in such a way, that in accordance with the relativity laws it will appear to be equal to the force of gravity acting upon the inhabitants of Earth. Thus the acting forces are only thus big, in order to give our fantasy the possibility to imagine the traveler as a human being. Since we have <math>\sqrt{1-v^{2}/c^{2}}</math> throughout, proper time flows four times slower for the traveler than for the inhabitants of the stars. Thus when he comes back to our solar system after 100 of our years, he will feel to have aged only by about 25 years. If he reaches an age of 75 years according to the development of his body and his own time experience, then this corresponds to a threefold return to our solar system, i.e. 300 of our Earth years. |} {{Lorentzbox|Text=a) Wiechert (1915)<ref name=wiechert15 /> later provided a short historical survey of the clock/twin paradox. He referred to the fact that already {{slink||Einstein 1905}} considered the case of two clocks ("Einstein's clock experiment"), and even though [[w:Hermann Minkowski|Minkowski]] himself didn't consider the case, his proper time formula provides the result in a straight forward manner. The latter was done by himself in lectures on 25 March and 23 May 1911, as well as by Langevin published in July 1911. Wiechert pointed out that he himself and Langevin used "humorist" examples in order to clarify the situation: While Wiechert argued that one has to make a journey in order to stay young, Langevin argued that one has to romp about in a laboratory in order to stay young. Both of them used human beings, arguing that their physical and mental life should have been influenced in the same way as any other process in nature. b) The dates given by Wiechert (1915) are not complete. The correct ones are: *Langevin's lecture on 10 April 1911, published in July. *Wiechert's lectures on 25 March and 23 May 1911, submitted on July 26, published in September. *He was still unaware of Einstein's lecture from January 1911, published in November 1911.}} |- !{{anchor|Müller 1911-HU}}[[w:Fritz Müller-Partenkirchen|Müller]] |- |The freelance writer and law student Fritz Müller (who was later known as [[w:Fritz Müller-Partenkirchen|Müller-Partenkirchen]]) attended Einstein's lecture and wrote a popular report about it in the German newspaper "[[w:Berliner Tageblatt|Berliner Tageblatt]]" on 16th and 23rd October 1911,<ref name=muller /> in which he gave further details (compare with {{slink||Lämmel 1911-HU}}). Regarding the clock/twin paradox he wrote: {| ! width=50% | Müller wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Zwei gleichgehende Uhren sollen je einen Beobachter haben und nebeneinander ruhen. Nun soll die eine mit ihrem Beobachter plötzlich mit Lichtgeschwindigkeit in den Weltenraum hinausreisen. Vorher haben die beiden vereinbart, sich alle Sekunden mit einem Lichtsignal die Zeit zu telegraphieren. [...] In unserem Grenzfall, wo die Reise mit Lichtgeschwindigkeit vor sich geht, müßte der ruhende Beobachter erklären, jene andere Uhr käme in der Zeit überhaupt nicht voran. Die Zeit stünde dort still. Tatsächlich kommen die Einsteinschen Gleichungen zu diesem Resultat. Für den mit der Uhr reisenden Beobachter, sagt Einstein, gelte dasselbe. Das heißt, im Urteil des Zurückbleibenden würde jener niemals alt. „Und wenn er auf einer gebrochenen Reiselinie wieder an seinen Ausgangspunkt zurückkehrte?" fragt man den Vortragenden in der Diskussion. – „So bliebe er in unserem Urteil so jung wie bei der Ausreise," erwidert Einstein mit vollem Ernst, „selbst wenn wir Zurückgebliebenen inzwischen Männer mit weißen Bärten geworden sind – die Gleichungen liefern für jede Richtung der Bewegung, auch für eine gebrochene Bewegung, unerschütterlich die selben Resultate." – Wir sehen einander an. Das klingt märchenhaft. Märchenhaft? Gewiß, die alten Märchen vom Mönch von Heisterbach, vom Rip van Winkle, von Urashima Taro steigen auf. Merkwürdig, wie die Volksphantasie bei den Deutschen, bei den Amerikanern, bei den Japanern in der gleichen Richtung gearbeitet hat – alle drei Märchen erzählen ja von Leuten, deren Leben still steht, viele hundert Jahre lang, während die andern altern. So fanden sie bei ihrer Rückkehr ein anderes Land und eine andere Generation. | style="padding: 0px 20px 0px 20px;" |Two synchronous clocks at rest next to each other, shall each be accompanied by an observer. Now one of them, together with its observer, suddenly travels into space at the speed of light. Previously, both have arranged that every second they telegraph their time to each other using light signals. [...] In our limiting case where the journey happens at light speed, the resting observer would have to declare that the other clock would not proceed in time at all. Time would stand still at this place. Einstein's equations indeed produce this result. As to the observer traveling with the clock, says Einstein, the same is true. That means in the judgment of the remaining one, the other one would never become old. Then the lecturer [i.e. Einstein] was asked in the discussion: "And if he comes back to his starting point on a curved travel path?", to which Einstein replied in full earnest: "Then in our judgment he would remain as young as he was at departure, even if we remaining ones became men with white beards in the meantime, the equations unshakably give the same result in every direction of motion, also for curved motion". We look at each other. That sounds fabulous. Fabulous? Of course, the old fairy tales of [[w:Heisterbach Abbey|w:The monk of Heisterbach]] or [[w:Rip Van Winkle]] or [[w:Urashima Tarō]] come forward. Strange, how the folk fantasy of the Germans, the Americans, the Japanese worked in the same direction, all three fairy tales indeed tell about people whose life stands still, many hundred years long, while the other ones grow old. Thus they found another country and another generation when they returned. |} {{Lorentzbox|Text=Müller's account confirms {{slink||Lämmel 1911-HU}} that Einstein indeed mentioned human beings, but his description also suggests that Einstein was the first to use mutually sent light signals. However, as this was published in October, it cannot be excluded that Müller's description of light signals was influenced by {{slink||Langevin 1911-HU}}, published in July, in which light signals were used as well.}} |} ==Twins from 1911 to 1920== We now provide a list of authors who employed ''twins'', i.e. ''two'' life forms or humans that initially were of ''same age'' when the round-trip began: {| class="wikitable" style="background-color:white;" |- ! Author !! Date !! Description |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> |1911 |Two life forms that begin their life at the ''same time'' (German: "Zwei Lebewesen [..] die ihr Leben gleichzeitig beginnen"), of which the moving one returns retarded in its progression with respect to the stationary one. |- |[[w:Paul Gruner|Gruner]]<ref name=gruner /> |1912 |Two persons of ''same age'' (French: "deux personnes du même âge"), of which the moving one returns less developed than stationary one. |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> |1913 |The moving life form returns younger than its ''former agemates'' (German: "ehemaligen Altersgenossen"). |- |[[w:Hermann Weyl|Weyl]]<ref name=weyl /> |Easter 1918 | {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Von zwei Zwillingsbrüdern, die sich in einem Weltpunkt A trennen, bleibe der eine in der Heimat (d. h. ruhe dauernd in einem tauglichen Bezugsraum), der andere aber unternehme Reisen, bei denen er Geschwindigkeiten (relativ zur »Heimat«) entwickelt, die der Lichtgeschwindigkeit nahekommen; dann wird sich der Reisende, wenn er dereinst in die Heimat zurückkehrt, als merklich jünger herausstellen denn der Seßhafte. |Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. |} {{Lorentzbox|Text=Weyl was the first to ''explicitly use twins'' in relation to the round-trip experiment. The fourth edition (1920) of that book was translated from German into English and French in 1922.}} |- |[[w:Albert Einstein|Einstein]]<ref name=einstein20 /> |1920/21 |{{Anchor|Einstein 1921-TW}} {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Trifft A wieder bei B ein, so kann es sich ereignen, daß der beharrende Zwilling inzwischen 60 Erdjahre alt geworden ist, während der zurückkehrende nur 15 Jahre zählt, oder sich gar noch im Säuglingsstadium befindet. [..] Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls -Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. |If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still. [..] In the case of these two twins, Einstein declared, we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures. |} {{Lorentzbox|Text=This was based on an interview of Einstein by Moszkowski. While the expression "clock paradox" was used since 1911/12 (see section {{slink||Paradoxical?}}), this seems to be the first time that it was rebranded as "twin paradox". The copyright mark indicates 1920, while the title page indicates 1921. The translation from German into English also appeared in 1921.}} |} ==Maximal proper time== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]] 1911 |{{anchor|Langevin 1911-PT}}In April 1911 (published July),<ref name=langevin1 /> he described the round-trip experiment without formulas using two portions of matter present at two events happening at the same place. The ''integration of proper time'' along the entire wordlines shows that the portion of matter that starts a closed cycle by receding and finally coming back, will have a ''smaller proper time'' than the one that stayed behind. In October 1911 (published 1912),<ref name=langevin2 /> Langevin again showed that the portion of matter that described a closed cycle will have a ''smaller proper time'' <math>R</math> than the one that stayed in an inertial frame, which is defined by the equation: :<math>\begin{matrix}V^{2}\left(t-t_{0}\right)^{2}=d^{2}-R\\ \left[d^{2}=\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}\right] \end{matrix}</math> |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> Lectures March-May 1911 submitted July published September |{{anchor|Wiechert 1911-PT}}Let two equal processes be observed in two equal material systems colocated in two moments (1) and (2), and let there velocities have been changed in arbitrarily different ways in the meantime. It follows that the ratio of advancement of those processes is given by the two intervals <math>\Delta\tau </math> of their respective ''proper times''. He concluded that any round-trip clock experiment can be easily comprehended from that theorem by computation. The corresponding integral is: :<math>\Delta\tau=\int_{1}^{2}d\tau=\int_{1}^{2}dt\sqrt{1-\frac{\mathfrak{v}^{2}}{c^{2}}}</math> |- |[[w:Eduard Study|Study]]<ref name=study /> June 1911 |Minkowski's concept of worldlines implies that the straight path between two points of the same worldline is the ''longest'' among all paths between those points, if the path length on a worldline is defined by the related proper time. {{Lorentzbox|Text=Study's book was purely mathematical without mentioning clocks or the round-trip experiment, alluding to his result only in a footnote.}} |- |[[w:Max von Laue|Laue]] 1911-13 |{{anchor|Laue 1911/12-PT}}In December 1911 (published 1912),<ref name=laue1 /> Laue showed without formulas that the round-trip experiment is represented by a curved worldline, which at worldpoint A decomposes into a row of curves, after which all of them will be re-united at worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the ''longest proper time.'' {{anchor|Laue 1912/13-PT}}In December 1912 (published 1913) in the second edition of this relativity book,<ref name=laue1 /> Laue described the proper time integral between events 1 and 2 of a slowly accelerated clock covering a broken line and a stationary clock covering a straight worldline. Of all worldlines covering 1 and 2, the straight line has the ''longest proper time''. Therefore the traveling clock in the round-trip experiment is retarded at reunion, because its curved worldline corresponds to a shorter proper time. This result he presented in terms of the following inequality, of which the right-hand side refers to the straight curve of the stationary clock, while all others possible curves are represented on left-hand side: :<math>\tfrac{1}{c}\int_{1}^{2}\sqrt{du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}<\tfrac{1}{c}\int_{1}^{2}du</math> {{Lorentzbox|Text={{anchor|Sommerfeld 1913-PT}}Similar treatments can be found in the textbooks of [[w:Arnold Sommerfeld|Sommerfeld]] (1913),<ref name=sommerfeld /> [[w:Hermann Weyl|Weyl]] (1918),<ref name=weyl /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Jean Becquerel|Becquerel]] (1922).<ref name=becqu1 />}} |} ==Triangle inequality== {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Alfred Robb|Robb]] 1914-1920 |{{anchor|Robb 1914-TR}}In 1914<ref name=robb1 /> he showed that there are three types of triangles formed by intervals in Minkowski space, depending on whether one deals with "separation lines" (spacelike intervals), "optical lines" (lightlike intervals), or "inertia lines" (timelike intervals representing the path of nonaccelerated particles defined by <math>{\scriptstyle \left(x_{1}-x_{0}\right)^{2}+\left(y_{1}-y_{0}\right)^{2}+\left(z_{1}-z_{0}\right)^{2}-c^{2}\left(t_{1}-t_{0}\right)^{2}<0}</math>). As to a triangle formed by inertia lines, he showed that the sum of a certain two sides is ''less'' than that of the third one. {{Lorentzbox|Text=So the triangle inequality derived from time-like intervals in Minkowski space is ''[[w:Triangle inequality#Reversal in Minkowski space|inverse]]'' to the inequality in Euclidean space. This inverse inequality directly represents the most simple variant of the twin paradox: the traveler follows two sides of the time-triangle, while the stay-at-home observer follows the third side indicating maximal proper time.}} [[File:RobbTriangle.svg|right|150px]] In 1920<ref name=robb2 /> Robb gave a numerical example of the triangle ABC with time-like intervals ("inertia lines") defined by coordinates :<math>\begin{matrix} & x & y & z & t\\ A\ & 0 & 0 & 0 & 0\\ B\ & 0 & 0 & 0 & 10\\ C\ & 4 & 0 & 0 & 5 \end{matrix}</math> which he plugged into :<math>\bar{s}^{2}=\left(t_{1}-t_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}-\left(y_{1}-y_{0}\right)^{2}-\left(z_{1}-z_{0}\right)^{2}</math> from which he obtained the sides AB=10, AC=3, CB=3 and the inequality <math>AC+CB<AB</math>. |- |[[w:Arthur Eddington|Eddington]]<ref name=edding2 /> 1922 |He distinguished between the "space-triangle" for spacelike intervals, and the "time-triangle" for time-like intervals. The latter is measured with a clock from A to B and from B to C, with the sum of those readings ''is always less'' than the reading of a clock measuring directly from A to C. In the ordinary space-triangle any two sides are together greater than the third side; in the time-triangle two sides are together ''less'' than the third side. |- |Rogers<ref name=rogers /> 1922 |He showed that the "pure time-triangle" C, A, B (in their proper time order) satisfies the relation <math>\cosh C=\tfrac{\alpha^{2}+\beta^{2}-\gamma^{2}}{2\alpha\beta}</math>, where <math>\cosh C</math> denotes the unit-scalar product of the vectors CA, CB, and <math>\alpha,\beta,\gamma </math> the real and positive intervals BC, CA, AB. Since <math>\alpha>\beta </math> and <math>\cosh C>1</math>, it follows that <math>\alpha>\beta+\gamma </math>. That is, "the greatest side of pure time-triangle is greater than the sum of the other two sides". It follows at once that the stationary value of the proper time integral is an "absolute maximum". |} ==Negligibility of proper acceleration== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |style="vertical-align:top" |[[w:Albert Einstein|Einstein]] 1905-1918 |In 1905,<ref name=einstein05 /> Einstein used velocity time dilation <math>\tau=t\sqrt{1-\left(\frac{v}{V}\right)^{2}}</math> to derive the retardation of a clock performing a round-trip with constant speed <math>v</math> along a polygonal path or a continuously curved line, without mentioning any influence of acceleration at turnaround. {{anchor|Einstein 1911-VA}} In 1911 (published 1912),<ref name=einstein3 /> Einstein said that special relativity doesn't say anything about what happened to the clock's pointer position during the acceleration that changes the clock's direction along the round-trip, yet the influence of this change must be getting smaller the longer the clock ''is moving uniformly'', i.e. the longer one chooses the dimensions of the path. {{anchor|Einstein 1912-VA}}In an unpublished manuscript on special relativity from 1912,<ref name=einst12manu /> he pointed out that any influence of acceleration during the round-trip experiment, can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygonal path. {{anchor|Einstein 1914a-VA}}In a letter from April 1914,<ref name=einstpetz /> Einstein showed that any ''finite'' acceleration at turnaround during the round-trip experiment can only influence the clock in a ''finite'' way, thus it can be neglected by minimizing the time of acceleration with respect to the time of uniform translation. So it ''must be concluded'' that the clock is retarded at reunion after traveling on a polygonal path. {{anchor|Einstein 1914b-VA}}During a conversation in May 1914,<ref name=rowe group=S /> Einstein is reported to have replied that the accelerations during the round-trip are "irrelevant for the amount of the time difference". (Compare with {{slink||Einstein 1914b-AC}}) {{anchor|Einstein 1918-VA}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918,<ref name=einstein18 /> Einstein pointed out that any effect of velocity changes at turnaround must be limited, thus the traveling clock must be retarded at reunion due to time dilation if one makes the path AB and back along the round-trip long enough. (Compare with {{slink||Einstein 1918-AC}}) |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> 1911 |{{Anchor|Wiechert 1911-VA}}[[File:WiechertTwin.svg|110px|right]] He demonstrated that differential aging along the round-trip cannot be caused during the passage from one velocity to another (i.e. acceleration) at turnaround, because the same result also follows when ''both'' A and B experience the ''same velocity changes'' with respect to another frame, only with the difference that B has relative velocities <math>+u</math> and <math>-u</math> for a long time, while A is brought after a short time from relative velocity <math>+u</math> to relative rest at which it remains a long time, and then it is brought to relative velocity <math>-u</math> for a short time. {{Lorentzbox|Text=He was probably the first to use an example in which both accelerate with same magnitude.}} |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> 1913 |{{anchor|Laue 1913-VA}}He showed that the problem of the influence of acceleration at turnaround in the round-trip experiment, can be eliminated by ''arbitrarily'' enlarging the time in inertial motion. {{Lorentzbox|Text=This is the same argument as given in {{slink||Einstein 1911-VA}}. The Einstein-Laue argument was also used by others such as [[w:Hans Thirring|Thirring]] (1921)<ref name=thirring /> or [[w:Max Born|Born]] (1921).<ref name=born />}} |- |[[w:Hendrik Lorentz|Lorentz]]<ref name=lorentz1 /> 1913 |He pointed out that any effect of acceleration on the traveling clock at turnaround, can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip. {{Lorentzbox|Text=Similarly, [[w:Wolfgang Pauli|Pauli]] (1921) stated that the arising infinitesimal accelerations at turnaround are certainly independent of the total travel time and ''therefore easy to eliminate''.<ref name=pauli />}} |} ==Relay (three brothers) experiment== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:de:Fritz Grünbaum (Physiker)|Grünbaum]]<ref name=gbaum /> 1911 |He discussed a one-way time dilation experiment in which the first clock is set into motion from the origin and then moving to the second clock. He argued that one can avoid the problem of acceleration experienced by the first clock when set into motion, by replacing it with a ''third'' clock that is already in motion with constant velocity and is synchronized at the origin with the first clock. {{Lorentzbox|Text=While Grünbaum didn't discuss round-trip experiments, his introduction of a third clock in order to avoid acceleration is the basis of the three-brother experiment.}} |- |style="vertical-align:top"|[[w:Emil Wiechert|Wiechert]] 1920-1922 |In 1920 (published 1921),<ref name=wiechert20 /> Wiechert explained how to completely remove acceleration from the round-trip experiment: Bodies A, B, C move undisturbed and non-accelerated in different directions. A and B pass each other at time (1), B and C pass each other at a later time (2), and C and A finally pass each other at an even later time (3). So in this setup, the condition of C is the continuation of the condition of B. On any of the three bodies one can count the oscillations of light of a certain spectral-line, in which case relativity predicts that the ''combined sum of all oscillations'' on B+C is smaller than the number of oscillations on A alone. Wiechert also held that one can replace the light oscillations by the life functions of human-like beings which live on A, B and C. For instance, while the inhabitants of B+C only had time for one meal, there were arbitrarily many generations on A who follow after each other by death and birth. [[File:Wiechert1922a.png|180px|right]] In 1921 (published 1922),<ref name=wiechert21 /> Wiechert extended his previous acceleration-free round-trip experiment to an arbitrary number of non-accelerated bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., which constitutes a "relay" (German: Stafette) starting from body A and back again. The first B passes A and moves away, and after some time the last B comes back to A. Since any B body continues the fate of the previous one, all bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., combined have emitted fewer oscillations than A alone during the relay race. Wiechert pointed out that instead of light oscillations one can also choose the aging of life forms. {{Lorentzbox|Text=Such relay experiments were later independently rediscovered in English language papers<ref name=debs group=S /> such as by Lange (1927)<ref group=S name=lange /> in which the brothers synchronize their times when they pass each other (“three brother experiment”).}} |} ==Acceleration as asymmetry indicator== While it was known that any direct influence of [[w:proper acceleration]] on clocks can be neglected in the computation of the inertial frame of the stay-at-home twin (see previous section {{slink||Negligibility of proper acceleration}}), the very fact that only one of them is accelerating is still useful as an asymmetry argument in order to show that there is no contradiction to the relativity principle. {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{Anchor|Langevin 1911-AC}}He derived differential aging in the round-trip experiment using the proper time integral along worldlines (see {{slink||Langevin 1911-PT}}) and used acceleration as an asymmetry indicator: The result of the round-trip experiment is "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". |- |[[w:Arnold Sommerfeld|Sommerfeld]]<ref name=sommerfeld /> 1913 |After he showed (see {{slink||Sommerfeld 1913-PT}}) that retardation of time in the round-trip experiment derived from the proper time integral rests on the assumption that the clock's rate ''only depends on its momentary velocity'' (now called "clock hypothesis"), he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle since one of the clocks has to be accelerated in order to come back, thus the retardation in the round-trip experiment does not demonstrate "motion", but "accelerated motion". |- |[[w:Hendrik Lorentz|Lorentz]] 1913<ref name=lorentz1 /> |After he derived differential aging in the round-trip experiment from velocity time dilation and pointed out the negligibility of proper acceleration for the computation, he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle, since one of them changes velocity and accelerates; the relativity principle does not require symmetry between inertial and non-inertial observers. |- |style="vertical-align:top"|[[w:Albert Einstein|Einstein]] 1914-1920 |{{anchor|Einstein 1914b-AC}} During a conversation in 1914,<ref name=rowe group=S /> Einstein is reported to have said that moving clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are ''irrelevant'' for the ''amount'' of the time difference, their ''presence'' nevertheless cause B to fall behind ("accelerated motions are absolute"). {{anchor|Einstein 1918-AC}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918<ref name=einstein18 />, Einstein pointed out the negligibility of velocity changes from the viewpoint of an inertial frame (see {{slink||Einstein 1918-VA}}). Then he used ''acceleration as an asymmetry indicator'' in order to show, that there is no contradiction to the relativity principle, because relativity only predicts the equivalence of non-accelerated inertial frames: "only K is such a frame while K' is temporarily accelerated, thus the retardation of U2 with respect to U1 cannot be used to construe a contradiction against the theory." {{anchor|Einstein 1920-AC}}Einstein is reported to have said in an interview from 1920:<ref name=einstein20 /> {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls-Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. Dieser Grund für das Jüngerbleiben des A ergibt sich vom Gesichtspunkt der speziellen Relativitätstheorie aus der Tatsache, daß das betreffende Geschöpf — und nur dieses — Beschleunigungen erlitten hat. | style="padding: 0px 20px 0px 20px;" |In the case of these two twins," Einstein declared, "we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures . This ground, which counts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations." |} In a discussion from 1922,<ref name=morand /> Einstein is reported to have said that there is no contradiction in the round-trip experiment (in terms of a train leaving the station and returning later): The relativity principle is not applicable to this case, because the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two frames having velocities in opposite direction is not an inertial frame. There is no reciprocity between a frame that changes direction and one that doesn't. |} ==Frame distribution as asymmetry indicator== Because any direct influence of proper acceleration on the traveling clock at turnaround can be neglected (see {{slink||Negligibility of proper acceleration}}), the importance of {{slink||Acceleration as asymmetry indicator}} is limited to the mere fact that it reveals that only the traveler was in a non-inertial frame as only he changed his inertial frames, thus instead of emphasizing the occurrence of proper acceleration at turnaround, it's possible to describe the asymmetry more geometrically by emphasizing the different distribution of inertial frames of the twins along their worldlines. {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Max von Laue|Laue]] 1911-1913 |{{Anchor|Laue 1911/12-VA}} In 1911/12,<ref name=laue1 /> he pointed out that during the time of separation, that clock is most advanced which was at rest in an inertial frame all the time; namely there is ''always one, and only one inertial frame'', in which the locations of separation and re-encounter lie in the same geometric point. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1911/12-PT}}). In 1912/13,<ref name=laue2 /> he argued that in the round-trip experiment, we indeed can decide, which one of the clocks was steadily at rest in one and the same reference system, and which one was in the meantime at rest in two or more such systems. Among them there is of course a real physical difference. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1912/13-PT}}). In 1913<ref name=laue3 /> Laue pointed out: {| !style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Aber nach unseren Voraussetzungen ruht während der Zeit der Trennung die erste Uhr in ''einem'' berechtigten Bezugssystem, die zweite hingegen ruht zwar sowohl bei der Hin- wie bei der Rückbewegung in berechtigten Bezugssystemen, aber notwendig in ''zwei verschiedenen. Deshalb'' unterscheiden sich beider Schicksale physikalisch. Ließe man die zweite Uhr in der ihr anfangs erteilten Bewegung und schickte man ihr dafür die erste Uhr nach einiger Zeit mit größerer Geschwindigkeit nach, so würde beim Zusammentreffen die erste gegen die zweite zurückgeblieben sein; denn jetzt hat die erste während der Trennung in zwei verschiedenen Systemen geruht. (Footnote: Dem naheliegenden Einwand, daß wir über den Gang einer Uhr während eines Geschwindigkeits''wechsels'' nichts aussagen können, begegnet man am einfachsten mit dem Hinweis, daß man die Zeiten der gleichförmigen Bewegung ''beliebig'' groß gegen die der Beschleunigung machen kann.) | style="padding: 0px 20px 0px 20px;" | However, by our presuppositions, one clock is at rest in ''one'' valid reference system during the time of separation, while the second one is at rest in valid reference systems both during the forward- and the backward motion, but necessarily in ''two different ones. Therefore'' the two fates differ physically. If the second clock remains in the motion which was given to it at the start, and if after some time it is followed by the first clock with greater velocity, then the first one would be retarded with respect to the second one at the encounter; since now it was the first one that was at rest in two different systems during the separation. (Footnote: The objection which is near at hand, that we cannot say anything about the rate of a clock during a velocity ''change'', can be met most simply by the allusion, that we can render the times of uniform motion ''arbitrarily'' great with respect to acceleration..) |} |- |[[w:Werner Bloch|Bloch]]<ref name=bloch /> September 1918 |{{anchor|Bloch 1918-VA}} He represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. |} ==Perspective of the traveler== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{anchor|Langevin 1911-LI}}[[Image:rstd4.gif|170px|right]] After deriving differential aging from the proper time integral in {{slink||Langevin 1911-PT}} and using human beings in {{slink||Langevin 1911-HU}}, he described the perspectives of both observers using light signals and the Doppler effect. When they separate they see each other live 200 times slower, while at return they see each other live 200 times faster. So ''from the explorer's viewpoint'', in the first year he sees the Earth perform the actions of two days, while in the second year he sees the Earth perform the actions of two centuries. The asymmetry can be seen by noticing, that the observer on Earth in 200 years sees the explorer performs the actions of 1 year. Then the explorer turns around, after which the observer on Earth in 2 days sees the projectile perform the actions of another year. {{Lorentzbox|Text=Langevin used <math>v=c\left(1-\tfrac{1}{20000}\right)</math>, producing Lorentz factor <math>\gamma\approx100</math> and Doppler factor <math>\sqrt{\tfrac{c+v}{c-v}}\approx200</math>.}} |- |[[w:Hendrik Lorentz|Lorentz]] Lectures published in 1913<ref name=lorentz1 /> Similar treatment in 1914<ref name=lorentz3 /> |{{anchor|Lorentz 1913/14-LI}}Described the round-trip experiment in terms of inertial observer A (equipped with clock K) and traveling observer B (equipped with clock K'). In the frame of A, clock K' is retarded with respect to K at reunion due to time dilation. He then described the perspective of the traveling observer B by using two-way propagation of light from K' to K and back to K', leading to three periods defined by the moment of B's turnaround: In the first period the light signals return to K' before turnaround; in the second period the signals are emitted before turnaround and return after turnaround; in the third period emission and return of the signals are both happening after turnaround. Lorentz showed that K is time dilated by a factor of <math>\sqrt{1-v^{2}/c^{2}}</math> with respect to K' in the first and third period, but in the second period K is ticking ''faster'' than K' by a factor of <math>\sqrt{\tfrac{c+v}{c-v}}</math> which overcompensates the dilation in the other periods and explains, even from the perspective of B, why K' is retarded with respect to K at reunion. {{Lorentzbox|Text=In a review of the German translation of Lorentz's book, Einstein (1914) didn't directly mention Lorentz's treatment of the twin paradox, but he wrote that nobody who is seriously interested in relativity should neglect to read that book.<ref name=einstlor /> [[w:Wolfgang Pauli|Pauli]] (1921) refers to Lorentz's book as one of three papers that analyze the twin paradox more closely.<ref name=pauli />}} |- |style="vertical-align:top"| [[w:Albert Einstein|Einstein]] 1916-1920 |{{anchor|Einstein 1916-EP}}In a lecture from 1916,<ref name=einstein16 /> of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of [[w:general relativity]]." {{anchor|Einstein 1918a-EP}}In a letter from September 1918,<ref name=einadl /> Einstein showed that general relativity makes the inertial frame K and and the accelerated frame K' of the clocks in the round-trip experiment "equally justified", explaining the time difference in K' by combining the influence of velocity and gravitational potential on clocks. {{anchor|Einstein 1918-EP}}In his famous "Dialog about Objections against the Theory of Relativity" from November 1918,<ref name=einstein18 /> aimed at clarifying misconceptions of the clock paradox, he explained that there is no paradox in special relativity because there is no symmetry between clock U1 at rest in inertial frame K and clock U2 at rest in accelerated frame K' (see {{slink||Einstein 1918-AC}}). Yet [[w:general relativity]] and the [[w:equivalence principle]] allow the treatment of this problem also from the standpoint of frame K', where clock U2 remains at rest all of the time while U1 makes the following movements: (1) It is accelerated by a homogeneous gravitational field in the negative direction, (2) it moves with constant velocity <math>-v</math>, (3) it is accelerated in the positive direction until it turns around and comes by with constant velocity <math>+v</math>, (4) it moves with velocity <math>+v</math>, (5) it is accelerated in the negative direction until it stops. Clock U1 is retarded with respect to U2 in periods 2) and 4) due to velocity time dilation, but this retardation is overcompensated by the faster rate of U1 during period 3), because U1 is at a higher gravitational potential. He argued that the computation (which he didn't provide) shows that the advance of U1 in period 3) is double its retardation during periods 2) and 4). Einstein concluded that by this consideration "the paradox is completely resolved". Using [[w:Mach's principle]], he pointed out that the gravitational field in K' might be induced by the masses of the universe that are accelerated in this frame. {{anchor|Einstein 1918b-EP}}In a letter to Einstein from December 1918, [[w:Max Jakob|Jakob]] doubted the result that the advance in period 3) is double the retardation during periods 2) and 4). Einstein responded by letter,<ref name=einstein18b /> in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). {{anchor|Einstein 1921-EP}}Einstein is reported to have said in an interview from 1920,<ref name=einstein20 /> that while acceleration explains the age difference between the stationary twin B and the traveling twin A in terms of special relativity (see {{slink||Einstein 1920-AC}}), the "proper" description in terms of general relativity is as follows: {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Eine tiefere Erfassung des Grundes ist indeß nur auf dem Boden der „Allgemeinen Relativitätstheorie" zu erlangen, die uns erkennen läßt, daß von A aus beurteilt ein Zentrifugalfeld existiert, von B aus betrachtet aber nicht; und dieses Feld hat einen Einfluß auf den relativen Ablauf und die Raschheit der Lebensvorgänge. | style="padding: 0px 20px 0px 20px;" | A proper grasp of the reason is furnished only when we adopt the general theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life." |} {{Lorentzbox|Text=a) Einstein's explanation was quickly adopted in the textbooks of [[w:Werner Bloch|Bloch]] (1920),<ref name=bloch2 /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Karl Bollert|Bollert]] (1921),<ref name=bollert1 /> [[w:Max Born|Born]] (1921),<ref name=born /> expressing the view that general relativity is "necessary" to provide the "complete" solution of the twin paradox. b) From a modern standpoint, however, Einstein's explanation has nothing to do with general relativity, but is rather an application of accelerated frames and "pseudo"-gravitational fields to flat Minkowski space of ''special'' relativity.<ref name=weiss group=S />}} |- |[[w:Hans Thirring|Thirring]]<ref name=thirring /> April 1921 |{{anchor|Thirring 1921-DS}}[[Image:Twin Paradox Minkowski Diagram.svg|right|200px]] He described the round-trip experiment by using two platforms K (clock A) and K' (clock B) each equipped with rows of clocks. He first demonstrated the symmetry of time dilation and the mutual relativity of simultaneity on the platforms and its effect on clock synchronization. The K clocks that B passes are all advanced because of <math>t'=\gamma\left(t-vx/c^{2}\right)</math>, and the same is true after turnaround since only the direction of velocity has to be changed in the Lorentz transformation <math>t'-t'_{0}=\gamma\left(t+vx/c^{2}\right)</math> leading to the effect of clock desynchronization, where <math>t'_{0}</math> is a constant depending on which clock one uses as standard for the new synchronization. He graphically showed using Minkowski diagrams, that this simultaneity jump due to desynchronization amounts to double the velocity time dilation during the inertial phases, explaining why A is more advanced than B at reunion. {{Lorentzbox|Text=Using clock B as synchronization standard, Thirring's constant is given by <math>t'_{0}=2l\gamma v/c^{2}=2t\gamma v^{2}/c^{2}</math> with <math>l=vt</math> as position of turnaround. A similar explanation was subsequently given by Langevin (1922).<ref name=morand />}} |} ==Curved spacetime== While the previous examples are defined in flat Minkowski spacetime and therefore can be fully discussed in terms of special relativity, [[general relativity]] is required when [[:w:spacetime curvature]] in the presence of mass and energy cannot be neglected any more.<ref name=koks group=S /> {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |[[w:Jean Becquerel|Becquerel]]<ref name=becqu1 /> 1922 |After defining gravitational time dilation <math>d\tau=\sqrt{1-\tfrac{2GM}{c^{2}r}}dt</math> in terms of the [[w:Schwarzschild metric]] around a material center, he discussed the following round-trip experiment: There are two identical clocks A and B placed next to each other, at a point very far from the material center, initially marking the same time <math>t</math>. Let us transport clock A to a point where the field is more intense, at a distance <math>r</math> from the center; this clock will measure time <math>\int d\tau</math> which is shorter than <math>\int dt</math>, thus it will run more slowly. If we bring clock A back to clock B, we will have to note that it is retarded with respect to B. |} ==Aether interpretations== [[w:Lorentz ether theory]] (LET) is empirically equivalent to special relativity since both models use the Lorentz transformation, thus the description of the twin paradox gives the same result as well. However, special relativity is preferred by the scientific community, because of the validity of the relativity principle in LET is only apparent due to a conspiracy of effects which makes the aether undetecable, and because the measured times and lengths in the aether are supposedly be giving the "true" values even though it is empirically impossible to determine which ones are true or apparent. {| class=wikitable style="background-color:white;{{text default color}};" |- ! style="width:150px" | Author !! Description |- |Langevin (1911)<ref name=langevin1 /> |He argued that it's true that uniform translation with respect to the aether has no experimental meaning in special relativity, though one can still speak of "absolute acceleration" with respect to an aether which he defined as the light carrying medium, so it was "premature to abandon the aether". The absolute nature of acceleration can be seen in the radiation of accelerated charges, as well as in the twin paradox in which the traveler that is more agitated or accelerated is younger at reunion. {{Lorentzbox|Text=Langevin didn't mention this aether interpretation in his later discussions of the twin paradox in 1911/12<ref name=langevin2 /> and 1919.<ref name=langevin3 />}} |- |style="vertical-align:top" |{{Anchor|Wiechert 1911b}}Wiechert (1911)<ref name=wiechert11 /> |Contrary to Langevin, he emphasized that differential aging can be attributed to the existence of absolute "velocities" which he called "strides" (German: Schreitungen, denoting the "absolute meaning" of non-accelerated motions) with respect to the aether, whereas he dismissed the role of accelerations. In other words, the clock's "strides" are not equivalent or anisotropic with respect to the aether, in contradiction to the "unconditional" relativity principle Einstein's which requires equivalence and symmetry. Wiechert proposed a "conditional" relativity principle in which the aether (in the sense of Lorentz) determines all processes in nature, thus the rate of clocks or processes is "really" altered during motion. {{Lorentzbox|Text=a) This aether interpretation was maintained by Wiechert also in subsequent publications in 1915-1922.<ref name=wiechert15 /><ref name=wiechert20 /><ref name=wiechert21 /> b) Wiechert's interpretation in terms of absolute non-accelerated motions was also independently given by others: [[s:fr:Georges Lechalas]] (1912/13)<ref name=lech /> argued that time dilation and asymmetric aging are the result of absolute speeds with respect to an aether, while criticizing Langevin's (1911) argument that only accelerations can indicate the aether and are responsible for the asymmetric aging; [[w:Edward Vermilye Huntington]] (1912)<ref name=hunt /> argued that the "famous paradoxes of the theory of relativity" represented by the reciprocal nature of length contraction and time dilation, appear as necessary consequences of perfectly natural and reasonable conventions for setting clocks and laying out coordinates, when the Lorentz transformation is derived and interpreted on the basis of a stationary aether in the sense of Lorentz. c) Laue (1911/12)<ref name=laue1 /> applauded Wiechert for the "particularly striking way" in which he demonstrated that asymmetric aging indeed follows from the relativity laws, yet he rejected Wiechert's aether interpretation and Wiechert's claim that asymmetric aging contradicts the "unconditional" relativity principle: Laue pointed out that the straight worldline connecting two events A and B is only "preferred" insofar as it indicates the maximal proper time between them, yet this preference is ''not'' the result of the natural laws employed, but is rather due to the choice of points A and B; by analogy, the geometric result that two points determine a straight line and thus a direction as well, doesn't refute the physical equivalence of all directions in space; finally, as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.}} |} ==Paradoxical?== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" | German original of [[w:Max von Laue|Laue]] (1911/12):<ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> ! English translation |- |Unter all den paradox erscheinenden Folgerungen aus der Zeittransformation der Relativitätstheorie gibt es wohl keine, gegen welche sich der natürliche Menschenverstand bei jedem, der der Sache noch ungewohnt ist, so sehr sträubt, wie gegen die, daß die Zeitangabe einer Uhr von ihrem Bewegungszustand abhängen soll. Schon in seiner grundlegenden Arbeit hat Einstein diese Paradoxie auf die Spitze getrieben in einem Gedankenexperiment, welches neuerdings von Langevin in einem auch sonst sehr lesenswerten Vortrage besonders hübsch erläutert worden ist. |Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. |- |colspan=2|{{Lorentzbox|Text=Laue was probably the first to denote the round-trip experiment as paradoxical (even though he pointed out that there are no real contradictions). Subsequently, [[:w:Paul Gruner|Gruner]] (1912)<ref name=gruner /> and others including Einstein (1918)<ref name=einstein18 /> explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas [[w:Rudolf Seeliger|Seeliger]] (1913)<ref name=seel /> spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon").}} |} ==Misunderstandings== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" padding=10 | German original by [[w:Otto Berg (scientist)|Berg]] (1910):<ref name=berg /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |Im Punkte <math>x = 0</math> des Systems S befinde sich eine Uhr, eine andere im Punkte <math>x'=0</math> von S'. Diese zweite bewege sich mit S' bis zum Punkte <math>x = a</math>, kehre dort um und bewege sich nun mit der Geschwindigkeit <math>v</math> zurück bis zum Punkte <math>x= 0</math>. Welche Zeit müssen beide Uhren in dem Moment angeben, wo sie sich wieder treffen? Wir beantworten diese Frage zunächst vom Standpunkt des Beobachters in S. Die Uhr in <math>x' = 0</math> hat sich mit der Geschwindigkeit <math>v</math> bis zum Punkte <math>x = a</math> bewegt; dazu brauchte sie die Zeit <math>\tau=\tfrac{a}{v}</math>. Zum Rückweg ist dieselbe Zeit nötig. Nach der Zeit <math>2\tau=2\tfrac{a}{v}</math> ist die Uhr also wieder im Punkte <math>x = 0</math> angelangt. Wir stellen uns nun auf den Standpunkt des Beobachters in S'. Für diesen führt nach dem Relativitätsprinzip das System S genau dieselben Bewegungen aus wie das System S' für den Beobachter in S, nur in entgegengesetzter Richtung. Die Zeit bis zum Zusammentreffen beider Uhren ist also im System S' ebenfalls gegeben durch <math>2\tau=2\tfrac{a}{v}</math>. Betrachtungen, die auf anschauliche Vorstellungen, wie Nachgehen von Uhren, gestützt sind, führen hier leicht zu Irrtümern, von denen auch die Fachlitteratur nicht frei ist. | style="padding: 0px 20px 0px 20px;" |There is a clock at point <math>x=0</math> of system S, and another one at point <math>x'=0</math> of S'. The second one moves together with S' until point <math>x=a</math>, turns around and now moves back with speed <math>v</math> to point <math>x=0</math>. Which time must both clocks indicate at the moment at which they encounter again? We answer this question at first from the standpoint of the observer in S. The clock at <math>x=0</math> has been moving with speed <math>v</math> until point <math>x=a</math>, for which it required time <math>\tau=\tfrac{a}{v}</math>. The same time is required for the way back. After time <math>2\tau=2\tfrac{a}{v}</math> the clock has thus arrived again at point <math>x=0</math>. Let's now take the standpoint of the observer in S'. In his view in accordance with the relativity principle, system S is conducting exactly the same motions as those of system S' with respect to the observer in S, only in opposite direction. Thus the time until the meeting of both clocks is given by <math>2\tau=2\tfrac{a}{v}</math> in system S' as well. Considerations based on illustrative notions, such as the retardation of clocks, easily lead to mistakes at this place, of which also the professional literature isn't free. |- |colspan=2|{{Lorentzbox|Text=a) Berg was probably the first to turn the relativity principle against asymmetric aging in the round-trip experiment, claiming that both clocks must indicate the same time at reunion. See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem. b) Berg's mistake also seems to be based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" padding=10 | German original by [[w:Otto Lehmann (physicist)|Lehmann]] (1910/11):<ref name=lehm /> ! English translation |- | style="padding: 0px 20px 0px 20px;" | Hat man zwei genau gleich gehende Uhren nebeneinander und bewegt nun die eine auf einer beliebigen Kurve bis wieder zur anderen zurück, welche Bewegung <math>t</math> Sekunden gedauert haben möge, so geht sie gegen diese um <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> oder annähernd <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> Sekunden zu spät, weil sie während der Bewegung auf langsameren Gang reguliert werden mußte, um mit der ruhenden Uhr in Übereinstimmung zu bleiben. | style="padding: 0px 20px 0px 20px;" | If there are two exactly identical clocks next to each other, and if one of them will be moved on an arbitrary curve until it comes back, which may have lasted <math>t</math> seconds, it [the moving clock] will lag behind the other one by <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> or approximately <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> seconds, because it [the moving clock] had to be regulated to a slower rate during motion in order to remain synchronous with the resting clock. |- |colspan=2|{{Lorentzbox|Text=a) So Lehmann erroneously thinks that the time difference at reunion is only the result of "regulating" the moving clock. This implies that he (like Berg) believed that special relativity predicts ''equal'' clock times at reunion if the moving clock would have been left ''unregulated'' during the round-trip. b) Lehmann's mistake (similar to Berg) seems to based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" | German original by [[w:Emil Wiechert|Wiechert]] (1911)<ref name=wiechert11 /> ! English translation |- |colspan=2| Even though he correctly derived differential clock aging in the round-trip experiment, he (like Berg and Lehmann) claimed that effects like time dilation are "apparent" if one admits Einstein's "unconditional" relativity principle in which there is no aether and all "strides" (i.e. non-accelerated motions) are physically equivalent, but they are "real" if one admits the existence of an aether in the framework of a "conditional" relativity principle in which all strides are physically non-equivalent or anisotropic. This led him to the following interpretation of the clock paradox: |- | style="padding: 0px 20px 0px 20px;" |[...] so muß am Schluß des Versuches B in seinem Fortschritt gegenüber A im Verhältnis <math>1:\sqrt{1-u^{2}/c^{2}}</math> zurückgeblieben sein. Und dieses Zurückbleiben ist unbedingt reell, denn die beiden Gebilde A und B können ja unter gleichen Umständen unmittelbar beieinander verglichen werden. Hier ist es ganz sicher ausgeschlossen, an einen Schein zu glauben, der durch unsere Auffassung der Zeit bewirkt wird. So ist denn also auch die Folgerung unabwendbar, daß für den Verlauf der Weltvorgänge die Schreitungen nicht gleichwertig sind, ''und damit sind wir von neuem zu einem Schluß gekommen, welcher der Unbedingtheit des Relativitätsprinzipes durchaus widerspricht.'' [...] Man kann den Versuch noch mannigfach variieren, z. B. so, daß A ebenso wie B zwei verschiedene Schreitungen, <math>+u</math> und <math>-u</math>, nacheinander inne hat. Wird dann zu A der Wert <math>u_{1}</math>, zu B der Wert <math>u_{2}</math>, zugeordnet, so muß der Vergleich von A und B am Schluß des Versuches ergeben, daß B oder A in seinem Fortschritt zurückgeblieben erscheint, je nachdem die Schreitungen <math>+u_{1}</math>, <math>-u_{1}</math>, oder <math>+u_{2}</math>, <math>-u_{2}</math> weiter auseinanderliegen. ''Vielleicht ist gerade diese Formulierung des Satzes besonders geeignet, um die Ungleichwertigkeit der verschiedenen Schreitungen klar und deutlich zu zeigen.'' | style="padding: 0px 20px 0px 20px;" | [...] thus B's progress must be retarded with respect to A's in the ratio <math>1:\sqrt{1-u^{2}/c^{2}}</math> at the end of the experiment. And this retardation is definitely real, since both bodies A and B indeed can be immediately compared side by side under the same conditions. Here it is certainly excluded to believe that this is an appearance due to our conception of time. Thus the consequence is unavoidable too, that the strides are not equivalent in the course of the world processes, ''and therefore we again came to a conclusion that completely contradicts the unconditionality of the relativity principle.'' [...] One can vary this experiment in many ways, for instance, so that A in the same way as B successively undergoes two different strides <math>+u</math> and <math>-u</math>. If we apply the value <math>u_{1}</math> to A and <math>u_{2}</math> to B, then the comparison of A and B at the end of the experiment must give the result, that B or A is retarded in its progress depending on whether the strides <math>+u_{2},-u_{2}</math> or <math>+u_{1},-u_{1}</math> are further apart. ''Probably it is precisely this formulation of the theorem that is particularly suitable to demonstrate the non-equivalence of the different strides clearly and explicitly.'' |- |colspan=2|{{Lorentzbox|Text=This interpretation was directly rebutted by Laue (1911/12) who demonstrated the geometrical meaning of differential aging in Minkowski space, see sections {{slink||Laue 1911/12-PT|Laue 1911/12-VA}}, showing that there is no need to assume non-equivalance or anisotropy of motions. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.<ref name=laue1 />}} |- ! style="width:50%" | German original by [[w:Norman Robert Campbell|Campbell]] (November 1911, published 1912)<ref name=camp /> ! English translation |- |colspan=2|After describing the round-trip experiment (as given by Wiechert) according to which the traveling clock B is retarded when it returns with respect to stationary clock A, he abandoned differential clock aging as follows: |- | style="padding: 0px 20px 0px 20px;" |Dieser Schluß ist nicht richtig. Die Beziehung zwischen <math>t</math>, der Ablesung an der Uhr auf A seitens des Beobachters auf A und <math>t'</math>, der Ablesung an der Uhr auf B seitens des Beobachters auf A, ist (unter der Annahme, daß zu Beginn des Versuchs <math>t=t'</math> ist) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. Der Unterschied zwischen <math>t'</math> and <math>t</math> ist eine Funktion von <math>z</math> und <math>v</math> allein. Wenn man diesen Größen ihre früheren Werte wiedergibt, indem man die beiden Uhren wieder zur Koinzidenz bringt, während sie relativ zueinander ruhen, so geht der Unterschied zwischen <math>t'</math> and <math>t</math> wieder auf null zurück, gleichviel, welche Werte <math>z</math> und <math>v</math> während der Zwischenzeit gehabt haben mögen. Wenn an irgendeinem Punkte der Bahn die Geschwindigkeit von B relativ zu A eine endliche plötzliche Änderung erfährt, so erfährt auch der Wert von <math>v</math> eine endliche plötzliche Änderung. | style="padding: 0px 20px 0px 20px;" |This conclusion is not correct. The relationship between <math>t</math> as the reading on the clock on A by the observer on A, and <math>t'</math> as the reading on the clock on B by the observer on A, is given by (assuming that <math>t=t'</math> at the beginning of the experiment) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. The difference between <math>t'</math> and <math>t</math> is a function of <math>z</math> and <math>v</math> alone. If these quantities are given their previous values by bringing the two clocks back to coincidence during which they are at rest relative to one another, the difference between <math>t'</math> and <math>t</math> goes back to zero, no matter what values <math>z</math> and <math>v</math> may have had in the meantime. If at any point on the path the speed of B experiences a finite sudden change relative to A, then the value of <math>t'</math> also undergoes a finite sudden change. |- |colspan=2|{{Lorentzbox|Text=a) So Campbell claims that any time difference during the outbound path is wiped out during the inbound path. His mistake is obvious: He is confusing coordinate differences stemming from the Lorentz transformation of ''events'' (which indeed depend on position and direction) with differences in ''clock aging'' derived from the proper time integral (which is ''accumulative'' and independent of position and direction.) b) As Campbell's paper was a reply to Wiechert, it's interesting to compare them: Campbell was correct in dismissing the aether but wrong in denying asymmetric aging, while Wiechert was correct in deriving asymmetric aging but wrong in requiring the aether. }} |- ! style="width:50%" | French original by [[w:Paul Gruner|Gruner]] (March 1912):<ref name=gruner /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |[...] deux personnes du même âge, se séparant dans des systèmes de « marche » très différents et retournant après un laps de temps assez long, constateront une différence d'âge très sensible. [...] le principe de relativité exige toujours la ''réciprocité parfaite'' des phénomènes entre deux systèmes qui possèdent un mouvement relatif. Si, dans l'exemple cité, les deux personnes du même âge se séparent avec une vitesse relative pour se retrouver plus tard, la constatation d'une différence d'âge sera parfaitement mutuelle : A dira positivement que B est resté en arrière dans son développement, et B affirmera avec le même droit que c'est A qui ne s'est pas développé assez vite. Ainsi le principe absolu de la relativité montre ses conséquences les plus extrèmes et il est clair que l'introduction de l’éther n'est plus en état de résoudre cette contradiction irréductible et inconcevable. | style="padding: 0px 20px 0px 20px;" | [...] two people of same age, separating into very different systems of motion and returning after a quite long period of time, will notice a very significant age difference. [...] the principle of relativity always requires the ''perfect reciprocity'' of the phenomenons between two systems that possess relative motion. When, in the cited example, the two persons of same age are separated by some relative velocity only to meet again later, the finding of an age difference will be perfectly mutual: A will positively say that B stayed behind in its development, and B will assert with same right that it was A who has not developed fast enough. By that, the absolute relativity principle shows its most extreme consequences and it is clear, that the introduction of the aether is no longer able to resolve this irreducible and inconceivable contradiction. |- |colspan=2|{{Lorentzbox|Text=Gruner was probably the first to claim that combining the round-trip experiment with the symmetry of time dilation leads to the contradictory situation, that both must attribute younger age to one another at reunion. At the end of his paper, we also find the expression "clock paradox" (French: paradoxe des horloges). See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem.}} |} ==Einstein's contributions== 1905:<ref name=einstein05 /> Introduction of the "peculiar" (German: eigentümlich) round-trip experiment with clocks in terms of a polygonal path as well as a continuously curved path, and an experiment comparing a clock at the pole with one at the equator. January 1911 (published November):<ref name=einstein11a /> In a lecture from January, Einstein extended the "funny" (German: drollig) round-trip experiment to living organisms. According to [[w:Rudolf Lämmel]] in April 1911<ref name=lammel /> and [[w:Fritz Müller-Partenkirchen|Fritz Müller]] in October 1911,<ref name=muller /> Einstein spoke of human beings as well. January 1911 (published January 1912):<ref name=einstein3 /> During a discussion with Einstein directly after the previous lecture, [[w:Fritz Müller-Partenkirchen|Fritz Müller]] claimed that any time difference during the round-trip should vanish at reunion, in analogy to the fact that the Lorentz contraction of a moving rod vanishes when it is at rest again. Einstein showed that the analogy is incorrect: While the clock rates are indeed the same again when they are mutually at rest, the clocks do not indicate the same time at reunion because "clocks are carriers of the time differential"; he went on to show that any possible influence of acceleration during the turnaround can be made negligible by elongating the constant velocity periods. 1912:<ref name=einst12manu /> In an unpublished manuscript on special relativity, Einstein showed that if system <math>\Sigma'</math> makes a round-trip along a polygon, then its inner processes will be retarded with respect to resting system <math>\Sigma </math> at reunion. He pointed out that any influence of acceleration can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygon. April 1914:<ref name=einstpetz /> [[w:Joseph Petzoldt]] criticized asymmetric clock aging in the round-trip experiment as a "fallback into absolutist way of thinking", claiming that special relativity requires that any difference between the clocks vanishes when their relative velocity is zero again, even though he added that any treatment of the clock paradox in special relativity is unrealistic anyway, since the theory only concerns uniform motions and therefore cannot handle velocity changes, so one has to modify the theory. Einstein responded by letter in which he praised Petzoldt's philosophical take on relativity, yet he rejected Petzoldt's conclusions concerning the clock paradox by showing that any finite acceleration at turnaround during the round-trip can only influence the clock in a finite way and therefore can be neglected by minimizing the time of acceleration with respect to the time of uniform translation, so it "must be concluded" that the clock traveling on a polygonal path is retarded at reunion. May 1914:<ref name=rowe group=S /> During a conversation with [[w:Ernst Gehrcke]] who claimed that the clock paradox contradicts the relativity principle, Einstein replied that clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are irrelevant for the amount of the time difference, their presence nevertheless cause B to fall behind ("accelerated motions are absolute in the theory of relativity"). 1916:<ref name=einstein16 /> In a lecture of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of general relativity." September 1918:<ref name=einadl /> In a letter to Einstein, [[w:Friedrich Adler (politician)|Friedrich Adler]] (while in prison for the [[w:Assassination of Karl von Stürgkh]]) claimed that the clock paradox which he described on a circular round-trip contradicts the special relativity principle, and also referred to the similar opinions of Berg and Petzoldt. Einstein responded by letter and explained that there is no contradiction as one of them accelerates; he then showed that general relativity makes both inertial frame K and accelerated frame K' equally justified, explaining the time difference in K' by combining the influence of velocity and gravitational potential, concluding that "Berg and Petzoldt were wrong". November 1918:<ref name=einstein18 /> In a fictitious dialogue between a relativity critic and a relativity apologist written by Einstein, the "critic" said that special relativity must predict differential clock aging in round-trip experiments, which was confirmed by the "relativist" who regretfully noted that even some pro-relativity authors tried to "circumvent this unavoidable result". Yet the critic claimed that this leads to a contradiction: From the viewpoint of K, clock U1 is at rest while the clock U2 was in motion and therefore returns being retarded with respect to U1, but from the viewpoint of K', clock U2 is at rest while clock U1 was in motion and therefore returns being retarded with respect to U2, which was rebutted by the relativist by pointing out the acceleration of U2. Then the critic claimed that this problem "rises again from the dead" in general relativity which allows to symmetrically treat both K and K', which was rebutted by the relativist using the equivalence principle: In K', the rate increase of U1 during turnaround period 3) is "the double" of its velocity time dilation in the inertial periods 2) and 4). December 1918:<ref name=einstein18b /> In a letter to Einstein, [[w:Max Jakob]] doubted the result from Einstein's dialogue, according to which the advance of U1 in period 3) is the double of its retardation during periods 2) and 4). Einstein responded by letter, in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). 1920:<ref name=einstein20 /> In conversations with [[w:Alexander Moszkowski]] between 1919 and 1920, Einstein argued that differential aging of the twins is rather a paradox of feeling, not a paradox of thought, because the latter would only arise if there were no reason for the asymmetric aging. The reason in special relativity lies in the fact that one of them suffered accelerations, while a deeper understanding of that question is obtained by using general relativity. Einstein argued that our "common sense" is located in the realm of feeling and analogy drawn from our ordinary experience; since there is no analogy to the example of the twins in our experience, it might appear paradoxical to the common sense, while it appears logical and necessary in light of intensified abstraction of the trained scientific mind. August 1920:<ref name=rowe group=S /> At an anti-relativity event organized by the right-wing agitator [[w:Paul Weyland]] during which [[w:antisemitic]] leaflets were distributed and [[w:swastika]]s offered at the entrance, a lecture was given by Gehrcke re-iterating his criticism of the twin paradox, claiming that the stationary first organism is old or even dead at reunion while the second organism was in motion and therefore stayed young, but from the standpoint of the second organism he himself is old or even dead while the first organism was in motion and stayed young, thus relativity is either contradictory or it leads to different realities and physical [[w:solipsism]]. Einstein who was present at that event, directly responded in a newspaper article;<ref name=einst20 /> after suspecting antisemitic motives of his critics, he specifically addressed Gehrcke's objections regarding the "well known example of the clocks (or twins)", remarking that the charge of solipsism will be "greeted by the experts as a joke", and characterized the claim that relativity requires mutual retardation of two co-located clocks as a "deliberate attempt to misinform the lay public". 1922:<ref name=morand /><ref name=nord /> [[w:Paul Painlevé]], Einstein and Langevin discussed the clock paradox at a meeting in Paris. Painlevé imagined a clock on a train that performs a round-trip with constant speed and returns being retarded with respect to the station clock, yet he claimed that the relativity principle also allows to say that the station clock performed the round-trip and returned being retarded with respect to the train clock, in contradiction to the previous result. Einstein replied that the relativity principle cannot be applied since the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two systems having velocities in opposite direction is not an inertial frame; there is no reciprocity between a frame that changes direction and one that doesn't. Langevin consequently gave a detailed analysis in terms of the Lorentz transformation. 1954:<ref name=einstein54 /> In a letter, Einstein explained the "well known clock paradoxon" using two clocks <math>B_{1}</math> and <math>B_{2}</math>; clock <math>B_{2}</math> has to reverse its speed in order to come back, thus it was initially at rest in inertial frame <math>S_{2}</math> and then at rest in <math>S_{2}^{+}</math>, whereas <math>B_{1}</math> constantly remains at rest in <math>S_{1}</math>, which explains the asymmetry between them. ==Historical references== <references> <ref name=einstein05>See p. 904f in: {{Citation |author=Einstein, A. |date=1905 |title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik |volume=322 |issue=10 |pages=891–921 |doi=10.1002/andp.19053221004|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 2, Document 23}}. See also: [https://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation at fourmilab].</ref> <ref name=einstein11a>See p. 10. in: {{Citation |author=Einstein, A. |title=Die Relativitäts-Theorie|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |issue=1-2|pages=1–14 |date=27 November 1911|orig-date=Lecture 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n11/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 17}}.<br /> The publication date 27 November 1911 can be seen on the [https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n5/mode/2up Title page and TOC of issue 1-2].</ref> <ref name=einstein3>Discussion between Einstien, Müller, Lämmel and others after the Zürich lecture: {{Citation |author=Einstein, A.; Müller, F., Lämmel, R.|title=Diskussion zu "Die Relativitäts-Theorie"|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |pages=II-IX |date=January 1912|orig-date=Lecture on 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n587/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 18, and in the corresponding English translation volume}}<br /> While the discussion already happened on January 1911, the publication followed one year later in January 1912 in the session proceedings (Sitzungsberichte) of the third issue, see [https://www.ngzh.ch/publikationen/vjs/56/3 Full issue Nr. 3] with [http://www.ngzh.ch/archiv/1911_56/56_1-2/56_3.pdf Title page and TOC] and the [http://www.ngzh.ch/archiv/1911_56/56_3/56_30.pdf Sitzungsberichte including Einstein's discussion on pp. II-IX]. </ref> <ref name=einst12manu>See p. 46 in: {{Citation |author=Einstein, A. |date=1912 |chapter=Document 1: Einstein's manuscript on the special theory of relativity|title=The collected papers of Albert Einstein|volume=4|pages=3-108|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstlor>{{Citation|author=Einstein, A.|date=1914|title=Review of "Lorentz, H. A. – Das Relativitätsprinzip" |journal=Die Naturwissenschaften|volume=2|pages=1018|url=https://archive.org/details/CAT31421305002/page/1018/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 6, Document 11}}</ref> <ref name=einstpetz>{{Citation |author=Einstein, A. |date=1914 |chapter=Document 5: Letter from Einstein to Petzoldt|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein16>See p. 423f in: {{Citation |author=Einstein, A. |date=1916 |title=Announcement of Einstein's lecture "Über einige anschauliche Überlegungen aus dem Gebiete der Relativitätstheorie"|journal=Berliner Sitzungsberichte|pages=423|volume=1916 (part 1)|url=https://archive.org/details/sitzungsberichte1916deutsch/page/423/mode/2up}}</ref> <ref name=einadl>Letter exchange between Einstein and Adler in which the critique on the clock paradox by Berg (1910) and Petzoldt (1914) was mentioned, together with the general relativity solution in terms of the gravitational potential, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Adler's letter in Document 620 and Einstein's reply in Document 628|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein18>Einstein discussed in terms of inertial frames (special relativity) on pp. 697f; accelerated frames (general relativity) on pp. 698f.; distant masses (Mach's principle) on pp. 700f. in: {{citation |author=Einstein, A.|title=[[s:de:Dialog über Einwände gegen die Relativitätstheorie|Dialog über Einwände gegen die Relativitätstheorie]]|date=November 1918|volume=6|issue=48|journal=Die Naturwissenschaften|pages=697-702|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 7, Document 13}}; See also English translation [[:s:Translation:Dialog about Objections against the Theory of Relativity|Dialog about Objections against the Theory of Relativity]] on Wikisource.</ref> <ref name=einstein18b>Letter exchange between Max Jakob and Einstein from December 1918, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Jakob's letter in Document 661c and Einstein's reply in Document 663a|title=The collected papers of Albert Einstein|volume=10|pages=189-190}}</ref> <ref name=einstein20>Interview of Einstein by Moszkowski, see p. 204f. in: {{citation |author=Moszkowski, A.|title=Einstein. Einblicke in seine Gedankenwelt|orig-date=Copyright date 1920 |date=1921|place=Hamburg|url=https://www.archive.org/details/einsteineinblick00moszuoft}}; See also English translation by H. L. Brose (1921): [https://archive.org/details/einsteinsearch00moszrich Einstein, the searcher], p. 206</ref> <ref name=einst20>{{Citation|author=Einstein, A.|date=27 August 1920|journal=Berliner Tageblatt|title=Meine Antwort - Ueber die anti-relativitätstheoretische G. m. b. H.|issue=402|pages=1-2|url=https://www.deutsche-digitale-bibliothek.de/newspaper/item/YH65KFT53MOG4SMXDXK4IVUPTR3QRY7Q?issuepage=1|quote=Reprinted in "The Collected Papers of Albert Einstein", Vol. 7, Document 45}}</ref> <ref name=einstein54>Letter from Einstein to N. V. Pope from March 1954; [[w:Albert Einstein Archives]], Object number 27-88 ([https://ein-web.adlibhosting.com/aea/Details/archive/110021626 Online dataset]); Scanned version as [https://groups.google.com/group/npachat/attach/d3121322d37764f2/Einstein%20letter.doc?part=0.1 Word document on Usenet] published by [https://groups.google.com/g/npachat/c/Haoib97d6OA/m/8mR30yITEtMJ Pope himself])</ref> <ref name=morand>Discussion between Painlevé, Einstein, and Langevin on p. 316ff in: {{citation |author=Morand, M.|title=Einstein au collège de france|date=April 1922|journal=La Nature|volume=50|issue=2511|pages=315-320|url=http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.102/319/100/620/5/613}}</ref> <ref name=lammel>{{Citation|author=Lämmel, R.|date=28 April 1911|title=Die Relativitäts-Lehre|journal=Neue Zürcher Zeitung|volume=117|pages=1|url=https://www.e-newspaperarchives.ch/?a=d&d=NZZ19110428-01.2.4.1}}; English translation of the part concering the twin pardox at [[:v:History of Topics in Special Relativity/Twin paradox#Lämmel 1911-Hum|Wikiversity:Early history of the twin paradox - Lämmel]]</ref> <ref name=lammel2>See p. 84ff in: {{Citation|author=Lämmel, R.|date=1921|orig-date=Preface December 1920|title=Die Grundlagen der Relativitätstheorie|place=Berlin|publisher=Springer|url=https://archive.org/details/diegrundlagende00lmgoog}}</ref> <ref name=langevin1>He derived differential aging from the proper time integral; pointed out that this demonstrates the "absolute nature of acceleration" with respect to an aether, see: {{citation |author=Langevin, P.|title=[[:s:fr:L’Évolution de l’espace et du temps|L’Évolution de l’espace et du temps]]|journal=Scientia |volume=X |pages=31–54 |date=July 1911|orig-date=Lecture 10 April 1911}}; English translation [[:s:en:Translation:The Evolution of Space and Time|The Evolution of Space and Time]] on Wikisource</ref> <ref name=langevin2>See p. 329 in: {{citation |author=Langevin, P. |title=Le temps, l'espace et la causalité dans la physique moderne |journal=Bulletin de la Société française de philosophie |volume=12 |orig-date=Lecture October 1911|date=1912|pages=1-28|url=http://ahp.li/1f7fc22d283fdf0deeca.pdf}}</ref> <ref name=langevin3>See p. 622f in: {{citation |author=Langevin, P. |title=Le Principe de relativité |journal=Bulletin de la société française des électriciens |volume=9 |date=1919 |pages=601-639|url=https://archive.org/details/bulletin-de-la-societe-francaise-des-electriciens-ser.-3-vol-9/page/600}}; Republished in 1922 as separate booklet: [[:s:fr:Le Principe de relativité|Le Principe de relativité]], Éditions Étienne Chiron</ref> <ref name=wiechert11>See p. 745f. general description and proper time; 757f. space travel; in: {{Citation |author=Wiechert, E. |date=September 1911|orig-date=Lectures March-May 1911, submitted 26 July|title=[[:s:de:Relativitätsprinzip und Äther|Relativitätsprinzip und Äther]]|journal=Physikalische Zeitschrift |volume=12 |issue=17-18 |pages=[https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/741 689-707] published September 1; [https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/789 737–758] published September 15}}</ref> <ref name=wiechert15>See p. 46 (Einstein, Langevin, Wiechert) and pp. 51f (Laue versus Wiechert) in: {{citation |author=Wiechert, E.|contribution=Die Mechanik im Rahmen der allgemeinen Physik| title=Die Kultur der Gegenwart: Physik|volume=3.3.1|date=1915 |orig-date=Submitted July 1914|pages=1–78|contribution-url=https://www.archive.org/details/physikunterredak00warbuoft}}</ref> <ref name=wiechert20>See p. 46f in: {{citation |author=Wiechert, E.|title=Der Äther im Weltbild der Physik|orig-date=Presented December 1920|date=1921|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse|pages=29-70|url=http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN00250586X}}</ref> <ref name=wiechert21>See p. 25ff in: {{citation |author=Wiechert, E.|title=[[:s:de:Prinzipielles über Äther und Relativität|Prinzipielles über Äther und Relativität]]|date=1922|orig-date=Lecture September 1921|journal=Physikalische Zeitschrift|volume=23|pages=25-28}}</ref> <ref name=muller>See p. 9 in: {{Citation|author=Müller, F.|date=October 1911|journal=Berliner Tageblatt|title=[[:s:de:Das Zeitproblem (1911)|Das Zeitproblem]]|pages=[https://www.deutsche-digitale-bibliothek.de/newspaper/item/2QKOIOLGNVQILTCEZQOGQPLTRVLPM5PZ?query=zeit&issuepage=9 Part 1 published 16 October 1911] and [https://www.deutsche-digitale-bibliothek.de/newspaper/item/IO44I6QBC4SVV5YUKUDSGXYIPQUXXBN5?query=zeit&issuepage=11 Part 2 published 23 October 1911]}}</ref> <ref name=gruner>See p. 253f in: {{Citation |author=Gruner, P. |title=[[:s:fr:Rapport sur la dernière discussion concernant le principe de la relativité et l’éther|Rapport sur la dernière discussion concernant le principe de la relativité et l’éther]] |journal=Archives des sciences physiques et naturelles |volume=33|issue=4 |pages=252-254 |date=March 1912}}</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=weyl>See p. 147f. in: {{Citation |author=Weyl, H. |date=March 1918|title=Raum-Zeit-Materie (first edition)|publisher=Berlin: Springer|url=https://archive.org/details/RaumZeitMaterieVolIMeinerFrauGewidmet}}; English translation of the 4th edition by H. Brose (1921): [https://www.gutenberg.org/ebooks/43006 Space—Time—Matter], pp. 278f.</ref> <ref name=gbaum>See footnote on p. 507 in: {{Citation|author=Grünbaum, F. |title=Über einige ideelle Versuche zum Relativitätsprinzip|journal=Physikalische Zeitschrift|volume=12|pages=500–509|date=1911|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/540}}</ref> <ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> <ref name=laue2>See p. 42f. for general description; p. 58f. in terms of proper time; in: {{Citation |author=Laue, M. v. |orig-date=Preface December 1912|date=1913 |title=Das Relativitätsprinzip (Second Edition) |publisher=Vieweg |place=Braunschweig|url=https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE4597082}}; See also English translation [[:s:Translation:The Principle of Relativity (Laue 1913)|The Principle of Relativity, Second edition, Part III]] on Wikisource</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=berg>See p. 369f in: {{Citation |author=Berg, O. |date=1910 |title=Das Relativitätsprinzip der Elektrodynamik |journal=Abhandlungen der Fries'schen Schule |volume=3 |issue=2|pages=333-382 |url=http://hdl.handle.net/2027/hvd.hnuynk?urlappend=%3Bseq=351}}</ref> <ref name=camp>See p. 123f in: {{Citation |author=Campbell, N. |title=Relativitätsprinzip und Äther: Eine Entgegnung an Herrn Wiechert |journal=Physikalische Zeitschrift |volume=13 |pages=120-128 |issue=3|orig-date=Submitted December 1911|date=February 1912|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/150}}. The is based on an English manuscript translated by Max Iklé, and Campbell's first name was Germanised as "Normann".</ref> <ref name=seel>{{Citation|author=Seeliger, R.|title=Review of "P. Gruner – Rapport sur la dernière discussion concernant le principe de la relativité et l'éther"|journal=Die Fortschritte der Physik|volume=68|issue=2|pages=336|date=1913|url=https://books.google.com/books?id=fSJGAQAAMAAJ&pg=PA336}}</ref> <ref name=study>See footnote on p. 111 in: {{citation |author=Study, E. |title=Vorlesungen über ausgewählte Gegenstände der Geometrie |date=June 1911|url=https://archive.org/details/vorlesungenber00studuoft|publisher=B.G. Teubner|place=Leipzig}} </ref> <ref name=robb1>See pp. 356ff. in: {{Citation|author=Robb, A.|date=1914|title=A theory of time and space|place=Cambridge|publisher=University Press|url=https://archive.org/details/theoryoftimespac00robbrich}} </ref> <ref name=robb2>See §12 in: {{citation |author=Robb, A. A.|title=The Straight Path|date=1920 |journal=Nature|pages=599|volume=104|issue=2623|url=https://archive.org/details/sim_nature-uk_1920-02-05_104_2623/page/598/mode/2up}}</ref> <ref name=edding2>See p. 22 in: {{Citation |author=Eddington, A. S. |date=1922 |title=The theory of relativity, and its influence on scientific thought |publisher=Oxford Clarendon Press |url=https://archive.org/details/cu31924005748573}}</ref> <ref name=rogers>{{citation |author=Rogers, R. A. P.|title=The Time-Triangle and Time-Triad in Special Relativity|date=November 1922|journal=Nature|volume=110|issue=2769|pages=698–699|url=https://archive.org/details/sim_nature-uk_1922-11-25_110_2769/page/698/mode/2up}}</ref> <ref name=lorentz1>See pp. 37f, 55ff in: {{citation |author=Lorentz, H. A.|date=1913|title=Het relativiteitsbeginsel : drie voordrachten gehouden in Teyler's stichting|publisher=De Erven Loosjes |place=Haarlem|url=https://resolver.kb.nl/resolve?urn=MMKB24:063387000:00005}}; German translation on pp. 31f, 47f in: {{citation |author=Lorentz, H. A.|date=1914| title=Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem|publisher=B.G. Teubner |place=Leipzig and Berlin|url=https://archive.org/details/bub_gb_89PPAAAAMAAJ}}; See also the transcription [[:s:de:Das Relativitätsprinzip (Lorentz)|Das Relativitätsprinzip]] on German Wikisource and the English translation [[:s:Translation:The Principle of Relativity (Lorentz)|The Principle of Relativity]] on English Wikisource</ref> <ref name=lorentz3>See §12 in: {{citation |author=Lorentz, H. A.|title=Considérations élémentaires sur le principe de relativité|date=1914 |journal=Revue générale des sciences pures et appliquées|pages=179-186|url=https://archive.org/details/revuegnraled25pari/page/178/mode/2up}}</ref> <ref name=bloch>See pp. 67 ff. in: {{Citation | author=Bloch, W.| date=September 1918|title=Einführung in die Relativitätstheorie| publisher=B. G. Teubner |url=https://hdl.handle.net/2027/njp.32101040276907}}</ref> <ref name=bloch2>See pp. 69ff. (special relativity) and 102ff. (general relativity) in: {{Citation | author=Bloch, W.| date=1920 |title=Einführung in die Relativitätstheorie (second edition)| publisher=B. G. Teubner |url=https://www.archive.org/details/einfhrungindier00blocgoog}}</ref> <ref name=bollert1>See p. 6 (special relativity), pp. 24-26 (EP) in: {{citation |author=Bollert, K.|title=Einstein’s Relativitätstheorie und ihre Stellung im System der Gesamterfahrung |date=April 1921|publisher=Steinkopff|url=https://archive.org/details/dbc.wroc.pl.001504}}</ref> <ref name=born>See pp. 190f. (special relativity), 250f (EP) in: {{Citation | author=Born, M.| date=1921 |title=Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Second edition)| publisher=Springer | place=Berlin|url=https://hdl.handle.net/2027/mdp.39015017387310}}; The [https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE5426498 first edition (1920)] of Born's book didn't include the twin paradox. English translation of the third edition by H. Brose (1924): [https://archive.org/details/einsteinstheoryo00born Einstein's theory of relativity]</ref> <ref name=pauli>See p. 558f (general description); p. 624f (proper time); p. 713f (accelerated frames); in: {{Citation |author=Pauli, W. |date=1921 |journal=Encyclopädie der Mathematischen Wissenschaften|title=Die Relativitätstheorie|pages=539–776|volume=5|issue=2 |url=http://resolver.sub.uni-goettingen.de/purl?PPN360709672}}; English translation by G. Field (1958): [https://books.google.com/books?id=rc3DAgAAQBAJ Theory of Relativity]</ref> <ref name=thirring>See p. 209ff in: {{citation |author=Thirring, H.|title=Über das Uhrenparadoxon in der Relativitätstheorie|date=April 1921|journal=Naturwissenschaften|volume=9|issue=18|pages=209-212|url=https://archive.org/details/sim_naturwissenschaften_1921-04-01_9_13/mode/2up}}</ref> <ref name=sommerfeld>See p. 71 in: {{citation |author=Sommerfeld, A. |date=May 1913|chapter=Remarks on Minkowski's "Space and Time"|title=Das Relativitätsprinzip|editor=Otto Blumenthal|pages=69-73|url=https://www.archive.org/details/dasrelativittsp00minkgoog}}</ref> <ref name=kopff>See pp. 45ff (special relativity and proper time); pp. 117ff (EP); pp. 189ff (Mach's principle), in: {{citation |author=Kopff, A.|title=Grundzüge der Einsteinschen Relativitätstheorie |date=February 1921|publisher=S. Hirzel|place=Leipzig|url=https://www.archive.org/details/grundzgedereins00kopfgoog}}; English translation by H. Levy (1923): [https://hdl.handle.net/2027/mdp.39015017188817 The mathematical theory of relativity].</ref> <ref name=becqu1>See p. 48ff (proper time), p. 240f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Le Principe de relativité et la théorie de la gravitation|Le Principe de relativité et la théorie de la gravitation]] |date=1922 |publisher=Gauthier-Villars|place=Paris}}; See also p. 57ff (proper time), p. 177f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Exposé élémentaire de la théorie d’Einstein et de sa généralisation|Exposé élémentaire de la théorie d’Einstein et de sa généralisation]]|date=1922 |publisher=Payot|place=Paris}}</ref> <ref name=nord>Discussion between Painlevé, Einstein, and Langevin on pp. 146ff in: {{citation |author=Nordmann, C.|title=[[s:fr:Einstein expose et discute sa théorie|Einstein expose et discute sa théorie]]|date=May 1922|journal=Revue des deux mondes|volume=IX|pages=129-166}}</ref> <ref name=lehm>{{Citation |author=Lehmann, Otto |orig-date=September 1910 |date=1911|title=Das Relativitätsprinzip der neue Fundamentalsatz der Physik |title-link=s:de:Das Relativitätsprinzip der neue Fundamentalsatz der Physik|journal=Verhandlungen des naturwissenschaften Vereins in Karlsruhe |volume=23 |pages=49-74}}</ref> <ref name=lech>See p. 19ff in: {{citation |author=Lechalas, G. |orig-date=Submitted December 1912|date=1913 |title=Le nouveau temps |journal=L’Année philosophique|volume=XXIII|pages=19-44|url=https://gallica.bnf.fr/ark:/12148/bpt6k255882z/f22.item}}</ref> <ref name=hunt>See pp. 494ff in: <br>{{Citation|author=Huntington, E. V. |year=1912 |title=A new approach to the theory of relativity|journal=Philosophical Magazine |volume=23|pages=494-512|url=https://archive.org/details/londonedinburg6231912lond/page/494/mode/2up}}</ref> </references> ==Secondary sources== <references group=S> <ref name=miller>{{Citation |author=Miller, A. I. |date=1981 |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |place=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}; See section 7.4.13 (Langevin, Wiechert, Laue, Einstein), footnotes 29-34 of chapter 7 (Petzoldt, Sommerfeld, Bergson, Einstein)</ref> <ref name=lange>{{Citation|author=Lange, L.|date=1927|title=The clock paradox of the theory of relativity|journal=The American Mathematical Monthly|volume=34|issue=1|pages=22-30|jstor=2299914}}</ref> <ref name=pes>{{Citation |author=Pesic, P. |date=2003 |title=Einstein and the twin paradox |journal=European Journal of Physics |volume=24 |issue=6 |pages=585–590 |doi=10.1088/0143-0807/24/6/004}}</ref> <ref name=during>{{Citation |author=During, É. |date=2014 |title=Langevin ou le paradoxe introuvable |journal=Revue de métaphysique et de morale |volume=84 |pages=513-527 |doi=10.3917/rmm.144.0513|doi-access=free}}; See pp. 515f (Langevin), 520f. (Einstein, Laue, Weyl, Painlevé).</ref> <ref name=debs>{{Citation |author=Debs, T. A., & Redhead, M. L. |title=The twin paradox and the conventionality of simultaneity |date=1996 |journal=American Journal of Physics |volume=64|issue=1| pages=384-392 |doi=10.1119/1.18252}}</ref> <ref name=alizzi>{{Citation |author=Alizzi, A., Sen, A., & Silagadze, Z. K.|title=Do moving clocks slow down? |year=2022 |journal=European Journal of Physics |volume=43|issue=6|pages=065601 |doi=10.1088/1361-6404/ac93ca|arxiv=2209.12654}}; Appendix B with reference to Lange and Halsbury</ref> <ref name=beng>{{Citation |author=Benguigui, L. G. |date=2020 |title=A Tale Of Two Twins: The Langevin Experiment Of A Traveler To A Star |publisher=World Scientific|isbn=9789811219115}}; See early solutions (Einstein, Langevin, Lorentz, Born/Kopff) and the Bergson controversy. A shorter version appeared in {{arxiv|1212.4414}}.</ref> <ref name=rowe>{{Citation|author=Rowe, D. E.|date=2006|title=Einstein's allies and enemies: Debating relativity in Germany 1916–1920|journal=Interactions: Mathematics, Physics and Philosophy|pages=231-280|publisher=Springer|doi=10.1007/978-1-4020-5195-1_8}}; Covering the criticism of Gehrcke starting with 1912; discussion between Einstein and Gehrcke in 1914; Einstein's dialogue (1918) as response to antirelativists; the Weyland event in 1920 and Einstein's response.</ref> <ref name=weiss>Weiss, W. (Physics FAQ): [https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html The Twin Paradox: The Equivalence Principle Analysis]</ref> <ref name=cuvaj>{{Citation |author=Cuvaj, C. |date=1971 |title=Paul Langevin and the theory of relativity|journal=Japanese studies in the history of science|volume=10| pages=113-142|url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf}}</ref> <ref name=koks>Koks, D. (2018): [https://math.ucr.edu/home/baez/physics/Relativity/SR/sr-gr.html Physics FAQ: Where is the Boundary between Special and General Relativity?]</ref> </references> [[Category:History of special relativity]] [[Category:Paradoxes]] t66m0vfo7vjar3kd5vh2gn76gd8epvc 2834539 2834526 2026-09-26T08:20:04Z D.H 52339 /* Historical references */ 2834539 wikitext text/x-wiki {| style="width:20%; font-size:13px;" align=right |{{../Other Topics (header)}} |} ==Early history of the twin paradox== {{Lorentzbox|Text={{center|Date of article creation: 9 November 2023; Last major revision: 26 September 2026}}}} a) When was the [[:w:twin paradox]] applied to life forms and human beings? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /><ref group=S name=during /> report that {{slink||Einstein 1911-HU}} discussed the aging of living organisms, and that {{slink||Langevin 1911-HU}} and {{slink||Wiechert 1911-HU}} explicitly discussed the aging of human beings. :*More details in sections {{slink||Human beings in 1911|Twins from 1911 to 1920}}, including newspaper articles from 1911 written by {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}} that clearly show that Einstein was the first to explicitly discuss the aging of human beings as well. b) Who was the first to formulate the principle of maximal proper time along straight worldlines, upon which differential aging in the standard twin paradox is based? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> mention Langevin (1911), Laue (1911). :*More details in section {{slink||Maximal proper time}} with the contributions of Langevin (1911), Wiechert (1911), Study (1911), Laue (1911-13). c) Who was the first to formulate [[w:Triangle inequality#Reversal in Minkowski space|inverse triangle inequality]] in Minkowski space, which represents the simplest version of the twin paradox? :*See details in section {{slink||Triangle inequality}} with the contributions of Robb (1914-20), Eddington (1922), Rogers (1922). d) Who was the first to show that any influence of proper acceleration on clocks can be neglected in the computation of the twin paradox from the viewpoint of the stay-at-home twin? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Einstein (1911), Laue (1913). :*More details in section {{slink||Negligibility of proper acceleration}} with the contributions of Einstein (1911), Wiechert (1911), Laue (1913), Lorentz (1913). e) Who was the first to introduce the three clock/brother example that completely removes acceleration from the clock/twin paradox? :*Historical accounts<ref group=S name=debs /><ref group=S name=alizzi /> date it back to Lange (1927) and Lord Halsbury (1957). :*More details in section {{slink||Relay (three brothers) experiment}} with the contributions of Grünbaum (1911) and Wiechert (1920-22). f) Who was the first to use acceleration as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref name=cuvaj group=S /><ref group=S name=pes /> mention Langevin (1911), Einstein (1918). :*More details in section {{slink||Acceleration as asymmetry indicator}} with the contributions of Langevin (1911), Sommerfeld (1913), Lorentz (1913), Einstein (1914-20). g) Who was the first to use different frame distribution as asymmetry indicator as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Laue (1911-13). :*More details in section {{slink||Frame distribution as asymmetry indicator}} with the contributions of Laue (1911-13), Bloch (1918). h) Who was the first to describe the perspective of the traveler? :*Historical accounts<ref group=S name=miller /><ref group=S name=beng /> mention Langevin (1911), Lorentz (1914), Einstein (1918). :*More details in section {{slink||Perspective of the traveler}} with the contributions of Langevin (1911), Lorentz (1913-14), Einstein (1918), Thirring (1921). i) Who was the first to describe a round-trip experiment in curved spacetime? :*See section {{slink||Curved spacetime}} with the contribution of Becquerel (1922). j) Who was the first to interprete the twin paradox in terms of an aether or absolute space? :*See section {{slink||Aether interpretations}} with the contribution of Langevin (1911), Wiechert (1911), Lechalas (1912). k) Who was the first to denote the round-trip experiment as paradoxical? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> point to Laue (1911). :*See section {{slink||Paradoxical?}} for details. l) Who was the first to misunderstand the twin paradox? :*See section {{slink||Misunderstandings}} with the contributions of Berg (1910), Wiechert (1911), Campbell (1911/12), Gruner (1912). m) What were Einstein's contributions? :*See section {{slink||Einstein's contributions}}. ==Human beings in 1911== {| class="wikitable" style="background-color:white;{{text default color}};" ![[w:Albert Einstein|Einstein]] |- |{{anchor|Einstein 1905}}In 1905<ref name=einstein05 /> he showed that a clock moving on a round-trip away from A and back along a polygonal or curved path, is retarded with respect to a clock stationary at A by approximately <math>\tfrac{1}{2}t(v/V)^{2}</math> at reunion. For example, a clock on the equator is retarded with respect to a clock on the pole. He described this consequence as being "peculiar" (German: eigentümlich). {{anchor|Einstein 1911-HU}}In a lecture given on January 1911<ref name=einstein11a /> (published in November), he extended this "funny" (German: drollig) experiment to living organisms: {| ! width=55% | Einstein wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Wenn wir z. B. einen lebenden Organismus in eine Schachtel hineinbrächten und ihn dieselbe Hin- und Herbewegung ausführen lassen wie vorher die Uhr, so könnte man es erreichen, dass dieser Organismus nach einem beliebig langen Fluge beliebig wenig geändert wieder an seinen ursprünglichen Ort zurückkehrt, während ganz entsprechend beschaffene Organismen, welche an den ursprünglichen Orten ruhend geblieben sind, bereits längst neuen Generationen Platz gemacht haben. Für den bewegten Organismus war die lange Zeit der Reise nur ein Augenblick, falls die Bewegung annähernd mit Lichtgeschwindigkeit erfolgte! | style="padding: 0px 20px 0px 20px;" |For example, if we put a living organism in a box and make it undergo the same back and forth movement as the clock before, we could achieve that this organism returns to its original location with arbitrary little change after a flight of arbitrary length, whereas completely identical organisms that remained at rest in the original location have long since made room for new generations. To the moving organism, the long journey was only a moment if the movement happened close to the speed of light! |} {{Lorentzbox|Text=Two participants of that lecture, {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}}, report that Einstein also talked about the aging of ''human beings''.}} |- !{{anchor|Lämmel 1911-HU}}[[w:Rudolf Lämmel|Lämmel]] |- |He attended Einstein's 1911 lecture and gave a popular report about it in the Swiss newspaper "[[w:Neue Zürcher Zeitung|Neue Zürcher Zeitung]]" published on 28 April 1911,<ref name=lammel /> including additional details. Regarding the round-trip clock experiment he wrote: {| ! width=50% | Lämmel wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bewegt sich eine Uhr mit Lichtgeschwindigkeit längs einer Geraden, auf der gerichtete Uhren stehen, so scheint die bewegte Uhr, beurteilt vom Standpunkt der ruhenden aus, im oben stizzierten Sinn, stillzustehen. Kehrt die Uhr, nach einem Ruck, mit Lichtgeschwindigkeit wieder zurück zur Zentral-Uhr, so ist, nach Einstein, für den Beobachter bei der Zentral-Uhr die Sache so, als ob ein mit der bewegten Uhr mitgeführter Beobachter (samt dessen Uhr) nicht gealtert hätte. Hinge also des letzteren Alter von den Angaben des ruhenden Beobachters ab, so könnte der von einer großen Reise ins Weltall zurückkehrende Beobachter bei der Zentral-Uhr spätere Generationen antreffen – er selber hätte nicht gealtert. Welche Bedeutung diese ''ad absurdum'' geführte Gedankenspielerei etwa hat, läßt sich heute nicht absehen – vielleicht, ja wahrscheinlich ist sie ohne jeden Einfluß auf die tatsächlichen Verhältnisse. Aber man sieht dabei immerhin, daß die Physik imstande ist, die kühnsten Träume der Phantasie noch – zu überbieten. | style="padding: 0px 20px 0px 20px;" |Let a clock be moving at speed of light along a line on which regulated clocks are standing, then the moving clock's hand appears to be standing still (in the sense described above) as judged from the standpoint of the resting one. If the clock, after one jolt, comes back with light speed to the central clock, then according to Einstein the matter presents itself to the observer at the central clock, as if the observer comoving with the clock (together with his clock itself) hasn't been grown older. Thus if the age of the latter would depend on the indications of the resting observer, the observer returning from a great journey into space could meet later generations at the central-clock – he himself hasn't been grown older. The importance of this play of thought led ''ad absurdum'' cannot be seen today – maybe, or even probably, it is without any influence on the actual situations. Though at least one can see that physics is able to – surpass – even the boldest dreams and fantasies. |} Lämmel in December 1920 (published 1921)<ref name=lammel2 /> again alluded to Einstein's lectures in Zürich (possibly the one from 1911, and maybe also later ones), describing a discussion between himself and Einstein. After Einstein concluded that the travelers who came back after their journey will probably meet their former contemporaries as old men while they themselves could have been away for only a few years, Lämmel objected that this conclusion is only drawn with respect to rods and clocks, but not with respect to living beings. Einstein responded though, that all processes in the blood, in the nerves etc. are eventually periodical oscillations, i.e. motions. Yet to any such motion the relativity principle applies, thus the conclusion regarding the unevenly rapid aging it permissive. {{Lorentzbox|Text=While the official publication of Einstein's January lecture ({{slink||Einstein 1911-HU}}) mentions the aging of organisms, Lämmel recalls the reference to the aging of a human space traveler ("observer returning from a great journey into space"). This means that Einstein was the first to use human beings in the clock/twin paradox on January 16 which was first published by Lämmel on April 28, 1911. In comparison, {{slink||Langevin 1911-HU}} used space travelers in a lecture on April 10 with publication in July, and {{slink||Wiechert 1911-HU}} used space travelers in lectures held between March 25 and May 23 with publication in July/September. It seems very unlikely that before April 28, Lämmel became somehow aware of the content of Langevin's or Wiechert's lectures held a few weeks earlier, in order to use them in his description of Einstein's lecture.}} |- !{{anchor|Langevin 1911-HU}}[[w:Paul Langevin|Langevin]] |- |On 10 April 1911, published July 1911,<ref name=langevin1 /> he held a now famous lecture popularizing the clock/twin paradox which he derived from the proper time integral as described in {{slink||Langevin 1911-PT}}. He demonstrated that a moving radioactive sample of radium is less evolved and less aged and therefore more active at return then the ones that remained in the laboratory. He also used light signals and the Doppler effect to visualize the effect. The most famous part concerned his description of the aging of human space travelers: {| ! width=50% | Langevin wrote ! [[:s:Translation:The Evolution of Space and Time|English Wikisource translation]] |- | style="padding: 0px 20px 0px 20px;" |Cette remarque fournit le moyen, à celui d’entre nous qui voudrait y consacrer deux années de sa vie, de savoir ce que sera la Terre dans deux cents ans, d’explorer l’avenir de la Terre en faisant dans la vie de celle-ci un saut en avant qui pour elle durera deux siècles et pour lui durera deux ans, mais ceci sans espoir de retour, sans possibilité de venir nous informer du résultat de son voyage puisque toute tentative du même genre ne pourrait que le transporter de plus en plus avant. Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse. Revenu à la Terre ayant vieilli de deux ans, il sortira de son arche et trouvera notre globe vieilli de deux cents ans si sa vitesse est restée dans l’intervalle inférieure d’un vingt-millième seulement à la vitesse de la lumière. Les faits expérimentaux les plus sûrement établis de la physique nous permettent d’affirmer qu’il en serait bien ainsi. | style="padding: 0px 20px 0px 20px;" |This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. |} {{Lorentzbox|Text=Reading his lecture in full, one finds the word "paradoxical" only in relation to the constancy of light speed, not on relation to the round-trip clock experiment.}} |- !{{anchor|Wiechert 1911-HU}}[[w:Emil Wiechert|Wiechert]] |- |In lectures on 25 March and 23 May 1911, submitted July and published September 1911,<ref name=wiechert11 /> he described the round-trip clock experiment with two equal clocks regulated to the same rate and brought to the same pointer position, or by introducing the same chemical process two times, or by introducing ''two life forms that began their life at the same time''. At the end of his paper he applied this to human travelers: {| ! width=50% | Wiechert wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Nehmen wir aber wieder eine Relativgeschwindigkeit an, die bis auf 3 Proz. der Lichtgeschwindigkeit nahekommt, dann wird das Verhältnis der empfundenen Zeitlängen wie 4:1. Das Bild mag etwas weiter noch ausgemalt werden. Denken wir uns, daß ein Beobachter durch den Raum unseres Sternhimmels mit dieser Geschwindigkeit in einer Kreisbahn mit einem Radius von 16 Lichtjahren fährt, dann wird er nach unserer Zeitrechnung nach je 100 Jahren wieder an unserem Sonnensystem vorüberkommen. In seinem Gefährt wird dabei die Zentrifugalkraft so auf ihn einwirken, daß sie gemäß den Relativitätsgesetzen der Einwirkung der Schwerkraft auf uns Erdenbewohner gleich erscheint. Es sind also die wirkenden Kräfte nur so groß, daß der Phantasie die Möglichkeit geboten wird, den Reisenden als menschliches Wesen zu denken. Da hier dauernd <math>\sqrt{1-v^{2}/c^{2}}</math> ist, fließt die Eigenzeit für den Reisenden viermal langsamer dahin, als für die Bewohner der Gestirne. Wenn er also nach 100 unserer Jahre wieder zu unserem Sonnensystem zurückkehrt, wird er sich selbst nur um 25 Jahre gealtert fühlen. Erreicht er nach der Entwicklung seines Körpers und nach seiner Zeitempfindung ein Alter von 75 Jahren, so entspricht dies doch einer dreimaligen Wiederkehr zu unserem Sonnensystem, also 300 unserer Erdenjahre. | style="padding: 0px 20px 0px 20px;" |Yet if we again assume a relative velocity approximating the speed of light by 3 percent, then the ratio of the experienced duration of time becomes 4:1. This image can be further extended. Let's imagine that an observer travels with that velocity on a circular path at a radius of 16 light years through the space of our galaxy, then according to our time calculation he passes by our solar system every 100 years. In his vehicle the centrifugal force will act on him in such a way, that in accordance with the relativity laws it will appear to be equal to the force of gravity acting upon the inhabitants of Earth. Thus the acting forces are only thus big, in order to give our fantasy the possibility to imagine the traveler as a human being. Since we have <math>\sqrt{1-v^{2}/c^{2}}</math> throughout, proper time flows four times slower for the traveler than for the inhabitants of the stars. Thus when he comes back to our solar system after 100 of our years, he will feel to have aged only by about 25 years. If he reaches an age of 75 years according to the development of his body and his own time experience, then this corresponds to a threefold return to our solar system, i.e. 300 of our Earth years. |} {{Lorentzbox|Text=a) Wiechert (1915)<ref name=wiechert15 /> later provided a short historical survey of the clock/twin paradox. He referred to the fact that already {{slink||Einstein 1905}} considered the case of two clocks ("Einstein's clock experiment"), and even though [[w:Hermann Minkowski|Minkowski]] himself didn't consider the case, his proper time formula provides the result in a straight forward manner. The latter was done by himself in lectures on 25 March and 23 May 1911, as well as by Langevin published in July 1911. Wiechert pointed out that he himself and Langevin used "humorist" examples in order to clarify the situation: While Wiechert argued that one has to make a journey in order to stay young, Langevin argued that one has to romp about in a laboratory in order to stay young. Both of them used human beings, arguing that their physical and mental life should have been influenced in the same way as any other process in nature. b) The dates given by Wiechert (1915) are not complete. The correct ones are: *Langevin's lecture on 10 April 1911, published in July. *Wiechert's lectures on 25 March and 23 May 1911, submitted on July 26, published in September. *He was still unaware of Einstein's lecture from January 1911, published in November 1911.}} |- !{{anchor|Müller 1911-HU}}[[w:Fritz Müller-Partenkirchen|Müller]] |- |The freelance writer and law student Fritz Müller (who was later known as [[w:Fritz Müller-Partenkirchen|Müller-Partenkirchen]]) attended Einstein's lecture and wrote a popular report about it in the German newspaper "[[w:Berliner Tageblatt|Berliner Tageblatt]]" on 16th and 23rd October 1911,<ref name=muller /> in which he gave further details (compare with {{slink||Lämmel 1911-HU}}). Regarding the clock/twin paradox he wrote: {| ! width=50% | Müller wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Zwei gleichgehende Uhren sollen je einen Beobachter haben und nebeneinander ruhen. Nun soll die eine mit ihrem Beobachter plötzlich mit Lichtgeschwindigkeit in den Weltenraum hinausreisen. Vorher haben die beiden vereinbart, sich alle Sekunden mit einem Lichtsignal die Zeit zu telegraphieren. [...] In unserem Grenzfall, wo die Reise mit Lichtgeschwindigkeit vor sich geht, müßte der ruhende Beobachter erklären, jene andere Uhr käme in der Zeit überhaupt nicht voran. Die Zeit stünde dort still. Tatsächlich kommen die Einsteinschen Gleichungen zu diesem Resultat. Für den mit der Uhr reisenden Beobachter, sagt Einstein, gelte dasselbe. Das heißt, im Urteil des Zurückbleibenden würde jener niemals alt. „Und wenn er auf einer gebrochenen Reiselinie wieder an seinen Ausgangspunkt zurückkehrte?" fragt man den Vortragenden in der Diskussion. – „So bliebe er in unserem Urteil so jung wie bei der Ausreise," erwidert Einstein mit vollem Ernst, „selbst wenn wir Zurückgebliebenen inzwischen Männer mit weißen Bärten geworden sind – die Gleichungen liefern für jede Richtung der Bewegung, auch für eine gebrochene Bewegung, unerschütterlich die selben Resultate." – Wir sehen einander an. Das klingt märchenhaft. Märchenhaft? Gewiß, die alten Märchen vom Mönch von Heisterbach, vom Rip van Winkle, von Urashima Taro steigen auf. Merkwürdig, wie die Volksphantasie bei den Deutschen, bei den Amerikanern, bei den Japanern in der gleichen Richtung gearbeitet hat – alle drei Märchen erzählen ja von Leuten, deren Leben still steht, viele hundert Jahre lang, während die andern altern. So fanden sie bei ihrer Rückkehr ein anderes Land und eine andere Generation. | style="padding: 0px 20px 0px 20px;" |Two synchronous clocks at rest next to each other, shall each be accompanied by an observer. Now one of them, together with its observer, suddenly travels into space at the speed of light. Previously, both have arranged that every second they telegraph their time to each other using light signals. [...] In our limiting case where the journey happens at light speed, the resting observer would have to declare that the other clock would not proceed in time at all. Time would stand still at this place. Einstein's equations indeed produce this result. As to the observer traveling with the clock, says Einstein, the same is true. That means in the judgment of the remaining one, the other one would never become old. Then the lecturer [i.e. Einstein] was asked in the discussion: "And if he comes back to his starting point on a curved travel path?", to which Einstein replied in full earnest: "Then in our judgment he would remain as young as he was at departure, even if we remaining ones became men with white beards in the meantime, the equations unshakably give the same result in every direction of motion, also for curved motion". We look at each other. That sounds fabulous. Fabulous? Of course, the old fairy tales of [[w:Heisterbach Abbey|w:The monk of Heisterbach]] or [[w:Rip Van Winkle]] or [[w:Urashima Tarō]] come forward. Strange, how the folk fantasy of the Germans, the Americans, the Japanese worked in the same direction, all three fairy tales indeed tell about people whose life stands still, many hundred years long, while the other ones grow old. Thus they found another country and another generation when they returned. |} {{Lorentzbox|Text=Müller's account confirms {{slink||Lämmel 1911-HU}} that Einstein indeed mentioned human beings, but his description also suggests that Einstein was the first to use mutually sent light signals. However, as this was published in October, it cannot be excluded that Müller's description of light signals was influenced by {{slink||Langevin 1911-HU}}, published in July, in which light signals were used as well.}} |} ==Twins from 1911 to 1920== We now provide a list of authors who employed ''twins'', i.e. ''two'' life forms or humans that initially were of ''same age'' when the round-trip began: {| class="wikitable" style="background-color:white;" |- ! Author !! Date !! Description |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> |1911 |Two life forms that begin their life at the ''same time'' (German: "Zwei Lebewesen [..] die ihr Leben gleichzeitig beginnen"), of which the moving one returns retarded in its progression with respect to the stationary one. |- |[[w:Paul Gruner|Gruner]]<ref name=gruner /> |1912 |Two persons of ''same age'' (French: "deux personnes du même âge"), of which the moving one returns less developed than stationary one. |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> |1913 |The moving life form returns younger than its ''former agemates'' (German: "ehemaligen Altersgenossen"). |- |[[w:Hermann Weyl|Weyl]]<ref name=weyl /> |Easter 1918 | {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Von zwei Zwillingsbrüdern, die sich in einem Weltpunkt A trennen, bleibe der eine in der Heimat (d. h. ruhe dauernd in einem tauglichen Bezugsraum), der andere aber unternehme Reisen, bei denen er Geschwindigkeiten (relativ zur »Heimat«) entwickelt, die der Lichtgeschwindigkeit nahekommen; dann wird sich der Reisende, wenn er dereinst in die Heimat zurückkehrt, als merklich jünger herausstellen denn der Seßhafte. |Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. |} {{Lorentzbox|Text=Weyl was the first to ''explicitly use twins'' in relation to the round-trip experiment. The fourth edition (1920) of that book was translated from German into English and French in 1922.}} |- |[[w:Albert Einstein|Einstein]]<ref name=einstein20 /> |1920/21 |{{Anchor|Einstein 1921-TW}} {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Trifft A wieder bei B ein, so kann es sich ereignen, daß der beharrende Zwilling inzwischen 60 Erdjahre alt geworden ist, während der zurückkehrende nur 15 Jahre zählt, oder sich gar noch im Säuglingsstadium befindet. [..] Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls -Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. |If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still. [..] In the case of these two twins, Einstein declared, we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures. |} {{Lorentzbox|Text=This was based on an interview of Einstein by Moszkowski. While the expression "clock paradox" was used since 1911/12 (see section {{slink||Paradoxical?}}), this seems to be the first time that it was rebranded as "twin paradox". The copyright mark indicates 1920, while the title page indicates 1921. The translation from German into English also appeared in 1921.}} |} ==Maximal proper time== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]] 1911 |{{anchor|Langevin 1911-PT}}In April 1911 (published July),<ref name=langevin1 /> he described the round-trip experiment without formulas using two portions of matter present at two events happening at the same place. The ''integration of proper time'' along the entire wordlines shows that the portion of matter that starts a closed cycle by receding and finally coming back, will have a ''smaller proper time'' than the one that stayed behind. In October 1911 (published 1912),<ref name=langevin2 /> Langevin again showed that the portion of matter that described a closed cycle will have a ''smaller proper time'' <math>R</math> than the one that stayed in an inertial frame, which is defined by the equation: :<math>\begin{matrix}V^{2}\left(t-t_{0}\right)^{2}=d^{2}-R\\ \left[d^{2}=\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}\right] \end{matrix}</math> |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> Lectures March-May 1911 submitted July published September |{{anchor|Wiechert 1911-PT}}Let two equal processes be observed in two equal material systems colocated in two moments (1) and (2), and let there velocities have been changed in arbitrarily different ways in the meantime. It follows that the ratio of advancement of those processes is given by the two intervals <math>\Delta\tau </math> of their respective ''proper times''. He concluded that any round-trip clock experiment can be easily comprehended from that theorem by computation. The corresponding integral is: :<math>\Delta\tau=\int_{1}^{2}d\tau=\int_{1}^{2}dt\sqrt{1-\frac{\mathfrak{v}^{2}}{c^{2}}}</math> |- |[[w:Eduard Study|Study]]<ref name=study /> June 1911 |Minkowski's concept of worldlines implies that the straight path between two points of the same worldline is the ''longest'' among all paths between those points, if the path length on a worldline is defined by the related proper time. {{Lorentzbox|Text=Study's book was purely mathematical without mentioning clocks or the round-trip experiment, alluding to his result only in a footnote.}} |- |[[w:Max von Laue|Laue]] 1911-13 |{{anchor|Laue 1911/12-PT}}In December 1911 (published 1912),<ref name=laue1 /> Laue showed without formulas that the round-trip experiment is represented by a curved worldline, which at worldpoint A decomposes into a row of curves, after which all of them will be re-united at worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the ''longest proper time.'' {{anchor|Laue 1912/13-PT}}In December 1912 (published 1913) in the second edition of this relativity book,<ref name=laue1 /> Laue described the proper time integral between events 1 and 2 of a slowly accelerated clock covering a broken line and a stationary clock covering a straight worldline. Of all worldlines covering 1 and 2, the straight line has the ''longest proper time''. Therefore the traveling clock in the round-trip experiment is retarded at reunion, because its curved worldline corresponds to a shorter proper time. This result he presented in terms of the following inequality, of which the right-hand side refers to the straight curve of the stationary clock, while all others possible curves are represented on left-hand side: :<math>\tfrac{1}{c}\int_{1}^{2}\sqrt{du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}<\tfrac{1}{c}\int_{1}^{2}du</math> {{Lorentzbox|Text={{anchor|Sommerfeld 1913-PT}}Similar treatments can be found in the textbooks of [[w:Arnold Sommerfeld|Sommerfeld]] (1913),<ref name=sommerfeld /> [[w:Hermann Weyl|Weyl]] (1918),<ref name=weyl /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Jean Becquerel|Becquerel]] (1922).<ref name=becqu1 />}} |} ==Triangle inequality== {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Alfred Robb|Robb]] 1914-1920 |{{anchor|Robb 1914-TR}}In 1914<ref name=robb1 /> he showed that there are three types of triangles formed by intervals in Minkowski space, depending on whether one deals with "separation lines" (spacelike intervals), "optical lines" (lightlike intervals), or "inertia lines" (timelike intervals representing the path of nonaccelerated particles defined by <math>{\scriptstyle \left(x_{1}-x_{0}\right)^{2}+\left(y_{1}-y_{0}\right)^{2}+\left(z_{1}-z_{0}\right)^{2}-c^{2}\left(t_{1}-t_{0}\right)^{2}<0}</math>). As to a triangle formed by inertia lines, he showed that the sum of a certain two sides is ''less'' than that of the third one. {{Lorentzbox|Text=So the triangle inequality derived from time-like intervals in Minkowski space is ''[[w:Triangle inequality#Reversal in Minkowski space|inverse]]'' to the inequality in Euclidean space. This inverse inequality directly represents the most simple variant of the twin paradox: the traveler follows two sides of the time-triangle, while the stay-at-home observer follows the third side indicating maximal proper time.}} [[File:RobbTriangle.svg|right|150px]] In 1920<ref name=robb2 /> Robb gave a numerical example of the triangle ABC with time-like intervals ("inertia lines") defined by coordinates :<math>\begin{matrix} & x & y & z & t\\ A\ & 0 & 0 & 0 & 0\\ B\ & 0 & 0 & 0 & 10\\ C\ & 4 & 0 & 0 & 5 \end{matrix}</math> which he plugged into :<math>\bar{s}^{2}=\left(t_{1}-t_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}-\left(y_{1}-y_{0}\right)^{2}-\left(z_{1}-z_{0}\right)^{2}</math> from which he obtained the sides AB=10, AC=3, CB=3 and the inequality <math>AC+CB<AB</math>. |- |[[w:Arthur Eddington|Eddington]]<ref name=edding2 /> 1922 |He distinguished between the "space-triangle" for spacelike intervals, and the "time-triangle" for time-like intervals. The latter is measured with a clock from A to B and from B to C, with the sum of those readings ''is always less'' than the reading of a clock measuring directly from A to C. In the ordinary space-triangle any two sides are together greater than the third side; in the time-triangle two sides are together ''less'' than the third side. |- |Rogers<ref name=rogers /> 1922 |He showed that the "pure time-triangle" C, A, B (in their proper time order) satisfies the relation <math>\cosh C=\tfrac{\alpha^{2}+\beta^{2}-\gamma^{2}}{2\alpha\beta}</math>, where <math>\cosh C</math> denotes the unit-scalar product of the vectors CA, CB, and <math>\alpha,\beta,\gamma </math> the real and positive intervals BC, CA, AB. Since <math>\alpha>\beta </math> and <math>\cosh C>1</math>, it follows that <math>\alpha>\beta+\gamma </math>. That is, "the greatest side of pure time-triangle is greater than the sum of the other two sides". It follows at once that the stationary value of the proper time integral is an "absolute maximum". |} ==Negligibility of proper acceleration== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |style="vertical-align:top" |[[w:Albert Einstein|Einstein]] 1905-1918 |In 1905,<ref name=einstein05 /> Einstein used velocity time dilation <math>\tau=t\sqrt{1-\left(\frac{v}{V}\right)^{2}}</math> to derive the retardation of a clock performing a round-trip with constant speed <math>v</math> along a polygonal path or a continuously curved line, without mentioning any influence of acceleration at turnaround. {{anchor|Einstein 1911-VA}} In 1911 (published 1912),<ref name=einstein3 /> Einstein said that special relativity doesn't say anything about what happened to the clock's pointer position during the acceleration that changes the clock's direction along the round-trip, yet the influence of this change must be getting smaller the longer the clock ''is moving uniformly'', i.e. the longer one chooses the dimensions of the path. {{anchor|Einstein 1912-VA}}In an unpublished manuscript on special relativity from 1912,<ref name=einst12manu /> he pointed out that any influence of acceleration during the round-trip experiment, can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygonal path. {{anchor|Einstein 1914a-VA}}In a letter from April 1914,<ref name=einstpetz /> Einstein showed that any ''finite'' acceleration at turnaround during the round-trip experiment can only influence the clock in a ''finite'' way, thus it can be neglected by minimizing the time of acceleration with respect to the time of uniform translation. So it ''must be concluded'' that the clock is retarded at reunion after traveling on a polygonal path. {{anchor|Einstein 1914b-VA}}During a conversation in May 1914,<ref name=rowe group=S /> Einstein is reported to have replied that the accelerations during the round-trip are "irrelevant for the amount of the time difference". (Compare with {{slink||Einstein 1914b-AC}}) {{anchor|Einstein 1918-VA}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918,<ref name=einstein18 /> Einstein pointed out that any effect of velocity changes at turnaround must be limited, thus the traveling clock must be retarded at reunion due to time dilation if one makes the path AB and back along the round-trip long enough. (Compare with {{slink||Einstein 1918-AC}}) |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> 1911 |{{Anchor|Wiechert 1911-VA}}[[File:WiechertTwin.svg|110px|right]] He demonstrated that differential aging along the round-trip cannot be caused during the passage from one velocity to another (i.e. acceleration) at turnaround, because the same result also follows when ''both'' A and B experience the ''same velocity changes'' with respect to another frame, only with the difference that B has relative velocities <math>+u</math> and <math>-u</math> for a long time, while A is brought after a short time from relative velocity <math>+u</math> to relative rest at which it remains a long time, and then it is brought to relative velocity <math>-u</math> for a short time. {{Lorentzbox|Text=He was probably the first to use an example in which both accelerate with same magnitude.}} |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> 1913 |{{anchor|Laue 1913-VA}}He showed that the problem of the influence of acceleration at turnaround in the round-trip experiment, can be eliminated by ''arbitrarily'' enlarging the time in inertial motion. {{Lorentzbox|Text=This is the same argument as given in {{slink||Einstein 1911-VA}}. The Einstein-Laue argument was also used by others such as [[w:Hans Thirring|Thirring]] (1921)<ref name=thirring /> or [[w:Max Born|Born]] (1921).<ref name=born />}} |- |[[w:Hendrik Lorentz|Lorentz]]<ref name=lorentz1 /> 1913 |He pointed out that any effect of acceleration on the traveling clock at turnaround, can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip. {{Lorentzbox|Text=Similarly, [[w:Wolfgang Pauli|Pauli]] (1921) stated that the arising infinitesimal accelerations at turnaround are certainly independent of the total travel time and ''therefore easy to eliminate''.<ref name=pauli />}} |} ==Relay (three brothers) experiment== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:de:Fritz Grünbaum (Physiker)|Grünbaum]]<ref name=gbaum /> 1911 |He discussed a one-way time dilation experiment in which the first clock is set into motion from the origin and then moving to the second clock. He argued that one can avoid the problem of acceleration experienced by the first clock when set into motion, by replacing it with a ''third'' clock that is already in motion with constant velocity and is synchronized at the origin with the first clock. {{Lorentzbox|Text=While Grünbaum didn't discuss round-trip experiments, his introduction of a third clock in order to avoid acceleration is the basis of the three-brother experiment.}} |- |style="vertical-align:top"|[[w:Emil Wiechert|Wiechert]] 1920-1922 |In 1920 (published 1921),<ref name=wiechert20 /> Wiechert explained how to completely remove acceleration from the round-trip experiment: Bodies A, B, C move undisturbed and non-accelerated in different directions. A and B pass each other at time (1), B and C pass each other at a later time (2), and C and A finally pass each other at an even later time (3). So in this setup, the condition of C is the continuation of the condition of B. On any of the three bodies one can count the oscillations of light of a certain spectral-line, in which case relativity predicts that the ''combined sum of all oscillations'' on B+C is smaller than the number of oscillations on A alone. Wiechert also held that one can replace the light oscillations by the life functions of human-like beings which live on A, B and C. For instance, while the inhabitants of B+C only had time for one meal, there were arbitrarily many generations on A who follow after each other by death and birth. [[File:Wiechert1922a.png|180px|right]] In 1921 (published 1922),<ref name=wiechert21 /> Wiechert extended his previous acceleration-free round-trip experiment to an arbitrary number of non-accelerated bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., which constitutes a "relay" (German: Stafette) starting from body A and back again. The first B passes A and moves away, and after some time the last B comes back to A. Since any B body continues the fate of the previous one, all bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., combined have emitted fewer oscillations than A alone during the relay race. Wiechert pointed out that instead of light oscillations one can also choose the aging of life forms. {{Lorentzbox|Text=Such relay experiments were later independently rediscovered in English language papers<ref name=debs group=S /> such as by Lange (1927)<ref group=S name=lange /> in which the brothers synchronize their times when they pass each other (“three brother experiment”).}} |} ==Acceleration as asymmetry indicator== While it was known that any direct influence of [[w:proper acceleration]] on clocks can be neglected in the computation of the inertial frame of the stay-at-home twin (see previous section {{slink||Negligibility of proper acceleration}}), the very fact that only one of them is accelerating is still useful as an asymmetry argument in order to show that there is no contradiction to the relativity principle. {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{Anchor|Langevin 1911-AC}}He derived differential aging in the round-trip experiment using the proper time integral along worldlines (see {{slink||Langevin 1911-PT}}) and used acceleration as an asymmetry indicator: The result of the round-trip experiment is "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". |- |[[w:Arnold Sommerfeld|Sommerfeld]]<ref name=sommerfeld /> 1913 |After he showed (see {{slink||Sommerfeld 1913-PT}}) that retardation of time in the round-trip experiment derived from the proper time integral rests on the assumption that the clock's rate ''only depends on its momentary velocity'' (now called "clock hypothesis"), he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle since one of the clocks has to be accelerated in order to come back, thus the retardation in the round-trip experiment does not demonstrate "motion", but "accelerated motion". |- |[[w:Hendrik Lorentz|Lorentz]] 1913<ref name=lorentz1 /> |After he derived differential aging in the round-trip experiment from velocity time dilation and pointed out the negligibility of proper acceleration for the computation, he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle, since one of them changes velocity and accelerates; the relativity principle does not require symmetry between inertial and non-inertial observers. |- |style="vertical-align:top"|[[w:Albert Einstein|Einstein]] 1914-1920 |{{anchor|Einstein 1914b-AC}} During a conversation in 1914,<ref name=rowe group=S /> Einstein is reported to have said that moving clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are ''irrelevant'' for the ''amount'' of the time difference, their ''presence'' nevertheless cause B to fall behind ("accelerated motions are absolute"). {{anchor|Einstein 1918-AC}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918<ref name=einstein18 />, Einstein pointed out the negligibility of velocity changes from the viewpoint of an inertial frame (see {{slink||Einstein 1918-VA}}). Then he used ''acceleration as an asymmetry indicator'' in order to show, that there is no contradiction to the relativity principle, because relativity only predicts the equivalence of non-accelerated inertial frames: "only K is such a frame while K' is temporarily accelerated, thus the retardation of U2 with respect to U1 cannot be used to construe a contradiction against the theory." {{anchor|Einstein 1920-AC}}Einstein is reported to have said in an interview from 1920:<ref name=einstein20 /> {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls-Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. Dieser Grund für das Jüngerbleiben des A ergibt sich vom Gesichtspunkt der speziellen Relativitätstheorie aus der Tatsache, daß das betreffende Geschöpf — und nur dieses — Beschleunigungen erlitten hat. | style="padding: 0px 20px 0px 20px;" |In the case of these two twins," Einstein declared, "we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures . This ground, which counts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations." |} In a discussion from 1922,<ref name=morand /> Einstein is reported to have said that there is no contradiction in the round-trip experiment (in terms of a train leaving the station and returning later): The relativity principle is not applicable to this case, because the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two frames having velocities in opposite direction is not an inertial frame. There is no reciprocity between a frame that changes direction and one that doesn't. |} ==Frame distribution as asymmetry indicator== Because any direct influence of proper acceleration on the traveling clock at turnaround can be neglected (see {{slink||Negligibility of proper acceleration}}), the importance of {{slink||Acceleration as asymmetry indicator}} is limited to the mere fact that it reveals that only the traveler was in a non-inertial frame as only he changed his inertial frames, thus instead of emphasizing the occurrence of proper acceleration at turnaround, it's possible to describe the asymmetry more geometrically by emphasizing the different distribution of inertial frames of the twins along their worldlines. {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Max von Laue|Laue]] 1911-1913 |{{Anchor|Laue 1911/12-VA}} In 1911/12,<ref name=laue1 /> he pointed out that during the time of separation, that clock is most advanced which was at rest in an inertial frame all the time; namely there is ''always one, and only one inertial frame'', in which the locations of separation and re-encounter lie in the same geometric point. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1911/12-PT}}). In 1912/13,<ref name=laue2 /> he argued that in the round-trip experiment, we indeed can decide, which one of the clocks was steadily at rest in one and the same reference system, and which one was in the meantime at rest in two or more such systems. Among them there is of course a real physical difference. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1912/13-PT}}). In 1913<ref name=laue3 /> Laue pointed out: {| !style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Aber nach unseren Voraussetzungen ruht während der Zeit der Trennung die erste Uhr in ''einem'' berechtigten Bezugssystem, die zweite hingegen ruht zwar sowohl bei der Hin- wie bei der Rückbewegung in berechtigten Bezugssystemen, aber notwendig in ''zwei verschiedenen. Deshalb'' unterscheiden sich beider Schicksale physikalisch. Ließe man die zweite Uhr in der ihr anfangs erteilten Bewegung und schickte man ihr dafür die erste Uhr nach einiger Zeit mit größerer Geschwindigkeit nach, so würde beim Zusammentreffen die erste gegen die zweite zurückgeblieben sein; denn jetzt hat die erste während der Trennung in zwei verschiedenen Systemen geruht. (Footnote: Dem naheliegenden Einwand, daß wir über den Gang einer Uhr während eines Geschwindigkeits''wechsels'' nichts aussagen können, begegnet man am einfachsten mit dem Hinweis, daß man die Zeiten der gleichförmigen Bewegung ''beliebig'' groß gegen die der Beschleunigung machen kann.) | style="padding: 0px 20px 0px 20px;" | However, by our presuppositions, one clock is at rest in ''one'' valid reference system during the time of separation, while the second one is at rest in valid reference systems both during the forward- and the backward motion, but necessarily in ''two different ones. Therefore'' the two fates differ physically. If the second clock remains in the motion which was given to it at the start, and if after some time it is followed by the first clock with greater velocity, then the first one would be retarded with respect to the second one at the encounter; since now it was the first one that was at rest in two different systems during the separation. (Footnote: The objection which is near at hand, that we cannot say anything about the rate of a clock during a velocity ''change'', can be met most simply by the allusion, that we can render the times of uniform motion ''arbitrarily'' great with respect to acceleration..) |} |- |[[w:Werner Bloch|Bloch]]<ref name=bloch /> September 1918 |{{anchor|Bloch 1918-VA}} He represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. |} ==Perspective of the traveler== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{anchor|Langevin 1911-LI}}[[Image:rstd4.gif|170px|right]] After deriving differential aging from the proper time integral in {{slink||Langevin 1911-PT}} and using human beings in {{slink||Langevin 1911-HU}}, he described the perspectives of both observers using light signals and the Doppler effect. When they separate they see each other live 200 times slower, while at return they see each other live 200 times faster. So ''from the explorer's viewpoint'', in the first year he sees the Earth perform the actions of two days, while in the second year he sees the Earth perform the actions of two centuries. The asymmetry can be seen by noticing, that the observer on Earth in 200 years sees the explorer performs the actions of 1 year. Then the explorer turns around, after which the observer on Earth in 2 days sees the projectile perform the actions of another year. {{Lorentzbox|Text=Langevin used <math>v=c\left(1-\tfrac{1}{20000}\right)</math>, producing Lorentz factor <math>\gamma\approx100</math> and Doppler factor <math>\sqrt{\tfrac{c+v}{c-v}}\approx200</math>.}} |- |[[w:Hendrik Lorentz|Lorentz]] Lectures published in 1913<ref name=lorentz1 /> Similar treatment in 1914<ref name=lorentz3 /> |{{anchor|Lorentz 1913/14-LI}}Described the round-trip experiment in terms of inertial observer A (equipped with clock K) and traveling observer B (equipped with clock K'). In the frame of A, clock K' is retarded with respect to K at reunion due to time dilation. He then described the perspective of the traveling observer B by using two-way propagation of light from K' to K and back to K', leading to three periods defined by the moment of B's turnaround: In the first period the light signals return to K' before turnaround; in the second period the signals are emitted before turnaround and return after turnaround; in the third period emission and return of the signals are both happening after turnaround. Lorentz showed that K is time dilated by a factor of <math>\sqrt{1-v^{2}/c^{2}}</math> with respect to K' in the first and third period, but in the second period K is ticking ''faster'' than K' by a factor of <math>\sqrt{\tfrac{c+v}{c-v}}</math> which overcompensates the dilation in the other periods and explains, even from the perspective of B, why K' is retarded with respect to K at reunion. {{Lorentzbox|Text=In a review of the German translation of Lorentz's book, Einstein (1914) didn't directly mention Lorentz's treatment of the twin paradox, but he wrote that nobody who is seriously interested in relativity should neglect to read that book.<ref name=einstlor /> [[w:Wolfgang Pauli|Pauli]] (1921) refers to Lorentz's book as one of three papers that analyze the twin paradox more closely.<ref name=pauli />}} |- |style="vertical-align:top"| [[w:Albert Einstein|Einstein]] 1916-1920 |{{anchor|Einstein 1916-EP}}In a lecture from 1916,<ref name=einstein16 /> of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of [[w:general relativity]]." {{anchor|Einstein 1918a-EP}}In a letter from September 1918,<ref name=einadl /> Einstein showed that general relativity makes the inertial frame K and and the accelerated frame K' of the clocks in the round-trip experiment "equally justified", explaining the time difference in K' by combining the influence of velocity and gravitational potential on clocks. {{anchor|Einstein 1918-EP}}In his famous "Dialog about Objections against the Theory of Relativity" from November 1918,<ref name=einstein18 /> aimed at clarifying misconceptions of the clock paradox, he explained that there is no paradox in special relativity because there is no symmetry between clock U1 at rest in inertial frame K and clock U2 at rest in accelerated frame K' (see {{slink||Einstein 1918-AC}}). Yet [[w:general relativity]] and the [[w:equivalence principle]] allow the treatment of this problem also from the standpoint of frame K', where clock U2 remains at rest all of the time while U1 makes the following movements: (1) It is accelerated by a homogeneous gravitational field in the negative direction, (2) it moves with constant velocity <math>-v</math>, (3) it is accelerated in the positive direction until it turns around and comes by with constant velocity <math>+v</math>, (4) it moves with velocity <math>+v</math>, (5) it is accelerated in the negative direction until it stops. Clock U1 is retarded with respect to U2 in periods 2) and 4) due to velocity time dilation, but this retardation is overcompensated by the faster rate of U1 during period 3), because U1 is at a higher gravitational potential. He argued that the computation (which he didn't provide) shows that the advance of U1 in period 3) is double its retardation during periods 2) and 4). Einstein concluded that by this consideration "the paradox is completely resolved". Using [[w:Mach's principle]], he pointed out that the gravitational field in K' might be induced by the masses of the universe that are accelerated in this frame. {{anchor|Einstein 1918b-EP}}In a letter to Einstein from December 1918, [[w:Max Jakob|Jakob]] doubted the result that the advance in period 3) is double the retardation during periods 2) and 4). Einstein responded by letter,<ref name=einstein18b /> in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). {{anchor|Einstein 1921-EP}}Einstein is reported to have said in an interview from 1920,<ref name=einstein20 /> that while acceleration explains the age difference between the stationary twin B and the traveling twin A in terms of special relativity (see {{slink||Einstein 1920-AC}}), the "proper" description in terms of general relativity is as follows: {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Eine tiefere Erfassung des Grundes ist indeß nur auf dem Boden der „Allgemeinen Relativitätstheorie" zu erlangen, die uns erkennen läßt, daß von A aus beurteilt ein Zentrifugalfeld existiert, von B aus betrachtet aber nicht; und dieses Feld hat einen Einfluß auf den relativen Ablauf und die Raschheit der Lebensvorgänge. | style="padding: 0px 20px 0px 20px;" | A proper grasp of the reason is furnished only when we adopt the general theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life." |} {{Lorentzbox|Text=a) Einstein's explanation was quickly adopted in the textbooks of [[w:Werner Bloch|Bloch]] (1920),<ref name=bloch2 /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Karl Bollert|Bollert]] (1921),<ref name=bollert1 /> [[w:Max Born|Born]] (1921),<ref name=born /> expressing the view that general relativity is "necessary" to provide the "complete" solution of the twin paradox. b) From a modern standpoint, however, Einstein's explanation has nothing to do with general relativity, but is rather an application of accelerated frames and "pseudo"-gravitational fields to flat Minkowski space of ''special'' relativity.<ref name=weiss group=S />}} |- |[[w:Hans Thirring|Thirring]]<ref name=thirring /> April 1921 |{{anchor|Thirring 1921-DS}}[[Image:Twin Paradox Minkowski Diagram.svg|right|200px]] He described the round-trip experiment by using two platforms K (clock A) and K' (clock B) each equipped with rows of clocks. He first demonstrated the symmetry of time dilation and the mutual relativity of simultaneity on the platforms and its effect on clock synchronization. The K clocks that B passes are all advanced because of <math>t'=\gamma\left(t-vx/c^{2}\right)</math>, and the same is true after turnaround since only the direction of velocity has to be changed in the Lorentz transformation <math>t'-t'_{0}=\gamma\left(t+vx/c^{2}\right)</math> leading to the effect of clock desynchronization, where <math>t'_{0}</math> is a constant depending on which clock one uses as standard for the new synchronization. He graphically showed using Minkowski diagrams, that this simultaneity jump due to desynchronization amounts to double the velocity time dilation during the inertial phases, explaining why A is more advanced than B at reunion. {{Lorentzbox|Text=Using clock B as synchronization standard, Thirring's constant is given by <math>t'_{0}=2l\gamma v/c^{2}=2t\gamma v^{2}/c^{2}</math> with <math>l=vt</math> as position of turnaround. A similar explanation was subsequently given by Langevin (1922).<ref name=morand />}} |} ==Curved spacetime== While the previous examples are defined in flat Minkowski spacetime and therefore can be fully discussed in terms of special relativity, [[general relativity]] is required when [[:w:spacetime curvature]] in the presence of mass and energy cannot be neglected any more.<ref name=koks group=S /> {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |[[w:Jean Becquerel|Becquerel]]<ref name=becqu1 /> 1922 |After defining gravitational time dilation <math>d\tau=\sqrt{1-\tfrac{2GM}{c^{2}r}}dt</math> in terms of the [[w:Schwarzschild metric]] around a material center, he discussed the following round-trip experiment: There are two identical clocks A and B placed next to each other, at a point very far from the material center, initially marking the same time <math>t</math>. Let us transport clock A to a point where the field is more intense, at a distance <math>r</math> from the center; this clock will measure time <math>\int d\tau</math> which is shorter than <math>\int dt</math>, thus it will run more slowly. If we bring clock A back to clock B, we will have to note that it is retarded with respect to B. |} ==Aether interpretations== [[w:Lorentz ether theory]] (LET) is empirically equivalent to special relativity since both models use the Lorentz transformation, thus the description of the twin paradox gives the same result as well. However, special relativity is preferred by the scientific community, because of the validity of the relativity principle in LET is only apparent due to a conspiracy of effects which makes the aether undetecable, and because the measured times and lengths in the aether are supposedly be giving the "true" values even though it is empirically impossible to determine which ones are true or apparent. {| class=wikitable style="background-color:white;{{text default color}};" |- ! style="width:150px" | Author !! Description |- |Langevin (1911)<ref name=langevin1 /> |He argued that it's true that uniform translation with respect to the aether has no experimental meaning in special relativity, though one can still speak of "absolute acceleration" with respect to an aether which he defined as the light carrying medium, so it was "premature to abandon the aether". The absolute nature of acceleration can be seen in the radiation of accelerated charges, as well as in the twin paradox in which the traveler that is more agitated or accelerated is younger at reunion. {{Lorentzbox|Text=Langevin didn't mention this aether interpretation in his later discussions of the twin paradox in 1911/12<ref name=langevin2 /> and 1919.<ref name=langevin3 />}} |- |style="vertical-align:top" |{{Anchor|Wiechert 1911b}}Wiechert (1911)<ref name=wiechert11 /> |Contrary to Langevin, he emphasized that differential aging can be attributed to the existence of absolute "velocities" which he called "strides" (German: Schreitungen, denoting the "absolute meaning" of non-accelerated motions) with respect to the aether, whereas he dismissed the role of accelerations. In other words, the clock's "strides" are not equivalent or anisotropic with respect to the aether, in contradiction to the "unconditional" relativity principle Einstein's which requires equivalence and symmetry. Wiechert proposed a "conditional" relativity principle in which the aether (in the sense of Lorentz) determines all processes in nature, thus the rate of clocks or processes is "really" altered during motion. {{Lorentzbox|Text=a) This aether interpretation was maintained by Wiechert also in subsequent publications in 1915-1922.<ref name=wiechert15 /><ref name=wiechert20 /><ref name=wiechert21 /> b) Wiechert's interpretation in terms of absolute non-accelerated motions was also independently given by others: [[s:fr:Georges Lechalas]] (1912/13)<ref name=lech /> argued that time dilation and asymmetric aging are the result of absolute speeds with respect to an aether, while criticizing Langevin's (1911) argument that only accelerations can indicate the aether and are responsible for the asymmetric aging; [[w:Edward Vermilye Huntington]] (1912)<ref name=hunt /> argued that the "famous paradoxes of the theory of relativity" represented by the reciprocal nature of length contraction and time dilation, appear as necessary consequences of perfectly natural and reasonable conventions for setting clocks and laying out coordinates, when the Lorentz transformation is derived and interpreted on the basis of a stationary aether in the sense of Lorentz. c) Laue (1911/12)<ref name=laue1 /> applauded Wiechert for the "particularly striking way" in which he demonstrated that asymmetric aging indeed follows from the relativity laws, yet he rejected Wiechert's aether interpretation and Wiechert's claim that asymmetric aging contradicts the "unconditional" relativity principle: Laue pointed out that the straight worldline connecting two events A and B is only "preferred" insofar as it indicates the maximal proper time between them, yet this preference is ''not'' the result of the natural laws employed, but is rather due to the choice of points A and B; by analogy, the geometric result that two points determine a straight line and thus a direction as well, doesn't refute the physical equivalence of all directions in space; finally, as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.}} |} ==Paradoxical?== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" | German original of [[w:Max von Laue|Laue]] (1911/12):<ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> ! English translation |- |Unter all den paradox erscheinenden Folgerungen aus der Zeittransformation der Relativitätstheorie gibt es wohl keine, gegen welche sich der natürliche Menschenverstand bei jedem, der der Sache noch ungewohnt ist, so sehr sträubt, wie gegen die, daß die Zeitangabe einer Uhr von ihrem Bewegungszustand abhängen soll. Schon in seiner grundlegenden Arbeit hat Einstein diese Paradoxie auf die Spitze getrieben in einem Gedankenexperiment, welches neuerdings von Langevin in einem auch sonst sehr lesenswerten Vortrage besonders hübsch erläutert worden ist. |Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. |- |colspan=2|{{Lorentzbox|Text=Laue was probably the first to denote the round-trip experiment as paradoxical (even though he pointed out that there are no real contradictions). Subsequently, [[:w:Paul Gruner|Gruner]] (1912)<ref name=gruner /> and others including Einstein (1918)<ref name=einstein18 /> explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas [[w:Rudolf Seeliger|Seeliger]] (1913)<ref name=seel /> spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon").}} |} ==Misunderstandings== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" padding=10 | German original by [[w:Otto Berg (scientist)|Berg]] (1910):<ref name=berg /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |Im Punkte <math>x = 0</math> des Systems S befinde sich eine Uhr, eine andere im Punkte <math>x'=0</math> von S'. Diese zweite bewege sich mit S' bis zum Punkte <math>x = a</math>, kehre dort um und bewege sich nun mit der Geschwindigkeit <math>v</math> zurück bis zum Punkte <math>x= 0</math>. Welche Zeit müssen beide Uhren in dem Moment angeben, wo sie sich wieder treffen? Wir beantworten diese Frage zunächst vom Standpunkt des Beobachters in S. Die Uhr in <math>x' = 0</math> hat sich mit der Geschwindigkeit <math>v</math> bis zum Punkte <math>x = a</math> bewegt; dazu brauchte sie die Zeit <math>\tau=\tfrac{a}{v}</math>. Zum Rückweg ist dieselbe Zeit nötig. Nach der Zeit <math>2\tau=2\tfrac{a}{v}</math> ist die Uhr also wieder im Punkte <math>x = 0</math> angelangt. Wir stellen uns nun auf den Standpunkt des Beobachters in S'. Für diesen führt nach dem Relativitätsprinzip das System S genau dieselben Bewegungen aus wie das System S' für den Beobachter in S, nur in entgegengesetzter Richtung. Die Zeit bis zum Zusammentreffen beider Uhren ist also im System S' ebenfalls gegeben durch <math>2\tau=2\tfrac{a}{v}</math>. Betrachtungen, die auf anschauliche Vorstellungen, wie Nachgehen von Uhren, gestützt sind, führen hier leicht zu Irrtümern, von denen auch die Fachlitteratur nicht frei ist. | style="padding: 0px 20px 0px 20px;" |There is a clock at point <math>x=0</math> of system S, and another one at point <math>x'=0</math> of S'. The second one moves together with S' until point <math>x=a</math>, turns around and now moves back with speed <math>v</math> to point <math>x=0</math>. Which time must both clocks indicate at the moment at which they encounter again? We answer this question at first from the standpoint of the observer in S. The clock at <math>x=0</math> has been moving with speed <math>v</math> until point <math>x=a</math>, for which it required time <math>\tau=\tfrac{a}{v}</math>. The same time is required for the way back. After time <math>2\tau=2\tfrac{a}{v}</math> the clock has thus arrived again at point <math>x=0</math>. Let's now take the standpoint of the observer in S'. In his view in accordance with the relativity principle, system S is conducting exactly the same motions as those of system S' with respect to the observer in S, only in opposite direction. Thus the time until the meeting of both clocks is given by <math>2\tau=2\tfrac{a}{v}</math> in system S' as well. Considerations based on illustrative notions, such as the retardation of clocks, easily lead to mistakes at this place, of which also the professional literature isn't free. |- |colspan=2|{{Lorentzbox|Text=a) Berg was probably the first to turn the relativity principle against asymmetric aging in the round-trip experiment, claiming that both clocks must indicate the same time at reunion. See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem. b) Berg's mistake also seems to be based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" padding=10 | German original by [[w:Otto Lehmann (physicist)|Lehmann]] (1910/11):<ref name=lehm /> ! English translation |- | style="padding: 0px 20px 0px 20px;" | Hat man zwei genau gleich gehende Uhren nebeneinander und bewegt nun die eine auf einer beliebigen Kurve bis wieder zur anderen zurück, welche Bewegung <math>t</math> Sekunden gedauert haben möge, so geht sie gegen diese um <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> oder annähernd <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> Sekunden zu spät, weil sie während der Bewegung auf langsameren Gang reguliert werden mußte, um mit der ruhenden Uhr in Übereinstimmung zu bleiben. | style="padding: 0px 20px 0px 20px;" | If there are two exactly identical clocks next to each other, and if one of them will be moved on an arbitrary curve until it comes back, which may have lasted <math>t</math> seconds, it [the moving clock] will lag behind the other one by <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> or approximately <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> seconds, because it [the moving clock] had to be regulated to a slower rate during motion in order to remain synchronous with the resting clock. |- |colspan=2|{{Lorentzbox|Text=a) So Lehmann erroneously thinks that the time difference at reunion is only the result of "regulating" the moving clock. This implies that he (like Berg) believed that special relativity predicts ''equal'' clock times at reunion if the moving clock would have been left ''unregulated'' during the round-trip. b) Lehmann's mistake (similar to Berg) seems to based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" | German original by [[w:Emil Wiechert|Wiechert]] (1911)<ref name=wiechert11 /> ! English translation |- |colspan=2| Even though he correctly derived differential clock aging in the round-trip experiment, he (like Berg and Lehmann) claimed that effects like time dilation are "apparent" if one admits Einstein's "unconditional" relativity principle in which there is no aether and all "strides" (i.e. non-accelerated motions) are physically equivalent, but they are "real" if one admits the existence of an aether in the framework of a "conditional" relativity principle in which all strides are physically non-equivalent or anisotropic. This led him to the following interpretation of the clock paradox: |- | style="padding: 0px 20px 0px 20px;" |[...] so muß am Schluß des Versuches B in seinem Fortschritt gegenüber A im Verhältnis <math>1:\sqrt{1-u^{2}/c^{2}}</math> zurückgeblieben sein. Und dieses Zurückbleiben ist unbedingt reell, denn die beiden Gebilde A und B können ja unter gleichen Umständen unmittelbar beieinander verglichen werden. Hier ist es ganz sicher ausgeschlossen, an einen Schein zu glauben, der durch unsere Auffassung der Zeit bewirkt wird. So ist denn also auch die Folgerung unabwendbar, daß für den Verlauf der Weltvorgänge die Schreitungen nicht gleichwertig sind, ''und damit sind wir von neuem zu einem Schluß gekommen, welcher der Unbedingtheit des Relativitätsprinzipes durchaus widerspricht.'' [...] Man kann den Versuch noch mannigfach variieren, z. B. so, daß A ebenso wie B zwei verschiedene Schreitungen, <math>+u</math> und <math>-u</math>, nacheinander inne hat. Wird dann zu A der Wert <math>u_{1}</math>, zu B der Wert <math>u_{2}</math>, zugeordnet, so muß der Vergleich von A und B am Schluß des Versuches ergeben, daß B oder A in seinem Fortschritt zurückgeblieben erscheint, je nachdem die Schreitungen <math>+u_{1}</math>, <math>-u_{1}</math>, oder <math>+u_{2}</math>, <math>-u_{2}</math> weiter auseinanderliegen. ''Vielleicht ist gerade diese Formulierung des Satzes besonders geeignet, um die Ungleichwertigkeit der verschiedenen Schreitungen klar und deutlich zu zeigen.'' | style="padding: 0px 20px 0px 20px;" | [...] thus B's progress must be retarded with respect to A's in the ratio <math>1:\sqrt{1-u^{2}/c^{2}}</math> at the end of the experiment. And this retardation is definitely real, since both bodies A and B indeed can be immediately compared side by side under the same conditions. Here it is certainly excluded to believe that this is an appearance due to our conception of time. Thus the consequence is unavoidable too, that the strides are not equivalent in the course of the world processes, ''and therefore we again came to a conclusion that completely contradicts the unconditionality of the relativity principle.'' [...] One can vary this experiment in many ways, for instance, so that A in the same way as B successively undergoes two different strides <math>+u</math> and <math>-u</math>. If we apply the value <math>u_{1}</math> to A and <math>u_{2}</math> to B, then the comparison of A and B at the end of the experiment must give the result, that B or A is retarded in its progress depending on whether the strides <math>+u_{2},-u_{2}</math> or <math>+u_{1},-u_{1}</math> are further apart. ''Probably it is precisely this formulation of the theorem that is particularly suitable to demonstrate the non-equivalence of the different strides clearly and explicitly.'' |- |colspan=2|{{Lorentzbox|Text=This interpretation was directly rebutted by Laue (1911/12) who demonstrated the geometrical meaning of differential aging in Minkowski space, see sections {{slink||Laue 1911/12-PT|Laue 1911/12-VA}}, showing that there is no need to assume non-equivalance or anisotropy of motions. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.<ref name=laue1 />}} |- ! style="width:50%" | German original by [[w:Norman Robert Campbell|Campbell]] (November 1911, published 1912)<ref name=camp /> ! English translation |- |colspan=2|After describing the round-trip experiment (as given by Wiechert) according to which the traveling clock B is retarded when it returns with respect to stationary clock A, he abandoned differential clock aging as follows: |- | style="padding: 0px 20px 0px 20px;" |Dieser Schluß ist nicht richtig. Die Beziehung zwischen <math>t</math>, der Ablesung an der Uhr auf A seitens des Beobachters auf A und <math>t'</math>, der Ablesung an der Uhr auf B seitens des Beobachters auf A, ist (unter der Annahme, daß zu Beginn des Versuchs <math>t=t'</math> ist) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. Der Unterschied zwischen <math>t'</math> and <math>t</math> ist eine Funktion von <math>z</math> und <math>v</math> allein. Wenn man diesen Größen ihre früheren Werte wiedergibt, indem man die beiden Uhren wieder zur Koinzidenz bringt, während sie relativ zueinander ruhen, so geht der Unterschied zwischen <math>t'</math> and <math>t</math> wieder auf null zurück, gleichviel, welche Werte <math>z</math> und <math>v</math> während der Zwischenzeit gehabt haben mögen. Wenn an irgendeinem Punkte der Bahn die Geschwindigkeit von B relativ zu A eine endliche plötzliche Änderung erfährt, so erfährt auch der Wert von <math>v</math> eine endliche plötzliche Änderung. | style="padding: 0px 20px 0px 20px;" |This conclusion is not correct. The relationship between <math>t</math> as the reading on the clock on A by the observer on A, and <math>t'</math> as the reading on the clock on B by the observer on A, is given by (assuming that <math>t=t'</math> at the beginning of the experiment) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. The difference between <math>t'</math> and <math>t</math> is a function of <math>z</math> and <math>v</math> alone. If these quantities are given their previous values by bringing the two clocks back to coincidence during which they are at rest relative to one another, the difference between <math>t'</math> and <math>t</math> goes back to zero, no matter what values <math>z</math> and <math>v</math> may have had in the meantime. If at any point on the path the speed of B experiences a finite sudden change relative to A, then the value of <math>t'</math> also undergoes a finite sudden change. |- |colspan=2|{{Lorentzbox|Text=a) So Campbell claims that any time difference during the outbound path is wiped out during the inbound path. His mistake is obvious: He is confusing coordinate differences stemming from the Lorentz transformation of ''events'' (which indeed depend on position and direction) with differences in ''clock aging'' derived from the proper time integral (which is ''accumulative'' and independent of position and direction.) b) As Campbell's paper was a reply to Wiechert, it's interesting to compare them: Campbell was correct in dismissing the aether but wrong in denying asymmetric aging, while Wiechert was correct in deriving asymmetric aging but wrong in requiring the aether. }} |- ! style="width:50%" | French original by [[w:Paul Gruner|Gruner]] (March 1912):<ref name=gruner /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |[...] deux personnes du même âge, se séparant dans des systèmes de « marche » très différents et retournant après un laps de temps assez long, constateront une différence d'âge très sensible. [...] le principe de relativité exige toujours la ''réciprocité parfaite'' des phénomènes entre deux systèmes qui possèdent un mouvement relatif. Si, dans l'exemple cité, les deux personnes du même âge se séparent avec une vitesse relative pour se retrouver plus tard, la constatation d'une différence d'âge sera parfaitement mutuelle : A dira positivement que B est resté en arrière dans son développement, et B affirmera avec le même droit que c'est A qui ne s'est pas développé assez vite. Ainsi le principe absolu de la relativité montre ses conséquences les plus extrèmes et il est clair que l'introduction de l’éther n'est plus en état de résoudre cette contradiction irréductible et inconcevable. | style="padding: 0px 20px 0px 20px;" | [...] two people of same age, separating into very different systems of motion and returning after a quite long period of time, will notice a very significant age difference. [...] the principle of relativity always requires the ''perfect reciprocity'' of the phenomenons between two systems that possess relative motion. When, in the cited example, the two persons of same age are separated by some relative velocity only to meet again later, the finding of an age difference will be perfectly mutual: A will positively say that B stayed behind in its development, and B will assert with same right that it was A who has not developed fast enough. By that, the absolute relativity principle shows its most extreme consequences and it is clear, that the introduction of the aether is no longer able to resolve this irreducible and inconceivable contradiction. |- |colspan=2|{{Lorentzbox|Text=Gruner was probably the first to claim that combining the round-trip experiment with the symmetry of time dilation leads to the contradictory situation, that both must attribute younger age to one another at reunion. At the end of his paper, we also find the expression "clock paradox" (French: paradoxe des horloges). See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem.}} |} ==Einstein's contributions== 1905:<ref name=einstein05 /> Introduction of the "peculiar" (German: eigentümlich) round-trip experiment with clocks in terms of a polygonal path as well as a continuously curved path, and an experiment comparing a clock at the pole with one at the equator. January 1911 (published November):<ref name=einstein11a /> In a lecture from January, Einstein extended the "funny" (German: drollig) round-trip experiment to living organisms. According to [[w:Rudolf Lämmel]] in April 1911<ref name=lammel /> and [[w:Fritz Müller-Partenkirchen|Fritz Müller]] in October 1911,<ref name=muller /> Einstein spoke of human beings as well. January 1911 (published January 1912):<ref name=einstein3 /> During a discussion with Einstein directly after the previous lecture, [[w:Fritz Müller-Partenkirchen|Fritz Müller]] claimed that any time difference during the round-trip should vanish at reunion, in analogy to the fact that the Lorentz contraction of a moving rod vanishes when it is at rest again. Einstein showed that the analogy is incorrect: While the clock rates are indeed the same again when they are mutually at rest, the clocks do not indicate the same time at reunion because "clocks are carriers of the time differential"; he went on to show that any possible influence of acceleration during the turnaround can be made negligible by elongating the constant velocity periods. 1912:<ref name=einst12manu /> In an unpublished manuscript on special relativity, Einstein showed that if system <math>\Sigma'</math> makes a round-trip along a polygon, then its inner processes will be retarded with respect to resting system <math>\Sigma </math> at reunion. He pointed out that any influence of acceleration can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygon. April 1914:<ref name=einstpetz /> [[w:Joseph Petzoldt]] criticized asymmetric clock aging in the round-trip experiment as a "fallback into absolutist way of thinking", claiming that special relativity requires that any difference between the clocks vanishes when their relative velocity is zero again, even though he added that any treatment of the clock paradox in special relativity is unrealistic anyway, since the theory only concerns uniform motions and therefore cannot handle velocity changes, so one has to modify the theory. Einstein responded by letter in which he praised Petzoldt's philosophical take on relativity, yet he rejected Petzoldt's conclusions concerning the clock paradox by showing that any finite acceleration at turnaround during the round-trip can only influence the clock in a finite way and therefore can be neglected by minimizing the time of acceleration with respect to the time of uniform translation, so it "must be concluded" that the clock traveling on a polygonal path is retarded at reunion. May 1914:<ref name=rowe group=S /> During a conversation with [[w:Ernst Gehrcke]] who claimed that the clock paradox contradicts the relativity principle, Einstein replied that clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are irrelevant for the amount of the time difference, their presence nevertheless cause B to fall behind ("accelerated motions are absolute in the theory of relativity"). 1916:<ref name=einstein16 /> In a lecture of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of general relativity." September 1918:<ref name=einadl /> In a letter to Einstein, [[w:Friedrich Adler (politician)|Friedrich Adler]] (while in prison for the [[w:Assassination of Karl von Stürgkh]]) claimed that the clock paradox which he described on a circular round-trip contradicts the special relativity principle, and also referred to the similar opinions of Berg and Petzoldt. Einstein responded by letter and explained that there is no contradiction as one of them accelerates; he then showed that general relativity makes both inertial frame K and accelerated frame K' equally justified, explaining the time difference in K' by combining the influence of velocity and gravitational potential, concluding that "Berg and Petzoldt were wrong". November 1918:<ref name=einstein18 /> In a fictitious dialogue between a relativity critic and a relativity apologist written by Einstein, the "critic" said that special relativity must predict differential clock aging in round-trip experiments, which was confirmed by the "relativist" who regretfully noted that even some pro-relativity authors tried to "circumvent this unavoidable result". Yet the critic claimed that this leads to a contradiction: From the viewpoint of K, clock U1 is at rest while the clock U2 was in motion and therefore returns being retarded with respect to U1, but from the viewpoint of K', clock U2 is at rest while clock U1 was in motion and therefore returns being retarded with respect to U2, which was rebutted by the relativist by pointing out the acceleration of U2. Then the critic claimed that this problem "rises again from the dead" in general relativity which allows to symmetrically treat both K and K', which was rebutted by the relativist using the equivalence principle: In K', the rate increase of U1 during turnaround period 3) is "the double" of its velocity time dilation in the inertial periods 2) and 4). December 1918:<ref name=einstein18b /> In a letter to Einstein, [[w:Max Jakob]] doubted the result from Einstein's dialogue, according to which the advance of U1 in period 3) is the double of its retardation during periods 2) and 4). Einstein responded by letter, in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). 1920:<ref name=einstein20 /> In conversations with [[w:Alexander Moszkowski]] between 1919 and 1920, Einstein argued that differential aging of the twins is rather a paradox of feeling, not a paradox of thought, because the latter would only arise if there were no reason for the asymmetric aging. The reason in special relativity lies in the fact that one of them suffered accelerations, while a deeper understanding of that question is obtained by using general relativity. Einstein argued that our "common sense" is located in the realm of feeling and analogy drawn from our ordinary experience; since there is no analogy to the example of the twins in our experience, it might appear paradoxical to the common sense, while it appears logical and necessary in light of intensified abstraction of the trained scientific mind. August 1920:<ref name=rowe group=S /> At an anti-relativity event organized by the right-wing agitator [[w:Paul Weyland]] during which [[w:antisemitic]] leaflets were distributed and [[w:swastika]]s offered at the entrance, a lecture was given by Gehrcke re-iterating his criticism of the twin paradox, claiming that the stationary first organism is old or even dead at reunion while the second organism was in motion and therefore stayed young, but from the standpoint of the second organism he himself is old or even dead while the first organism was in motion and stayed young, thus relativity is either contradictory or it leads to different realities and physical [[w:solipsism]]. Einstein who was present at that event, directly responded in a newspaper article;<ref name=einst20 /> after suspecting antisemitic motives of his critics, he specifically addressed Gehrcke's objections regarding the "well known example of the clocks (or twins)", remarking that the charge of solipsism will be "greeted by the experts as a joke", and characterized the claim that relativity requires mutual retardation of two co-located clocks as a "deliberate attempt to misinform the lay public". 1922:<ref name=morand /><ref name=nord /> [[w:Paul Painlevé]], Einstein and Langevin discussed the clock paradox at a meeting in Paris. Painlevé imagined a clock on a train that performs a round-trip with constant speed and returns being retarded with respect to the station clock, yet he claimed that the relativity principle also allows to say that the station clock performed the round-trip and returned being retarded with respect to the train clock, in contradiction to the previous result. Einstein replied that the relativity principle cannot be applied since the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two systems having velocities in opposite direction is not an inertial frame; there is no reciprocity between a frame that changes direction and one that doesn't. Langevin consequently gave a detailed analysis in terms of the Lorentz transformation. 1954:<ref name=einstein54 /> In a letter, Einstein explained the "well known clock paradoxon" using two clocks <math>B_{1}</math> and <math>B_{2}</math>; clock <math>B_{2}</math> has to reverse its speed in order to come back, thus it was initially at rest in inertial frame <math>S_{2}</math> and then at rest in <math>S_{2}^{+}</math>, whereas <math>B_{1}</math> constantly remains at rest in <math>S_{1}</math>, which explains the asymmetry between them. ==Historical references== <references> <ref name=einstein05>See p. 904f in: {{Citation |author=Einstein, A. |date=1905 |title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik |volume=322 |issue=10 |pages=891–921 |doi=10.1002/andp.19053221004|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 2, Document 23}}. See also: [https://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation at fourmilab].</ref> <ref name=einstein11a>See p. 10. in: {{Citation |author=Einstein, A. |title=Die Relativitäts-Theorie|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |issue=1-2|pages=1–14 |date=27 November 1911|orig-date=Lecture 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n11/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 17}}.<br /> The publication date 27 November 1911 can be seen on the [https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n5/mode/2up Title page and TOC of issue 1-2].</ref> <ref name=einstein3>Discussion between Einstien, Müller, Lämmel and others after the Zürich lecture: {{Citation |author=Einstein, A.; Müller, F., Lämmel, R.|title=Diskussion zu "Die Relativitäts-Theorie"|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |pages=II-IX |date=January 1912|orig-date=Lecture on 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n587/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 18, and in the corresponding English translation volume}}<br /> While the discussion already happened on January 1911, the publication followed one year later in January 1912 in the session proceedings (Sitzungsberichte) of the third issue, see [https://www.ngzh.ch/publikationen/vjs/56/3 Full issue Nr. 3] with [http://www.ngzh.ch/archiv/1911_56/56_1-2/56_3.pdf Title page and TOC] and the [http://www.ngzh.ch/archiv/1911_56/56_3/56_30.pdf Sitzungsberichte including Einstein's discussion on pp. II-IX]. </ref> <ref name=einst12manu>See p. 46 in: {{Citation |author=Einstein, A. |date=1912 |chapter=Document 1: Einstein's manuscript on the special theory of relativity|title=The collected papers of Albert Einstein|volume=4|pages=3-108|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstlor>{{Citation|author=Einstein, A.|date=1914|title=Review of "Lorentz, H. A. – Das Relativitätsprinzip" |journal=Die Naturwissenschaften|volume=2|pages=1018|url=https://archive.org/details/CAT31421305002/page/1018/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 6, Document 11}}</ref> <ref name=einstpetz>{{Citation |author=Einstein, A. |date=1914 |chapter=Document 5: Letter from Einstein to Petzoldt|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein16>See p. 423f in: {{Citation |author=Einstein, A. |date=1916 |title=Announcement of Einstein's lecture "Über einige anschauliche Überlegungen aus dem Gebiete der Relativitätstheorie"|journal=Berliner Sitzungsberichte|pages=423|volume=1916 (part 1)|url=https://archive.org/details/sitzungsberichte1916deutsch/page/423/mode/2up}}</ref> <ref name=einadl>Letter exchange between Einstein and Adler in which the critique on the clock paradox by Berg (1910) and Petzoldt (1914) was mentioned, together with the general relativity solution in terms of the gravitational potential, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Adler's letter in Document 620 and Einstein's reply in Document 628|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein18>Einstein discussed in terms of inertial frames (special relativity) on pp. 697f; accelerated frames (general relativity) on pp. 698f.; distant masses (Mach's principle) on pp. 700f. in: {{citation |author=Einstein, A.|title=[[s:de:Dialog über Einwände gegen die Relativitätstheorie|Dialog über Einwände gegen die Relativitätstheorie]]|date=November 1918|volume=6|issue=48|journal=Die Naturwissenschaften|pages=697-702|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 7, Document 13}}; See also English translation [[:s:Translation:Dialog about Objections against the Theory of Relativity|Dialog about Objections against the Theory of Relativity]] on Wikisource.</ref> <ref name=einstein18b>Letter exchange between Max Jakob and Einstein from December 1918, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Jakob's letter in Document 661c and Einstein's reply in Document 663a|title=The collected papers of Albert Einstein|volume=10|pages=189-190}}</ref> <ref name=einstein20>Interview of Einstein by Moszkowski, see p. 204f. in: {{citation |author=Moszkowski, A.|title=Einstein. Einblicke in seine Gedankenwelt|orig-date=Copyright date 1920 |date=1921|place=Hamburg|url=https://www.archive.org/details/einsteineinblick00moszuoft}}; See also English translation by H. L. Brose (1921): [https://archive.org/details/einsteinsearch00moszrich Einstein, the searcher], p. 206</ref> <ref name=einst20>{{Citation|author=Einstein, A.|date=27 August 1920|journal=Berliner Tageblatt|title=Meine Antwort - Ueber die anti-relativitätstheoretische G. m. b. H.|issue=402|pages=1-2|url=https://www.deutsche-digitale-bibliothek.de/newspaper/item/YH65KFT53MOG4SMXDXK4IVUPTR3QRY7Q?issuepage=1|quote=Reprinted in "The Collected Papers of Albert Einstein", Vol. 7, Document 45}}</ref> <ref name=einstein54>Letter from Einstein to N. V. Pope from March 1954; [[w:Albert Einstein Archives]], Object number 27-88 ([https://ein-web.adlibhosting.com/aea/Details/archive/110021626 Online dataset]); Scanned version as [https://groups.google.com/group/npachat/attach/d3121322d37764f2/Einstein%20letter.doc?part=0.1 Word document on Usenet] published by [https://groups.google.com/g/npachat/c/Haoib97d6OA/m/8mR30yITEtMJ Pope himself])</ref> <ref name=morand>Discussion between Painlevé, Einstein, and Langevin on p. 316ff in: {{citation |author=Morand, M.|title=Einstein au collège de france|date=April 1922|journal=La Nature|volume=50|issue=2511|pages=315-320|url=http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.102/319/100/620/5/613}}</ref> <ref name=lammel>{{Citation|author=Lämmel, R.|date=28 April 1911|title=Die Relativitäts-Lehre|journal=Neue Zürcher Zeitung|volume=117|pages=1|url=https://www.e-newspaperarchives.ch/?a=d&d=NZZ19110428-01.2.4.1}}; English translation of the part concering the twin pardox at [[:v:History of Topics in Special Relativity/Twin paradox#Lämmel 1911-Hum|Wikiversity:Early history of the twin paradox - Lämmel]]</ref> <ref name=lammel2>See p. 84ff in: {{Citation|author=Lämmel, R.|date=1921|orig-date=Preface December 1920|title=Die Grundlagen der Relativitätstheorie|place=Berlin|publisher=Springer|url=https://archive.org/details/diegrundlagende00lmgoog}}</ref> <ref name=langevin1>He derived differential aging from the proper time integral; pointed out that this demonstrates the "absolute nature of acceleration" with respect to an aether, see: {{citation |author=Langevin, P.|title=[[:s:fr:L’Évolution de l’espace et du temps|L’Évolution de l’espace et du temps]]|journal=Scientia |volume=X |pages=31–54 |date=July 1911|orig-date=Lecture 10 April 1911}}; English translation [[:s:en:Translation:The Evolution of Space and Time|The Evolution of Space and Time]] on Wikisource</ref> <ref name=langevin2>See p. 329 in: {{citation |author=Langevin, P. |title=Le temps, l'espace et la causalité dans la physique moderne |journal=Bulletin de la Société française de philosophie |volume=12 |orig-date=Lecture October 1911|date=1912|pages=1-28|url=http://ahp.li/1f7fc22d283fdf0deeca.pdf}}</ref> <ref name=langevin3>See p. 622f in: {{citation |author=Langevin, P. |title=Le Principe de relativité |journal=Bulletin de la société française des électriciens |volume=9 |date=1919 |pages=601-639|url=https://archive.org/details/bulletin-de-la-societe-francaise-des-electriciens-ser.-3-vol-9/page/600}}; Republished in 1922 as separate booklet: [[:s:fr:Le Principe de relativité|Le Principe de relativité]], Éditions Étienne Chiron</ref> <ref name=wiechert11>See p. 745f. general description and proper time; 757f. space travel; in: {{Citation |author=Wiechert, E. |date=September 1911|orig-date=Lectures March-May 1911, submitted 26 July|title=[[:s:de:Relativitätsprinzip und Äther|Relativitätsprinzip und Äther]]|journal=Physikalische Zeitschrift |volume=12 |issue=17-18 |pages=[https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/741 689-707] published September 1; [https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/789 737–758] published September 15}}</ref> <ref name=wiechert15>See p. 46 (Einstein, Langevin, Wiechert) and pp. 51f (Laue versus Wiechert) in: {{citation |author=Wiechert, E.|contribution=Die Mechanik im Rahmen der allgemeinen Physik| title=Die Kultur der Gegenwart: Physik|volume=3.3.1|date=1915 |orig-date=Submitted July 1914|pages=1–78|contribution-url=https://www.archive.org/details/physikunterredak00warbuoft}}</ref> <ref name=wiechert20>See p. 46f in: {{citation |author=Wiechert, E.|title=Der Äther im Weltbild der Physik|orig-date=Presented December 1920|date=1921|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse|pages=29-70|url=http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN00250586X}}</ref> <ref name=wiechert21>See p. 25ff in: {{citation |author=Wiechert, E.|title=[[:s:de:Prinzipielles über Äther und Relativität|Prinzipielles über Äther und Relativität]]|date=1922|orig-date=Lecture September 1921|journal=Physikalische Zeitschrift|volume=23|pages=25-28}}</ref> <ref name=muller>See p. 9 in: {{Citation|author=Müller, F.|date=October 1911|journal=Berliner Tageblatt|title=[[:s:de:Das Zeitproblem (1911)|Das Zeitproblem]]|pages=[https://www.deutsche-digitale-bibliothek.de/newspaper/item/2QKOIOLGNVQILTCEZQOGQPLTRVLPM5PZ?query=zeit&issuepage=9 Part 1 published 16 October 1911] and [https://www.deutsche-digitale-bibliothek.de/newspaper/item/IO44I6QBC4SVV5YUKUDSGXYIPQUXXBN5?query=zeit&issuepage=11 Part 2 published 23 October 1911]}}</ref> <ref name=gruner>See p. 253f in: {{Citation |author=Gruner, P. |title=[[:s:fr:Rapport sur la dernière discussion concernant le principe de la relativité et l’éther|Rapport sur la dernière discussion concernant le principe de la relativité et l’éther]] |journal=Archives des sciences physiques et naturelles |volume=33|issue=4 |pages=252-254 |date=March 1912}}</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=weyl>See p. 147f. in: {{Citation |author=Weyl, H. |date=March 1918|title=Raum-Zeit-Materie (first edition)|publisher=Berlin: Springer|url=https://archive.org/details/RaumZeitMaterieVolIMeinerFrauGewidmet}}; English translation of the 4th edition by H. Brose (1921): [https://www.gutenberg.org/ebooks/43006 Space—Time—Matter], pp. 278f.</ref> <ref name=gbaum>See footnote on p. 507 in: {{Citation|author=Grünbaum, F. |title=Über einige ideelle Versuche zum Relativitätsprinzip|journal=Physikalische Zeitschrift|volume=12|pages=500–509|date=1911|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/540}}</ref> <ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> <ref name=laue2>See p. 42f. for general description; p. 58f. in terms of proper time; in: {{Citation |author=Laue, M. v. |orig-date=Preface December 1912|date=1913 |title=Das Relativitätsprinzip (Second Edition) |publisher=Vieweg |place=Braunschweig|url=https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE4597082}}; See also English translation [[:s:Translation:The Principle of Relativity (Laue 1913)|The Principle of Relativity, Second edition, Part III]] on Wikisource</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=berg>See p. 369f in: {{Citation |author=Berg, O. |date=1910 |title=Das Relativitätsprinzip der Elektrodynamik |journal=Abhandlungen der Fries'schen Schule |volume=3 |issue=2|pages=333-382 |url=http://hdl.handle.net/2027/hvd.hnuynk?urlappend=%3Bseq=351}}</ref> <ref name=camp>See p. 123f in: {{Citation |author=Campbell, N. |title=Relativitätsprinzip und Äther: Eine Entgegnung an Herrn Wiechert |journal=Physikalische Zeitschrift |volume=13 |pages=120-128 |issue=3|orig-date=Submitted December 1911|date=February 1912|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/150}}. The is based on an English manuscript translated by Max Iklé, and Campbell's first name was Germanised as "Normann".</ref> <ref name=seel>{{Citation|author=Seeliger, R.|title=Review of "P. Gruner – Rapport sur la dernière discussion concernant le principe de la relativité et l'éther"|journal=Die Fortschritte der Physik|volume=68|issue=2|pages=336|date=1913|url=https://books.google.com/books?id=fSJGAQAAMAAJ&pg=PA336}}</ref> <ref name=study>See footnote on p. 111 in: {{citation |author=Study, E. |title=Vorlesungen über ausgewählte Gegenstände der Geometrie |date=June 1911|url=https://archive.org/details/vorlesungenber00studuoft|publisher=B.G. Teubner|place=Leipzig}} </ref> <ref name=robb1>See pp. 356ff. in: {{Citation|author=Robb, A.|date=1914|title=A theory of time and space|place=Cambridge|publisher=University Press|url=https://archive.org/details/theoryoftimespac00robbrich}} </ref> <ref name=robb2>See §12 in: {{citation |author=Robb, A. A.|title=The Straight Path|date=1920 |journal=Nature|pages=599|volume=104|issue=2623|url=https://archive.org/details/sim_nature-uk_1920-02-05_104_2623/page/598/mode/2up}}</ref> <ref name=edding2>See p. 22 in: {{Citation |author=Eddington, A. S. |date=1922 |title=The theory of relativity, and its influence on scientific thought |publisher=Oxford Clarendon Press |url=https://archive.org/details/cu31924005748573}}</ref> <ref name=rogers>{{citation |author=Rogers, R. A. P.|title=The Time-Triangle and Time-Triad in Special Relativity|date=November 1922|journal=Nature|volume=110|issue=2769|pages=698–699|url=https://archive.org/details/sim_nature-uk_1922-11-25_110_2769/page/698/mode/2up}}</ref> <ref name=lorentz1>See pp. 37f, 55ff in: {{citation |author=Lorentz, H. A.|date=1913|title=Het relativiteitsbeginsel : drie voordrachten gehouden in Teyler's stichting|publisher=De Erven Loosjes |place=Haarlem|url=https://resolver.kb.nl/resolve?urn=MMKB24:063387000:00005}}; German translation on pp. 31f, 47f in: {{citation |author=Lorentz, H. A.|date=1914| title=Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem|publisher=B.G. Teubner |place=Leipzig and Berlin|url=https://archive.org/details/bub_gb_89PPAAAAMAAJ}}; See also the transcription [[:s:de:Das Relativitätsprinzip (Lorentz)|Das Relativitätsprinzip]] on German Wikisource and the English translation [[:s:Translation:The Principle of Relativity (Lorentz)|The Principle of Relativity]] on English Wikisource</ref> <ref name=lorentz3>See §12 in: {{citation |author=Lorentz, H. A.|title=Considérations élémentaires sur le principe de relativité|date=1914 |journal=Revue générale des sciences pures et appliquées|pages=179-186|url=https://archive.org/details/revuegnraled25pari/page/178/mode/2up}}</ref> <ref name=bloch>See pp. 67 ff. in: {{Citation | author=Bloch, W.| date=September 1918|title=Einführung in die Relativitätstheorie| publisher=B. G. Teubner |url=https://hdl.handle.net/2027/njp.32101040276907}}</ref> <ref name=bloch2>See pp. 69ff. (special relativity) and 102ff. (general relativity) in: {{Citation | author=Bloch, W.| date=1920 |title=Einführung in die Relativitätstheorie (second edition)| publisher=B. G. Teubner |url=https://www.archive.org/details/einfhrungindier00blocgoog}}</ref> <ref name=bollert1>See p. 6 (special relativity), pp. 24-26 (EP) in: {{citation |author=Bollert, K.|title=Einstein’s Relativitätstheorie und ihre Stellung im System der Gesamterfahrung |date=April 1921|publisher=Steinkopff|url=https://archive.org/details/dbc.wroc.pl.001504}}</ref> <ref name=born>See pp. 190f. (special relativity), 250f (EP) in: {{Citation | author=Born, M.| date=1921 |title=Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Second edition)| publisher=Springer | place=Berlin|url=https://hdl.handle.net/2027/mdp.39015017387310}}; The [https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE5426498 first edition (1920)] of Born's book didn't include the twin paradox. English translation of the third edition by H. Brose (1924): [https://archive.org/details/einsteinstheoryo00born Einstein's theory of relativity]</ref> <ref name=pauli>See p. 558f (general description); p. 624f (proper time); p. 713f (accelerated frames); in: {{Citation |author=Pauli, W. |date=1921 |journal=Encyclopädie der Mathematischen Wissenschaften|title=Die Relativitätstheorie|pages=539–776|volume=5|issue=2 |url=http://resolver.sub.uni-goettingen.de/purl?PPN360709672}}; English translation by G. Field (1958): [https://books.google.com/books?id=rc3DAgAAQBAJ Theory of Relativity]</ref> <ref name=thirring>See p. 209ff in: {{citation |author=Thirring, H.|title=Über das Uhrenparadoxon in der Relativitätstheorie|date=April 1921|journal=Naturwissenschaften|volume=9|issue=18|pages=209-212|url=https://archive.org/details/sim_naturwissenschaften_1921-04-01_9_13/mode/2up}}</ref> <ref name=sommerfeld>See p. 71 in: {{citation |author=Sommerfeld, A. |date=May 1913|chapter=Remarks on Minkowski's "Space and Time"|title=Das Relativitätsprinzip|editor=Otto Blumenthal|pages=69-73|url=https://www.archive.org/details/dasrelativittsp00minkgoog}}</ref> <ref name=kopff>See pp. 45ff (special relativity and proper time); pp. 117ff (EP); pp. 189ff (Mach's principle), in: {{citation |author=Kopff, A.|title=Grundzüge der Einsteinschen Relativitätstheorie |date=February 1921|publisher=S. Hirzel|place=Leipzig|url=https://www.archive.org/details/grundzgedereins00kopfgoog}}; English translation by H. Levy (1923): [https://hdl.handle.net/2027/mdp.39015017188817 The mathematical theory of relativity].</ref> <ref name=becqu1>See p. 48ff (proper time), p. 240f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Le Principe de relativité et la théorie de la gravitation|Le Principe de relativité et la théorie de la gravitation]] |date=1922 |publisher=Gauthier-Villars|place=Paris}}; See also p. 57ff (proper time), p. 177f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Exposé élémentaire de la théorie d’Einstein et de sa généralisation|Exposé élémentaire de la théorie d’Einstein et de sa généralisation]]|date=1922 |publisher=Payot|place=Paris}}</ref> <ref name=nord>Discussion between Painlevé, Einstein, and Langevin on pp. 146ff in: {{citation |author=Nordmann, C.|title=[[s:fr:Einstein expose et discute sa théorie|Einstein expose et discute sa théorie]]|date=May 1922|journal=Revue des deux mondes|volume=IX|pages=129-166}}</ref> <ref name=lehm>{{Citation |author=Lehmann, Otto |orig-date=September 1910 |date=1911|title=Das Relativitätsprinzip der neue Fundamentalsatz der Physik |title-link=s:de:Das Relativitätsprinzip der neue Fundamentalsatz der Physik|journal=Verhandlungen des naturwissenschaften Vereins in Karlsruhe |volume=23 |pages=49-74}}</ref> <ref name=lech>See p. 19ff in: {{citation |author=Lechalas, G. |orig-date=Submitted December 1912|date=1913 |title=Le nouveau temps |journal=L’Année philosophique|volume=XXIII|pages=19-44|url=https://gallica.bnf.fr/ark:/12148/bpt6k255882z/f22.item}}</ref> <ref name=hunt>See pp. 494ff in: {{Citation|author=Huntington, E. V. |year=1912 |title=A new approach to the theory of relativity|journal=Philosophical Magazine |volume=23|pages=494-512|url=https://archive.org/details/londonedinburg6231912lond/page/494/mode/2up}}</ref> </references> ==Secondary sources== <references group=S> <ref name=miller>{{Citation |author=Miller, A. I. |date=1981 |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |place=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}; See section 7.4.13 (Langevin, Wiechert, Laue, Einstein), footnotes 29-34 of chapter 7 (Petzoldt, Sommerfeld, Bergson, Einstein)</ref> <ref name=lange>{{Citation|author=Lange, L.|date=1927|title=The clock paradox of the theory of relativity|journal=The American Mathematical Monthly|volume=34|issue=1|pages=22-30|jstor=2299914}}</ref> <ref name=pes>{{Citation |author=Pesic, P. |date=2003 |title=Einstein and the twin paradox |journal=European Journal of Physics |volume=24 |issue=6 |pages=585–590 |doi=10.1088/0143-0807/24/6/004}}</ref> <ref name=during>{{Citation |author=During, É. |date=2014 |title=Langevin ou le paradoxe introuvable |journal=Revue de métaphysique et de morale |volume=84 |pages=513-527 |doi=10.3917/rmm.144.0513|doi-access=free}}; See pp. 515f (Langevin), 520f. (Einstein, Laue, Weyl, Painlevé).</ref> <ref name=debs>{{Citation |author=Debs, T. A., & Redhead, M. L. |title=The twin paradox and the conventionality of simultaneity |date=1996 |journal=American Journal of Physics |volume=64|issue=1| pages=384-392 |doi=10.1119/1.18252}}</ref> <ref name=alizzi>{{Citation |author=Alizzi, A., Sen, A., & Silagadze, Z. K.|title=Do moving clocks slow down? |year=2022 |journal=European Journal of Physics |volume=43|issue=6|pages=065601 |doi=10.1088/1361-6404/ac93ca|arxiv=2209.12654}}; Appendix B with reference to Lange and Halsbury</ref> <ref name=beng>{{Citation |author=Benguigui, L. G. |date=2020 |title=A Tale Of Two Twins: The Langevin Experiment Of A Traveler To A Star |publisher=World Scientific|isbn=9789811219115}}; See early solutions (Einstein, Langevin, Lorentz, Born/Kopff) and the Bergson controversy. A shorter version appeared in {{arxiv|1212.4414}}.</ref> <ref name=rowe>{{Citation|author=Rowe, D. E.|date=2006|title=Einstein's allies and enemies: Debating relativity in Germany 1916–1920|journal=Interactions: Mathematics, Physics and Philosophy|pages=231-280|publisher=Springer|doi=10.1007/978-1-4020-5195-1_8}}; Covering the criticism of Gehrcke starting with 1912; discussion between Einstein and Gehrcke in 1914; Einstein's dialogue (1918) as response to antirelativists; the Weyland event in 1920 and Einstein's response.</ref> <ref name=weiss>Weiss, W. (Physics FAQ): [https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html The Twin Paradox: The Equivalence Principle Analysis]</ref> <ref name=cuvaj>{{Citation |author=Cuvaj, C. |date=1971 |title=Paul Langevin and the theory of relativity|journal=Japanese studies in the history of science|volume=10| pages=113-142|url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf}}</ref> <ref name=koks>Koks, D. (2018): [https://math.ucr.edu/home/baez/physics/Relativity/SR/sr-gr.html Physics FAQ: Where is the Boundary between Special and General Relativity?]</ref> </references> [[Category:History of special relativity]] [[Category:Paradoxes]] f7sllro6eb1b1znu8v0s53ms2ni0iyy 2834540 2834539 2026-09-26T08:40:08Z D.H 52339 /* Paradoxical? */ + 2834540 wikitext text/x-wiki {| style="width:20%; font-size:13px;" align=right |{{../Other Topics (header)}} |} ==Early history of the twin paradox== {{Lorentzbox|Text={{center|Date of article creation: 9 November 2023; Last major revision: 26 September 2026}}}} a) When was the [[:w:twin paradox]] applied to life forms and human beings? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /><ref group=S name=during /> report that {{slink||Einstein 1911-HU}} discussed the aging of living organisms, and that {{slink||Langevin 1911-HU}} and {{slink||Wiechert 1911-HU}} explicitly discussed the aging of human beings. :*More details in sections {{slink||Human beings in 1911|Twins from 1911 to 1920}}, including newspaper articles from 1911 written by {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}} that clearly show that Einstein was the first to explicitly discuss the aging of human beings as well. b) Who was the first to formulate the principle of maximal proper time along straight worldlines, upon which differential aging in the standard twin paradox is based? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> mention Langevin (1911), Laue (1911). :*More details in section {{slink||Maximal proper time}} with the contributions of Langevin (1911), Wiechert (1911), Study (1911), Laue (1911-13). c) Who was the first to formulate [[w:Triangle inequality#Reversal in Minkowski space|inverse triangle inequality]] in Minkowski space, which represents the simplest version of the twin paradox? :*See details in section {{slink||Triangle inequality}} with the contributions of Robb (1914-20), Eddington (1922), Rogers (1922). d) Who was the first to show that any influence of proper acceleration on clocks can be neglected in the computation of the twin paradox from the viewpoint of the stay-at-home twin? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Einstein (1911), Laue (1913). :*More details in section {{slink||Negligibility of proper acceleration}} with the contributions of Einstein (1911), Wiechert (1911), Laue (1913), Lorentz (1913). e) Who was the first to introduce the three clock/brother example that completely removes acceleration from the clock/twin paradox? :*Historical accounts<ref group=S name=debs /><ref group=S name=alizzi /> date it back to Lange (1927) and Lord Halsbury (1957). :*More details in section {{slink||Relay (three brothers) experiment}} with the contributions of Grünbaum (1911) and Wiechert (1920-22). f) Who was the first to use acceleration as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref name=cuvaj group=S /><ref group=S name=pes /> mention Langevin (1911), Einstein (1918). :*More details in section {{slink||Acceleration as asymmetry indicator}} with the contributions of Langevin (1911), Sommerfeld (1913), Lorentz (1913), Einstein (1914-20). g) Who was the first to use different frame distribution as asymmetry indicator as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Laue (1911-13). :*More details in section {{slink||Frame distribution as asymmetry indicator}} with the contributions of Laue (1911-13), Bloch (1918). h) Who was the first to describe the perspective of the traveler? :*Historical accounts<ref group=S name=miller /><ref group=S name=beng /> mention Langevin (1911), Lorentz (1914), Einstein (1918). :*More details in section {{slink||Perspective of the traveler}} with the contributions of Langevin (1911), Lorentz (1913-14), Einstein (1918), Thirring (1921). i) Who was the first to describe a round-trip experiment in curved spacetime? :*See section {{slink||Curved spacetime}} with the contribution of Becquerel (1922). j) Who was the first to interprete the twin paradox in terms of an aether or absolute space? :*See section {{slink||Aether interpretations}} with the contribution of Langevin (1911), Wiechert (1911), Lechalas (1912). k) Who was the first to denote the round-trip experiment as paradoxical? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> point to Laue (1911). :*See section {{slink||Paradoxical?}} for details. l) Who was the first to misunderstand the twin paradox? :*See section {{slink||Misunderstandings}} with the contributions of Berg (1910), Wiechert (1911), Campbell (1911/12), Gruner (1912). m) What were Einstein's contributions? :*See section {{slink||Einstein's contributions}}. ==Human beings in 1911== {| class="wikitable" style="background-color:white;{{text default color}};" ![[w:Albert Einstein|Einstein]] |- |{{anchor|Einstein 1905}}In 1905<ref name=einstein05 /> he showed that a clock moving on a round-trip away from A and back along a polygonal or curved path, is retarded with respect to a clock stationary at A by approximately <math>\tfrac{1}{2}t(v/V)^{2}</math> at reunion. For example, a clock on the equator is retarded with respect to a clock on the pole. He described this consequence as being "peculiar" (German: eigentümlich). {{anchor|Einstein 1911-HU}}In a lecture given on January 1911<ref name=einstein11a /> (published in November), he extended this "funny" (German: drollig) experiment to living organisms: {| ! width=55% | Einstein wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Wenn wir z. B. einen lebenden Organismus in eine Schachtel hineinbrächten und ihn dieselbe Hin- und Herbewegung ausführen lassen wie vorher die Uhr, so könnte man es erreichen, dass dieser Organismus nach einem beliebig langen Fluge beliebig wenig geändert wieder an seinen ursprünglichen Ort zurückkehrt, während ganz entsprechend beschaffene Organismen, welche an den ursprünglichen Orten ruhend geblieben sind, bereits längst neuen Generationen Platz gemacht haben. Für den bewegten Organismus war die lange Zeit der Reise nur ein Augenblick, falls die Bewegung annähernd mit Lichtgeschwindigkeit erfolgte! | style="padding: 0px 20px 0px 20px;" |For example, if we put a living organism in a box and make it undergo the same back and forth movement as the clock before, we could achieve that this organism returns to its original location with arbitrary little change after a flight of arbitrary length, whereas completely identical organisms that remained at rest in the original location have long since made room for new generations. To the moving organism, the long journey was only a moment if the movement happened close to the speed of light! |} {{Lorentzbox|Text=Two participants of that lecture, {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}}, report that Einstein also talked about the aging of ''human beings''.}} |- !{{anchor|Lämmel 1911-HU}}[[w:Rudolf Lämmel|Lämmel]] |- |He attended Einstein's 1911 lecture and gave a popular report about it in the Swiss newspaper "[[w:Neue Zürcher Zeitung|Neue Zürcher Zeitung]]" published on 28 April 1911,<ref name=lammel /> including additional details. Regarding the round-trip clock experiment he wrote: {| ! width=50% | Lämmel wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bewegt sich eine Uhr mit Lichtgeschwindigkeit längs einer Geraden, auf der gerichtete Uhren stehen, so scheint die bewegte Uhr, beurteilt vom Standpunkt der ruhenden aus, im oben stizzierten Sinn, stillzustehen. Kehrt die Uhr, nach einem Ruck, mit Lichtgeschwindigkeit wieder zurück zur Zentral-Uhr, so ist, nach Einstein, für den Beobachter bei der Zentral-Uhr die Sache so, als ob ein mit der bewegten Uhr mitgeführter Beobachter (samt dessen Uhr) nicht gealtert hätte. Hinge also des letzteren Alter von den Angaben des ruhenden Beobachters ab, so könnte der von einer großen Reise ins Weltall zurückkehrende Beobachter bei der Zentral-Uhr spätere Generationen antreffen – er selber hätte nicht gealtert. Welche Bedeutung diese ''ad absurdum'' geführte Gedankenspielerei etwa hat, läßt sich heute nicht absehen – vielleicht, ja wahrscheinlich ist sie ohne jeden Einfluß auf die tatsächlichen Verhältnisse. Aber man sieht dabei immerhin, daß die Physik imstande ist, die kühnsten Träume der Phantasie noch – zu überbieten. | style="padding: 0px 20px 0px 20px;" |Let a clock be moving at speed of light along a line on which regulated clocks are standing, then the moving clock's hand appears to be standing still (in the sense described above) as judged from the standpoint of the resting one. If the clock, after one jolt, comes back with light speed to the central clock, then according to Einstein the matter presents itself to the observer at the central clock, as if the observer comoving with the clock (together with his clock itself) hasn't been grown older. Thus if the age of the latter would depend on the indications of the resting observer, the observer returning from a great journey into space could meet later generations at the central-clock – he himself hasn't been grown older. The importance of this play of thought led ''ad absurdum'' cannot be seen today – maybe, or even probably, it is without any influence on the actual situations. Though at least one can see that physics is able to – surpass – even the boldest dreams and fantasies. |} Lämmel in December 1920 (published 1921)<ref name=lammel2 /> again alluded to Einstein's lectures in Zürich (possibly the one from 1911, and maybe also later ones), describing a discussion between himself and Einstein. After Einstein concluded that the travelers who came back after their journey will probably meet their former contemporaries as old men while they themselves could have been away for only a few years, Lämmel objected that this conclusion is only drawn with respect to rods and clocks, but not with respect to living beings. Einstein responded though, that all processes in the blood, in the nerves etc. are eventually periodical oscillations, i.e. motions. Yet to any such motion the relativity principle applies, thus the conclusion regarding the unevenly rapid aging it permissive. {{Lorentzbox|Text=While the official publication of Einstein's January lecture ({{slink||Einstein 1911-HU}}) mentions the aging of organisms, Lämmel recalls the reference to the aging of a human space traveler ("observer returning from a great journey into space"). This means that Einstein was the first to use human beings in the clock/twin paradox on January 16 which was first published by Lämmel on April 28, 1911. In comparison, {{slink||Langevin 1911-HU}} used space travelers in a lecture on April 10 with publication in July, and {{slink||Wiechert 1911-HU}} used space travelers in lectures held between March 25 and May 23 with publication in July/September. It seems very unlikely that before April 28, Lämmel became somehow aware of the content of Langevin's or Wiechert's lectures held a few weeks earlier, in order to use them in his description of Einstein's lecture.}} |- !{{anchor|Langevin 1911-HU}}[[w:Paul Langevin|Langevin]] |- |On 10 April 1911, published July 1911,<ref name=langevin1 /> he held a now famous lecture popularizing the clock/twin paradox which he derived from the proper time integral as described in {{slink||Langevin 1911-PT}}. He demonstrated that a moving radioactive sample of radium is less evolved and less aged and therefore more active at return then the ones that remained in the laboratory. He also used light signals and the Doppler effect to visualize the effect. The most famous part concerned his description of the aging of human space travelers: {| ! width=50% | Langevin wrote ! [[:s:Translation:The Evolution of Space and Time|English Wikisource translation]] |- | style="padding: 0px 20px 0px 20px;" |Cette remarque fournit le moyen, à celui d’entre nous qui voudrait y consacrer deux années de sa vie, de savoir ce que sera la Terre dans deux cents ans, d’explorer l’avenir de la Terre en faisant dans la vie de celle-ci un saut en avant qui pour elle durera deux siècles et pour lui durera deux ans, mais ceci sans espoir de retour, sans possibilité de venir nous informer du résultat de son voyage puisque toute tentative du même genre ne pourrait que le transporter de plus en plus avant. Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse. Revenu à la Terre ayant vieilli de deux ans, il sortira de son arche et trouvera notre globe vieilli de deux cents ans si sa vitesse est restée dans l’intervalle inférieure d’un vingt-millième seulement à la vitesse de la lumière. Les faits expérimentaux les plus sûrement établis de la physique nous permettent d’affirmer qu’il en serait bien ainsi. | style="padding: 0px 20px 0px 20px;" |This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. |} {{Lorentzbox|Text=Reading his lecture in full, one finds the word "paradoxical" only in relation to the constancy of light speed, not on relation to the round-trip clock experiment.}} |- !{{anchor|Wiechert 1911-HU}}[[w:Emil Wiechert|Wiechert]] |- |In lectures on 25 March and 23 May 1911, submitted July and published September 1911,<ref name=wiechert11 /> he described the round-trip clock experiment with two equal clocks regulated to the same rate and brought to the same pointer position, or by introducing the same chemical process two times, or by introducing ''two life forms that began their life at the same time''. At the end of his paper he applied this to human travelers: {| ! width=50% | Wiechert wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Nehmen wir aber wieder eine Relativgeschwindigkeit an, die bis auf 3 Proz. der Lichtgeschwindigkeit nahekommt, dann wird das Verhältnis der empfundenen Zeitlängen wie 4:1. Das Bild mag etwas weiter noch ausgemalt werden. Denken wir uns, daß ein Beobachter durch den Raum unseres Sternhimmels mit dieser Geschwindigkeit in einer Kreisbahn mit einem Radius von 16 Lichtjahren fährt, dann wird er nach unserer Zeitrechnung nach je 100 Jahren wieder an unserem Sonnensystem vorüberkommen. In seinem Gefährt wird dabei die Zentrifugalkraft so auf ihn einwirken, daß sie gemäß den Relativitätsgesetzen der Einwirkung der Schwerkraft auf uns Erdenbewohner gleich erscheint. Es sind also die wirkenden Kräfte nur so groß, daß der Phantasie die Möglichkeit geboten wird, den Reisenden als menschliches Wesen zu denken. Da hier dauernd <math>\sqrt{1-v^{2}/c^{2}}</math> ist, fließt die Eigenzeit für den Reisenden viermal langsamer dahin, als für die Bewohner der Gestirne. Wenn er also nach 100 unserer Jahre wieder zu unserem Sonnensystem zurückkehrt, wird er sich selbst nur um 25 Jahre gealtert fühlen. Erreicht er nach der Entwicklung seines Körpers und nach seiner Zeitempfindung ein Alter von 75 Jahren, so entspricht dies doch einer dreimaligen Wiederkehr zu unserem Sonnensystem, also 300 unserer Erdenjahre. | style="padding: 0px 20px 0px 20px;" |Yet if we again assume a relative velocity approximating the speed of light by 3 percent, then the ratio of the experienced duration of time becomes 4:1. This image can be further extended. Let's imagine that an observer travels with that velocity on a circular path at a radius of 16 light years through the space of our galaxy, then according to our time calculation he passes by our solar system every 100 years. In his vehicle the centrifugal force will act on him in such a way, that in accordance with the relativity laws it will appear to be equal to the force of gravity acting upon the inhabitants of Earth. Thus the acting forces are only thus big, in order to give our fantasy the possibility to imagine the traveler as a human being. Since we have <math>\sqrt{1-v^{2}/c^{2}}</math> throughout, proper time flows four times slower for the traveler than for the inhabitants of the stars. Thus when he comes back to our solar system after 100 of our years, he will feel to have aged only by about 25 years. If he reaches an age of 75 years according to the development of his body and his own time experience, then this corresponds to a threefold return to our solar system, i.e. 300 of our Earth years. |} {{Lorentzbox|Text=a) Wiechert (1915)<ref name=wiechert15 /> later provided a short historical survey of the clock/twin paradox. He referred to the fact that already {{slink||Einstein 1905}} considered the case of two clocks ("Einstein's clock experiment"), and even though [[w:Hermann Minkowski|Minkowski]] himself didn't consider the case, his proper time formula provides the result in a straight forward manner. The latter was done by himself in lectures on 25 March and 23 May 1911, as well as by Langevin published in July 1911. Wiechert pointed out that he himself and Langevin used "humorist" examples in order to clarify the situation: While Wiechert argued that one has to make a journey in order to stay young, Langevin argued that one has to romp about in a laboratory in order to stay young. Both of them used human beings, arguing that their physical and mental life should have been influenced in the same way as any other process in nature. b) The dates given by Wiechert (1915) are not complete. The correct ones are: *Langevin's lecture on 10 April 1911, published in July. *Wiechert's lectures on 25 March and 23 May 1911, submitted on July 26, published in September. *He was still unaware of Einstein's lecture from January 1911, published in November 1911.}} |- !{{anchor|Müller 1911-HU}}[[w:Fritz Müller-Partenkirchen|Müller]] |- |The freelance writer and law student Fritz Müller (who was later known as [[w:Fritz Müller-Partenkirchen|Müller-Partenkirchen]]) attended Einstein's lecture and wrote a popular report about it in the German newspaper "[[w:Berliner Tageblatt|Berliner Tageblatt]]" on 16th and 23rd October 1911,<ref name=muller /> in which he gave further details (compare with {{slink||Lämmel 1911-HU}}). Regarding the clock/twin paradox he wrote: {| ! width=50% | Müller wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Zwei gleichgehende Uhren sollen je einen Beobachter haben und nebeneinander ruhen. Nun soll die eine mit ihrem Beobachter plötzlich mit Lichtgeschwindigkeit in den Weltenraum hinausreisen. Vorher haben die beiden vereinbart, sich alle Sekunden mit einem Lichtsignal die Zeit zu telegraphieren. [...] In unserem Grenzfall, wo die Reise mit Lichtgeschwindigkeit vor sich geht, müßte der ruhende Beobachter erklären, jene andere Uhr käme in der Zeit überhaupt nicht voran. Die Zeit stünde dort still. Tatsächlich kommen die Einsteinschen Gleichungen zu diesem Resultat. Für den mit der Uhr reisenden Beobachter, sagt Einstein, gelte dasselbe. Das heißt, im Urteil des Zurückbleibenden würde jener niemals alt. „Und wenn er auf einer gebrochenen Reiselinie wieder an seinen Ausgangspunkt zurückkehrte?" fragt man den Vortragenden in der Diskussion. – „So bliebe er in unserem Urteil so jung wie bei der Ausreise," erwidert Einstein mit vollem Ernst, „selbst wenn wir Zurückgebliebenen inzwischen Männer mit weißen Bärten geworden sind – die Gleichungen liefern für jede Richtung der Bewegung, auch für eine gebrochene Bewegung, unerschütterlich die selben Resultate." – Wir sehen einander an. Das klingt märchenhaft. Märchenhaft? Gewiß, die alten Märchen vom Mönch von Heisterbach, vom Rip van Winkle, von Urashima Taro steigen auf. Merkwürdig, wie die Volksphantasie bei den Deutschen, bei den Amerikanern, bei den Japanern in der gleichen Richtung gearbeitet hat – alle drei Märchen erzählen ja von Leuten, deren Leben still steht, viele hundert Jahre lang, während die andern altern. So fanden sie bei ihrer Rückkehr ein anderes Land und eine andere Generation. | style="padding: 0px 20px 0px 20px;" |Two synchronous clocks at rest next to each other, shall each be accompanied by an observer. Now one of them, together with its observer, suddenly travels into space at the speed of light. Previously, both have arranged that every second they telegraph their time to each other using light signals. [...] In our limiting case where the journey happens at light speed, the resting observer would have to declare that the other clock would not proceed in time at all. Time would stand still at this place. Einstein's equations indeed produce this result. As to the observer traveling with the clock, says Einstein, the same is true. That means in the judgment of the remaining one, the other one would never become old. Then the lecturer [i.e. Einstein] was asked in the discussion: "And if he comes back to his starting point on a curved travel path?", to which Einstein replied in full earnest: "Then in our judgment he would remain as young as he was at departure, even if we remaining ones became men with white beards in the meantime, the equations unshakably give the same result in every direction of motion, also for curved motion". We look at each other. That sounds fabulous. Fabulous? Of course, the old fairy tales of [[w:Heisterbach Abbey|w:The monk of Heisterbach]] or [[w:Rip Van Winkle]] or [[w:Urashima Tarō]] come forward. Strange, how the folk fantasy of the Germans, the Americans, the Japanese worked in the same direction, all three fairy tales indeed tell about people whose life stands still, many hundred years long, while the other ones grow old. Thus they found another country and another generation when they returned. |} {{Lorentzbox|Text=Müller's account confirms {{slink||Lämmel 1911-HU}} that Einstein indeed mentioned human beings, but his description also suggests that Einstein was the first to use mutually sent light signals. However, as this was published in October, it cannot be excluded that Müller's description of light signals was influenced by {{slink||Langevin 1911-HU}}, published in July, in which light signals were used as well.}} |} ==Twins from 1911 to 1920== We now provide a list of authors who employed ''twins'', i.e. ''two'' life forms or humans that initially were of ''same age'' when the round-trip began: {| class="wikitable" style="background-color:white;" |- ! Author !! Date !! Description |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> |1911 |Two life forms that begin their life at the ''same time'' (German: "Zwei Lebewesen [..] die ihr Leben gleichzeitig beginnen"), of which the moving one returns retarded in its progression with respect to the stationary one. |- |[[w:Paul Gruner|Gruner]]<ref name=gruner /> |1912 |Two persons of ''same age'' (French: "deux personnes du même âge"), of which the moving one returns less developed than stationary one. |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> |1913 |The moving life form returns younger than its ''former agemates'' (German: "ehemaligen Altersgenossen"). |- |[[w:Hermann Weyl|Weyl]]<ref name=weyl /> |Easter 1918 | {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Von zwei Zwillingsbrüdern, die sich in einem Weltpunkt A trennen, bleibe der eine in der Heimat (d. h. ruhe dauernd in einem tauglichen Bezugsraum), der andere aber unternehme Reisen, bei denen er Geschwindigkeiten (relativ zur »Heimat«) entwickelt, die der Lichtgeschwindigkeit nahekommen; dann wird sich der Reisende, wenn er dereinst in die Heimat zurückkehrt, als merklich jünger herausstellen denn der Seßhafte. |Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. |} {{Lorentzbox|Text=Weyl was the first to ''explicitly use twins'' in relation to the round-trip experiment. The fourth edition (1920) of that book was translated from German into English and French in 1922.}} |- |[[w:Albert Einstein|Einstein]]<ref name=einstein20 /> |1920/21 |{{Anchor|Einstein 1921-TW}} {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Trifft A wieder bei B ein, so kann es sich ereignen, daß der beharrende Zwilling inzwischen 60 Erdjahre alt geworden ist, während der zurückkehrende nur 15 Jahre zählt, oder sich gar noch im Säuglingsstadium befindet. [..] Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls -Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. |If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still. [..] In the case of these two twins, Einstein declared, we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures. |} {{Lorentzbox|Text=This was based on an interview of Einstein by Moszkowski. While the expression "clock paradox" was used since 1911/12 (see section {{slink||Paradoxical?}}), this seems to be the first time that it was rebranded as "twin paradox". The copyright mark indicates 1920, while the title page indicates 1921. The translation from German into English also appeared in 1921.}} |} ==Maximal proper time== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]] 1911 |{{anchor|Langevin 1911-PT}}In April 1911 (published July),<ref name=langevin1 /> he described the round-trip experiment without formulas using two portions of matter present at two events happening at the same place. The ''integration of proper time'' along the entire wordlines shows that the portion of matter that starts a closed cycle by receding and finally coming back, will have a ''smaller proper time'' than the one that stayed behind. In October 1911 (published 1912),<ref name=langevin2 /> Langevin again showed that the portion of matter that described a closed cycle will have a ''smaller proper time'' <math>R</math> than the one that stayed in an inertial frame, which is defined by the equation: :<math>\begin{matrix}V^{2}\left(t-t_{0}\right)^{2}=d^{2}-R\\ \left[d^{2}=\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}\right] \end{matrix}</math> |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> Lectures March-May 1911 submitted July published September |{{anchor|Wiechert 1911-PT}}Let two equal processes be observed in two equal material systems colocated in two moments (1) and (2), and let there velocities have been changed in arbitrarily different ways in the meantime. It follows that the ratio of advancement of those processes is given by the two intervals <math>\Delta\tau </math> of their respective ''proper times''. He concluded that any round-trip clock experiment can be easily comprehended from that theorem by computation. The corresponding integral is: :<math>\Delta\tau=\int_{1}^{2}d\tau=\int_{1}^{2}dt\sqrt{1-\frac{\mathfrak{v}^{2}}{c^{2}}}</math> |- |[[w:Eduard Study|Study]]<ref name=study /> June 1911 |Minkowski's concept of worldlines implies that the straight path between two points of the same worldline is the ''longest'' among all paths between those points, if the path length on a worldline is defined by the related proper time. {{Lorentzbox|Text=Study's book was purely mathematical without mentioning clocks or the round-trip experiment, alluding to his result only in a footnote.}} |- |[[w:Max von Laue|Laue]] 1911-13 |{{anchor|Laue 1911/12-PT}}In December 1911 (published 1912),<ref name=laue1 /> Laue showed without formulas that the round-trip experiment is represented by a curved worldline, which at worldpoint A decomposes into a row of curves, after which all of them will be re-united at worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the ''longest proper time.'' {{anchor|Laue 1912/13-PT}}In December 1912 (published 1913) in the second edition of this relativity book,<ref name=laue1 /> Laue described the proper time integral between events 1 and 2 of a slowly accelerated clock covering a broken line and a stationary clock covering a straight worldline. Of all worldlines covering 1 and 2, the straight line has the ''longest proper time''. Therefore the traveling clock in the round-trip experiment is retarded at reunion, because its curved worldline corresponds to a shorter proper time. This result he presented in terms of the following inequality, of which the right-hand side refers to the straight curve of the stationary clock, while all others possible curves are represented on left-hand side: :<math>\tfrac{1}{c}\int_{1}^{2}\sqrt{du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}<\tfrac{1}{c}\int_{1}^{2}du</math> {{Lorentzbox|Text={{anchor|Sommerfeld 1913-PT}}Similar treatments can be found in the textbooks of [[w:Arnold Sommerfeld|Sommerfeld]] (1913),<ref name=sommerfeld /> [[w:Hermann Weyl|Weyl]] (1918),<ref name=weyl /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Jean Becquerel|Becquerel]] (1922).<ref name=becqu1 />}} |} ==Triangle inequality== {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Alfred Robb|Robb]] 1914-1920 |{{anchor|Robb 1914-TR}}In 1914<ref name=robb1 /> he showed that there are three types of triangles formed by intervals in Minkowski space, depending on whether one deals with "separation lines" (spacelike intervals), "optical lines" (lightlike intervals), or "inertia lines" (timelike intervals representing the path of nonaccelerated particles defined by <math>{\scriptstyle \left(x_{1}-x_{0}\right)^{2}+\left(y_{1}-y_{0}\right)^{2}+\left(z_{1}-z_{0}\right)^{2}-c^{2}\left(t_{1}-t_{0}\right)^{2}<0}</math>). As to a triangle formed by inertia lines, he showed that the sum of a certain two sides is ''less'' than that of the third one. {{Lorentzbox|Text=So the triangle inequality derived from time-like intervals in Minkowski space is ''[[w:Triangle inequality#Reversal in Minkowski space|inverse]]'' to the inequality in Euclidean space. This inverse inequality directly represents the most simple variant of the twin paradox: the traveler follows two sides of the time-triangle, while the stay-at-home observer follows the third side indicating maximal proper time.}} [[File:RobbTriangle.svg|right|150px]] In 1920<ref name=robb2 /> Robb gave a numerical example of the triangle ABC with time-like intervals ("inertia lines") defined by coordinates :<math>\begin{matrix} & x & y & z & t\\ A\ & 0 & 0 & 0 & 0\\ B\ & 0 & 0 & 0 & 10\\ C\ & 4 & 0 & 0 & 5 \end{matrix}</math> which he plugged into :<math>\bar{s}^{2}=\left(t_{1}-t_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}-\left(y_{1}-y_{0}\right)^{2}-\left(z_{1}-z_{0}\right)^{2}</math> from which he obtained the sides AB=10, AC=3, CB=3 and the inequality <math>AC+CB<AB</math>. |- |[[w:Arthur Eddington|Eddington]]<ref name=edding2 /> 1922 |He distinguished between the "space-triangle" for spacelike intervals, and the "time-triangle" for time-like intervals. The latter is measured with a clock from A to B and from B to C, with the sum of those readings ''is always less'' than the reading of a clock measuring directly from A to C. In the ordinary space-triangle any two sides are together greater than the third side; in the time-triangle two sides are together ''less'' than the third side. |- |Rogers<ref name=rogers /> 1922 |He showed that the "pure time-triangle" C, A, B (in their proper time order) satisfies the relation <math>\cosh C=\tfrac{\alpha^{2}+\beta^{2}-\gamma^{2}}{2\alpha\beta}</math>, where <math>\cosh C</math> denotes the unit-scalar product of the vectors CA, CB, and <math>\alpha,\beta,\gamma </math> the real and positive intervals BC, CA, AB. Since <math>\alpha>\beta </math> and <math>\cosh C>1</math>, it follows that <math>\alpha>\beta+\gamma </math>. That is, "the greatest side of pure time-triangle is greater than the sum of the other two sides". It follows at once that the stationary value of the proper time integral is an "absolute maximum". |} ==Negligibility of proper acceleration== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |style="vertical-align:top" |[[w:Albert Einstein|Einstein]] 1905-1918 |In 1905,<ref name=einstein05 /> Einstein used velocity time dilation <math>\tau=t\sqrt{1-\left(\frac{v}{V}\right)^{2}}</math> to derive the retardation of a clock performing a round-trip with constant speed <math>v</math> along a polygonal path or a continuously curved line, without mentioning any influence of acceleration at turnaround. {{anchor|Einstein 1911-VA}} In 1911 (published 1912),<ref name=einstein3 /> Einstein said that special relativity doesn't say anything about what happened to the clock's pointer position during the acceleration that changes the clock's direction along the round-trip, yet the influence of this change must be getting smaller the longer the clock ''is moving uniformly'', i.e. the longer one chooses the dimensions of the path. {{anchor|Einstein 1912-VA}}In an unpublished manuscript on special relativity from 1912,<ref name=einst12manu /> he pointed out that any influence of acceleration during the round-trip experiment, can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygonal path. {{anchor|Einstein 1914a-VA}}In a letter from April 1914,<ref name=einstpetz /> Einstein showed that any ''finite'' acceleration at turnaround during the round-trip experiment can only influence the clock in a ''finite'' way, thus it can be neglected by minimizing the time of acceleration with respect to the time of uniform translation. So it ''must be concluded'' that the clock is retarded at reunion after traveling on a polygonal path. {{anchor|Einstein 1914b-VA}}During a conversation in May 1914,<ref name=rowe group=S /> Einstein is reported to have replied that the accelerations during the round-trip are "irrelevant for the amount of the time difference". (Compare with {{slink||Einstein 1914b-AC}}) {{anchor|Einstein 1918-VA}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918,<ref name=einstein18 /> Einstein pointed out that any effect of velocity changes at turnaround must be limited, thus the traveling clock must be retarded at reunion due to time dilation if one makes the path AB and back along the round-trip long enough. (Compare with {{slink||Einstein 1918-AC}}) |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> 1911 |{{Anchor|Wiechert 1911-VA}}[[File:WiechertTwin.svg|110px|right]] He demonstrated that differential aging along the round-trip cannot be caused during the passage from one velocity to another (i.e. acceleration) at turnaround, because the same result also follows when ''both'' A and B experience the ''same velocity changes'' with respect to another frame, only with the difference that B has relative velocities <math>+u</math> and <math>-u</math> for a long time, while A is brought after a short time from relative velocity <math>+u</math> to relative rest at which it remains a long time, and then it is brought to relative velocity <math>-u</math> for a short time. {{Lorentzbox|Text=He was probably the first to use an example in which both accelerate with same magnitude.}} |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> 1913 |{{anchor|Laue 1913-VA}}He showed that the problem of the influence of acceleration at turnaround in the round-trip experiment, can be eliminated by ''arbitrarily'' enlarging the time in inertial motion. {{Lorentzbox|Text=This is the same argument as given in {{slink||Einstein 1911-VA}}. The Einstein-Laue argument was also used by others such as [[w:Hans Thirring|Thirring]] (1921)<ref name=thirring /> or [[w:Max Born|Born]] (1921).<ref name=born />}} |- |[[w:Hendrik Lorentz|Lorentz]]<ref name=lorentz1 /> 1913 |He pointed out that any effect of acceleration on the traveling clock at turnaround, can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip. {{Lorentzbox|Text=Similarly, [[w:Wolfgang Pauli|Pauli]] (1921) stated that the arising infinitesimal accelerations at turnaround are certainly independent of the total travel time and ''therefore easy to eliminate''.<ref name=pauli />}} |} ==Relay (three brothers) experiment== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:de:Fritz Grünbaum (Physiker)|Grünbaum]]<ref name=gbaum /> 1911 |He discussed a one-way time dilation experiment in which the first clock is set into motion from the origin and then moving to the second clock. He argued that one can avoid the problem of acceleration experienced by the first clock when set into motion, by replacing it with a ''third'' clock that is already in motion with constant velocity and is synchronized at the origin with the first clock. {{Lorentzbox|Text=While Grünbaum didn't discuss round-trip experiments, his introduction of a third clock in order to avoid acceleration is the basis of the three-brother experiment.}} |- |style="vertical-align:top"|[[w:Emil Wiechert|Wiechert]] 1920-1922 |In 1920 (published 1921),<ref name=wiechert20 /> Wiechert explained how to completely remove acceleration from the round-trip experiment: Bodies A, B, C move undisturbed and non-accelerated in different directions. A and B pass each other at time (1), B and C pass each other at a later time (2), and C and A finally pass each other at an even later time (3). So in this setup, the condition of C is the continuation of the condition of B. On any of the three bodies one can count the oscillations of light of a certain spectral-line, in which case relativity predicts that the ''combined sum of all oscillations'' on B+C is smaller than the number of oscillations on A alone. Wiechert also held that one can replace the light oscillations by the life functions of human-like beings which live on A, B and C. For instance, while the inhabitants of B+C only had time for one meal, there were arbitrarily many generations on A who follow after each other by death and birth. [[File:Wiechert1922a.png|180px|right]] In 1921 (published 1922),<ref name=wiechert21 /> Wiechert extended his previous acceleration-free round-trip experiment to an arbitrary number of non-accelerated bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., which constitutes a "relay" (German: Stafette) starting from body A and back again. The first B passes A and moves away, and after some time the last B comes back to A. Since any B body continues the fate of the previous one, all bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., combined have emitted fewer oscillations than A alone during the relay race. Wiechert pointed out that instead of light oscillations one can also choose the aging of life forms. {{Lorentzbox|Text=Such relay experiments were later independently rediscovered in English language papers<ref name=debs group=S /> such as by Lange (1927)<ref group=S name=lange /> in which the brothers synchronize their times when they pass each other (“three brother experiment”).}} |} ==Acceleration as asymmetry indicator== While it was known that any direct influence of [[w:proper acceleration]] on clocks can be neglected in the computation of the inertial frame of the stay-at-home twin (see previous section {{slink||Negligibility of proper acceleration}}), the very fact that only one of them is accelerating is still useful as an asymmetry argument in order to show that there is no contradiction to the relativity principle. {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{Anchor|Langevin 1911-AC}}He derived differential aging in the round-trip experiment using the proper time integral along worldlines (see {{slink||Langevin 1911-PT}}) and used acceleration as an asymmetry indicator: The result of the round-trip experiment is "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". |- |[[w:Arnold Sommerfeld|Sommerfeld]]<ref name=sommerfeld /> 1913 |After he showed (see {{slink||Sommerfeld 1913-PT}}) that retardation of time in the round-trip experiment derived from the proper time integral rests on the assumption that the clock's rate ''only depends on its momentary velocity'' (now called "clock hypothesis"), he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle since one of the clocks has to be accelerated in order to come back, thus the retardation in the round-trip experiment does not demonstrate "motion", but "accelerated motion". |- |[[w:Hendrik Lorentz|Lorentz]] 1913<ref name=lorentz1 /> |After he derived differential aging in the round-trip experiment from velocity time dilation and pointed out the negligibility of proper acceleration for the computation, he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle, since one of them changes velocity and accelerates; the relativity principle does not require symmetry between inertial and non-inertial observers. |- |style="vertical-align:top"|[[w:Albert Einstein|Einstein]] 1914-1920 |{{anchor|Einstein 1914b-AC}} During a conversation in 1914,<ref name=rowe group=S /> Einstein is reported to have said that moving clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are ''irrelevant'' for the ''amount'' of the time difference, their ''presence'' nevertheless cause B to fall behind ("accelerated motions are absolute"). {{anchor|Einstein 1918-AC}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918<ref name=einstein18 />, Einstein pointed out the negligibility of velocity changes from the viewpoint of an inertial frame (see {{slink||Einstein 1918-VA}}). Then he used ''acceleration as an asymmetry indicator'' in order to show, that there is no contradiction to the relativity principle, because relativity only predicts the equivalence of non-accelerated inertial frames: "only K is such a frame while K' is temporarily accelerated, thus the retardation of U2 with respect to U1 cannot be used to construe a contradiction against the theory." {{anchor|Einstein 1920-AC}}Einstein is reported to have said in an interview from 1920:<ref name=einstein20 /> {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls-Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. Dieser Grund für das Jüngerbleiben des A ergibt sich vom Gesichtspunkt der speziellen Relativitätstheorie aus der Tatsache, daß das betreffende Geschöpf — und nur dieses — Beschleunigungen erlitten hat. | style="padding: 0px 20px 0px 20px;" |In the case of these two twins," Einstein declared, "we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures . This ground, which counts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations." |} In a discussion from 1922,<ref name=morand /> Einstein is reported to have said that there is no contradiction in the round-trip experiment (in terms of a train leaving the station and returning later): The relativity principle is not applicable to this case, because the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two frames having velocities in opposite direction is not an inertial frame. There is no reciprocity between a frame that changes direction and one that doesn't. |} ==Frame distribution as asymmetry indicator== Because any direct influence of proper acceleration on the traveling clock at turnaround can be neglected (see {{slink||Negligibility of proper acceleration}}), the importance of {{slink||Acceleration as asymmetry indicator}} is limited to the mere fact that it reveals that only the traveler was in a non-inertial frame as only he changed his inertial frames, thus instead of emphasizing the occurrence of proper acceleration at turnaround, it's possible to describe the asymmetry more geometrically by emphasizing the different distribution of inertial frames of the twins along their worldlines. {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Max von Laue|Laue]] 1911-1913 |{{Anchor|Laue 1911/12-VA}} In 1911/12,<ref name=laue1 /> he pointed out that during the time of separation, that clock is most advanced which was at rest in an inertial frame all the time; namely there is ''always one, and only one inertial frame'', in which the locations of separation and re-encounter lie in the same geometric point. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1911/12-PT}}). In 1912/13,<ref name=laue2 /> he argued that in the round-trip experiment, we indeed can decide, which one of the clocks was steadily at rest in one and the same reference system, and which one was in the meantime at rest in two or more such systems. Among them there is of course a real physical difference. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1912/13-PT}}). In 1913<ref name=laue3 /> Laue pointed out: {| !style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Aber nach unseren Voraussetzungen ruht während der Zeit der Trennung die erste Uhr in ''einem'' berechtigten Bezugssystem, die zweite hingegen ruht zwar sowohl bei der Hin- wie bei der Rückbewegung in berechtigten Bezugssystemen, aber notwendig in ''zwei verschiedenen. Deshalb'' unterscheiden sich beider Schicksale physikalisch. Ließe man die zweite Uhr in der ihr anfangs erteilten Bewegung und schickte man ihr dafür die erste Uhr nach einiger Zeit mit größerer Geschwindigkeit nach, so würde beim Zusammentreffen die erste gegen die zweite zurückgeblieben sein; denn jetzt hat die erste während der Trennung in zwei verschiedenen Systemen geruht. (Footnote: Dem naheliegenden Einwand, daß wir über den Gang einer Uhr während eines Geschwindigkeits''wechsels'' nichts aussagen können, begegnet man am einfachsten mit dem Hinweis, daß man die Zeiten der gleichförmigen Bewegung ''beliebig'' groß gegen die der Beschleunigung machen kann.) | style="padding: 0px 20px 0px 20px;" | However, by our presuppositions, one clock is at rest in ''one'' valid reference system during the time of separation, while the second one is at rest in valid reference systems both during the forward- and the backward motion, but necessarily in ''two different ones. Therefore'' the two fates differ physically. If the second clock remains in the motion which was given to it at the start, and if after some time it is followed by the first clock with greater velocity, then the first one would be retarded with respect to the second one at the encounter; since now it was the first one that was at rest in two different systems during the separation. (Footnote: The objection which is near at hand, that we cannot say anything about the rate of a clock during a velocity ''change'', can be met most simply by the allusion, that we can render the times of uniform motion ''arbitrarily'' great with respect to acceleration..) |} |- |[[w:Werner Bloch|Bloch]]<ref name=bloch /> September 1918 |{{anchor|Bloch 1918-VA}} He represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. |} ==Perspective of the traveler== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{anchor|Langevin 1911-LI}}[[Image:rstd4.gif|170px|right]] After deriving differential aging from the proper time integral in {{slink||Langevin 1911-PT}} and using human beings in {{slink||Langevin 1911-HU}}, he described the perspectives of both observers using light signals and the Doppler effect. When they separate they see each other live 200 times slower, while at return they see each other live 200 times faster. So ''from the explorer's viewpoint'', in the first year he sees the Earth perform the actions of two days, while in the second year he sees the Earth perform the actions of two centuries. The asymmetry can be seen by noticing, that the observer on Earth in 200 years sees the explorer performs the actions of 1 year. Then the explorer turns around, after which the observer on Earth in 2 days sees the projectile perform the actions of another year. {{Lorentzbox|Text=Langevin used <math>v=c\left(1-\tfrac{1}{20000}\right)</math>, producing Lorentz factor <math>\gamma\approx100</math> and Doppler factor <math>\sqrt{\tfrac{c+v}{c-v}}\approx200</math>.}} |- |[[w:Hendrik Lorentz|Lorentz]] Lectures published in 1913<ref name=lorentz1 /> Similar treatment in 1914<ref name=lorentz3 /> |{{anchor|Lorentz 1913/14-LI}}Described the round-trip experiment in terms of inertial observer A (equipped with clock K) and traveling observer B (equipped with clock K'). In the frame of A, clock K' is retarded with respect to K at reunion due to time dilation. He then described the perspective of the traveling observer B by using two-way propagation of light from K' to K and back to K', leading to three periods defined by the moment of B's turnaround: In the first period the light signals return to K' before turnaround; in the second period the signals are emitted before turnaround and return after turnaround; in the third period emission and return of the signals are both happening after turnaround. Lorentz showed that K is time dilated by a factor of <math>\sqrt{1-v^{2}/c^{2}}</math> with respect to K' in the first and third period, but in the second period K is ticking ''faster'' than K' by a factor of <math>\sqrt{\tfrac{c+v}{c-v}}</math> which overcompensates the dilation in the other periods and explains, even from the perspective of B, why K' is retarded with respect to K at reunion. {{Lorentzbox|Text=In a review of the German translation of Lorentz's book, Einstein (1914) didn't directly mention Lorentz's treatment of the twin paradox, but he wrote that nobody who is seriously interested in relativity should neglect to read that book.<ref name=einstlor /> [[w:Wolfgang Pauli|Pauli]] (1921) refers to Lorentz's book as one of three papers that analyze the twin paradox more closely.<ref name=pauli />}} |- |style="vertical-align:top"| [[w:Albert Einstein|Einstein]] 1916-1920 |{{anchor|Einstein 1916-EP}}In a lecture from 1916,<ref name=einstein16 /> of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of [[w:general relativity]]." {{anchor|Einstein 1918a-EP}}In a letter from September 1918,<ref name=einadl /> Einstein showed that general relativity makes the inertial frame K and and the accelerated frame K' of the clocks in the round-trip experiment "equally justified", explaining the time difference in K' by combining the influence of velocity and gravitational potential on clocks. {{anchor|Einstein 1918-EP}}In his famous "Dialog about Objections against the Theory of Relativity" from November 1918,<ref name=einstein18 /> aimed at clarifying misconceptions of the clock paradox, he explained that there is no paradox in special relativity because there is no symmetry between clock U1 at rest in inertial frame K and clock U2 at rest in accelerated frame K' (see {{slink||Einstein 1918-AC}}). Yet [[w:general relativity]] and the [[w:equivalence principle]] allow the treatment of this problem also from the standpoint of frame K', where clock U2 remains at rest all of the time while U1 makes the following movements: (1) It is accelerated by a homogeneous gravitational field in the negative direction, (2) it moves with constant velocity <math>-v</math>, (3) it is accelerated in the positive direction until it turns around and comes by with constant velocity <math>+v</math>, (4) it moves with velocity <math>+v</math>, (5) it is accelerated in the negative direction until it stops. Clock U1 is retarded with respect to U2 in periods 2) and 4) due to velocity time dilation, but this retardation is overcompensated by the faster rate of U1 during period 3), because U1 is at a higher gravitational potential. He argued that the computation (which he didn't provide) shows that the advance of U1 in period 3) is double its retardation during periods 2) and 4). Einstein concluded that by this consideration "the paradox is completely resolved". Using [[w:Mach's principle]], he pointed out that the gravitational field in K' might be induced by the masses of the universe that are accelerated in this frame. {{anchor|Einstein 1918b-EP}}In a letter to Einstein from December 1918, [[w:Max Jakob|Jakob]] doubted the result that the advance in period 3) is double the retardation during periods 2) and 4). Einstein responded by letter,<ref name=einstein18b /> in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). {{anchor|Einstein 1921-EP}}Einstein is reported to have said in an interview from 1920,<ref name=einstein20 /> that while acceleration explains the age difference between the stationary twin B and the traveling twin A in terms of special relativity (see {{slink||Einstein 1920-AC}}), the "proper" description in terms of general relativity is as follows: {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Eine tiefere Erfassung des Grundes ist indeß nur auf dem Boden der „Allgemeinen Relativitätstheorie" zu erlangen, die uns erkennen läßt, daß von A aus beurteilt ein Zentrifugalfeld existiert, von B aus betrachtet aber nicht; und dieses Feld hat einen Einfluß auf den relativen Ablauf und die Raschheit der Lebensvorgänge. | style="padding: 0px 20px 0px 20px;" | A proper grasp of the reason is furnished only when we adopt the general theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life." |} {{Lorentzbox|Text=a) Einstein's explanation was quickly adopted in the textbooks of [[w:Werner Bloch|Bloch]] (1920),<ref name=bloch2 /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Karl Bollert|Bollert]] (1921),<ref name=bollert1 /> [[w:Max Born|Born]] (1921),<ref name=born /> expressing the view that general relativity is "necessary" to provide the "complete" solution of the twin paradox. b) From a modern standpoint, however, Einstein's explanation has nothing to do with general relativity, but is rather an application of accelerated frames and "pseudo"-gravitational fields to flat Minkowski space of ''special'' relativity.<ref name=weiss group=S />}} |- |[[w:Hans Thirring|Thirring]]<ref name=thirring /> April 1921 |{{anchor|Thirring 1921-DS}}[[Image:Twin Paradox Minkowski Diagram.svg|right|200px]] He described the round-trip experiment by using two platforms K (clock A) and K' (clock B) each equipped with rows of clocks. He first demonstrated the symmetry of time dilation and the mutual relativity of simultaneity on the platforms and its effect on clock synchronization. The K clocks that B passes are all advanced because of <math>t'=\gamma\left(t-vx/c^{2}\right)</math>, and the same is true after turnaround since only the direction of velocity has to be changed in the Lorentz transformation <math>t'-t'_{0}=\gamma\left(t+vx/c^{2}\right)</math> leading to the effect of clock desynchronization, where <math>t'_{0}</math> is a constant depending on which clock one uses as standard for the new synchronization. He graphically showed using Minkowski diagrams, that this simultaneity jump due to desynchronization amounts to double the velocity time dilation during the inertial phases, explaining why A is more advanced than B at reunion. {{Lorentzbox|Text=Using clock B as synchronization standard, Thirring's constant is given by <math>t'_{0}=2l\gamma v/c^{2}=2t\gamma v^{2}/c^{2}</math> with <math>l=vt</math> as position of turnaround. A similar explanation was subsequently given by Langevin (1922).<ref name=morand />}} |} ==Curved spacetime== While the previous examples are defined in flat Minkowski spacetime and therefore can be fully discussed in terms of special relativity, [[general relativity]] is required when [[:w:spacetime curvature]] in the presence of mass and energy cannot be neglected any more.<ref name=koks group=S /> {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |[[w:Jean Becquerel|Becquerel]]<ref name=becqu1 /> 1922 |After defining gravitational time dilation <math>d\tau=\sqrt{1-\tfrac{2GM}{c^{2}r}}dt</math> in terms of the [[w:Schwarzschild metric]] around a material center, he discussed the following round-trip experiment: There are two identical clocks A and B placed next to each other, at a point very far from the material center, initially marking the same time <math>t</math>. Let us transport clock A to a point where the field is more intense, at a distance <math>r</math> from the center; this clock will measure time <math>\int d\tau</math> which is shorter than <math>\int dt</math>, thus it will run more slowly. If we bring clock A back to clock B, we will have to note that it is retarded with respect to B. |} ==Aether interpretations== [[w:Lorentz ether theory]] (LET) is empirically equivalent to special relativity since both models use the Lorentz transformation, thus the description of the twin paradox gives the same result as well. However, special relativity is preferred by the scientific community, because of the validity of the relativity principle in LET is only apparent due to a conspiracy of effects which makes the aether undetecable, and because the measured times and lengths in the aether are supposedly be giving the "true" values even though it is empirically impossible to determine which ones are true or apparent. {| class=wikitable style="background-color:white;{{text default color}};" |- ! style="width:150px" | Author !! Description |- |Langevin (1911)<ref name=langevin1 /> |He argued that it's true that uniform translation with respect to the aether has no experimental meaning in special relativity, though one can still speak of "absolute acceleration" with respect to an aether which he defined as the light carrying medium, so it was "premature to abandon the aether". The absolute nature of acceleration can be seen in the radiation of accelerated charges, as well as in the twin paradox in which the traveler that is more agitated or accelerated is younger at reunion. {{Lorentzbox|Text=Langevin didn't mention this aether interpretation in his later discussions of the twin paradox in 1911/12<ref name=langevin2 /> and 1919.<ref name=langevin3 />}} |- |style="vertical-align:top" |{{Anchor|Wiechert 1911b}}Wiechert (1911)<ref name=wiechert11 /> |Contrary to Langevin, he emphasized that differential aging can be attributed to the existence of absolute "velocities" which he called "strides" (German: Schreitungen, denoting the "absolute meaning" of non-accelerated motions) with respect to the aether, whereas he dismissed the role of accelerations. In other words, the clock's "strides" are not equivalent or anisotropic with respect to the aether, in contradiction to the "unconditional" relativity principle Einstein's which requires equivalence and symmetry. Wiechert proposed a "conditional" relativity principle in which the aether (in the sense of Lorentz) determines all processes in nature, thus the rate of clocks or processes is "really" altered during motion. {{Lorentzbox|Text=a) This aether interpretation was maintained by Wiechert also in subsequent publications in 1915-1922.<ref name=wiechert15 /><ref name=wiechert20 /><ref name=wiechert21 /> b) Wiechert's interpretation in terms of absolute non-accelerated motions was also independently given by others: [[s:fr:Georges Lechalas]] (1912/13)<ref name=lech /> argued that time dilation and asymmetric aging are the result of absolute speeds with respect to an aether, while criticizing Langevin's (1911) argument that only accelerations can indicate the aether and are responsible for the asymmetric aging; [[w:Edward Vermilye Huntington]] (1912)<ref name=hunt /> argued that the "famous paradoxes of the theory of relativity" represented by the reciprocal nature of length contraction and time dilation, appear as necessary consequences of perfectly natural and reasonable conventions for setting clocks and laying out coordinates, when the Lorentz transformation is derived and interpreted on the basis of a stationary aether in the sense of Lorentz. c) Laue (1911/12)<ref name=laue1 /> applauded Wiechert for the "particularly striking way" in which he demonstrated that asymmetric aging indeed follows from the relativity laws, yet he rejected Wiechert's aether interpretation and Wiechert's claim that asymmetric aging contradicts the "unconditional" relativity principle: Laue pointed out that the straight worldline connecting two events A and B is only "preferred" insofar as it indicates the maximal proper time between them, yet this preference is ''not'' the result of the natural laws employed, but is rather due to the choice of points A and B; by analogy, the geometric result that two points determine a straight line and thus a direction as well, doesn't refute the physical equivalence of all directions in space; finally, as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.}} |} ==Paradoxical?== Even though Einstein (1905)<ref name=einstein05 /> denoted the round-trip experiment as "peculiar" (German: eigentümlich) he saw nothing contradictory in it. Without mentioning the round-trip experiment, [[w:Paul Gruner]] in May 1910<ref name=gruner10 /> denoted the effect that clocks in relative motion are not showing the same time when they meet as the "great paradox" of relativity (German: Grosse Paradoxie), and [[w:Max von Laue]] in May 1911<ref name=laue0 /> wrote that some consequences of the relativity of time occasionally indeed look "paradoxical" (German: paradox). Eventually, Laue in November 1911 (published 1912)<ref name=laue1 /> was the ''first to specifically denote the round-trip experiment'' as a "paradox" (German: Paradoxie): {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" | German original of [[w:Max von Laue|Laue]] (1911/12):<ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> ! English translation |- |Unter all den paradox erscheinenden Folgerungen aus der Zeittransformation der Relativitätstheorie gibt es wohl keine, gegen welche sich der natürliche Menschenverstand bei jedem, der der Sache noch ungewohnt ist, so sehr sträubt, wie gegen die, daß die Zeitangabe einer Uhr von ihrem Bewegungszustand abhängen soll. Schon in seiner grundlegenden Arbeit hat Einstein diese Paradoxie auf die Spitze getrieben in einem Gedankenexperiment, welches neuerdings von Langevin in einem auch sonst sehr lesenswerten Vortrage besonders hübsch erläutert worden ist. |Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. |- |colspan=2|{{Lorentzbox|Text=Subsequently, [[w:Paul Gruner]] (1912)<ref name=gruner /> and others including Einstein (1918)<ref name=einstein18 /> explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas [[w:Rudolf Seeliger]] (1913)<ref name=seel /> spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon").}} |} ==Misunderstandings== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" padding=10 | German original by [[w:Otto Berg (scientist)|Berg]] (1910):<ref name=berg /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |Im Punkte <math>x = 0</math> des Systems S befinde sich eine Uhr, eine andere im Punkte <math>x'=0</math> von S'. Diese zweite bewege sich mit S' bis zum Punkte <math>x = a</math>, kehre dort um und bewege sich nun mit der Geschwindigkeit <math>v</math> zurück bis zum Punkte <math>x= 0</math>. Welche Zeit müssen beide Uhren in dem Moment angeben, wo sie sich wieder treffen? Wir beantworten diese Frage zunächst vom Standpunkt des Beobachters in S. Die Uhr in <math>x' = 0</math> hat sich mit der Geschwindigkeit <math>v</math> bis zum Punkte <math>x = a</math> bewegt; dazu brauchte sie die Zeit <math>\tau=\tfrac{a}{v}</math>. Zum Rückweg ist dieselbe Zeit nötig. Nach der Zeit <math>2\tau=2\tfrac{a}{v}</math> ist die Uhr also wieder im Punkte <math>x = 0</math> angelangt. Wir stellen uns nun auf den Standpunkt des Beobachters in S'. Für diesen führt nach dem Relativitätsprinzip das System S genau dieselben Bewegungen aus wie das System S' für den Beobachter in S, nur in entgegengesetzter Richtung. Die Zeit bis zum Zusammentreffen beider Uhren ist also im System S' ebenfalls gegeben durch <math>2\tau=2\tfrac{a}{v}</math>. Betrachtungen, die auf anschauliche Vorstellungen, wie Nachgehen von Uhren, gestützt sind, führen hier leicht zu Irrtümern, von denen auch die Fachlitteratur nicht frei ist. | style="padding: 0px 20px 0px 20px;" |There is a clock at point <math>x=0</math> of system S, and another one at point <math>x'=0</math> of S'. The second one moves together with S' until point <math>x=a</math>, turns around and now moves back with speed <math>v</math> to point <math>x=0</math>. Which time must both clocks indicate at the moment at which they encounter again? We answer this question at first from the standpoint of the observer in S. The clock at <math>x=0</math> has been moving with speed <math>v</math> until point <math>x=a</math>, for which it required time <math>\tau=\tfrac{a}{v}</math>. The same time is required for the way back. After time <math>2\tau=2\tfrac{a}{v}</math> the clock has thus arrived again at point <math>x=0</math>. Let's now take the standpoint of the observer in S'. In his view in accordance with the relativity principle, system S is conducting exactly the same motions as those of system S' with respect to the observer in S, only in opposite direction. Thus the time until the meeting of both clocks is given by <math>2\tau=2\tfrac{a}{v}</math> in system S' as well. Considerations based on illustrative notions, such as the retardation of clocks, easily lead to mistakes at this place, of which also the professional literature isn't free. |- |colspan=2|{{Lorentzbox|Text=a) Berg was probably the first to turn the relativity principle against asymmetric aging in the round-trip experiment, claiming that both clocks must indicate the same time at reunion. See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem. b) Berg's mistake also seems to be based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" padding=10 | German original by [[w:Otto Lehmann (physicist)|Lehmann]] (1910/11):<ref name=lehm /> ! English translation |- | style="padding: 0px 20px 0px 20px;" | Hat man zwei genau gleich gehende Uhren nebeneinander und bewegt nun die eine auf einer beliebigen Kurve bis wieder zur anderen zurück, welche Bewegung <math>t</math> Sekunden gedauert haben möge, so geht sie gegen diese um <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> oder annähernd <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> Sekunden zu spät, weil sie während der Bewegung auf langsameren Gang reguliert werden mußte, um mit der ruhenden Uhr in Übereinstimmung zu bleiben. | style="padding: 0px 20px 0px 20px;" | If there are two exactly identical clocks next to each other, and if one of them will be moved on an arbitrary curve until it comes back, which may have lasted <math>t</math> seconds, it [the moving clock] will lag behind the other one by <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> or approximately <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> seconds, because it [the moving clock] had to be regulated to a slower rate during motion in order to remain synchronous with the resting clock. |- |colspan=2|{{Lorentzbox|Text=a) So Lehmann erroneously thinks that the time difference at reunion is only the result of "regulating" the moving clock. This implies that he (like Berg) believed that special relativity predicts ''equal'' clock times at reunion if the moving clock would have been left ''unregulated'' during the round-trip. b) Lehmann's mistake (similar to Berg) seems to based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" | German original by [[w:Emil Wiechert|Wiechert]] (1911)<ref name=wiechert11 /> ! English translation |- |colspan=2| Even though he correctly derived differential clock aging in the round-trip experiment, he (like Berg and Lehmann) claimed that effects like time dilation are "apparent" if one admits Einstein's "unconditional" relativity principle in which there is no aether and all "strides" (i.e. non-accelerated motions) are physically equivalent, but they are "real" if one admits the existence of an aether in the framework of a "conditional" relativity principle in which all strides are physically non-equivalent or anisotropic. This led him to the following interpretation of the clock paradox: |- | style="padding: 0px 20px 0px 20px;" |[...] so muß am Schluß des Versuches B in seinem Fortschritt gegenüber A im Verhältnis <math>1:\sqrt{1-u^{2}/c^{2}}</math> zurückgeblieben sein. Und dieses Zurückbleiben ist unbedingt reell, denn die beiden Gebilde A und B können ja unter gleichen Umständen unmittelbar beieinander verglichen werden. Hier ist es ganz sicher ausgeschlossen, an einen Schein zu glauben, der durch unsere Auffassung der Zeit bewirkt wird. So ist denn also auch die Folgerung unabwendbar, daß für den Verlauf der Weltvorgänge die Schreitungen nicht gleichwertig sind, ''und damit sind wir von neuem zu einem Schluß gekommen, welcher der Unbedingtheit des Relativitätsprinzipes durchaus widerspricht.'' [...] Man kann den Versuch noch mannigfach variieren, z. B. so, daß A ebenso wie B zwei verschiedene Schreitungen, <math>+u</math> und <math>-u</math>, nacheinander inne hat. Wird dann zu A der Wert <math>u_{1}</math>, zu B der Wert <math>u_{2}</math>, zugeordnet, so muß der Vergleich von A und B am Schluß des Versuches ergeben, daß B oder A in seinem Fortschritt zurückgeblieben erscheint, je nachdem die Schreitungen <math>+u_{1}</math>, <math>-u_{1}</math>, oder <math>+u_{2}</math>, <math>-u_{2}</math> weiter auseinanderliegen. ''Vielleicht ist gerade diese Formulierung des Satzes besonders geeignet, um die Ungleichwertigkeit der verschiedenen Schreitungen klar und deutlich zu zeigen.'' | style="padding: 0px 20px 0px 20px;" | [...] thus B's progress must be retarded with respect to A's in the ratio <math>1:\sqrt{1-u^{2}/c^{2}}</math> at the end of the experiment. And this retardation is definitely real, since both bodies A and B indeed can be immediately compared side by side under the same conditions. Here it is certainly excluded to believe that this is an appearance due to our conception of time. Thus the consequence is unavoidable too, that the strides are not equivalent in the course of the world processes, ''and therefore we again came to a conclusion that completely contradicts the unconditionality of the relativity principle.'' [...] One can vary this experiment in many ways, for instance, so that A in the same way as B successively undergoes two different strides <math>+u</math> and <math>-u</math>. If we apply the value <math>u_{1}</math> to A and <math>u_{2}</math> to B, then the comparison of A and B at the end of the experiment must give the result, that B or A is retarded in its progress depending on whether the strides <math>+u_{2},-u_{2}</math> or <math>+u_{1},-u_{1}</math> are further apart. ''Probably it is precisely this formulation of the theorem that is particularly suitable to demonstrate the non-equivalence of the different strides clearly and explicitly.'' |- |colspan=2|{{Lorentzbox|Text=This interpretation was directly rebutted by Laue (1911/12) who demonstrated the geometrical meaning of differential aging in Minkowski space, see sections {{slink||Laue 1911/12-PT|Laue 1911/12-VA}}, showing that there is no need to assume non-equivalance or anisotropy of motions. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.<ref name=laue1 />}} |- ! style="width:50%" | German original by [[w:Norman Robert Campbell|Campbell]] (November 1911, published 1912)<ref name=camp /> ! English translation |- |colspan=2|After describing the round-trip experiment (as given by Wiechert) according to which the traveling clock B is retarded when it returns with respect to stationary clock A, he abandoned differential clock aging as follows: |- | style="padding: 0px 20px 0px 20px;" |Dieser Schluß ist nicht richtig. Die Beziehung zwischen <math>t</math>, der Ablesung an der Uhr auf A seitens des Beobachters auf A und <math>t'</math>, der Ablesung an der Uhr auf B seitens des Beobachters auf A, ist (unter der Annahme, daß zu Beginn des Versuchs <math>t=t'</math> ist) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. Der Unterschied zwischen <math>t'</math> and <math>t</math> ist eine Funktion von <math>z</math> und <math>v</math> allein. Wenn man diesen Größen ihre früheren Werte wiedergibt, indem man die beiden Uhren wieder zur Koinzidenz bringt, während sie relativ zueinander ruhen, so geht der Unterschied zwischen <math>t'</math> and <math>t</math> wieder auf null zurück, gleichviel, welche Werte <math>z</math> und <math>v</math> während der Zwischenzeit gehabt haben mögen. Wenn an irgendeinem Punkte der Bahn die Geschwindigkeit von B relativ zu A eine endliche plötzliche Änderung erfährt, so erfährt auch der Wert von <math>v</math> eine endliche plötzliche Änderung. | style="padding: 0px 20px 0px 20px;" |This conclusion is not correct. The relationship between <math>t</math> as the reading on the clock on A by the observer on A, and <math>t'</math> as the reading on the clock on B by the observer on A, is given by (assuming that <math>t=t'</math> at the beginning of the experiment) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. The difference between <math>t'</math> and <math>t</math> is a function of <math>z</math> and <math>v</math> alone. If these quantities are given their previous values by bringing the two clocks back to coincidence during which they are at rest relative to one another, the difference between <math>t'</math> and <math>t</math> goes back to zero, no matter what values <math>z</math> and <math>v</math> may have had in the meantime. If at any point on the path the speed of B experiences a finite sudden change relative to A, then the value of <math>t'</math> also undergoes a finite sudden change. |- |colspan=2|{{Lorentzbox|Text=a) So Campbell claims that any time difference during the outbound path is wiped out during the inbound path. His mistake is obvious: He is confusing coordinate differences stemming from the Lorentz transformation of ''events'' (which indeed depend on position and direction) with differences in ''clock aging'' derived from the proper time integral (which is ''accumulative'' and independent of position and direction.) b) As Campbell's paper was a reply to Wiechert, it's interesting to compare them: Campbell was correct in dismissing the aether but wrong in denying asymmetric aging, while Wiechert was correct in deriving asymmetric aging but wrong in requiring the aether. }} |- ! style="width:50%" | French original by [[w:Paul Gruner|Gruner]] (March 1912):<ref name=gruner /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |[...] deux personnes du même âge, se séparant dans des systèmes de « marche » très différents et retournant après un laps de temps assez long, constateront une différence d'âge très sensible. [...] le principe de relativité exige toujours la ''réciprocité parfaite'' des phénomènes entre deux systèmes qui possèdent un mouvement relatif. Si, dans l'exemple cité, les deux personnes du même âge se séparent avec une vitesse relative pour se retrouver plus tard, la constatation d'une différence d'âge sera parfaitement mutuelle : A dira positivement que B est resté en arrière dans son développement, et B affirmera avec le même droit que c'est A qui ne s'est pas développé assez vite. Ainsi le principe absolu de la relativité montre ses conséquences les plus extrèmes et il est clair que l'introduction de l’éther n'est plus en état de résoudre cette contradiction irréductible et inconcevable. | style="padding: 0px 20px 0px 20px;" | [...] two people of same age, separating into very different systems of motion and returning after a quite long period of time, will notice a very significant age difference. [...] the principle of relativity always requires the ''perfect reciprocity'' of the phenomenons between two systems that possess relative motion. When, in the cited example, the two persons of same age are separated by some relative velocity only to meet again later, the finding of an age difference will be perfectly mutual: A will positively say that B stayed behind in its development, and B will assert with same right that it was A who has not developed fast enough. By that, the absolute relativity principle shows its most extreme consequences and it is clear, that the introduction of the aether is no longer able to resolve this irreducible and inconceivable contradiction. |- |colspan=2|{{Lorentzbox|Text=Gruner was probably the first to claim that combining the round-trip experiment with the symmetry of time dilation leads to the contradictory situation, that both must attribute younger age to one another at reunion. At the end of his paper, we also find the expression "clock paradox" (French: paradoxe des horloges). See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem.}} |} ==Einstein's contributions== 1905:<ref name=einstein05 /> Introduction of the "peculiar" (German: eigentümlich) round-trip experiment with clocks in terms of a polygonal path as well as a continuously curved path, and an experiment comparing a clock at the pole with one at the equator. January 1911 (published November):<ref name=einstein11a /> In a lecture from January, Einstein extended the "funny" (German: drollig) round-trip experiment to living organisms. According to [[w:Rudolf Lämmel]] in April 1911<ref name=lammel /> and [[w:Fritz Müller-Partenkirchen|Fritz Müller]] in October 1911,<ref name=muller /> Einstein spoke of human beings as well. January 1911 (published January 1912):<ref name=einstein3 /> During a discussion with Einstein directly after the previous lecture, [[w:Fritz Müller-Partenkirchen|Fritz Müller]] claimed that any time difference during the round-trip should vanish at reunion, in analogy to the fact that the Lorentz contraction of a moving rod vanishes when it is at rest again. Einstein showed that the analogy is incorrect: While the clock rates are indeed the same again when they are mutually at rest, the clocks do not indicate the same time at reunion because "clocks are carriers of the time differential"; he went on to show that any possible influence of acceleration during the turnaround can be made negligible by elongating the constant velocity periods. 1912:<ref name=einst12manu /> In an unpublished manuscript on special relativity, Einstein showed that if system <math>\Sigma'</math> makes a round-trip along a polygon, then its inner processes will be retarded with respect to resting system <math>\Sigma </math> at reunion. He pointed out that any influence of acceleration can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygon. April 1914:<ref name=einstpetz /> [[w:Joseph Petzoldt]] criticized asymmetric clock aging in the round-trip experiment as a "fallback into absolutist way of thinking", claiming that special relativity requires that any difference between the clocks vanishes when their relative velocity is zero again, even though he added that any treatment of the clock paradox in special relativity is unrealistic anyway, since the theory only concerns uniform motions and therefore cannot handle velocity changes, so one has to modify the theory. Einstein responded by letter in which he praised Petzoldt's philosophical take on relativity, yet he rejected Petzoldt's conclusions concerning the clock paradox by showing that any finite acceleration at turnaround during the round-trip can only influence the clock in a finite way and therefore can be neglected by minimizing the time of acceleration with respect to the time of uniform translation, so it "must be concluded" that the clock traveling on a polygonal path is retarded at reunion. May 1914:<ref name=rowe group=S /> During a conversation with [[w:Ernst Gehrcke]] who claimed that the clock paradox contradicts the relativity principle, Einstein replied that clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are irrelevant for the amount of the time difference, their presence nevertheless cause B to fall behind ("accelerated motions are absolute in the theory of relativity"). 1916:<ref name=einstein16 /> In a lecture of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of general relativity." September 1918:<ref name=einadl /> In a letter to Einstein, [[w:Friedrich Adler (politician)|Friedrich Adler]] (while in prison for the [[w:Assassination of Karl von Stürgkh]]) claimed that the clock paradox which he described on a circular round-trip contradicts the special relativity principle, and also referred to the similar opinions of Berg and Petzoldt. Einstein responded by letter and explained that there is no contradiction as one of them accelerates; he then showed that general relativity makes both inertial frame K and accelerated frame K' equally justified, explaining the time difference in K' by combining the influence of velocity and gravitational potential, concluding that "Berg and Petzoldt were wrong". November 1918:<ref name=einstein18 /> In a fictitious dialogue between a relativity critic and a relativity apologist written by Einstein, the "critic" said that special relativity must predict differential clock aging in round-trip experiments, which was confirmed by the "relativist" who regretfully noted that even some pro-relativity authors tried to "circumvent this unavoidable result". Yet the critic claimed that this leads to a contradiction: From the viewpoint of K, clock U1 is at rest while the clock U2 was in motion and therefore returns being retarded with respect to U1, but from the viewpoint of K', clock U2 is at rest while clock U1 was in motion and therefore returns being retarded with respect to U2, which was rebutted by the relativist by pointing out the acceleration of U2. Then the critic claimed that this problem "rises again from the dead" in general relativity which allows to symmetrically treat both K and K', which was rebutted by the relativist using the equivalence principle: In K', the rate increase of U1 during turnaround period 3) is "the double" of its velocity time dilation in the inertial periods 2) and 4). December 1918:<ref name=einstein18b /> In a letter to Einstein, [[w:Max Jakob]] doubted the result from Einstein's dialogue, according to which the advance of U1 in period 3) is the double of its retardation during periods 2) and 4). Einstein responded by letter, in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). 1920:<ref name=einstein20 /> In conversations with [[w:Alexander Moszkowski]] between 1919 and 1920, Einstein argued that differential aging of the twins is rather a paradox of feeling, not a paradox of thought, because the latter would only arise if there were no reason for the asymmetric aging. The reason in special relativity lies in the fact that one of them suffered accelerations, while a deeper understanding of that question is obtained by using general relativity. Einstein argued that our "common sense" is located in the realm of feeling and analogy drawn from our ordinary experience; since there is no analogy to the example of the twins in our experience, it might appear paradoxical to the common sense, while it appears logical and necessary in light of intensified abstraction of the trained scientific mind. August 1920:<ref name=rowe group=S /> At an anti-relativity event organized by the right-wing agitator [[w:Paul Weyland]] during which [[w:antisemitic]] leaflets were distributed and [[w:swastika]]s offered at the entrance, a lecture was given by Gehrcke re-iterating his criticism of the twin paradox, claiming that the stationary first organism is old or even dead at reunion while the second organism was in motion and therefore stayed young, but from the standpoint of the second organism he himself is old or even dead while the first organism was in motion and stayed young, thus relativity is either contradictory or it leads to different realities and physical [[w:solipsism]]. Einstein who was present at that event, directly responded in a newspaper article;<ref name=einst20 /> after suspecting antisemitic motives of his critics, he specifically addressed Gehrcke's objections regarding the "well known example of the clocks (or twins)", remarking that the charge of solipsism will be "greeted by the experts as a joke", and characterized the claim that relativity requires mutual retardation of two co-located clocks as a "deliberate attempt to misinform the lay public". 1922:<ref name=morand /><ref name=nord /> [[w:Paul Painlevé]], Einstein and Langevin discussed the clock paradox at a meeting in Paris. Painlevé imagined a clock on a train that performs a round-trip with constant speed and returns being retarded with respect to the station clock, yet he claimed that the relativity principle also allows to say that the station clock performed the round-trip and returned being retarded with respect to the train clock, in contradiction to the previous result. Einstein replied that the relativity principle cannot be applied since the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two systems having velocities in opposite direction is not an inertial frame; there is no reciprocity between a frame that changes direction and one that doesn't. Langevin consequently gave a detailed analysis in terms of the Lorentz transformation. 1954:<ref name=einstein54 /> In a letter, Einstein explained the "well known clock paradoxon" using two clocks <math>B_{1}</math> and <math>B_{2}</math>; clock <math>B_{2}</math> has to reverse its speed in order to come back, thus it was initially at rest in inertial frame <math>S_{2}</math> and then at rest in <math>S_{2}^{+}</math>, whereas <math>B_{1}</math> constantly remains at rest in <math>S_{1}</math>, which explains the asymmetry between them. ==Historical references== <references> <ref name=einstein05>See p. 904f in: {{Citation |author=Einstein, A. |date=1905 |title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik |volume=322 |issue=10 |pages=891–921 |doi=10.1002/andp.19053221004|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 2, Document 23}}. See also: [https://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation at fourmilab].</ref> <ref name=einstein11a>See p. 10. in: {{Citation |author=Einstein, A. |title=Die Relativitäts-Theorie|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |issue=1-2|pages=1–14 |date=27 November 1911|orig-date=Lecture 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n11/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 17}}.<br /> The publication date 27 November 1911 can be seen on the [https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n5/mode/2up Title page and TOC of issue 1-2].</ref> <ref name=einstein3>Discussion between Einstien, Müller, Lämmel and others after the Zürich lecture: {{Citation |author=Einstein, A.; Müller, F., Lämmel, R.|title=Diskussion zu "Die Relativitäts-Theorie"|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |pages=II-IX |date=January 1912|orig-date=Lecture on 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n587/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 18, and in the corresponding English translation volume}}<br /> While the discussion already happened on January 1911, the publication followed one year later in January 1912 in the session proceedings (Sitzungsberichte) of the third issue, see [https://www.ngzh.ch/publikationen/vjs/56/3 Full issue Nr. 3] with [http://www.ngzh.ch/archiv/1911_56/56_1-2/56_3.pdf Title page and TOC] and the [http://www.ngzh.ch/archiv/1911_56/56_3/56_30.pdf Sitzungsberichte including Einstein's discussion on pp. II-IX]. </ref> <ref name=einst12manu>See p. 46 in: {{Citation |author=Einstein, A. |date=1912 |chapter=Document 1: Einstein's manuscript on the special theory of relativity|title=The collected papers of Albert Einstein|volume=4|pages=3-108|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstlor>{{Citation|author=Einstein, A.|date=1914|title=Review of "Lorentz, H. A. – Das Relativitätsprinzip" |journal=Die Naturwissenschaften|volume=2|pages=1018|url=https://archive.org/details/CAT31421305002/page/1018/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 6, Document 11}}</ref> <ref name=einstpetz>{{Citation |author=Einstein, A. |date=1914 |chapter=Document 5: Letter from Einstein to Petzoldt|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein16>See p. 423f in: {{Citation |author=Einstein, A. |date=1916 |title=Announcement of Einstein's lecture "Über einige anschauliche Überlegungen aus dem Gebiete der Relativitätstheorie"|journal=Berliner Sitzungsberichte|pages=423|volume=1916 (part 1)|url=https://archive.org/details/sitzungsberichte1916deutsch/page/423/mode/2up}}</ref> <ref name=einadl>Letter exchange between Einstein and Adler in which the critique on the clock paradox by Berg (1910) and Petzoldt (1914) was mentioned, together with the general relativity solution in terms of the gravitational potential, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Adler's letter in Document 620 and Einstein's reply in Document 628|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein18>Einstein discussed in terms of inertial frames (special relativity) on pp. 697f; accelerated frames (general relativity) on pp. 698f.; distant masses (Mach's principle) on pp. 700f. in: {{citation |author=Einstein, A.|title=[[s:de:Dialog über Einwände gegen die Relativitätstheorie|Dialog über Einwände gegen die Relativitätstheorie]]|date=November 1918|volume=6|issue=48|journal=Die Naturwissenschaften|pages=697-702|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 7, Document 13}}; See also English translation [[:s:Translation:Dialog about Objections against the Theory of Relativity|Dialog about Objections against the Theory of Relativity]] on Wikisource.</ref> <ref name=einstein18b>Letter exchange between Max Jakob and Einstein from December 1918, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Jakob's letter in Document 661c and Einstein's reply in Document 663a|title=The collected papers of Albert Einstein|volume=10|pages=189-190}}</ref> <ref name=einstein20>Interview of Einstein by Moszkowski, see p. 204f. in: {{citation |author=Moszkowski, A.|title=Einstein. Einblicke in seine Gedankenwelt|orig-date=Copyright date 1920 |date=1921|place=Hamburg|url=https://www.archive.org/details/einsteineinblick00moszuoft}}; See also English translation by H. L. Brose (1921): [https://archive.org/details/einsteinsearch00moszrich Einstein, the searcher], p. 206</ref> <ref name=einst20>{{Citation|author=Einstein, A.|date=27 August 1920|journal=Berliner Tageblatt|title=Meine Antwort - Ueber die anti-relativitätstheoretische G. m. b. H.|issue=402|pages=1-2|url=https://www.deutsche-digitale-bibliothek.de/newspaper/item/YH65KFT53MOG4SMXDXK4IVUPTR3QRY7Q?issuepage=1|quote=Reprinted in "The Collected Papers of Albert Einstein", Vol. 7, Document 45}}</ref> <ref name=einstein54>Letter from Einstein to N. V. Pope from March 1954; [[w:Albert Einstein Archives]], Object number 27-88 ([https://ein-web.adlibhosting.com/aea/Details/archive/110021626 Online dataset]); Scanned version as [https://groups.google.com/group/npachat/attach/d3121322d37764f2/Einstein%20letter.doc?part=0.1 Word document on Usenet] published by [https://groups.google.com/g/npachat/c/Haoib97d6OA/m/8mR30yITEtMJ Pope himself])</ref> <ref name=morand>Discussion between Painlevé, Einstein, and Langevin on p. 316ff in: {{citation |author=Morand, M.|title=Einstein au collège de france|date=April 1922|journal=La Nature|volume=50|issue=2511|pages=315-320|url=http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.102/319/100/620/5/613}}</ref> <ref name=lammel>{{Citation|author=Lämmel, R.|date=28 April 1911|title=Die Relativitäts-Lehre|journal=Neue Zürcher Zeitung|volume=117|pages=1|url=https://www.e-newspaperarchives.ch/?a=d&d=NZZ19110428-01.2.4.1}}; English translation of the part concering the twin pardox at [[:v:History of Topics in Special Relativity/Twin paradox#Lämmel 1911-Hum|Wikiversity:Early history of the twin paradox - Lämmel]]</ref> <ref name=lammel2>See p. 84ff in: {{Citation|author=Lämmel, R.|date=1921|orig-date=Preface December 1920|title=Die Grundlagen der Relativitätstheorie|place=Berlin|publisher=Springer|url=https://archive.org/details/diegrundlagende00lmgoog}}</ref> <ref name=langevin1>He derived differential aging from the proper time integral; pointed out that this demonstrates the "absolute nature of acceleration" with respect to an aether, see: {{citation |author=Langevin, P.|title=[[:s:fr:L’Évolution de l’espace et du temps|L’Évolution de l’espace et du temps]]|journal=Scientia |volume=X |pages=31–54 |date=July 1911|orig-date=Lecture 10 April 1911}}; English translation [[:s:en:Translation:The Evolution of Space and Time|The Evolution of Space and Time]] on Wikisource</ref> <ref name=langevin2>See p. 329 in: {{citation |author=Langevin, P. |title=Le temps, l'espace et la causalité dans la physique moderne |journal=Bulletin de la Société française de philosophie |volume=12 |orig-date=Lecture October 1911|date=1912|pages=1-28|url=http://ahp.li/1f7fc22d283fdf0deeca.pdf}}</ref> <ref name=langevin3>See p. 622f in: {{citation |author=Langevin, P. |title=Le Principe de relativité |journal=Bulletin de la société française des électriciens |volume=9 |date=1919 |pages=601-639|url=https://archive.org/details/bulletin-de-la-societe-francaise-des-electriciens-ser.-3-vol-9/page/600}}; Republished in 1922 as separate booklet: [[:s:fr:Le Principe de relativité|Le Principe de relativité]], Éditions Étienne Chiron</ref> <ref name=wiechert11>See p. 745f. general description and proper time; 757f. space travel; in: {{Citation |author=Wiechert, E. |date=September 1911|orig-date=Lectures March-May 1911, submitted 26 July|title=[[:s:de:Relativitätsprinzip und Äther|Relativitätsprinzip und Äther]]|journal=Physikalische Zeitschrift |volume=12 |issue=17-18 |pages=[https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/741 689-707] published September 1; [https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/789 737–758] published September 15}}</ref> <ref name=wiechert15>See p. 46 (Einstein, Langevin, Wiechert) and pp. 51f (Laue versus Wiechert) in: {{citation |author=Wiechert, E.|contribution=Die Mechanik im Rahmen der allgemeinen Physik| title=Die Kultur der Gegenwart: Physik|volume=3.3.1|date=1915 |orig-date=Submitted July 1914|pages=1–78|contribution-url=https://www.archive.org/details/physikunterredak00warbuoft}}</ref> <ref name=wiechert20>See p. 46f in: {{citation |author=Wiechert, E.|title=Der Äther im Weltbild der Physik|orig-date=Presented December 1920|date=1921|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse|pages=29-70|url=http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN00250586X}}</ref> <ref name=wiechert21>See p. 25ff in: {{citation |author=Wiechert, E.|title=[[:s:de:Prinzipielles über Äther und Relativität|Prinzipielles über Äther und Relativität]]|date=1922|orig-date=Lecture September 1921|journal=Physikalische Zeitschrift|volume=23|pages=25-28}}</ref> <ref name=muller>See p. 9 in: {{Citation|author=Müller, F.|date=October 1911|journal=Berliner Tageblatt|title=[[:s:de:Das Zeitproblem (1911)|Das Zeitproblem]]|pages=[https://www.deutsche-digitale-bibliothek.de/newspaper/item/2QKOIOLGNVQILTCEZQOGQPLTRVLPM5PZ?query=zeit&issuepage=9 Part 1 published 16 October 1911] and [https://www.deutsche-digitale-bibliothek.de/newspaper/item/IO44I6QBC4SVV5YUKUDSGXYIPQUXXBN5?query=zeit&issuepage=11 Part 2 published 23 October 1911]}}</ref> <ref name=gruner>See p. 253f in: {{Citation |author=Gruner, P. |title=[[:s:fr:Rapport sur la dernière discussion concernant le principe de la relativité et l’éther|Rapport sur la dernière discussion concernant le principe de la relativité et l’éther]] |journal=Archives des sciences physiques et naturelles |volume=33|issue=4 |pages=252-254 |date=March 1912}}</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=weyl>See p. 147f. in: {{Citation |author=Weyl, H. |date=March 1918|title=Raum-Zeit-Materie (first edition)|publisher=Berlin: Springer|url=https://archive.org/details/RaumZeitMaterieVolIMeinerFrauGewidmet}}; English translation of the 4th edition by H. Brose (1921): [https://www.gutenberg.org/ebooks/43006 Space—Time—Matter], pp. 278f.</ref> <ref name=gbaum>See footnote on p. 507 in: {{Citation|author=Grünbaum, F. |title=Über einige ideelle Versuche zum Relativitätsprinzip|journal=Physikalische Zeitschrift|volume=12|pages=500–509|date=1911|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/540}}</ref> <ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> <ref name=laue2>See p. 42f. for general description; p. 58f. in terms of proper time; in: {{Citation |author=Laue, M. v. |orig-date=Preface December 1912|date=1913 |title=Das Relativitätsprinzip (Second Edition) |publisher=Vieweg |place=Braunschweig|url=https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE4597082}}; See also English translation [[:s:Translation:The Principle of Relativity (Laue 1913)|The Principle of Relativity, Second edition, Part III]] on Wikisource</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=berg>See p. 369f in: {{Citation |author=Berg, O. |date=1910 |title=Das Relativitätsprinzip der Elektrodynamik |journal=Abhandlungen der Fries'schen Schule |volume=3 |issue=2|pages=333-382 |url=http://hdl.handle.net/2027/hvd.hnuynk?urlappend=%3Bseq=351}}</ref> <ref name=camp>See p. 123f in: {{Citation |author=Campbell, N. |title=Relativitätsprinzip und Äther: Eine Entgegnung an Herrn Wiechert |journal=Physikalische Zeitschrift |volume=13 |pages=120-128 |issue=3|orig-date=Submitted December 1911|date=February 1912|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/150}}. The is based on an English manuscript translated by Max Iklé, and Campbell's first name was Germanised as "Normann".</ref> <ref name=seel>{{Citation|author=Seeliger, R.|title=Review of "P. Gruner – Rapport sur la dernière discussion concernant le principe de la relativité et l'éther"|journal=Die Fortschritte der Physik|volume=68|issue=2|pages=336|date=1913|url=https://books.google.com/books?id=fSJGAQAAMAAJ&pg=PA336}}</ref> <ref name=study>See footnote on p. 111 in: {{citation |author=Study, E. |title=Vorlesungen über ausgewählte Gegenstände der Geometrie |date=June 1911|url=https://archive.org/details/vorlesungenber00studuoft|publisher=B.G. Teubner|place=Leipzig}} </ref> <ref name=robb1>See pp. 356ff. in: {{Citation|author=Robb, A.|date=1914|title=A theory of time and space|place=Cambridge|publisher=University Press|url=https://archive.org/details/theoryoftimespac00robbrich}} </ref> <ref name=robb2>See §12 in: {{citation |author=Robb, A. A.|title=The Straight Path|date=1920 |journal=Nature|pages=599|volume=104|issue=2623|url=https://archive.org/details/sim_nature-uk_1920-02-05_104_2623/page/598/mode/2up}}</ref> <ref name=edding2>See p. 22 in: {{Citation |author=Eddington, A. S. |date=1922 |title=The theory of relativity, and its influence on scientific thought |publisher=Oxford Clarendon Press |url=https://archive.org/details/cu31924005748573}}</ref> <ref name=rogers>{{citation |author=Rogers, R. A. P.|title=The Time-Triangle and Time-Triad in Special Relativity|date=November 1922|journal=Nature|volume=110|issue=2769|pages=698–699|url=https://archive.org/details/sim_nature-uk_1922-11-25_110_2769/page/698/mode/2up}}</ref> <ref name=lorentz1>See pp. 37f, 55ff in: {{citation |author=Lorentz, H. A.|date=1913|title=Het relativiteitsbeginsel : drie voordrachten gehouden in Teyler's stichting|publisher=De Erven Loosjes |place=Haarlem|url=https://resolver.kb.nl/resolve?urn=MMKB24:063387000:00005}}; German translation on pp. 31f, 47f in: {{citation |author=Lorentz, H. A.|date=1914| title=Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem|publisher=B.G. Teubner |place=Leipzig and Berlin|url=https://archive.org/details/bub_gb_89PPAAAAMAAJ}}; See also the transcription [[:s:de:Das Relativitätsprinzip (Lorentz)|Das Relativitätsprinzip]] on German Wikisource and the English translation [[:s:Translation:The Principle of Relativity (Lorentz)|The Principle of Relativity]] on English Wikisource</ref> <ref name=lorentz3>See §12 in: {{citation |author=Lorentz, H. A.|title=Considérations élémentaires sur le principe de relativité|date=1914 |journal=Revue générale des sciences pures et appliquées|pages=179-186|url=https://archive.org/details/revuegnraled25pari/page/178/mode/2up}}</ref> <ref name=bloch>See pp. 67 ff. in: {{Citation | author=Bloch, W.| date=September 1918|title=Einführung in die Relativitätstheorie| publisher=B. G. Teubner |url=https://hdl.handle.net/2027/njp.32101040276907}}</ref> <ref name=bloch2>See pp. 69ff. (special relativity) and 102ff. (general relativity) in: {{Citation | author=Bloch, W.| date=1920 |title=Einführung in die Relativitätstheorie (second edition)| publisher=B. G. Teubner |url=https://www.archive.org/details/einfhrungindier00blocgoog}}</ref> <ref name=bollert1>See p. 6 (special relativity), pp. 24-26 (EP) in: {{citation |author=Bollert, K.|title=Einstein’s Relativitätstheorie und ihre Stellung im System der Gesamterfahrung |date=April 1921|publisher=Steinkopff|url=https://archive.org/details/dbc.wroc.pl.001504}}</ref> <ref name=born>See pp. 190f. (special relativity), 250f (EP) in: {{Citation | author=Born, M.| date=1921 |title=Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Second edition)| publisher=Springer | place=Berlin|url=https://hdl.handle.net/2027/mdp.39015017387310}}; The [https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE5426498 first edition (1920)] of Born's book didn't include the twin paradox. English translation of the third edition by H. Brose (1924): [https://archive.org/details/einsteinstheoryo00born Einstein's theory of relativity]</ref> <ref name=pauli>See p. 558f (general description); p. 624f (proper time); p. 713f (accelerated frames); in: {{Citation |author=Pauli, W. |date=1921 |journal=Encyclopädie der Mathematischen Wissenschaften|title=Die Relativitätstheorie|pages=539–776|volume=5|issue=2 |url=http://resolver.sub.uni-goettingen.de/purl?PPN360709672}}; English translation by G. Field (1958): [https://books.google.com/books?id=rc3DAgAAQBAJ Theory of Relativity]</ref> <ref name=thirring>See p. 209ff in: {{citation |author=Thirring, H.|title=Über das Uhrenparadoxon in der Relativitätstheorie|date=April 1921|journal=Naturwissenschaften|volume=9|issue=18|pages=209-212|url=https://archive.org/details/sim_naturwissenschaften_1921-04-01_9_13/mode/2up}}</ref> <ref name=sommerfeld>See p. 71 in: {{citation |author=Sommerfeld, A. |date=May 1913|chapter=Remarks on Minkowski's "Space and Time"|title=Das Relativitätsprinzip|editor=Otto Blumenthal|pages=69-73|url=https://www.archive.org/details/dasrelativittsp00minkgoog}}</ref> <ref name=kopff>See pp. 45ff (special relativity and proper time); pp. 117ff (EP); pp. 189ff (Mach's principle), in: {{citation |author=Kopff, A.|title=Grundzüge der Einsteinschen Relativitätstheorie |date=February 1921|publisher=S. Hirzel|place=Leipzig|url=https://www.archive.org/details/grundzgedereins00kopfgoog}}; English translation by H. Levy (1923): [https://hdl.handle.net/2027/mdp.39015017188817 The mathematical theory of relativity].</ref> <ref name=becqu1>See p. 48ff (proper time), p. 240f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Le Principe de relativité et la théorie de la gravitation|Le Principe de relativité et la théorie de la gravitation]] |date=1922 |publisher=Gauthier-Villars|place=Paris}}; See also p. 57ff (proper time), p. 177f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Exposé élémentaire de la théorie d’Einstein et de sa généralisation|Exposé élémentaire de la théorie d’Einstein et de sa généralisation]]|date=1922 |publisher=Payot|place=Paris}}</ref> <ref name=nord>Discussion between Painlevé, Einstein, and Langevin on pp. 146ff in: {{citation |author=Nordmann, C.|title=[[s:fr:Einstein expose et discute sa théorie|Einstein expose et discute sa théorie]]|date=May 1922|journal=Revue des deux mondes|volume=IX|pages=129-166}}</ref> <ref name=lehm>{{Citation |author=Lehmann, Otto |orig-date=September 1910 |date=1911|title=Das Relativitätsprinzip der neue Fundamentalsatz der Physik |title-link=s:de:Das Relativitätsprinzip der neue Fundamentalsatz der Physik|journal=Verhandlungen des naturwissenschaften Vereins in Karlsruhe |volume=23 |pages=49-74}}</ref> <ref name=lech>See p. 19ff in: {{citation |author=Lechalas, G. |orig-date=Submitted December 1912|date=1913 |title=Le nouveau temps |journal=L’Année philosophique|volume=XXIII|pages=19-44|url=https://gallica.bnf.fr/ark:/12148/bpt6k255882z/f22.item}}</ref> <ref name=hunt>See pp. 494ff in: {{Citation|author=Huntington, E. V. |year=1912 |title=A new approach to the theory of relativity|journal=Philosophical Magazine |volume=23|pages=494-512|url=https://archive.org/details/londonedinburg6231912lond/page/494/mode/2up}}</ref> </references> ==Secondary sources== <references group=S> <ref name=miller>{{Citation |author=Miller, A. I. |date=1981 |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |place=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}; See section 7.4.13 (Langevin, Wiechert, Laue, Einstein), footnotes 29-34 of chapter 7 (Petzoldt, Sommerfeld, Bergson, Einstein)</ref> <ref name=lange>{{Citation|author=Lange, L.|date=1927|title=The clock paradox of the theory of relativity|journal=The American Mathematical Monthly|volume=34|issue=1|pages=22-30|jstor=2299914}}</ref> <ref name=pes>{{Citation |author=Pesic, P. |date=2003 |title=Einstein and the twin paradox |journal=European Journal of Physics |volume=24 |issue=6 |pages=585–590 |doi=10.1088/0143-0807/24/6/004}}</ref> <ref name=during>{{Citation |author=During, É. |date=2014 |title=Langevin ou le paradoxe introuvable |journal=Revue de métaphysique et de morale |volume=84 |pages=513-527 |doi=10.3917/rmm.144.0513|doi-access=free}}; See pp. 515f (Langevin), 520f. (Einstein, Laue, Weyl, Painlevé).</ref> <ref name=debs>{{Citation |author=Debs, T. A., & Redhead, M. L. |title=The twin paradox and the conventionality of simultaneity |date=1996 |journal=American Journal of Physics |volume=64|issue=1| pages=384-392 |doi=10.1119/1.18252}}</ref> <ref name=alizzi>{{Citation |author=Alizzi, A., Sen, A., & Silagadze, Z. K.|title=Do moving clocks slow down? |year=2022 |journal=European Journal of Physics |volume=43|issue=6|pages=065601 |doi=10.1088/1361-6404/ac93ca|arxiv=2209.12654}}; Appendix B with reference to Lange and Halsbury</ref> <ref name=beng>{{Citation |author=Benguigui, L. G. |date=2020 |title=A Tale Of Two Twins: The Langevin Experiment Of A Traveler To A Star |publisher=World Scientific|isbn=9789811219115}}; See early solutions (Einstein, Langevin, Lorentz, Born/Kopff) and the Bergson controversy. A shorter version appeared in {{arxiv|1212.4414}}.</ref> <ref name=rowe>{{Citation|author=Rowe, D. E.|date=2006|title=Einstein's allies and enemies: Debating relativity in Germany 1916–1920|journal=Interactions: Mathematics, Physics and Philosophy|pages=231-280|publisher=Springer|doi=10.1007/978-1-4020-5195-1_8}}; Covering the criticism of Gehrcke starting with 1912; discussion between Einstein and Gehrcke in 1914; Einstein's dialogue (1918) as response to antirelativists; the Weyland event in 1920 and Einstein's response.</ref> <ref name=weiss>Weiss, W. (Physics FAQ): [https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html The Twin Paradox: The Equivalence Principle Analysis]</ref> <ref name=cuvaj>{{Citation |author=Cuvaj, C. |date=1971 |title=Paul Langevin and the theory of relativity|journal=Japanese studies in the history of science|volume=10| pages=113-142|url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf}}</ref> <ref name=koks>Koks, D. (2018): [https://math.ucr.edu/home/baez/physics/Relativity/SR/sr-gr.html Physics FAQ: Where is the Boundary between Special and General Relativity?]</ref> </references> [[Category:History of special relativity]] [[Category:Paradoxes]] o2tj8natkuh97trqq3ydlu6qel2xa4q 2834541 2834540 2026-09-26T08:42:35Z D.H 52339 /* Historical references */ + 2834541 wikitext text/x-wiki {| style="width:20%; font-size:13px;" align=right |{{../Other Topics (header)}} |} ==Early history of the twin paradox== {{Lorentzbox|Text={{center|Date of article creation: 9 November 2023; Last major revision: 26 September 2026}}}} a) When was the [[:w:twin paradox]] applied to life forms and human beings? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /><ref group=S name=during /> report that {{slink||Einstein 1911-HU}} discussed the aging of living organisms, and that {{slink||Langevin 1911-HU}} and {{slink||Wiechert 1911-HU}} explicitly discussed the aging of human beings. :*More details in sections {{slink||Human beings in 1911|Twins from 1911 to 1920}}, including newspaper articles from 1911 written by {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}} that clearly show that Einstein was the first to explicitly discuss the aging of human beings as well. b) Who was the first to formulate the principle of maximal proper time along straight worldlines, upon which differential aging in the standard twin paradox is based? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> mention Langevin (1911), Laue (1911). :*More details in section {{slink||Maximal proper time}} with the contributions of Langevin (1911), Wiechert (1911), Study (1911), Laue (1911-13). c) Who was the first to formulate [[w:Triangle inequality#Reversal in Minkowski space|inverse triangle inequality]] in Minkowski space, which represents the simplest version of the twin paradox? :*See details in section {{slink||Triangle inequality}} with the contributions of Robb (1914-20), Eddington (1922), Rogers (1922). d) Who was the first to show that any influence of proper acceleration on clocks can be neglected in the computation of the twin paradox from the viewpoint of the stay-at-home twin? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Einstein (1911), Laue (1913). :*More details in section {{slink||Negligibility of proper acceleration}} with the contributions of Einstein (1911), Wiechert (1911), Laue (1913), Lorentz (1913). e) Who was the first to introduce the three clock/brother example that completely removes acceleration from the clock/twin paradox? :*Historical accounts<ref group=S name=debs /><ref group=S name=alizzi /> date it back to Lange (1927) and Lord Halsbury (1957). :*More details in section {{slink||Relay (three brothers) experiment}} with the contributions of Grünbaum (1911) and Wiechert (1920-22). f) Who was the first to use acceleration as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref name=cuvaj group=S /><ref group=S name=pes /> mention Langevin (1911), Einstein (1918). :*More details in section {{slink||Acceleration as asymmetry indicator}} with the contributions of Langevin (1911), Sommerfeld (1913), Lorentz (1913), Einstein (1914-20). g) Who was the first to use different frame distribution as asymmetry indicator as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Laue (1911-13). :*More details in section {{slink||Frame distribution as asymmetry indicator}} with the contributions of Laue (1911-13), Bloch (1918). h) Who was the first to describe the perspective of the traveler? :*Historical accounts<ref group=S name=miller /><ref group=S name=beng /> mention Langevin (1911), Lorentz (1914), Einstein (1918). :*More details in section {{slink||Perspective of the traveler}} with the contributions of Langevin (1911), Lorentz (1913-14), Einstein (1918), Thirring (1921). i) Who was the first to describe a round-trip experiment in curved spacetime? :*See section {{slink||Curved spacetime}} with the contribution of Becquerel (1922). j) Who was the first to interprete the twin paradox in terms of an aether or absolute space? :*See section {{slink||Aether interpretations}} with the contribution of Langevin (1911), Wiechert (1911), Lechalas (1912). k) Who was the first to denote the round-trip experiment as paradoxical? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> point to Laue (1911). :*See section {{slink||Paradoxical?}} for details. l) Who was the first to misunderstand the twin paradox? :*See section {{slink||Misunderstandings}} with the contributions of Berg (1910), Wiechert (1911), Campbell (1911/12), Gruner (1912). m) What were Einstein's contributions? :*See section {{slink||Einstein's contributions}}. ==Human beings in 1911== {| class="wikitable" style="background-color:white;{{text default color}};" ![[w:Albert Einstein|Einstein]] |- |{{anchor|Einstein 1905}}In 1905<ref name=einstein05 /> he showed that a clock moving on a round-trip away from A and back along a polygonal or curved path, is retarded with respect to a clock stationary at A by approximately <math>\tfrac{1}{2}t(v/V)^{2}</math> at reunion. For example, a clock on the equator is retarded with respect to a clock on the pole. He described this consequence as being "peculiar" (German: eigentümlich). {{anchor|Einstein 1911-HU}}In a lecture given on January 1911<ref name=einstein11a /> (published in November), he extended this "funny" (German: drollig) experiment to living organisms: {| ! width=55% | Einstein wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Wenn wir z. B. einen lebenden Organismus in eine Schachtel hineinbrächten und ihn dieselbe Hin- und Herbewegung ausführen lassen wie vorher die Uhr, so könnte man es erreichen, dass dieser Organismus nach einem beliebig langen Fluge beliebig wenig geändert wieder an seinen ursprünglichen Ort zurückkehrt, während ganz entsprechend beschaffene Organismen, welche an den ursprünglichen Orten ruhend geblieben sind, bereits längst neuen Generationen Platz gemacht haben. Für den bewegten Organismus war die lange Zeit der Reise nur ein Augenblick, falls die Bewegung annähernd mit Lichtgeschwindigkeit erfolgte! | style="padding: 0px 20px 0px 20px;" |For example, if we put a living organism in a box and make it undergo the same back and forth movement as the clock before, we could achieve that this organism returns to its original location with arbitrary little change after a flight of arbitrary length, whereas completely identical organisms that remained at rest in the original location have long since made room for new generations. To the moving organism, the long journey was only a moment if the movement happened close to the speed of light! |} {{Lorentzbox|Text=Two participants of that lecture, {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}}, report that Einstein also talked about the aging of ''human beings''.}} |- !{{anchor|Lämmel 1911-HU}}[[w:Rudolf Lämmel|Lämmel]] |- |He attended Einstein's 1911 lecture and gave a popular report about it in the Swiss newspaper "[[w:Neue Zürcher Zeitung|Neue Zürcher Zeitung]]" published on 28 April 1911,<ref name=lammel /> including additional details. Regarding the round-trip clock experiment he wrote: {| ! width=50% | Lämmel wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bewegt sich eine Uhr mit Lichtgeschwindigkeit längs einer Geraden, auf der gerichtete Uhren stehen, so scheint die bewegte Uhr, beurteilt vom Standpunkt der ruhenden aus, im oben stizzierten Sinn, stillzustehen. Kehrt die Uhr, nach einem Ruck, mit Lichtgeschwindigkeit wieder zurück zur Zentral-Uhr, so ist, nach Einstein, für den Beobachter bei der Zentral-Uhr die Sache so, als ob ein mit der bewegten Uhr mitgeführter Beobachter (samt dessen Uhr) nicht gealtert hätte. Hinge also des letzteren Alter von den Angaben des ruhenden Beobachters ab, so könnte der von einer großen Reise ins Weltall zurückkehrende Beobachter bei der Zentral-Uhr spätere Generationen antreffen – er selber hätte nicht gealtert. Welche Bedeutung diese ''ad absurdum'' geführte Gedankenspielerei etwa hat, läßt sich heute nicht absehen – vielleicht, ja wahrscheinlich ist sie ohne jeden Einfluß auf die tatsächlichen Verhältnisse. Aber man sieht dabei immerhin, daß die Physik imstande ist, die kühnsten Träume der Phantasie noch – zu überbieten. | style="padding: 0px 20px 0px 20px;" |Let a clock be moving at speed of light along a line on which regulated clocks are standing, then the moving clock's hand appears to be standing still (in the sense described above) as judged from the standpoint of the resting one. If the clock, after one jolt, comes back with light speed to the central clock, then according to Einstein the matter presents itself to the observer at the central clock, as if the observer comoving with the clock (together with his clock itself) hasn't been grown older. Thus if the age of the latter would depend on the indications of the resting observer, the observer returning from a great journey into space could meet later generations at the central-clock – he himself hasn't been grown older. The importance of this play of thought led ''ad absurdum'' cannot be seen today – maybe, or even probably, it is without any influence on the actual situations. Though at least one can see that physics is able to – surpass – even the boldest dreams and fantasies. |} Lämmel in December 1920 (published 1921)<ref name=lammel2 /> again alluded to Einstein's lectures in Zürich (possibly the one from 1911, and maybe also later ones), describing a discussion between himself and Einstein. After Einstein concluded that the travelers who came back after their journey will probably meet their former contemporaries as old men while they themselves could have been away for only a few years, Lämmel objected that this conclusion is only drawn with respect to rods and clocks, but not with respect to living beings. Einstein responded though, that all processes in the blood, in the nerves etc. are eventually periodical oscillations, i.e. motions. Yet to any such motion the relativity principle applies, thus the conclusion regarding the unevenly rapid aging it permissive. {{Lorentzbox|Text=While the official publication of Einstein's January lecture ({{slink||Einstein 1911-HU}}) mentions the aging of organisms, Lämmel recalls the reference to the aging of a human space traveler ("observer returning from a great journey into space"). This means that Einstein was the first to use human beings in the clock/twin paradox on January 16 which was first published by Lämmel on April 28, 1911. In comparison, {{slink||Langevin 1911-HU}} used space travelers in a lecture on April 10 with publication in July, and {{slink||Wiechert 1911-HU}} used space travelers in lectures held between March 25 and May 23 with publication in July/September. It seems very unlikely that before April 28, Lämmel became somehow aware of the content of Langevin's or Wiechert's lectures held a few weeks earlier, in order to use them in his description of Einstein's lecture.}} |- !{{anchor|Langevin 1911-HU}}[[w:Paul Langevin|Langevin]] |- |On 10 April 1911, published July 1911,<ref name=langevin1 /> he held a now famous lecture popularizing the clock/twin paradox which he derived from the proper time integral as described in {{slink||Langevin 1911-PT}}. He demonstrated that a moving radioactive sample of radium is less evolved and less aged and therefore more active at return then the ones that remained in the laboratory. He also used light signals and the Doppler effect to visualize the effect. The most famous part concerned his description of the aging of human space travelers: {| ! width=50% | Langevin wrote ! [[:s:Translation:The Evolution of Space and Time|English Wikisource translation]] |- | style="padding: 0px 20px 0px 20px;" |Cette remarque fournit le moyen, à celui d’entre nous qui voudrait y consacrer deux années de sa vie, de savoir ce que sera la Terre dans deux cents ans, d’explorer l’avenir de la Terre en faisant dans la vie de celle-ci un saut en avant qui pour elle durera deux siècles et pour lui durera deux ans, mais ceci sans espoir de retour, sans possibilité de venir nous informer du résultat de son voyage puisque toute tentative du même genre ne pourrait que le transporter de plus en plus avant. Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse. Revenu à la Terre ayant vieilli de deux ans, il sortira de son arche et trouvera notre globe vieilli de deux cents ans si sa vitesse est restée dans l’intervalle inférieure d’un vingt-millième seulement à la vitesse de la lumière. Les faits expérimentaux les plus sûrement établis de la physique nous permettent d’affirmer qu’il en serait bien ainsi. | style="padding: 0px 20px 0px 20px;" |This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. |} {{Lorentzbox|Text=Reading his lecture in full, one finds the word "paradoxical" only in relation to the constancy of light speed, not on relation to the round-trip clock experiment.}} |- !{{anchor|Wiechert 1911-HU}}[[w:Emil Wiechert|Wiechert]] |- |In lectures on 25 March and 23 May 1911, submitted July and published September 1911,<ref name=wiechert11 /> he described the round-trip clock experiment with two equal clocks regulated to the same rate and brought to the same pointer position, or by introducing the same chemical process two times, or by introducing ''two life forms that began their life at the same time''. At the end of his paper he applied this to human travelers: {| ! width=50% | Wiechert wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Nehmen wir aber wieder eine Relativgeschwindigkeit an, die bis auf 3 Proz. der Lichtgeschwindigkeit nahekommt, dann wird das Verhältnis der empfundenen Zeitlängen wie 4:1. Das Bild mag etwas weiter noch ausgemalt werden. Denken wir uns, daß ein Beobachter durch den Raum unseres Sternhimmels mit dieser Geschwindigkeit in einer Kreisbahn mit einem Radius von 16 Lichtjahren fährt, dann wird er nach unserer Zeitrechnung nach je 100 Jahren wieder an unserem Sonnensystem vorüberkommen. In seinem Gefährt wird dabei die Zentrifugalkraft so auf ihn einwirken, daß sie gemäß den Relativitätsgesetzen der Einwirkung der Schwerkraft auf uns Erdenbewohner gleich erscheint. Es sind also die wirkenden Kräfte nur so groß, daß der Phantasie die Möglichkeit geboten wird, den Reisenden als menschliches Wesen zu denken. Da hier dauernd <math>\sqrt{1-v^{2}/c^{2}}</math> ist, fließt die Eigenzeit für den Reisenden viermal langsamer dahin, als für die Bewohner der Gestirne. Wenn er also nach 100 unserer Jahre wieder zu unserem Sonnensystem zurückkehrt, wird er sich selbst nur um 25 Jahre gealtert fühlen. Erreicht er nach der Entwicklung seines Körpers und nach seiner Zeitempfindung ein Alter von 75 Jahren, so entspricht dies doch einer dreimaligen Wiederkehr zu unserem Sonnensystem, also 300 unserer Erdenjahre. | style="padding: 0px 20px 0px 20px;" |Yet if we again assume a relative velocity approximating the speed of light by 3 percent, then the ratio of the experienced duration of time becomes 4:1. This image can be further extended. Let's imagine that an observer travels with that velocity on a circular path at a radius of 16 light years through the space of our galaxy, then according to our time calculation he passes by our solar system every 100 years. In his vehicle the centrifugal force will act on him in such a way, that in accordance with the relativity laws it will appear to be equal to the force of gravity acting upon the inhabitants of Earth. Thus the acting forces are only thus big, in order to give our fantasy the possibility to imagine the traveler as a human being. Since we have <math>\sqrt{1-v^{2}/c^{2}}</math> throughout, proper time flows four times slower for the traveler than for the inhabitants of the stars. Thus when he comes back to our solar system after 100 of our years, he will feel to have aged only by about 25 years. If he reaches an age of 75 years according to the development of his body and his own time experience, then this corresponds to a threefold return to our solar system, i.e. 300 of our Earth years. |} {{Lorentzbox|Text=a) Wiechert (1915)<ref name=wiechert15 /> later provided a short historical survey of the clock/twin paradox. He referred to the fact that already {{slink||Einstein 1905}} considered the case of two clocks ("Einstein's clock experiment"), and even though [[w:Hermann Minkowski|Minkowski]] himself didn't consider the case, his proper time formula provides the result in a straight forward manner. The latter was done by himself in lectures on 25 March and 23 May 1911, as well as by Langevin published in July 1911. Wiechert pointed out that he himself and Langevin used "humorist" examples in order to clarify the situation: While Wiechert argued that one has to make a journey in order to stay young, Langevin argued that one has to romp about in a laboratory in order to stay young. Both of them used human beings, arguing that their physical and mental life should have been influenced in the same way as any other process in nature. b) The dates given by Wiechert (1915) are not complete. The correct ones are: *Langevin's lecture on 10 April 1911, published in July. *Wiechert's lectures on 25 March and 23 May 1911, submitted on July 26, published in September. *He was still unaware of Einstein's lecture from January 1911, published in November 1911.}} |- !{{anchor|Müller 1911-HU}}[[w:Fritz Müller-Partenkirchen|Müller]] |- |The freelance writer and law student Fritz Müller (who was later known as [[w:Fritz Müller-Partenkirchen|Müller-Partenkirchen]]) attended Einstein's lecture and wrote a popular report about it in the German newspaper "[[w:Berliner Tageblatt|Berliner Tageblatt]]" on 16th and 23rd October 1911,<ref name=muller /> in which he gave further details (compare with {{slink||Lämmel 1911-HU}}). Regarding the clock/twin paradox he wrote: {| ! width=50% | Müller wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Zwei gleichgehende Uhren sollen je einen Beobachter haben und nebeneinander ruhen. Nun soll die eine mit ihrem Beobachter plötzlich mit Lichtgeschwindigkeit in den Weltenraum hinausreisen. Vorher haben die beiden vereinbart, sich alle Sekunden mit einem Lichtsignal die Zeit zu telegraphieren. [...] In unserem Grenzfall, wo die Reise mit Lichtgeschwindigkeit vor sich geht, müßte der ruhende Beobachter erklären, jene andere Uhr käme in der Zeit überhaupt nicht voran. Die Zeit stünde dort still. Tatsächlich kommen die Einsteinschen Gleichungen zu diesem Resultat. Für den mit der Uhr reisenden Beobachter, sagt Einstein, gelte dasselbe. Das heißt, im Urteil des Zurückbleibenden würde jener niemals alt. „Und wenn er auf einer gebrochenen Reiselinie wieder an seinen Ausgangspunkt zurückkehrte?" fragt man den Vortragenden in der Diskussion. – „So bliebe er in unserem Urteil so jung wie bei der Ausreise," erwidert Einstein mit vollem Ernst, „selbst wenn wir Zurückgebliebenen inzwischen Männer mit weißen Bärten geworden sind – die Gleichungen liefern für jede Richtung der Bewegung, auch für eine gebrochene Bewegung, unerschütterlich die selben Resultate." – Wir sehen einander an. Das klingt märchenhaft. Märchenhaft? Gewiß, die alten Märchen vom Mönch von Heisterbach, vom Rip van Winkle, von Urashima Taro steigen auf. Merkwürdig, wie die Volksphantasie bei den Deutschen, bei den Amerikanern, bei den Japanern in der gleichen Richtung gearbeitet hat – alle drei Märchen erzählen ja von Leuten, deren Leben still steht, viele hundert Jahre lang, während die andern altern. So fanden sie bei ihrer Rückkehr ein anderes Land und eine andere Generation. | style="padding: 0px 20px 0px 20px;" |Two synchronous clocks at rest next to each other, shall each be accompanied by an observer. Now one of them, together with its observer, suddenly travels into space at the speed of light. Previously, both have arranged that every second they telegraph their time to each other using light signals. [...] In our limiting case where the journey happens at light speed, the resting observer would have to declare that the other clock would not proceed in time at all. Time would stand still at this place. Einstein's equations indeed produce this result. As to the observer traveling with the clock, says Einstein, the same is true. That means in the judgment of the remaining one, the other one would never become old. Then the lecturer [i.e. Einstein] was asked in the discussion: "And if he comes back to his starting point on a curved travel path?", to which Einstein replied in full earnest: "Then in our judgment he would remain as young as he was at departure, even if we remaining ones became men with white beards in the meantime, the equations unshakably give the same result in every direction of motion, also for curved motion". We look at each other. That sounds fabulous. Fabulous? Of course, the old fairy tales of [[w:Heisterbach Abbey|w:The monk of Heisterbach]] or [[w:Rip Van Winkle]] or [[w:Urashima Tarō]] come forward. Strange, how the folk fantasy of the Germans, the Americans, the Japanese worked in the same direction, all three fairy tales indeed tell about people whose life stands still, many hundred years long, while the other ones grow old. Thus they found another country and another generation when they returned. |} {{Lorentzbox|Text=Müller's account confirms {{slink||Lämmel 1911-HU}} that Einstein indeed mentioned human beings, but his description also suggests that Einstein was the first to use mutually sent light signals. However, as this was published in October, it cannot be excluded that Müller's description of light signals was influenced by {{slink||Langevin 1911-HU}}, published in July, in which light signals were used as well.}} |} ==Twins from 1911 to 1920== We now provide a list of authors who employed ''twins'', i.e. ''two'' life forms or humans that initially were of ''same age'' when the round-trip began: {| class="wikitable" style="background-color:white;" |- ! Author !! Date !! Description |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> |1911 |Two life forms that begin their life at the ''same time'' (German: "Zwei Lebewesen [..] die ihr Leben gleichzeitig beginnen"), of which the moving one returns retarded in its progression with respect to the stationary one. |- |[[w:Paul Gruner|Gruner]]<ref name=gruner /> |1912 |Two persons of ''same age'' (French: "deux personnes du même âge"), of which the moving one returns less developed than stationary one. |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> |1913 |The moving life form returns younger than its ''former agemates'' (German: "ehemaligen Altersgenossen"). |- |[[w:Hermann Weyl|Weyl]]<ref name=weyl /> |Easter 1918 | {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Von zwei Zwillingsbrüdern, die sich in einem Weltpunkt A trennen, bleibe der eine in der Heimat (d. h. ruhe dauernd in einem tauglichen Bezugsraum), der andere aber unternehme Reisen, bei denen er Geschwindigkeiten (relativ zur »Heimat«) entwickelt, die der Lichtgeschwindigkeit nahekommen; dann wird sich der Reisende, wenn er dereinst in die Heimat zurückkehrt, als merklich jünger herausstellen denn der Seßhafte. |Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. |} {{Lorentzbox|Text=Weyl was the first to ''explicitly use twins'' in relation to the round-trip experiment. The fourth edition (1920) of that book was translated from German into English and French in 1922.}} |- |[[w:Albert Einstein|Einstein]]<ref name=einstein20 /> |1920/21 |{{Anchor|Einstein 1921-TW}} {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Trifft A wieder bei B ein, so kann es sich ereignen, daß der beharrende Zwilling inzwischen 60 Erdjahre alt geworden ist, während der zurückkehrende nur 15 Jahre zählt, oder sich gar noch im Säuglingsstadium befindet. [..] Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls -Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. |If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still. [..] In the case of these two twins, Einstein declared, we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures. |} {{Lorentzbox|Text=This was based on an interview of Einstein by Moszkowski. While the expression "clock paradox" was used since 1911/12 (see section {{slink||Paradoxical?}}), this seems to be the first time that it was rebranded as "twin paradox". The copyright mark indicates 1920, while the title page indicates 1921. The translation from German into English also appeared in 1921.}} |} ==Maximal proper time== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]] 1911 |{{anchor|Langevin 1911-PT}}In April 1911 (published July),<ref name=langevin1 /> he described the round-trip experiment without formulas using two portions of matter present at two events happening at the same place. The ''integration of proper time'' along the entire wordlines shows that the portion of matter that starts a closed cycle by receding and finally coming back, will have a ''smaller proper time'' than the one that stayed behind. In October 1911 (published 1912),<ref name=langevin2 /> Langevin again showed that the portion of matter that described a closed cycle will have a ''smaller proper time'' <math>R</math> than the one that stayed in an inertial frame, which is defined by the equation: :<math>\begin{matrix}V^{2}\left(t-t_{0}\right)^{2}=d^{2}-R\\ \left[d^{2}=\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}\right] \end{matrix}</math> |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> Lectures March-May 1911 submitted July published September |{{anchor|Wiechert 1911-PT}}Let two equal processes be observed in two equal material systems colocated in two moments (1) and (2), and let there velocities have been changed in arbitrarily different ways in the meantime. It follows that the ratio of advancement of those processes is given by the two intervals <math>\Delta\tau </math> of their respective ''proper times''. He concluded that any round-trip clock experiment can be easily comprehended from that theorem by computation. The corresponding integral is: :<math>\Delta\tau=\int_{1}^{2}d\tau=\int_{1}^{2}dt\sqrt{1-\frac{\mathfrak{v}^{2}}{c^{2}}}</math> |- |[[w:Eduard Study|Study]]<ref name=study /> June 1911 |Minkowski's concept of worldlines implies that the straight path between two points of the same worldline is the ''longest'' among all paths between those points, if the path length on a worldline is defined by the related proper time. {{Lorentzbox|Text=Study's book was purely mathematical without mentioning clocks or the round-trip experiment, alluding to his result only in a footnote.}} |- |[[w:Max von Laue|Laue]] 1911-13 |{{anchor|Laue 1911/12-PT}}In December 1911 (published 1912),<ref name=laue1 /> Laue showed without formulas that the round-trip experiment is represented by a curved worldline, which at worldpoint A decomposes into a row of curves, after which all of them will be re-united at worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the ''longest proper time.'' {{anchor|Laue 1912/13-PT}}In December 1912 (published 1913) in the second edition of this relativity book,<ref name=laue1 /> Laue described the proper time integral between events 1 and 2 of a slowly accelerated clock covering a broken line and a stationary clock covering a straight worldline. Of all worldlines covering 1 and 2, the straight line has the ''longest proper time''. Therefore the traveling clock in the round-trip experiment is retarded at reunion, because its curved worldline corresponds to a shorter proper time. This result he presented in terms of the following inequality, of which the right-hand side refers to the straight curve of the stationary clock, while all others possible curves are represented on left-hand side: :<math>\tfrac{1}{c}\int_{1}^{2}\sqrt{du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}<\tfrac{1}{c}\int_{1}^{2}du</math> {{Lorentzbox|Text={{anchor|Sommerfeld 1913-PT}}Similar treatments can be found in the textbooks of [[w:Arnold Sommerfeld|Sommerfeld]] (1913),<ref name=sommerfeld /> [[w:Hermann Weyl|Weyl]] (1918),<ref name=weyl /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Jean Becquerel|Becquerel]] (1922).<ref name=becqu1 />}} |} ==Triangle inequality== {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Alfred Robb|Robb]] 1914-1920 |{{anchor|Robb 1914-TR}}In 1914<ref name=robb1 /> he showed that there are three types of triangles formed by intervals in Minkowski space, depending on whether one deals with "separation lines" (spacelike intervals), "optical lines" (lightlike intervals), or "inertia lines" (timelike intervals representing the path of nonaccelerated particles defined by <math>{\scriptstyle \left(x_{1}-x_{0}\right)^{2}+\left(y_{1}-y_{0}\right)^{2}+\left(z_{1}-z_{0}\right)^{2}-c^{2}\left(t_{1}-t_{0}\right)^{2}<0}</math>). As to a triangle formed by inertia lines, he showed that the sum of a certain two sides is ''less'' than that of the third one. {{Lorentzbox|Text=So the triangle inequality derived from time-like intervals in Minkowski space is ''[[w:Triangle inequality#Reversal in Minkowski space|inverse]]'' to the inequality in Euclidean space. This inverse inequality directly represents the most simple variant of the twin paradox: the traveler follows two sides of the time-triangle, while the stay-at-home observer follows the third side indicating maximal proper time.}} [[File:RobbTriangle.svg|right|150px]] In 1920<ref name=robb2 /> Robb gave a numerical example of the triangle ABC with time-like intervals ("inertia lines") defined by coordinates :<math>\begin{matrix} & x & y & z & t\\ A\ & 0 & 0 & 0 & 0\\ B\ & 0 & 0 & 0 & 10\\ C\ & 4 & 0 & 0 & 5 \end{matrix}</math> which he plugged into :<math>\bar{s}^{2}=\left(t_{1}-t_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}-\left(y_{1}-y_{0}\right)^{2}-\left(z_{1}-z_{0}\right)^{2}</math> from which he obtained the sides AB=10, AC=3, CB=3 and the inequality <math>AC+CB<AB</math>. |- |[[w:Arthur Eddington|Eddington]]<ref name=edding2 /> 1922 |He distinguished between the "space-triangle" for spacelike intervals, and the "time-triangle" for time-like intervals. The latter is measured with a clock from A to B and from B to C, with the sum of those readings ''is always less'' than the reading of a clock measuring directly from A to C. In the ordinary space-triangle any two sides are together greater than the third side; in the time-triangle two sides are together ''less'' than the third side. |- |Rogers<ref name=rogers /> 1922 |He showed that the "pure time-triangle" C, A, B (in their proper time order) satisfies the relation <math>\cosh C=\tfrac{\alpha^{2}+\beta^{2}-\gamma^{2}}{2\alpha\beta}</math>, where <math>\cosh C</math> denotes the unit-scalar product of the vectors CA, CB, and <math>\alpha,\beta,\gamma </math> the real and positive intervals BC, CA, AB. Since <math>\alpha>\beta </math> and <math>\cosh C>1</math>, it follows that <math>\alpha>\beta+\gamma </math>. That is, "the greatest side of pure time-triangle is greater than the sum of the other two sides". It follows at once that the stationary value of the proper time integral is an "absolute maximum". |} ==Negligibility of proper acceleration== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |style="vertical-align:top" |[[w:Albert Einstein|Einstein]] 1905-1918 |In 1905,<ref name=einstein05 /> Einstein used velocity time dilation <math>\tau=t\sqrt{1-\left(\frac{v}{V}\right)^{2}}</math> to derive the retardation of a clock performing a round-trip with constant speed <math>v</math> along a polygonal path or a continuously curved line, without mentioning any influence of acceleration at turnaround. {{anchor|Einstein 1911-VA}} In 1911 (published 1912),<ref name=einstein3 /> Einstein said that special relativity doesn't say anything about what happened to the clock's pointer position during the acceleration that changes the clock's direction along the round-trip, yet the influence of this change must be getting smaller the longer the clock ''is moving uniformly'', i.e. the longer one chooses the dimensions of the path. {{anchor|Einstein 1912-VA}}In an unpublished manuscript on special relativity from 1912,<ref name=einst12manu /> he pointed out that any influence of acceleration during the round-trip experiment, can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygonal path. {{anchor|Einstein 1914a-VA}}In a letter from April 1914,<ref name=einstpetz /> Einstein showed that any ''finite'' acceleration at turnaround during the round-trip experiment can only influence the clock in a ''finite'' way, thus it can be neglected by minimizing the time of acceleration with respect to the time of uniform translation. So it ''must be concluded'' that the clock is retarded at reunion after traveling on a polygonal path. {{anchor|Einstein 1914b-VA}}During a conversation in May 1914,<ref name=rowe group=S /> Einstein is reported to have replied that the accelerations during the round-trip are "irrelevant for the amount of the time difference". (Compare with {{slink||Einstein 1914b-AC}}) {{anchor|Einstein 1918-VA}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918,<ref name=einstein18 /> Einstein pointed out that any effect of velocity changes at turnaround must be limited, thus the traveling clock must be retarded at reunion due to time dilation if one makes the path AB and back along the round-trip long enough. (Compare with {{slink||Einstein 1918-AC}}) |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> 1911 |{{Anchor|Wiechert 1911-VA}}[[File:WiechertTwin.svg|110px|right]] He demonstrated that differential aging along the round-trip cannot be caused during the passage from one velocity to another (i.e. acceleration) at turnaround, because the same result also follows when ''both'' A and B experience the ''same velocity changes'' with respect to another frame, only with the difference that B has relative velocities <math>+u</math> and <math>-u</math> for a long time, while A is brought after a short time from relative velocity <math>+u</math> to relative rest at which it remains a long time, and then it is brought to relative velocity <math>-u</math> for a short time. {{Lorentzbox|Text=He was probably the first to use an example in which both accelerate with same magnitude.}} |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> 1913 |{{anchor|Laue 1913-VA}}He showed that the problem of the influence of acceleration at turnaround in the round-trip experiment, can be eliminated by ''arbitrarily'' enlarging the time in inertial motion. {{Lorentzbox|Text=This is the same argument as given in {{slink||Einstein 1911-VA}}. The Einstein-Laue argument was also used by others such as [[w:Hans Thirring|Thirring]] (1921)<ref name=thirring /> or [[w:Max Born|Born]] (1921).<ref name=born />}} |- |[[w:Hendrik Lorentz|Lorentz]]<ref name=lorentz1 /> 1913 |He pointed out that any effect of acceleration on the traveling clock at turnaround, can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip. {{Lorentzbox|Text=Similarly, [[w:Wolfgang Pauli|Pauli]] (1921) stated that the arising infinitesimal accelerations at turnaround are certainly independent of the total travel time and ''therefore easy to eliminate''.<ref name=pauli />}} |} ==Relay (three brothers) experiment== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:de:Fritz Grünbaum (Physiker)|Grünbaum]]<ref name=gbaum /> 1911 |He discussed a one-way time dilation experiment in which the first clock is set into motion from the origin and then moving to the second clock. He argued that one can avoid the problem of acceleration experienced by the first clock when set into motion, by replacing it with a ''third'' clock that is already in motion with constant velocity and is synchronized at the origin with the first clock. {{Lorentzbox|Text=While Grünbaum didn't discuss round-trip experiments, his introduction of a third clock in order to avoid acceleration is the basis of the three-brother experiment.}} |- |style="vertical-align:top"|[[w:Emil Wiechert|Wiechert]] 1920-1922 |In 1920 (published 1921),<ref name=wiechert20 /> Wiechert explained how to completely remove acceleration from the round-trip experiment: Bodies A, B, C move undisturbed and non-accelerated in different directions. A and B pass each other at time (1), B and C pass each other at a later time (2), and C and A finally pass each other at an even later time (3). So in this setup, the condition of C is the continuation of the condition of B. On any of the three bodies one can count the oscillations of light of a certain spectral-line, in which case relativity predicts that the ''combined sum of all oscillations'' on B+C is smaller than the number of oscillations on A alone. Wiechert also held that one can replace the light oscillations by the life functions of human-like beings which live on A, B and C. For instance, while the inhabitants of B+C only had time for one meal, there were arbitrarily many generations on A who follow after each other by death and birth. [[File:Wiechert1922a.png|180px|right]] In 1921 (published 1922),<ref name=wiechert21 /> Wiechert extended his previous acceleration-free round-trip experiment to an arbitrary number of non-accelerated bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., which constitutes a "relay" (German: Stafette) starting from body A and back again. The first B passes A and moves away, and after some time the last B comes back to A. Since any B body continues the fate of the previous one, all bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., combined have emitted fewer oscillations than A alone during the relay race. Wiechert pointed out that instead of light oscillations one can also choose the aging of life forms. {{Lorentzbox|Text=Such relay experiments were later independently rediscovered in English language papers<ref name=debs group=S /> such as by Lange (1927)<ref group=S name=lange /> in which the brothers synchronize their times when they pass each other (“three brother experiment”).}} |} ==Acceleration as asymmetry indicator== While it was known that any direct influence of [[w:proper acceleration]] on clocks can be neglected in the computation of the inertial frame of the stay-at-home twin (see previous section {{slink||Negligibility of proper acceleration}}), the very fact that only one of them is accelerating is still useful as an asymmetry argument in order to show that there is no contradiction to the relativity principle. {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{Anchor|Langevin 1911-AC}}He derived differential aging in the round-trip experiment using the proper time integral along worldlines (see {{slink||Langevin 1911-PT}}) and used acceleration as an asymmetry indicator: The result of the round-trip experiment is "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". |- |[[w:Arnold Sommerfeld|Sommerfeld]]<ref name=sommerfeld /> 1913 |After he showed (see {{slink||Sommerfeld 1913-PT}}) that retardation of time in the round-trip experiment derived from the proper time integral rests on the assumption that the clock's rate ''only depends on its momentary velocity'' (now called "clock hypothesis"), he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle since one of the clocks has to be accelerated in order to come back, thus the retardation in the round-trip experiment does not demonstrate "motion", but "accelerated motion". |- |[[w:Hendrik Lorentz|Lorentz]] 1913<ref name=lorentz1 /> |After he derived differential aging in the round-trip experiment from velocity time dilation and pointed out the negligibility of proper acceleration for the computation, he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle, since one of them changes velocity and accelerates; the relativity principle does not require symmetry between inertial and non-inertial observers. |- |style="vertical-align:top"|[[w:Albert Einstein|Einstein]] 1914-1920 |{{anchor|Einstein 1914b-AC}} During a conversation in 1914,<ref name=rowe group=S /> Einstein is reported to have said that moving clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are ''irrelevant'' for the ''amount'' of the time difference, their ''presence'' nevertheless cause B to fall behind ("accelerated motions are absolute"). {{anchor|Einstein 1918-AC}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918<ref name=einstein18 />, Einstein pointed out the negligibility of velocity changes from the viewpoint of an inertial frame (see {{slink||Einstein 1918-VA}}). Then he used ''acceleration as an asymmetry indicator'' in order to show, that there is no contradiction to the relativity principle, because relativity only predicts the equivalence of non-accelerated inertial frames: "only K is such a frame while K' is temporarily accelerated, thus the retardation of U2 with respect to U1 cannot be used to construe a contradiction against the theory." {{anchor|Einstein 1920-AC}}Einstein is reported to have said in an interview from 1920:<ref name=einstein20 /> {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls-Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. Dieser Grund für das Jüngerbleiben des A ergibt sich vom Gesichtspunkt der speziellen Relativitätstheorie aus der Tatsache, daß das betreffende Geschöpf — und nur dieses — Beschleunigungen erlitten hat. | style="padding: 0px 20px 0px 20px;" |In the case of these two twins," Einstein declared, "we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures . This ground, which counts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations." |} In a discussion from 1922,<ref name=morand /> Einstein is reported to have said that there is no contradiction in the round-trip experiment (in terms of a train leaving the station and returning later): The relativity principle is not applicable to this case, because the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two frames having velocities in opposite direction is not an inertial frame. There is no reciprocity between a frame that changes direction and one that doesn't. |} ==Frame distribution as asymmetry indicator== Because any direct influence of proper acceleration on the traveling clock at turnaround can be neglected (see {{slink||Negligibility of proper acceleration}}), the importance of {{slink||Acceleration as asymmetry indicator}} is limited to the mere fact that it reveals that only the traveler was in a non-inertial frame as only he changed his inertial frames, thus instead of emphasizing the occurrence of proper acceleration at turnaround, it's possible to describe the asymmetry more geometrically by emphasizing the different distribution of inertial frames of the twins along their worldlines. {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Max von Laue|Laue]] 1911-1913 |{{Anchor|Laue 1911/12-VA}} In 1911/12,<ref name=laue1 /> he pointed out that during the time of separation, that clock is most advanced which was at rest in an inertial frame all the time; namely there is ''always one, and only one inertial frame'', in which the locations of separation and re-encounter lie in the same geometric point. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1911/12-PT}}). In 1912/13,<ref name=laue2 /> he argued that in the round-trip experiment, we indeed can decide, which one of the clocks was steadily at rest in one and the same reference system, and which one was in the meantime at rest in two or more such systems. Among them there is of course a real physical difference. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1912/13-PT}}). In 1913<ref name=laue3 /> Laue pointed out: {| !style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Aber nach unseren Voraussetzungen ruht während der Zeit der Trennung die erste Uhr in ''einem'' berechtigten Bezugssystem, die zweite hingegen ruht zwar sowohl bei der Hin- wie bei der Rückbewegung in berechtigten Bezugssystemen, aber notwendig in ''zwei verschiedenen. Deshalb'' unterscheiden sich beider Schicksale physikalisch. Ließe man die zweite Uhr in der ihr anfangs erteilten Bewegung und schickte man ihr dafür die erste Uhr nach einiger Zeit mit größerer Geschwindigkeit nach, so würde beim Zusammentreffen die erste gegen die zweite zurückgeblieben sein; denn jetzt hat die erste während der Trennung in zwei verschiedenen Systemen geruht. (Footnote: Dem naheliegenden Einwand, daß wir über den Gang einer Uhr während eines Geschwindigkeits''wechsels'' nichts aussagen können, begegnet man am einfachsten mit dem Hinweis, daß man die Zeiten der gleichförmigen Bewegung ''beliebig'' groß gegen die der Beschleunigung machen kann.) | style="padding: 0px 20px 0px 20px;" | However, by our presuppositions, one clock is at rest in ''one'' valid reference system during the time of separation, while the second one is at rest in valid reference systems both during the forward- and the backward motion, but necessarily in ''two different ones. Therefore'' the two fates differ physically. If the second clock remains in the motion which was given to it at the start, and if after some time it is followed by the first clock with greater velocity, then the first one would be retarded with respect to the second one at the encounter; since now it was the first one that was at rest in two different systems during the separation. (Footnote: The objection which is near at hand, that we cannot say anything about the rate of a clock during a velocity ''change'', can be met most simply by the allusion, that we can render the times of uniform motion ''arbitrarily'' great with respect to acceleration..) |} |- |[[w:Werner Bloch|Bloch]]<ref name=bloch /> September 1918 |{{anchor|Bloch 1918-VA}} He represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. |} ==Perspective of the traveler== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{anchor|Langevin 1911-LI}}[[Image:rstd4.gif|170px|right]] After deriving differential aging from the proper time integral in {{slink||Langevin 1911-PT}} and using human beings in {{slink||Langevin 1911-HU}}, he described the perspectives of both observers using light signals and the Doppler effect. When they separate they see each other live 200 times slower, while at return they see each other live 200 times faster. So ''from the explorer's viewpoint'', in the first year he sees the Earth perform the actions of two days, while in the second year he sees the Earth perform the actions of two centuries. The asymmetry can be seen by noticing, that the observer on Earth in 200 years sees the explorer performs the actions of 1 year. Then the explorer turns around, after which the observer on Earth in 2 days sees the projectile perform the actions of another year. {{Lorentzbox|Text=Langevin used <math>v=c\left(1-\tfrac{1}{20000}\right)</math>, producing Lorentz factor <math>\gamma\approx100</math> and Doppler factor <math>\sqrt{\tfrac{c+v}{c-v}}\approx200</math>.}} |- |[[w:Hendrik Lorentz|Lorentz]] Lectures published in 1913<ref name=lorentz1 /> Similar treatment in 1914<ref name=lorentz3 /> |{{anchor|Lorentz 1913/14-LI}}Described the round-trip experiment in terms of inertial observer A (equipped with clock K) and traveling observer B (equipped with clock K'). In the frame of A, clock K' is retarded with respect to K at reunion due to time dilation. He then described the perspective of the traveling observer B by using two-way propagation of light from K' to K and back to K', leading to three periods defined by the moment of B's turnaround: In the first period the light signals return to K' before turnaround; in the second period the signals are emitted before turnaround and return after turnaround; in the third period emission and return of the signals are both happening after turnaround. Lorentz showed that K is time dilated by a factor of <math>\sqrt{1-v^{2}/c^{2}}</math> with respect to K' in the first and third period, but in the second period K is ticking ''faster'' than K' by a factor of <math>\sqrt{\tfrac{c+v}{c-v}}</math> which overcompensates the dilation in the other periods and explains, even from the perspective of B, why K' is retarded with respect to K at reunion. {{Lorentzbox|Text=In a review of the German translation of Lorentz's book, Einstein (1914) didn't directly mention Lorentz's treatment of the twin paradox, but he wrote that nobody who is seriously interested in relativity should neglect to read that book.<ref name=einstlor /> [[w:Wolfgang Pauli|Pauli]] (1921) refers to Lorentz's book as one of three papers that analyze the twin paradox more closely.<ref name=pauli />}} |- |style="vertical-align:top"| [[w:Albert Einstein|Einstein]] 1916-1920 |{{anchor|Einstein 1916-EP}}In a lecture from 1916,<ref name=einstein16 /> of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of [[w:general relativity]]." {{anchor|Einstein 1918a-EP}}In a letter from September 1918,<ref name=einadl /> Einstein showed that general relativity makes the inertial frame K and and the accelerated frame K' of the clocks in the round-trip experiment "equally justified", explaining the time difference in K' by combining the influence of velocity and gravitational potential on clocks. {{anchor|Einstein 1918-EP}}In his famous "Dialog about Objections against the Theory of Relativity" from November 1918,<ref name=einstein18 /> aimed at clarifying misconceptions of the clock paradox, he explained that there is no paradox in special relativity because there is no symmetry between clock U1 at rest in inertial frame K and clock U2 at rest in accelerated frame K' (see {{slink||Einstein 1918-AC}}). Yet [[w:general relativity]] and the [[w:equivalence principle]] allow the treatment of this problem also from the standpoint of frame K', where clock U2 remains at rest all of the time while U1 makes the following movements: (1) It is accelerated by a homogeneous gravitational field in the negative direction, (2) it moves with constant velocity <math>-v</math>, (3) it is accelerated in the positive direction until it turns around and comes by with constant velocity <math>+v</math>, (4) it moves with velocity <math>+v</math>, (5) it is accelerated in the negative direction until it stops. Clock U1 is retarded with respect to U2 in periods 2) and 4) due to velocity time dilation, but this retardation is overcompensated by the faster rate of U1 during period 3), because U1 is at a higher gravitational potential. He argued that the computation (which he didn't provide) shows that the advance of U1 in period 3) is double its retardation during periods 2) and 4). Einstein concluded that by this consideration "the paradox is completely resolved". Using [[w:Mach's principle]], he pointed out that the gravitational field in K' might be induced by the masses of the universe that are accelerated in this frame. {{anchor|Einstein 1918b-EP}}In a letter to Einstein from December 1918, [[w:Max Jakob|Jakob]] doubted the result that the advance in period 3) is double the retardation during periods 2) and 4). Einstein responded by letter,<ref name=einstein18b /> in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). {{anchor|Einstein 1921-EP}}Einstein is reported to have said in an interview from 1920,<ref name=einstein20 /> that while acceleration explains the age difference between the stationary twin B and the traveling twin A in terms of special relativity (see {{slink||Einstein 1920-AC}}), the "proper" description in terms of general relativity is as follows: {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Eine tiefere Erfassung des Grundes ist indeß nur auf dem Boden der „Allgemeinen Relativitätstheorie" zu erlangen, die uns erkennen läßt, daß von A aus beurteilt ein Zentrifugalfeld existiert, von B aus betrachtet aber nicht; und dieses Feld hat einen Einfluß auf den relativen Ablauf und die Raschheit der Lebensvorgänge. | style="padding: 0px 20px 0px 20px;" | A proper grasp of the reason is furnished only when we adopt the general theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life." |} {{Lorentzbox|Text=a) Einstein's explanation was quickly adopted in the textbooks of [[w:Werner Bloch|Bloch]] (1920),<ref name=bloch2 /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Karl Bollert|Bollert]] (1921),<ref name=bollert1 /> [[w:Max Born|Born]] (1921),<ref name=born /> expressing the view that general relativity is "necessary" to provide the "complete" solution of the twin paradox. b) From a modern standpoint, however, Einstein's explanation has nothing to do with general relativity, but is rather an application of accelerated frames and "pseudo"-gravitational fields to flat Minkowski space of ''special'' relativity.<ref name=weiss group=S />}} |- |[[w:Hans Thirring|Thirring]]<ref name=thirring /> April 1921 |{{anchor|Thirring 1921-DS}}[[Image:Twin Paradox Minkowski Diagram.svg|right|200px]] He described the round-trip experiment by using two platforms K (clock A) and K' (clock B) each equipped with rows of clocks. He first demonstrated the symmetry of time dilation and the mutual relativity of simultaneity on the platforms and its effect on clock synchronization. The K clocks that B passes are all advanced because of <math>t'=\gamma\left(t-vx/c^{2}\right)</math>, and the same is true after turnaround since only the direction of velocity has to be changed in the Lorentz transformation <math>t'-t'_{0}=\gamma\left(t+vx/c^{2}\right)</math> leading to the effect of clock desynchronization, where <math>t'_{0}</math> is a constant depending on which clock one uses as standard for the new synchronization. He graphically showed using Minkowski diagrams, that this simultaneity jump due to desynchronization amounts to double the velocity time dilation during the inertial phases, explaining why A is more advanced than B at reunion. {{Lorentzbox|Text=Using clock B as synchronization standard, Thirring's constant is given by <math>t'_{0}=2l\gamma v/c^{2}=2t\gamma v^{2}/c^{2}</math> with <math>l=vt</math> as position of turnaround. A similar explanation was subsequently given by Langevin (1922).<ref name=morand />}} |} ==Curved spacetime== While the previous examples are defined in flat Minkowski spacetime and therefore can be fully discussed in terms of special relativity, [[general relativity]] is required when [[:w:spacetime curvature]] in the presence of mass and energy cannot be neglected any more.<ref name=koks group=S /> {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |[[w:Jean Becquerel|Becquerel]]<ref name=becqu1 /> 1922 |After defining gravitational time dilation <math>d\tau=\sqrt{1-\tfrac{2GM}{c^{2}r}}dt</math> in terms of the [[w:Schwarzschild metric]] around a material center, he discussed the following round-trip experiment: There are two identical clocks A and B placed next to each other, at a point very far from the material center, initially marking the same time <math>t</math>. Let us transport clock A to a point where the field is more intense, at a distance <math>r</math> from the center; this clock will measure time <math>\int d\tau</math> which is shorter than <math>\int dt</math>, thus it will run more slowly. If we bring clock A back to clock B, we will have to note that it is retarded with respect to B. |} ==Aether interpretations== [[w:Lorentz ether theory]] (LET) is empirically equivalent to special relativity since both models use the Lorentz transformation, thus the description of the twin paradox gives the same result as well. However, special relativity is preferred by the scientific community, because of the validity of the relativity principle in LET is only apparent due to a conspiracy of effects which makes the aether undetecable, and because the measured times and lengths in the aether are supposedly be giving the "true" values even though it is empirically impossible to determine which ones are true or apparent. {| class=wikitable style="background-color:white;{{text default color}};" |- ! style="width:150px" | Author !! Description |- |Langevin (1911)<ref name=langevin1 /> |He argued that it's true that uniform translation with respect to the aether has no experimental meaning in special relativity, though one can still speak of "absolute acceleration" with respect to an aether which he defined as the light carrying medium, so it was "premature to abandon the aether". The absolute nature of acceleration can be seen in the radiation of accelerated charges, as well as in the twin paradox in which the traveler that is more agitated or accelerated is younger at reunion. {{Lorentzbox|Text=Langevin didn't mention this aether interpretation in his later discussions of the twin paradox in 1911/12<ref name=langevin2 /> and 1919.<ref name=langevin3 />}} |- |style="vertical-align:top" |{{Anchor|Wiechert 1911b}}Wiechert (1911)<ref name=wiechert11 /> |Contrary to Langevin, he emphasized that differential aging can be attributed to the existence of absolute "velocities" which he called "strides" (German: Schreitungen, denoting the "absolute meaning" of non-accelerated motions) with respect to the aether, whereas he dismissed the role of accelerations. In other words, the clock's "strides" are not equivalent or anisotropic with respect to the aether, in contradiction to the "unconditional" relativity principle Einstein's which requires equivalence and symmetry. Wiechert proposed a "conditional" relativity principle in which the aether (in the sense of Lorentz) determines all processes in nature, thus the rate of clocks or processes is "really" altered during motion. {{Lorentzbox|Text=a) This aether interpretation was maintained by Wiechert also in subsequent publications in 1915-1922.<ref name=wiechert15 /><ref name=wiechert20 /><ref name=wiechert21 /> b) Wiechert's interpretation in terms of absolute non-accelerated motions was also independently given by others: [[s:fr:Georges Lechalas]] (1912/13)<ref name=lech /> argued that time dilation and asymmetric aging are the result of absolute speeds with respect to an aether, while criticizing Langevin's (1911) argument that only accelerations can indicate the aether and are responsible for the asymmetric aging; [[w:Edward Vermilye Huntington]] (1912)<ref name=hunt /> argued that the "famous paradoxes of the theory of relativity" represented by the reciprocal nature of length contraction and time dilation, appear as necessary consequences of perfectly natural and reasonable conventions for setting clocks and laying out coordinates, when the Lorentz transformation is derived and interpreted on the basis of a stationary aether in the sense of Lorentz. c) Laue (1911/12)<ref name=laue1 /> applauded Wiechert for the "particularly striking way" in which he demonstrated that asymmetric aging indeed follows from the relativity laws, yet he rejected Wiechert's aether interpretation and Wiechert's claim that asymmetric aging contradicts the "unconditional" relativity principle: Laue pointed out that the straight worldline connecting two events A and B is only "preferred" insofar as it indicates the maximal proper time between them, yet this preference is ''not'' the result of the natural laws employed, but is rather due to the choice of points A and B; by analogy, the geometric result that two points determine a straight line and thus a direction as well, doesn't refute the physical equivalence of all directions in space; finally, as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.}} |} ==Paradoxical?== Even though Einstein (1905)<ref name=einstein05 /> denoted the round-trip experiment as "peculiar" (German: eigentümlich) he saw nothing contradictory in it. Without mentioning the round-trip experiment, [[w:Paul Gruner]] in May 1910<ref name=gruner10 /> denoted the effect that clocks in relative motion are not showing the same time when they meet as the "great paradox" of relativity (German: Grosse Paradoxie), and [[w:Max von Laue]] in May 1911<ref name=laue0 /> wrote that some consequences of the relativity of time occasionally indeed look "paradoxical" (German: paradox). Eventually, Laue in November 1911 (published 1912)<ref name=laue1 /> was the ''first to specifically denote the round-trip experiment'' as a "paradox" (German: Paradoxie): {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" | German original of [[w:Max von Laue|Laue]] (1911/12):<ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> ! English translation |- |Unter all den paradox erscheinenden Folgerungen aus der Zeittransformation der Relativitätstheorie gibt es wohl keine, gegen welche sich der natürliche Menschenverstand bei jedem, der der Sache noch ungewohnt ist, so sehr sträubt, wie gegen die, daß die Zeitangabe einer Uhr von ihrem Bewegungszustand abhängen soll. Schon in seiner grundlegenden Arbeit hat Einstein diese Paradoxie auf die Spitze getrieben in einem Gedankenexperiment, welches neuerdings von Langevin in einem auch sonst sehr lesenswerten Vortrage besonders hübsch erläutert worden ist. |Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. |- |colspan=2|{{Lorentzbox|Text=Subsequently, [[w:Paul Gruner]] (1912)<ref name=gruner /> and others including Einstein (1918)<ref name=einstein18 /> explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas [[w:Rudolf Seeliger]] (1913)<ref name=seel /> spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon").}} |} ==Misunderstandings== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" padding=10 | German original by [[w:Otto Berg (scientist)|Berg]] (1910):<ref name=berg /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |Im Punkte <math>x = 0</math> des Systems S befinde sich eine Uhr, eine andere im Punkte <math>x'=0</math> von S'. Diese zweite bewege sich mit S' bis zum Punkte <math>x = a</math>, kehre dort um und bewege sich nun mit der Geschwindigkeit <math>v</math> zurück bis zum Punkte <math>x= 0</math>. Welche Zeit müssen beide Uhren in dem Moment angeben, wo sie sich wieder treffen? Wir beantworten diese Frage zunächst vom Standpunkt des Beobachters in S. Die Uhr in <math>x' = 0</math> hat sich mit der Geschwindigkeit <math>v</math> bis zum Punkte <math>x = a</math> bewegt; dazu brauchte sie die Zeit <math>\tau=\tfrac{a}{v}</math>. Zum Rückweg ist dieselbe Zeit nötig. Nach der Zeit <math>2\tau=2\tfrac{a}{v}</math> ist die Uhr also wieder im Punkte <math>x = 0</math> angelangt. Wir stellen uns nun auf den Standpunkt des Beobachters in S'. Für diesen führt nach dem Relativitätsprinzip das System S genau dieselben Bewegungen aus wie das System S' für den Beobachter in S, nur in entgegengesetzter Richtung. Die Zeit bis zum Zusammentreffen beider Uhren ist also im System S' ebenfalls gegeben durch <math>2\tau=2\tfrac{a}{v}</math>. Betrachtungen, die auf anschauliche Vorstellungen, wie Nachgehen von Uhren, gestützt sind, führen hier leicht zu Irrtümern, von denen auch die Fachlitteratur nicht frei ist. | style="padding: 0px 20px 0px 20px;" |There is a clock at point <math>x=0</math> of system S, and another one at point <math>x'=0</math> of S'. The second one moves together with S' until point <math>x=a</math>, turns around and now moves back with speed <math>v</math> to point <math>x=0</math>. Which time must both clocks indicate at the moment at which they encounter again? We answer this question at first from the standpoint of the observer in S. The clock at <math>x=0</math> has been moving with speed <math>v</math> until point <math>x=a</math>, for which it required time <math>\tau=\tfrac{a}{v}</math>. The same time is required for the way back. After time <math>2\tau=2\tfrac{a}{v}</math> the clock has thus arrived again at point <math>x=0</math>. Let's now take the standpoint of the observer in S'. In his view in accordance with the relativity principle, system S is conducting exactly the same motions as those of system S' with respect to the observer in S, only in opposite direction. Thus the time until the meeting of both clocks is given by <math>2\tau=2\tfrac{a}{v}</math> in system S' as well. Considerations based on illustrative notions, such as the retardation of clocks, easily lead to mistakes at this place, of which also the professional literature isn't free. |- |colspan=2|{{Lorentzbox|Text=a) Berg was probably the first to turn the relativity principle against asymmetric aging in the round-trip experiment, claiming that both clocks must indicate the same time at reunion. See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem. b) Berg's mistake also seems to be based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" padding=10 | German original by [[w:Otto Lehmann (physicist)|Lehmann]] (1910/11):<ref name=lehm /> ! English translation |- | style="padding: 0px 20px 0px 20px;" | Hat man zwei genau gleich gehende Uhren nebeneinander und bewegt nun die eine auf einer beliebigen Kurve bis wieder zur anderen zurück, welche Bewegung <math>t</math> Sekunden gedauert haben möge, so geht sie gegen diese um <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> oder annähernd <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> Sekunden zu spät, weil sie während der Bewegung auf langsameren Gang reguliert werden mußte, um mit der ruhenden Uhr in Übereinstimmung zu bleiben. | style="padding: 0px 20px 0px 20px;" | If there are two exactly identical clocks next to each other, and if one of them will be moved on an arbitrary curve until it comes back, which may have lasted <math>t</math> seconds, it [the moving clock] will lag behind the other one by <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> or approximately <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> seconds, because it [the moving clock] had to be regulated to a slower rate during motion in order to remain synchronous with the resting clock. |- |colspan=2|{{Lorentzbox|Text=a) So Lehmann erroneously thinks that the time difference at reunion is only the result of "regulating" the moving clock. This implies that he (like Berg) believed that special relativity predicts ''equal'' clock times at reunion if the moving clock would have been left ''unregulated'' during the round-trip. b) Lehmann's mistake (similar to Berg) seems to based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" | German original by [[w:Emil Wiechert|Wiechert]] (1911)<ref name=wiechert11 /> ! English translation |- |colspan=2| Even though he correctly derived differential clock aging in the round-trip experiment, he (like Berg and Lehmann) claimed that effects like time dilation are "apparent" if one admits Einstein's "unconditional" relativity principle in which there is no aether and all "strides" (i.e. non-accelerated motions) are physically equivalent, but they are "real" if one admits the existence of an aether in the framework of a "conditional" relativity principle in which all strides are physically non-equivalent or anisotropic. This led him to the following interpretation of the clock paradox: |- | style="padding: 0px 20px 0px 20px;" |[...] so muß am Schluß des Versuches B in seinem Fortschritt gegenüber A im Verhältnis <math>1:\sqrt{1-u^{2}/c^{2}}</math> zurückgeblieben sein. Und dieses Zurückbleiben ist unbedingt reell, denn die beiden Gebilde A und B können ja unter gleichen Umständen unmittelbar beieinander verglichen werden. Hier ist es ganz sicher ausgeschlossen, an einen Schein zu glauben, der durch unsere Auffassung der Zeit bewirkt wird. So ist denn also auch die Folgerung unabwendbar, daß für den Verlauf der Weltvorgänge die Schreitungen nicht gleichwertig sind, ''und damit sind wir von neuem zu einem Schluß gekommen, welcher der Unbedingtheit des Relativitätsprinzipes durchaus widerspricht.'' [...] Man kann den Versuch noch mannigfach variieren, z. B. so, daß A ebenso wie B zwei verschiedene Schreitungen, <math>+u</math> und <math>-u</math>, nacheinander inne hat. Wird dann zu A der Wert <math>u_{1}</math>, zu B der Wert <math>u_{2}</math>, zugeordnet, so muß der Vergleich von A und B am Schluß des Versuches ergeben, daß B oder A in seinem Fortschritt zurückgeblieben erscheint, je nachdem die Schreitungen <math>+u_{1}</math>, <math>-u_{1}</math>, oder <math>+u_{2}</math>, <math>-u_{2}</math> weiter auseinanderliegen. ''Vielleicht ist gerade diese Formulierung des Satzes besonders geeignet, um die Ungleichwertigkeit der verschiedenen Schreitungen klar und deutlich zu zeigen.'' | style="padding: 0px 20px 0px 20px;" | [...] thus B's progress must be retarded with respect to A's in the ratio <math>1:\sqrt{1-u^{2}/c^{2}}</math> at the end of the experiment. And this retardation is definitely real, since both bodies A and B indeed can be immediately compared side by side under the same conditions. Here it is certainly excluded to believe that this is an appearance due to our conception of time. Thus the consequence is unavoidable too, that the strides are not equivalent in the course of the world processes, ''and therefore we again came to a conclusion that completely contradicts the unconditionality of the relativity principle.'' [...] One can vary this experiment in many ways, for instance, so that A in the same way as B successively undergoes two different strides <math>+u</math> and <math>-u</math>. If we apply the value <math>u_{1}</math> to A and <math>u_{2}</math> to B, then the comparison of A and B at the end of the experiment must give the result, that B or A is retarded in its progress depending on whether the strides <math>+u_{2},-u_{2}</math> or <math>+u_{1},-u_{1}</math> are further apart. ''Probably it is precisely this formulation of the theorem that is particularly suitable to demonstrate the non-equivalence of the different strides clearly and explicitly.'' |- |colspan=2|{{Lorentzbox|Text=This interpretation was directly rebutted by Laue (1911/12) who demonstrated the geometrical meaning of differential aging in Minkowski space, see sections {{slink||Laue 1911/12-PT|Laue 1911/12-VA}}, showing that there is no need to assume non-equivalance or anisotropy of motions. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.<ref name=laue1 />}} |- ! style="width:50%" | German original by [[w:Norman Robert Campbell|Campbell]] (November 1911, published 1912)<ref name=camp /> ! English translation |- |colspan=2|After describing the round-trip experiment (as given by Wiechert) according to which the traveling clock B is retarded when it returns with respect to stationary clock A, he abandoned differential clock aging as follows: |- | style="padding: 0px 20px 0px 20px;" |Dieser Schluß ist nicht richtig. Die Beziehung zwischen <math>t</math>, der Ablesung an der Uhr auf A seitens des Beobachters auf A und <math>t'</math>, der Ablesung an der Uhr auf B seitens des Beobachters auf A, ist (unter der Annahme, daß zu Beginn des Versuchs <math>t=t'</math> ist) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. Der Unterschied zwischen <math>t'</math> and <math>t</math> ist eine Funktion von <math>z</math> und <math>v</math> allein. Wenn man diesen Größen ihre früheren Werte wiedergibt, indem man die beiden Uhren wieder zur Koinzidenz bringt, während sie relativ zueinander ruhen, so geht der Unterschied zwischen <math>t'</math> and <math>t</math> wieder auf null zurück, gleichviel, welche Werte <math>z</math> und <math>v</math> während der Zwischenzeit gehabt haben mögen. Wenn an irgendeinem Punkte der Bahn die Geschwindigkeit von B relativ zu A eine endliche plötzliche Änderung erfährt, so erfährt auch der Wert von <math>v</math> eine endliche plötzliche Änderung. | style="padding: 0px 20px 0px 20px;" |This conclusion is not correct. The relationship between <math>t</math> as the reading on the clock on A by the observer on A, and <math>t'</math> as the reading on the clock on B by the observer on A, is given by (assuming that <math>t=t'</math> at the beginning of the experiment) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. The difference between <math>t'</math> and <math>t</math> is a function of <math>z</math> and <math>v</math> alone. If these quantities are given their previous values by bringing the two clocks back to coincidence during which they are at rest relative to one another, the difference between <math>t'</math> and <math>t</math> goes back to zero, no matter what values <math>z</math> and <math>v</math> may have had in the meantime. If at any point on the path the speed of B experiences a finite sudden change relative to A, then the value of <math>t'</math> also undergoes a finite sudden change. |- |colspan=2|{{Lorentzbox|Text=a) So Campbell claims that any time difference during the outbound path is wiped out during the inbound path. His mistake is obvious: He is confusing coordinate differences stemming from the Lorentz transformation of ''events'' (which indeed depend on position and direction) with differences in ''clock aging'' derived from the proper time integral (which is ''accumulative'' and independent of position and direction.) b) As Campbell's paper was a reply to Wiechert, it's interesting to compare them: Campbell was correct in dismissing the aether but wrong in denying asymmetric aging, while Wiechert was correct in deriving asymmetric aging but wrong in requiring the aether. }} |- ! style="width:50%" | French original by [[w:Paul Gruner|Gruner]] (March 1912):<ref name=gruner /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |[...] deux personnes du même âge, se séparant dans des systèmes de « marche » très différents et retournant après un laps de temps assez long, constateront une différence d'âge très sensible. [...] le principe de relativité exige toujours la ''réciprocité parfaite'' des phénomènes entre deux systèmes qui possèdent un mouvement relatif. Si, dans l'exemple cité, les deux personnes du même âge se séparent avec une vitesse relative pour se retrouver plus tard, la constatation d'une différence d'âge sera parfaitement mutuelle : A dira positivement que B est resté en arrière dans son développement, et B affirmera avec le même droit que c'est A qui ne s'est pas développé assez vite. Ainsi le principe absolu de la relativité montre ses conséquences les plus extrèmes et il est clair que l'introduction de l’éther n'est plus en état de résoudre cette contradiction irréductible et inconcevable. | style="padding: 0px 20px 0px 20px;" | [...] two people of same age, separating into very different systems of motion and returning after a quite long period of time, will notice a very significant age difference. [...] the principle of relativity always requires the ''perfect reciprocity'' of the phenomenons between two systems that possess relative motion. When, in the cited example, the two persons of same age are separated by some relative velocity only to meet again later, the finding of an age difference will be perfectly mutual: A will positively say that B stayed behind in its development, and B will assert with same right that it was A who has not developed fast enough. By that, the absolute relativity principle shows its most extreme consequences and it is clear, that the introduction of the aether is no longer able to resolve this irreducible and inconceivable contradiction. |- |colspan=2|{{Lorentzbox|Text=Gruner was probably the first to claim that combining the round-trip experiment with the symmetry of time dilation leads to the contradictory situation, that both must attribute younger age to one another at reunion. At the end of his paper, we also find the expression "clock paradox" (French: paradoxe des horloges). See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem.}} |} ==Einstein's contributions== 1905:<ref name=einstein05 /> Introduction of the "peculiar" (German: eigentümlich) round-trip experiment with clocks in terms of a polygonal path as well as a continuously curved path, and an experiment comparing a clock at the pole with one at the equator. January 1911 (published November):<ref name=einstein11a /> In a lecture from January, Einstein extended the "funny" (German: drollig) round-trip experiment to living organisms. According to [[w:Rudolf Lämmel]] in April 1911<ref name=lammel /> and [[w:Fritz Müller-Partenkirchen|Fritz Müller]] in October 1911,<ref name=muller /> Einstein spoke of human beings as well. January 1911 (published January 1912):<ref name=einstein3 /> During a discussion with Einstein directly after the previous lecture, [[w:Fritz Müller-Partenkirchen|Fritz Müller]] claimed that any time difference during the round-trip should vanish at reunion, in analogy to the fact that the Lorentz contraction of a moving rod vanishes when it is at rest again. Einstein showed that the analogy is incorrect: While the clock rates are indeed the same again when they are mutually at rest, the clocks do not indicate the same time at reunion because "clocks are carriers of the time differential"; he went on to show that any possible influence of acceleration during the turnaround can be made negligible by elongating the constant velocity periods. 1912:<ref name=einst12manu /> In an unpublished manuscript on special relativity, Einstein showed that if system <math>\Sigma'</math> makes a round-trip along a polygon, then its inner processes will be retarded with respect to resting system <math>\Sigma </math> at reunion. He pointed out that any influence of acceleration can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygon. April 1914:<ref name=einstpetz /> [[w:Joseph Petzoldt]] criticized asymmetric clock aging in the round-trip experiment as a "fallback into absolutist way of thinking", claiming that special relativity requires that any difference between the clocks vanishes when their relative velocity is zero again, even though he added that any treatment of the clock paradox in special relativity is unrealistic anyway, since the theory only concerns uniform motions and therefore cannot handle velocity changes, so one has to modify the theory. Einstein responded by letter in which he praised Petzoldt's philosophical take on relativity, yet he rejected Petzoldt's conclusions concerning the clock paradox by showing that any finite acceleration at turnaround during the round-trip can only influence the clock in a finite way and therefore can be neglected by minimizing the time of acceleration with respect to the time of uniform translation, so it "must be concluded" that the clock traveling on a polygonal path is retarded at reunion. May 1914:<ref name=rowe group=S /> During a conversation with [[w:Ernst Gehrcke]] who claimed that the clock paradox contradicts the relativity principle, Einstein replied that clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are irrelevant for the amount of the time difference, their presence nevertheless cause B to fall behind ("accelerated motions are absolute in the theory of relativity"). 1916:<ref name=einstein16 /> In a lecture of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of general relativity." September 1918:<ref name=einadl /> In a letter to Einstein, [[w:Friedrich Adler (politician)|Friedrich Adler]] (while in prison for the [[w:Assassination of Karl von Stürgkh]]) claimed that the clock paradox which he described on a circular round-trip contradicts the special relativity principle, and also referred to the similar opinions of Berg and Petzoldt. Einstein responded by letter and explained that there is no contradiction as one of them accelerates; he then showed that general relativity makes both inertial frame K and accelerated frame K' equally justified, explaining the time difference in K' by combining the influence of velocity and gravitational potential, concluding that "Berg and Petzoldt were wrong". November 1918:<ref name=einstein18 /> In a fictitious dialogue between a relativity critic and a relativity apologist written by Einstein, the "critic" said that special relativity must predict differential clock aging in round-trip experiments, which was confirmed by the "relativist" who regretfully noted that even some pro-relativity authors tried to "circumvent this unavoidable result". Yet the critic claimed that this leads to a contradiction: From the viewpoint of K, clock U1 is at rest while the clock U2 was in motion and therefore returns being retarded with respect to U1, but from the viewpoint of K', clock U2 is at rest while clock U1 was in motion and therefore returns being retarded with respect to U2, which was rebutted by the relativist by pointing out the acceleration of U2. Then the critic claimed that this problem "rises again from the dead" in general relativity which allows to symmetrically treat both K and K', which was rebutted by the relativist using the equivalence principle: In K', the rate increase of U1 during turnaround period 3) is "the double" of its velocity time dilation in the inertial periods 2) and 4). December 1918:<ref name=einstein18b /> In a letter to Einstein, [[w:Max Jakob]] doubted the result from Einstein's dialogue, according to which the advance of U1 in period 3) is the double of its retardation during periods 2) and 4). Einstein responded by letter, in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). 1920:<ref name=einstein20 /> In conversations with [[w:Alexander Moszkowski]] between 1919 and 1920, Einstein argued that differential aging of the twins is rather a paradox of feeling, not a paradox of thought, because the latter would only arise if there were no reason for the asymmetric aging. The reason in special relativity lies in the fact that one of them suffered accelerations, while a deeper understanding of that question is obtained by using general relativity. Einstein argued that our "common sense" is located in the realm of feeling and analogy drawn from our ordinary experience; since there is no analogy to the example of the twins in our experience, it might appear paradoxical to the common sense, while it appears logical and necessary in light of intensified abstraction of the trained scientific mind. August 1920:<ref name=rowe group=S /> At an anti-relativity event organized by the right-wing agitator [[w:Paul Weyland]] during which [[w:antisemitic]] leaflets were distributed and [[w:swastika]]s offered at the entrance, a lecture was given by Gehrcke re-iterating his criticism of the twin paradox, claiming that the stationary first organism is old or even dead at reunion while the second organism was in motion and therefore stayed young, but from the standpoint of the second organism he himself is old or even dead while the first organism was in motion and stayed young, thus relativity is either contradictory or it leads to different realities and physical [[w:solipsism]]. Einstein who was present at that event, directly responded in a newspaper article;<ref name=einst20 /> after suspecting antisemitic motives of his critics, he specifically addressed Gehrcke's objections regarding the "well known example of the clocks (or twins)", remarking that the charge of solipsism will be "greeted by the experts as a joke", and characterized the claim that relativity requires mutual retardation of two co-located clocks as a "deliberate attempt to misinform the lay public". 1922:<ref name=morand /><ref name=nord /> [[w:Paul Painlevé]], Einstein and Langevin discussed the clock paradox at a meeting in Paris. Painlevé imagined a clock on a train that performs a round-trip with constant speed and returns being retarded with respect to the station clock, yet he claimed that the relativity principle also allows to say that the station clock performed the round-trip and returned being retarded with respect to the train clock, in contradiction to the previous result. Einstein replied that the relativity principle cannot be applied since the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two systems having velocities in opposite direction is not an inertial frame; there is no reciprocity between a frame that changes direction and one that doesn't. Langevin consequently gave a detailed analysis in terms of the Lorentz transformation. 1954:<ref name=einstein54 /> In a letter, Einstein explained the "well known clock paradoxon" using two clocks <math>B_{1}</math> and <math>B_{2}</math>; clock <math>B_{2}</math> has to reverse its speed in order to come back, thus it was initially at rest in inertial frame <math>S_{2}</math> and then at rest in <math>S_{2}^{+}</math>, whereas <math>B_{1}</math> constantly remains at rest in <math>S_{1}</math>, which explains the asymmetry between them. ==Historical references== <references> <ref name=einstein05>See p. 904f in: {{Citation |author=Einstein, A. |date=1905 |title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik |volume=322 |issue=10 |pages=891–921 |doi=10.1002/andp.19053221004|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 2, Document 23}}. See also: [https://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation at fourmilab].</ref> <ref name=einstein11a>See p. 10. in: {{Citation |author=Einstein, A. |title=Die Relativitäts-Theorie|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |issue=1-2|pages=1–14 |date=27 November 1911|orig-date=Lecture 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n11/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 17}}.<br /> The publication date 27 November 1911 can be seen on the [https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n5/mode/2up Title page and TOC of issue 1-2].</ref> <ref name=einstein3>Discussion between Einstien, Müller, Lämmel and others after the Zürich lecture: {{Citation |author=Einstein, A.; Müller, F., Lämmel, R.|title=Diskussion zu "Die Relativitäts-Theorie"|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |pages=II-IX |date=January 1912|orig-date=Lecture on 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n587/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 18, and in the corresponding English translation volume}}<br /> While the discussion already happened on January 1911, the publication followed one year later in January 1912 in the session proceedings (Sitzungsberichte) of the third issue, see [https://www.ngzh.ch/publikationen/vjs/56/3 Full issue Nr. 3] with [http://www.ngzh.ch/archiv/1911_56/56_1-2/56_3.pdf Title page and TOC] and the [http://www.ngzh.ch/archiv/1911_56/56_3/56_30.pdf Sitzungsberichte including Einstein's discussion on pp. II-IX]. </ref> <ref name=einst12manu>See p. 46 in: {{Citation |author=Einstein, A. |date=1912 |chapter=Document 1: Einstein's manuscript on the special theory of relativity|title=The collected papers of Albert Einstein|volume=4|pages=3-108|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstlor>{{Citation|author=Einstein, A.|date=1914|title=Review of "Lorentz, H. A. – Das Relativitätsprinzip" |journal=Die Naturwissenschaften|volume=2|pages=1018|url=https://archive.org/details/CAT31421305002/page/1018/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 6, Document 11}}</ref> <ref name=einstpetz>{{Citation |author=Einstein, A. |date=1914 |chapter=Document 5: Letter from Einstein to Petzoldt|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein16>See p. 423f in: {{Citation |author=Einstein, A. |date=1916 |title=Announcement of Einstein's lecture "Über einige anschauliche Überlegungen aus dem Gebiete der Relativitätstheorie"|journal=Berliner Sitzungsberichte|pages=423|volume=1916 (part 1)|url=https://archive.org/details/sitzungsberichte1916deutsch/page/423/mode/2up}}</ref> <ref name=einadl>Letter exchange between Einstein and Adler in which the critique on the clock paradox by Berg (1910) and Petzoldt (1914) was mentioned, together with the general relativity solution in terms of the gravitational potential, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Adler's letter in Document 620 and Einstein's reply in Document 628|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein18>Einstein discussed in terms of inertial frames (special relativity) on pp. 697f; accelerated frames (general relativity) on pp. 698f.; distant masses (Mach's principle) on pp. 700f. in: {{citation |author=Einstein, A.|title=[[s:de:Dialog über Einwände gegen die Relativitätstheorie|Dialog über Einwände gegen die Relativitätstheorie]]|date=November 1918|volume=6|issue=48|journal=Die Naturwissenschaften|pages=697-702|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 7, Document 13}}; See also English translation [[:s:Translation:Dialog about Objections against the Theory of Relativity|Dialog about Objections against the Theory of Relativity]] on Wikisource.</ref> <ref name=einstein18b>Letter exchange between Max Jakob and Einstein from December 1918, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Jakob's letter in Document 661c and Einstein's reply in Document 663a|title=The collected papers of Albert Einstein|volume=10|pages=189-190}}</ref> <ref name=einstein20>Interview of Einstein by Moszkowski, see p. 204f. in: {{citation |author=Moszkowski, A.|title=Einstein. Einblicke in seine Gedankenwelt|orig-date=Copyright date 1920 |date=1921|place=Hamburg|url=https://www.archive.org/details/einsteineinblick00moszuoft}}; See also English translation by H. L. Brose (1921): [https://archive.org/details/einsteinsearch00moszrich Einstein, the searcher], p. 206</ref> <ref name=einst20>{{Citation|author=Einstein, A.|date=27 August 1920|journal=Berliner Tageblatt|title=Meine Antwort - Ueber die anti-relativitätstheoretische G. m. b. H.|issue=402|pages=1-2|url=https://www.deutsche-digitale-bibliothek.de/newspaper/item/YH65KFT53MOG4SMXDXK4IVUPTR3QRY7Q?issuepage=1|quote=Reprinted in "The Collected Papers of Albert Einstein", Vol. 7, Document 45}}</ref> <ref name=einstein54>Letter from Einstein to N. V. Pope from March 1954; [[w:Albert Einstein Archives]], Object number 27-88 ([https://ein-web.adlibhosting.com/aea/Details/archive/110021626 Online dataset]); Scanned version as [https://groups.google.com/group/npachat/attach/d3121322d37764f2/Einstein%20letter.doc?part=0.1 Word document on Usenet] published by [https://groups.google.com/g/npachat/c/Haoib97d6OA/m/8mR30yITEtMJ Pope himself])</ref> <ref name=morand>Discussion between Painlevé, Einstein, and Langevin on p. 316ff in: {{citation |author=Morand, M.|title=Einstein au collège de france|date=April 1922|journal=La Nature|volume=50|issue=2511|pages=315-320|url=http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.102/319/100/620/5/613}}</ref> <ref name=lammel>{{Citation|author=Lämmel, R.|date=28 April 1911|title=Die Relativitäts-Lehre|journal=Neue Zürcher Zeitung|volume=117|pages=1|url=https://www.e-newspaperarchives.ch/?a=d&d=NZZ19110428-01.2.4.1}}; English translation of the part concering the twin pardox at [[:v:History of Topics in Special Relativity/Twin paradox#Lämmel 1911-Hum|Wikiversity:Early history of the twin paradox - Lämmel]]</ref> <ref name=lammel2>See p. 84ff in: {{Citation|author=Lämmel, R.|date=1921|orig-date=Preface December 1920|title=Die Grundlagen der Relativitätstheorie|place=Berlin|publisher=Springer|url=https://archive.org/details/diegrundlagende00lmgoog}}</ref> <ref name=langevin1>He derived differential aging from the proper time integral; pointed out that this demonstrates the "absolute nature of acceleration" with respect to an aether, see: {{citation |author=Langevin, P.|title=[[:s:fr:L’Évolution de l’espace et du temps|L’Évolution de l’espace et du temps]]|journal=Scientia |volume=X |pages=31–54 |date=July 1911|orig-date=Lecture 10 April 1911}}; English translation [[:s:en:Translation:The Evolution of Space and Time|The Evolution of Space and Time]] on Wikisource</ref> <ref name=langevin2>See p. 329 in: {{citation |author=Langevin, P. |title=Le temps, l'espace et la causalité dans la physique moderne |journal=Bulletin de la Société française de philosophie |volume=12 |orig-date=Lecture October 1911|date=1912|pages=1-28|url=http://ahp.li/1f7fc22d283fdf0deeca.pdf}}</ref> <ref name=langevin3>See p. 622f in: {{citation |author=Langevin, P. |title=Le Principe de relativité |journal=Bulletin de la société française des électriciens |volume=9 |date=1919 |pages=601-639|url=https://archive.org/details/bulletin-de-la-societe-francaise-des-electriciens-ser.-3-vol-9/page/600}}; Republished in 1922 as separate booklet: [[:s:fr:Le Principe de relativité|Le Principe de relativité]], Éditions Étienne Chiron</ref> <ref name=wiechert11>See p. 745f. general description and proper time; 757f. space travel; in: {{Citation |author=Wiechert, E. |date=September 1911|orig-date=Lectures March-May 1911, submitted 26 July|title=[[:s:de:Relativitätsprinzip und Äther|Relativitätsprinzip und Äther]]|journal=Physikalische Zeitschrift |volume=12 |issue=17-18 |pages=[https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/741 689-707] published September 1; [https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/789 737–758] published September 15}}</ref> <ref name=wiechert15>See p. 46 (Einstein, Langevin, Wiechert) and pp. 51f (Laue versus Wiechert) in: {{citation |author=Wiechert, E.|contribution=Die Mechanik im Rahmen der allgemeinen Physik| title=Die Kultur der Gegenwart: Physik|volume=3.3.1|date=1915 |orig-date=Submitted July 1914|pages=1–78|contribution-url=https://www.archive.org/details/physikunterredak00warbuoft}}</ref> <ref name=wiechert20>See p. 46f in: {{citation |author=Wiechert, E.|title=Der Äther im Weltbild der Physik|orig-date=Presented December 1920|date=1921|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse|pages=29-70|url=http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN00250586X}}</ref> <ref name=wiechert21>See p. 25ff in: {{citation |author=Wiechert, E.|title=[[:s:de:Prinzipielles über Äther und Relativität|Prinzipielles über Äther und Relativität]]|date=1922|orig-date=Lecture September 1921|journal=Physikalische Zeitschrift|volume=23|pages=25-28}}</ref> <ref name=muller>See p. 9 in: {{Citation|author=Müller, F.|date=October 1911|journal=Berliner Tageblatt|title=[[:s:de:Das Zeitproblem (1911)|Das Zeitproblem]]|pages=[https://www.deutsche-digitale-bibliothek.de/newspaper/item/2QKOIOLGNVQILTCEZQOGQPLTRVLPM5PZ?query=zeit&issuepage=9 Part 1 published 16 October 1911] and [https://www.deutsche-digitale-bibliothek.de/newspaper/item/IO44I6QBC4SVV5YUKUDSGXYIPQUXXBN5?query=zeit&issuepage=11 Part 2 published 23 October 1911]}}</ref> <ref name=gruner10>See p. 89 in: {{Citation |author=Gruner, P. |title=Elementare Darlegung der Relativitätstheorie |journal=Mitteilungen der Naturforschenden Gesellschaft Bern |issue=1751 |pages=82-103 |date=May 1912|doi=10.5169/seals-319208}}</ref> <ref name=gruner>See p. 253f in: {{Citation |author=Gruner, P. |title=[[:s:fr:Rapport sur la dernière discussion concernant le principe de la relativité et l’éther|Rapport sur la dernière discussion concernant le principe de la relativité et l’éther]] |journal=Archives des sciences physiques et naturelles |volume=33|issue=4 |pages=252-254 |date=March 1912}}</ref> <ref name=weyl>See p. 147f. in: {{Citation |author=Weyl, H. |date=March 1918|title=Raum-Zeit-Materie (first edition)|publisher=Berlin: Springer|url=https://archive.org/details/RaumZeitMaterieVolIMeinerFrauGewidmet}}; English translation of the 4th edition by H. Brose (1921): [https://www.gutenberg.org/ebooks/43006 Space—Time—Matter], pp. 278f.</ref> <ref name=gbaum>See footnote on p. 507 in: {{Citation|author=Grünbaum, F. |title=Über einige ideelle Versuche zum Relativitätsprinzip|journal=Physikalische Zeitschrift|volume=12|pages=500–509|date=1911|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/540}}</ref> <ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> <ref name=laue2>See p. 42f. for general description; p. 58f. in terms of proper time; in: {{Citation |author=Laue, M. v. |orig-date=Preface December 1912|date=1913 |title=Das Relativitätsprinzip (Second Edition) |publisher=Vieweg |place=Braunschweig|url=https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE4597082}}; See also English translation [[:s:Translation:The Principle of Relativity (Laue 1913)|The Principle of Relativity, Second edition, Part III]] on Wikisource</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=laue0>See preface in: {{Citation |author=Laue, M. v. |date=May 1911|title=Das Relativitätsprinzip (First Edition) |publisher=Vieweg |place=Braunschweig|url=https://archive.org/details/dasrelativittsp00lauegoog}}</ref> <ref name=berg>See p. 369f in: {{Citation |author=Berg, O. |date=1910 |title=Das Relativitätsprinzip der Elektrodynamik |journal=Abhandlungen der Fries'schen Schule |volume=3 |issue=2|pages=333-382 |url=http://hdl.handle.net/2027/hvd.hnuynk?urlappend=%3Bseq=351}}</ref> <ref name=camp>See p. 123f in: {{Citation |author=Campbell, N. |title=Relativitätsprinzip und Äther: Eine Entgegnung an Herrn Wiechert |journal=Physikalische Zeitschrift |volume=13 |pages=120-128 |issue=3|orig-date=Submitted December 1911|date=February 1912|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/150}}. The is based on an English manuscript translated by Max Iklé, and Campbell's first name was Germanised as "Normann".</ref> <ref name=seel>{{Citation|author=Seeliger, R.|title=Review of "P. Gruner – Rapport sur la dernière discussion concernant le principe de la relativité et l'éther"|journal=Die Fortschritte der Physik|volume=68|issue=2|pages=336|date=1913|url=https://books.google.com/books?id=fSJGAQAAMAAJ&pg=PA336}}</ref> <ref name=study>See footnote on p. 111 in: {{citation |author=Study, E. |title=Vorlesungen über ausgewählte Gegenstände der Geometrie |date=June 1911|url=https://archive.org/details/vorlesungenber00studuoft|publisher=B.G. Teubner|place=Leipzig}} </ref> <ref name=robb1>See pp. 356ff. in: {{Citation|author=Robb, A.|date=1914|title=A theory of time and space|place=Cambridge|publisher=University Press|url=https://archive.org/details/theoryoftimespac00robbrich}} </ref> <ref name=robb2>See §12 in: {{citation |author=Robb, A. A.|title=The Straight Path|date=1920 |journal=Nature|pages=599|volume=104|issue=2623|url=https://archive.org/details/sim_nature-uk_1920-02-05_104_2623/page/598/mode/2up}}</ref> <ref name=edding2>See p. 22 in: {{Citation |author=Eddington, A. S. |date=1922 |title=The theory of relativity, and its influence on scientific thought |publisher=Oxford Clarendon Press |url=https://archive.org/details/cu31924005748573}}</ref> <ref name=rogers>{{citation |author=Rogers, R. A. P.|title=The Time-Triangle and Time-Triad in Special Relativity|date=November 1922|journal=Nature|volume=110|issue=2769|pages=698–699|url=https://archive.org/details/sim_nature-uk_1922-11-25_110_2769/page/698/mode/2up}}</ref> <ref name=lorentz1>See pp. 37f, 55ff in: {{citation |author=Lorentz, H. A.|date=1913|title=Het relativiteitsbeginsel : drie voordrachten gehouden in Teyler's stichting|publisher=De Erven Loosjes |place=Haarlem|url=https://resolver.kb.nl/resolve?urn=MMKB24:063387000:00005}}; German translation on pp. 31f, 47f in: {{citation |author=Lorentz, H. A.|date=1914| title=Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem|publisher=B.G. Teubner |place=Leipzig and Berlin|url=https://archive.org/details/bub_gb_89PPAAAAMAAJ}}; See also the transcription [[:s:de:Das Relativitätsprinzip (Lorentz)|Das Relativitätsprinzip]] on German Wikisource and the English translation [[:s:Translation:The Principle of Relativity (Lorentz)|The Principle of Relativity]] on English Wikisource</ref> <ref name=lorentz3>See §12 in: {{citation |author=Lorentz, H. A.|title=Considérations élémentaires sur le principe de relativité|date=1914 |journal=Revue générale des sciences pures et appliquées|pages=179-186|url=https://archive.org/details/revuegnraled25pari/page/178/mode/2up}}</ref> <ref name=bloch>See pp. 67 ff. in: {{Citation | author=Bloch, W.| date=September 1918|title=Einführung in die Relativitätstheorie| publisher=B. G. Teubner |url=https://hdl.handle.net/2027/njp.32101040276907}}</ref> <ref name=bloch2>See pp. 69ff. (special relativity) and 102ff. (general relativity) in: {{Citation | author=Bloch, W.| date=1920 |title=Einführung in die Relativitätstheorie (second edition)| publisher=B. G. Teubner |url=https://www.archive.org/details/einfhrungindier00blocgoog}}</ref> <ref name=bollert1>See p. 6 (special relativity), pp. 24-26 (EP) in: {{citation |author=Bollert, K.|title=Einstein’s Relativitätstheorie und ihre Stellung im System der Gesamterfahrung |date=April 1921|publisher=Steinkopff|url=https://archive.org/details/dbc.wroc.pl.001504}}</ref> <ref name=born>See pp. 190f. (special relativity), 250f (EP) in: {{Citation | author=Born, M.| date=1921 |title=Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Second edition)| publisher=Springer | place=Berlin|url=https://hdl.handle.net/2027/mdp.39015017387310}}; The [https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE5426498 first edition (1920)] of Born's book didn't include the twin paradox. English translation of the third edition by H. Brose (1924): [https://archive.org/details/einsteinstheoryo00born Einstein's theory of relativity]</ref> <ref name=pauli>See p. 558f (general description); p. 624f (proper time); p. 713f (accelerated frames); in: {{Citation |author=Pauli, W. |date=1921 |journal=Encyclopädie der Mathematischen Wissenschaften|title=Die Relativitätstheorie|pages=539–776|volume=5|issue=2 |url=http://resolver.sub.uni-goettingen.de/purl?PPN360709672}}; English translation by G. Field (1958): [https://books.google.com/books?id=rc3DAgAAQBAJ Theory of Relativity]</ref> <ref name=thirring>See p. 209ff in: {{citation |author=Thirring, H.|title=Über das Uhrenparadoxon in der Relativitätstheorie|date=April 1921|journal=Naturwissenschaften|volume=9|issue=18|pages=209-212|url=https://archive.org/details/sim_naturwissenschaften_1921-04-01_9_13/mode/2up}}</ref> <ref name=sommerfeld>See p. 71 in: {{citation |author=Sommerfeld, A. |date=May 1913|chapter=Remarks on Minkowski's "Space and Time"|title=Das Relativitätsprinzip|editor=Otto Blumenthal|pages=69-73|url=https://www.archive.org/details/dasrelativittsp00minkgoog}}</ref> <ref name=kopff>See pp. 45ff (special relativity and proper time); pp. 117ff (EP); pp. 189ff (Mach's principle), in: {{citation |author=Kopff, A.|title=Grundzüge der Einsteinschen Relativitätstheorie |date=February 1921|publisher=S. Hirzel|place=Leipzig|url=https://www.archive.org/details/grundzgedereins00kopfgoog}}; English translation by H. Levy (1923): [https://hdl.handle.net/2027/mdp.39015017188817 The mathematical theory of relativity].</ref> <ref name=becqu1>See p. 48ff (proper time), p. 240f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Le Principe de relativité et la théorie de la gravitation|Le Principe de relativité et la théorie de la gravitation]] |date=1922 |publisher=Gauthier-Villars|place=Paris}}; See also p. 57ff (proper time), p. 177f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Exposé élémentaire de la théorie d’Einstein et de sa généralisation|Exposé élémentaire de la théorie d’Einstein et de sa généralisation]]|date=1922 |publisher=Payot|place=Paris}}</ref> <ref name=nord>Discussion between Painlevé, Einstein, and Langevin on pp. 146ff in: {{citation |author=Nordmann, C.|title=[[s:fr:Einstein expose et discute sa théorie|Einstein expose et discute sa théorie]]|date=May 1922|journal=Revue des deux mondes|volume=IX|pages=129-166}}</ref> <ref name=lehm>{{Citation |author=Lehmann, Otto |orig-date=September 1910 |date=1911|title=Das Relativitätsprinzip der neue Fundamentalsatz der Physik |title-link=s:de:Das Relativitätsprinzip der neue Fundamentalsatz der Physik|journal=Verhandlungen des naturwissenschaften Vereins in Karlsruhe |volume=23 |pages=49-74}}</ref> <ref name=lech>See p. 19ff in: {{citation |author=Lechalas, G. |orig-date=Submitted December 1912|date=1913 |title=Le nouveau temps |journal=L’Année philosophique|volume=XXIII|pages=19-44|url=https://gallica.bnf.fr/ark:/12148/bpt6k255882z/f22.item}}</ref> <ref name=hunt>See pp. 494ff in: {{Citation|author=Huntington, E. V. |year=1912 |title=A new approach to the theory of relativity|journal=Philosophical Magazine |volume=23|pages=494-512|url=https://archive.org/details/londonedinburg6231912lond/page/494/mode/2up}}</ref> </references> ==Secondary sources== <references group=S> <ref name=miller>{{Citation |author=Miller, A. I. |date=1981 |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |place=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}; See section 7.4.13 (Langevin, Wiechert, Laue, Einstein), footnotes 29-34 of chapter 7 (Petzoldt, Sommerfeld, Bergson, Einstein)</ref> <ref name=lange>{{Citation|author=Lange, L.|date=1927|title=The clock paradox of the theory of relativity|journal=The American Mathematical Monthly|volume=34|issue=1|pages=22-30|jstor=2299914}}</ref> <ref name=pes>{{Citation |author=Pesic, P. |date=2003 |title=Einstein and the twin paradox |journal=European Journal of Physics |volume=24 |issue=6 |pages=585–590 |doi=10.1088/0143-0807/24/6/004}}</ref> <ref name=during>{{Citation |author=During, É. |date=2014 |title=Langevin ou le paradoxe introuvable |journal=Revue de métaphysique et de morale |volume=84 |pages=513-527 |doi=10.3917/rmm.144.0513|doi-access=free}}; See pp. 515f (Langevin), 520f. (Einstein, Laue, Weyl, Painlevé).</ref> <ref name=debs>{{Citation |author=Debs, T. A., & Redhead, M. L. |title=The twin paradox and the conventionality of simultaneity |date=1996 |journal=American Journal of Physics |volume=64|issue=1| pages=384-392 |doi=10.1119/1.18252}}</ref> <ref name=alizzi>{{Citation |author=Alizzi, A., Sen, A., & Silagadze, Z. K.|title=Do moving clocks slow down? |year=2022 |journal=European Journal of Physics |volume=43|issue=6|pages=065601 |doi=10.1088/1361-6404/ac93ca|arxiv=2209.12654}}; Appendix B with reference to Lange and Halsbury</ref> <ref name=beng>{{Citation |author=Benguigui, L. G. |date=2020 |title=A Tale Of Two Twins: The Langevin Experiment Of A Traveler To A Star |publisher=World Scientific|isbn=9789811219115}}; See early solutions (Einstein, Langevin, Lorentz, Born/Kopff) and the Bergson controversy. A shorter version appeared in {{arxiv|1212.4414}}.</ref> <ref name=rowe>{{Citation|author=Rowe, D. E.|date=2006|title=Einstein's allies and enemies: Debating relativity in Germany 1916–1920|journal=Interactions: Mathematics, Physics and Philosophy|pages=231-280|publisher=Springer|doi=10.1007/978-1-4020-5195-1_8}}; Covering the criticism of Gehrcke starting with 1912; discussion between Einstein and Gehrcke in 1914; Einstein's dialogue (1918) as response to antirelativists; the Weyland event in 1920 and Einstein's response.</ref> <ref name=weiss>Weiss, W. (Physics FAQ): [https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html The Twin Paradox: The Equivalence Principle Analysis]</ref> <ref name=cuvaj>{{Citation |author=Cuvaj, C. |date=1971 |title=Paul Langevin and the theory of relativity|journal=Japanese studies in the history of science|volume=10| pages=113-142|url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf}}</ref> <ref name=koks>Koks, D. (2018): [https://math.ucr.edu/home/baez/physics/Relativity/SR/sr-gr.html Physics FAQ: Where is the Boundary between Special and General Relativity?]</ref> </references> [[Category:History of special relativity]] [[Category:Paradoxes]] 5r159ytxbqnbzubv4c509685qwhiyzk 2834542 2834541 2026-09-26T10:19:44Z D.H 52339 2834542 wikitext text/x-wiki {| style="width:20%; font-size:13px;" align=right |{{../Other Topics (header)}} |} ==Early history of the twin paradox== {{Lorentzbox|Text={{center|Date of article creation: 9 November 2023; Last major revision: 26 September 2026}}}} a) When was the [[:w:twin paradox]] applied to life forms and human beings? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /><ref group=S name=during /> report that {{slink||Einstein 1911-HU}} discussed the aging of living organisms, and that {{slink||Langevin 1911-HU}} and {{slink||Wiechert 1911-HU}} explicitly discussed the aging of human beings. :*More details in sections {{slink||Human beings in 1911|Twins from 1911 to 1920}}, including newspaper articles from 1911 written by {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}} that clearly show that Einstein was the first to explicitly discuss the aging of human beings as well. b) Who was the first to formulate the principle of maximal proper time along straight worldlines, upon which differential aging in the standard twin paradox is based? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> mention Langevin (1911), Laue (1911). :*More details in section {{slink||Maximal proper time}} with the contributions of Langevin (1911), Wiechert (1911), Study (1911), Laue (1911-13). c) Who was the first to formulate [[w:Triangle inequality#Reversal in Minkowski space|inverse triangle inequality]] in Minkowski space, which represents the simplest version of the twin paradox? :*See details in section {{slink||Triangle inequality}} with the contributions of Robb (1914-20), Eddington (1922), Rogers (1922). d) Who was the first to show that any influence of proper acceleration on clocks can be neglected in the computation of the twin paradox from the viewpoint of the stay-at-home twin? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Einstein (1911), Laue (1913). :*More details in section {{slink||Negligibility of proper acceleration}} with the contributions of Einstein (1911), Wiechert (1911), Laue (1913), Lorentz (1913). e) Who was the first to introduce the three clock/brother example that completely removes acceleration from the clock/twin paradox? :*Historical accounts<ref group=S name=debs /><ref group=S name=alizzi /> date it back to Lange (1927) and Lord Halsbury (1957). :*More details in section {{slink||Relay (three brothers) experiment}} with the contributions of Grünbaum (1911) and Wiechert (1920-22). f) Who was the first to use acceleration as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref name=cuvaj group=S /><ref group=S name=pes /> mention Langevin (1911), Einstein (1918). :*More details in section {{slink||Acceleration as asymmetry indicator}} with the contributions of Langevin (1911), Sommerfeld (1913), Lorentz (1913), Einstein (1914-20). g) Who was the first to use different frame distribution as asymmetry indicator as an asymmetry indicator? :*Historical accounts<ref group=S name=miller /><ref group=S name=pes /> mention Laue (1911-13). :*More details in section {{slink||Frame distribution as asymmetry indicator}} with the contributions of Laue (1911-13), Bloch (1918). h) Who was the first to describe the perspective of the traveler? :*Historical accounts<ref group=S name=miller /><ref group=S name=beng /> mention Langevin (1911), Lorentz (1914), Einstein (1918). :*More details in section {{slink||Perspective of the traveler}} with the contributions of Langevin (1911), Lorentz (1913-14), Einstein (1918), Thirring (1921). i) Who was the first to describe a round-trip experiment in curved spacetime? :*See section {{slink||Curved spacetime}} with the contribution of Becquerel (1922). j) Who was the first to interprete the twin paradox in terms of an aether or absolute space? :*See section {{slink||Aether interpretations}} with the contribution of Langevin (1911), Wiechert (1911), Lechalas (1912). k) Who was the first to denote the round-trip experiment as paradoxical? :*Historical accounts<ref group=S name=miller /><ref group=S name=during /> point to Laue (1911). :*See section {{slink||Paradoxical?}} for details. l) Who was the first to misunderstand the twin paradox? :*See section {{slink||Misunderstandings}} with the contributions of Berg (1910), Wiechert (1911), Campbell (1911/12), Gruner (1912). m) What were Einstein's contributions? :*See section {{slink||Einstein's contributions}}. ==Human beings in 1911== {| class="wikitable" style="background-color:white;{{text default color}};" ![[w:Albert Einstein|Einstein]] |- |{{anchor|Einstein 1905}}In 1905<ref name=einstein05 /> he showed that a clock moving on a round-trip away from A and back along a polygonal or curved path, is retarded with respect to a clock stationary at A by approximately <math>\tfrac{1}{2}t(v/V)^{2}</math> at reunion. For example, a clock on the equator is retarded with respect to a clock on the pole. He described this consequence as being "peculiar" (German: eigentümlich). {{anchor|Einstein 1911-HU}}In a lecture given on January 1911<ref name=einstein11a /> (published in November), he extended this "funny" (German: drollig) experiment to living organisms: {| ! width=55% | Einstein wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Wenn wir z. B. einen lebenden Organismus in eine Schachtel hineinbrächten und ihn dieselbe Hin- und Herbewegung ausführen lassen wie vorher die Uhr, so könnte man es erreichen, dass dieser Organismus nach einem beliebig langen Fluge beliebig wenig geändert wieder an seinen ursprünglichen Ort zurückkehrt, während ganz entsprechend beschaffene Organismen, welche an den ursprünglichen Orten ruhend geblieben sind, bereits längst neuen Generationen Platz gemacht haben. Für den bewegten Organismus war die lange Zeit der Reise nur ein Augenblick, falls die Bewegung annähernd mit Lichtgeschwindigkeit erfolgte! | style="padding: 0px 20px 0px 20px;" |For example, if we put a living organism in a box and make it undergo the same back and forth movement as the clock before, we could achieve that this organism returns to its original location with arbitrary little change after a flight of arbitrary length, whereas completely identical organisms that remained at rest in the original location have long since made room for new generations. To the moving organism, the long journey was only a moment if the movement happened close to the speed of light! |} {{Lorentzbox|Text=Two participants of that lecture, {{slink||Lämmel 1911-HU}} and {{slink||Müller 1911-HU}}, report that Einstein also talked about the aging of ''human beings''.}} |- !{{anchor|Lämmel 1911-HU}}[[w:Rudolf Lämmel|Lämmel]] |- |He attended Einstein's 1911 lecture and gave a popular report about it in the Swiss newspaper "[[w:Neue Zürcher Zeitung|Neue Zürcher Zeitung]]" published on 28 April 1911,<ref name=lammel /> including additional details. Regarding the round-trip clock experiment he wrote: {| ! width=50% | Lämmel wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bewegt sich eine Uhr mit Lichtgeschwindigkeit längs einer Geraden, auf der gerichtete Uhren stehen, so scheint die bewegte Uhr, beurteilt vom Standpunkt der ruhenden aus, im oben stizzierten Sinn, stillzustehen. Kehrt die Uhr, nach einem Ruck, mit Lichtgeschwindigkeit wieder zurück zur Zentral-Uhr, so ist, nach Einstein, für den Beobachter bei der Zentral-Uhr die Sache so, als ob ein mit der bewegten Uhr mitgeführter Beobachter (samt dessen Uhr) nicht gealtert hätte. Hinge also des letzteren Alter von den Angaben des ruhenden Beobachters ab, so könnte der von einer großen Reise ins Weltall zurückkehrende Beobachter bei der Zentral-Uhr spätere Generationen antreffen – er selber hätte nicht gealtert. Welche Bedeutung diese ''ad absurdum'' geführte Gedankenspielerei etwa hat, läßt sich heute nicht absehen – vielleicht, ja wahrscheinlich ist sie ohne jeden Einfluß auf die tatsächlichen Verhältnisse. Aber man sieht dabei immerhin, daß die Physik imstande ist, die kühnsten Träume der Phantasie noch – zu überbieten. | style="padding: 0px 20px 0px 20px;" |Let a clock be moving at speed of light along a line on which regulated clocks are standing, then the moving clock's hand appears to be standing still (in the sense described above) as judged from the standpoint of the resting one. If the clock, after one jolt, comes back with light speed to the central clock, then according to Einstein the matter presents itself to the observer at the central clock, as if the observer comoving with the clock (together with his clock itself) hasn't been grown older. Thus if the age of the latter would depend on the indications of the resting observer, the observer returning from a great journey into space could meet later generations at the central-clock – he himself hasn't been grown older. The importance of this play of thought led ''ad absurdum'' cannot be seen today – maybe, or even probably, it is without any influence on the actual situations. Though at least one can see that physics is able to – surpass – even the boldest dreams and fantasies. |} Lämmel in December 1920 (published 1921)<ref name=lammel2 /> again alluded to Einstein's lectures in Zürich (possibly the one from 1911, and maybe also later ones), describing a discussion between himself and Einstein. After Einstein concluded that the travelers who came back after their journey will probably meet their former contemporaries as old men while they themselves could have been away for only a few years, Lämmel objected that this conclusion is only drawn with respect to rods and clocks, but not with respect to living beings. Einstein responded though, that all processes in the blood, in the nerves etc. are eventually periodical oscillations, i.e. motions. Yet to any such motion the relativity principle applies, thus the conclusion regarding the unevenly rapid aging it permissive. {{Lorentzbox|Text=While the official publication of Einstein's January lecture ({{slink||Einstein 1911-HU}}) mentions the aging of organisms, Lämmel recalls the reference to the aging of a human space traveler ("observer returning from a great journey into space"). This means that Einstein was the first to use human beings in the clock/twin paradox on January 16 which was first published by Lämmel on April 28, 1911. In comparison, {{slink||Langevin 1911-HU}} used space travelers in a lecture on April 10 with publication in July, and {{slink||Wiechert 1911-HU}} used space travelers in lectures held between March 25 and May 23 with publication in July/September. It seems very unlikely that before April 28, Lämmel became somehow aware of the content of Langevin's or Wiechert's lectures held a few weeks earlier, in order to use them in his description of Einstein's lecture.}} |- !{{anchor|Langevin 1911-HU}}[[w:Paul Langevin|Langevin]] |- |On 10 April 1911, published July 1911,<ref name=langevin1 /> he held a now famous lecture popularizing the clock/twin paradox which he derived from the proper time integral as described in {{slink||Langevin 1911-PT}}. He demonstrated that a moving radioactive sample of radium is less evolved and less aged and therefore more active at return then the ones that remained in the laboratory. He also used light signals and the Doppler effect to visualize the effect. The most famous part concerned his description of the aging of human space travelers: {| ! width=50% | Langevin wrote ! [[:s:Translation:The Evolution of Space and Time|English Wikisource translation]] |- | style="padding: 0px 20px 0px 20px;" |Cette remarque fournit le moyen, à celui d’entre nous qui voudrait y consacrer deux années de sa vie, de savoir ce que sera la Terre dans deux cents ans, d’explorer l’avenir de la Terre en faisant dans la vie de celle-ci un saut en avant qui pour elle durera deux siècles et pour lui durera deux ans, mais ceci sans espoir de retour, sans possibilité de venir nous informer du résultat de son voyage puisque toute tentative du même genre ne pourrait que le transporter de plus en plus avant. Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse. Revenu à la Terre ayant vieilli de deux ans, il sortira de son arche et trouvera notre globe vieilli de deux cents ans si sa vitesse est restée dans l’intervalle inférieure d’un vingt-millième seulement à la vitesse de la lumière. Les faits expérimentaux les plus sûrement établis de la physique nous permettent d’affirmer qu’il en serait bien ainsi. | style="padding: 0px 20px 0px 20px;" |This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. |} {{Lorentzbox|Text=Reading his lecture in full, one finds the word "paradoxical" only in relation to the constancy of light speed, not on relation to the round-trip clock experiment.}} |- !{{anchor|Wiechert 1911-HU}}[[w:Emil Wiechert|Wiechert]] |- |In lectures on 25 March and 23 May 1911, submitted July and published September 1911,<ref name=wiechert11 /> he described the round-trip clock experiment with two equal clocks regulated to the same rate and brought to the same pointer position, or by introducing the same chemical process two times, or by introducing ''two life forms that began their life at the same time''. At the end of his paper he applied this to human travelers: {| ! width=50% | Wiechert wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Nehmen wir aber wieder eine Relativgeschwindigkeit an, die bis auf 3 Proz. der Lichtgeschwindigkeit nahekommt, dann wird das Verhältnis der empfundenen Zeitlängen wie 4:1. Das Bild mag etwas weiter noch ausgemalt werden. Denken wir uns, daß ein Beobachter durch den Raum unseres Sternhimmels mit dieser Geschwindigkeit in einer Kreisbahn mit einem Radius von 16 Lichtjahren fährt, dann wird er nach unserer Zeitrechnung nach je 100 Jahren wieder an unserem Sonnensystem vorüberkommen. In seinem Gefährt wird dabei die Zentrifugalkraft so auf ihn einwirken, daß sie gemäß den Relativitätsgesetzen der Einwirkung der Schwerkraft auf uns Erdenbewohner gleich erscheint. Es sind also die wirkenden Kräfte nur so groß, daß der Phantasie die Möglichkeit geboten wird, den Reisenden als menschliches Wesen zu denken. Da hier dauernd <math>\sqrt{1-v^{2}/c^{2}}</math> ist, fließt die Eigenzeit für den Reisenden viermal langsamer dahin, als für die Bewohner der Gestirne. Wenn er also nach 100 unserer Jahre wieder zu unserem Sonnensystem zurückkehrt, wird er sich selbst nur um 25 Jahre gealtert fühlen. Erreicht er nach der Entwicklung seines Körpers und nach seiner Zeitempfindung ein Alter von 75 Jahren, so entspricht dies doch einer dreimaligen Wiederkehr zu unserem Sonnensystem, also 300 unserer Erdenjahre. | style="padding: 0px 20px 0px 20px;" |Yet if we again assume a relative velocity approximating the speed of light by 3 percent, then the ratio of the experienced duration of time becomes 4:1. This image can be further extended. Let's imagine that an observer travels with that velocity on a circular path at a radius of 16 light years through the space of our galaxy, then according to our time calculation he passes by our solar system every 100 years. In his vehicle the centrifugal force will act on him in such a way, that in accordance with the relativity laws it will appear to be equal to the force of gravity acting upon the inhabitants of Earth. Thus the acting forces are only thus big, in order to give our fantasy the possibility to imagine the traveler as a human being. Since we have <math>\sqrt{1-v^{2}/c^{2}}</math> throughout, proper time flows four times slower for the traveler than for the inhabitants of the stars. Thus when he comes back to our solar system after 100 of our years, he will feel to have aged only by about 25 years. If he reaches an age of 75 years according to the development of his body and his own time experience, then this corresponds to a threefold return to our solar system, i.e. 300 of our Earth years. |} {{Lorentzbox|Text=a) Wiechert (1915)<ref name=wiechert15 /> later provided a short historical survey of the clock/twin paradox. He referred to the fact that already {{slink||Einstein 1905}} considered the case of two clocks ("Einstein's clock experiment"), and even though [[w:Hermann Minkowski|Minkowski]] himself didn't consider the case, his proper time formula provides the result in a straight forward manner. The latter was done by himself in lectures on 25 March and 23 May 1911, as well as by Langevin published in July 1911. Wiechert pointed out that he himself and Langevin used "humorist" examples in order to clarify the situation: While Wiechert argued that one has to make a journey in order to stay young, Langevin argued that one has to romp about in a laboratory in order to stay young. Both of them used human beings, arguing that their physical and mental life should have been influenced in the same way as any other process in nature. b) The dates given by Wiechert (1915) are not complete. The correct ones are: *Langevin's lecture on 10 April 1911, published in July. *Wiechert's lectures on 25 March and 23 May 1911, submitted on July 26, published in September. *He was still unaware of Einstein's lecture from January 1911, published in November 1911.}} |- !{{anchor|Müller 1911-HU}}[[w:Fritz Müller-Partenkirchen|Müller]] |- |The freelance writer and law student Fritz Müller (who was later known as [[w:Fritz Müller-Partenkirchen|Müller-Partenkirchen]]) attended Einstein's lecture and wrote a popular report about it in the German newspaper "[[w:Berliner Tageblatt|Berliner Tageblatt]]" on 16th and 23rd October 1911,<ref name=muller /> in which he gave further details (compare with {{slink||Lämmel 1911-HU}}). Regarding the clock/twin paradox he wrote: {| ! width=50% | Müller wrote ! English translation |- | style="padding: 0px 20px 0px 20px;" |Zwei gleichgehende Uhren sollen je einen Beobachter haben und nebeneinander ruhen. Nun soll die eine mit ihrem Beobachter plötzlich mit Lichtgeschwindigkeit in den Weltenraum hinausreisen. Vorher haben die beiden vereinbart, sich alle Sekunden mit einem Lichtsignal die Zeit zu telegraphieren. [...] In unserem Grenzfall, wo die Reise mit Lichtgeschwindigkeit vor sich geht, müßte der ruhende Beobachter erklären, jene andere Uhr käme in der Zeit überhaupt nicht voran. Die Zeit stünde dort still. Tatsächlich kommen die Einsteinschen Gleichungen zu diesem Resultat. Für den mit der Uhr reisenden Beobachter, sagt Einstein, gelte dasselbe. Das heißt, im Urteil des Zurückbleibenden würde jener niemals alt. „Und wenn er auf einer gebrochenen Reiselinie wieder an seinen Ausgangspunkt zurückkehrte?" fragt man den Vortragenden in der Diskussion. – „So bliebe er in unserem Urteil so jung wie bei der Ausreise," erwidert Einstein mit vollem Ernst, „selbst wenn wir Zurückgebliebenen inzwischen Männer mit weißen Bärten geworden sind – die Gleichungen liefern für jede Richtung der Bewegung, auch für eine gebrochene Bewegung, unerschütterlich die selben Resultate." – Wir sehen einander an. Das klingt märchenhaft. Märchenhaft? Gewiß, die alten Märchen vom Mönch von Heisterbach, vom Rip van Winkle, von Urashima Taro steigen auf. Merkwürdig, wie die Volksphantasie bei den Deutschen, bei den Amerikanern, bei den Japanern in der gleichen Richtung gearbeitet hat – alle drei Märchen erzählen ja von Leuten, deren Leben still steht, viele hundert Jahre lang, während die andern altern. So fanden sie bei ihrer Rückkehr ein anderes Land und eine andere Generation. | style="padding: 0px 20px 0px 20px;" |Two synchronous clocks at rest next to each other, shall each be accompanied by an observer. Now one of them, together with its observer, suddenly travels into space at the speed of light. Previously, both have arranged that every second they telegraph their time to each other using light signals. [...] In our limiting case where the journey happens at light speed, the resting observer would have to declare that the other clock would not proceed in time at all. Time would stand still at this place. Einstein's equations indeed produce this result. As to the observer traveling with the clock, says Einstein, the same is true. That means in the judgment of the remaining one, the other one would never become old. Then the lecturer [i.e. Einstein] was asked in the discussion: "And if he comes back to his starting point on a curved travel path?", to which Einstein replied in full earnest: "Then in our judgment he would remain as young as he was at departure, even if we remaining ones became men with white beards in the meantime, the equations unshakably give the same result in every direction of motion, also for curved motion". We look at each other. That sounds fabulous. Fabulous? Of course, the old fairy tales of [[w:Heisterbach Abbey|w:The monk of Heisterbach]] or [[w:Rip Van Winkle]] or [[w:Urashima Tarō]] come forward. Strange, how the folk fantasy of the Germans, the Americans, the Japanese worked in the same direction, all three fairy tales indeed tell about people whose life stands still, many hundred years long, while the other ones grow old. Thus they found another country and another generation when they returned. |} {{Lorentzbox|Text=Müller's account confirms {{slink||Lämmel 1911-HU}} that Einstein indeed mentioned human beings, but his description also suggests that Einstein was the first to use mutually sent light signals. However, as this was published in October, it cannot be excluded that Müller's description of light signals was influenced by {{slink||Langevin 1911-HU}}, published in July, in which light signals were used as well.}} |} ==Twins from 1911 to 1920== We now provide a list of authors who employed ''twins'', i.e. ''two'' life forms or humans that initially were of ''same age'' when the round-trip began: {| class="wikitable" style="background-color:white;" |- ! Author !! Date !! Description |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> |1911 |Two life forms that begin their life at the ''same time'' (German: "Zwei Lebewesen [..] die ihr Leben gleichzeitig beginnen"), of which the moving one returns retarded in its progression with respect to the stationary one. |- |[[w:Paul Gruner|Gruner]]<ref name=gruner /> |1912 |Two persons of ''same age'' (French: "deux personnes du même âge"), of which the moving one returns less developed than stationary one. |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> |1913 |The moving life form returns younger than its ''former agemates'' (German: "ehemaligen Altersgenossen"). |- |[[w:Hermann Weyl|Weyl]]<ref name=weyl /> |Easter 1918 | {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Von zwei Zwillingsbrüdern, die sich in einem Weltpunkt A trennen, bleibe der eine in der Heimat (d. h. ruhe dauernd in einem tauglichen Bezugsraum), der andere aber unternehme Reisen, bei denen er Geschwindigkeiten (relativ zur »Heimat«) entwickelt, die der Lichtgeschwindigkeit nahekommen; dann wird sich der Reisende, wenn er dereinst in die Heimat zurückkehrt, als merklich jünger herausstellen denn der Seßhafte. |Suppose we have two twin-brothers who take leave from one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to “home”) that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home. |} {{Lorentzbox|Text=Weyl was the first to ''explicitly use twins'' in relation to the round-trip experiment. The fourth edition (1920) of that book was translated from German into English and French in 1922.}} |- |[[w:Albert Einstein|Einstein]]<ref name=einstein20 /> |1920/21 |{{Anchor|Einstein 1921-TW}} {| ! width=50% | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Trifft A wieder bei B ein, so kann es sich ereignen, daß der beharrende Zwilling inzwischen 60 Erdjahre alt geworden ist, während der zurückkehrende nur 15 Jahre zählt, oder sich gar noch im Säuglingsstadium befindet. [..] Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls -Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. |If A then returns to B, it may happen that the twin who stayed at home is now sixty years old, whereas the wanderer is only fifteen years of age, or is perhaps only an infant still. [..] In the case of these two twins, Einstein declared, we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures. |} {{Lorentzbox|Text=This was based on an interview of Einstein by Moszkowski. While the expression "clock paradox" was used since 1911/12 (see section {{slink||Paradoxical?}}), this seems to be the first time that it was rebranded as "twin paradox". The copyright mark indicates 1920, while the title page indicates 1921. The translation from German into English also appeared in 1921.}} |} ==Maximal proper time== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]] 1911 |{{anchor|Langevin 1911-PT}}In April 1911 (published July),<ref name=langevin1 /> he described the round-trip experiment without formulas using two portions of matter present at two events happening at the same place. The ''integration of proper time'' along the entire wordlines shows that the portion of matter that starts a closed cycle by receding and finally coming back, will have a ''smaller proper time'' than the one that stayed behind. In October 1911 (published 1912),<ref name=langevin2 /> Langevin again showed that the portion of matter that described a closed cycle will have a ''smaller proper time'' <math>R</math> than the one that stayed in an inertial frame, which is defined by the equation: :<math>\begin{matrix}V^{2}\left(t-t_{0}\right)^{2}=d^{2}-R\\ \left[d^{2}=\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}\right] \end{matrix}</math> |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> Lectures March-May 1911 submitted July published September |{{anchor|Wiechert 1911-PT}}Let two equal processes be observed in two equal material systems colocated in two moments (1) and (2), and let there velocities have been changed in arbitrarily different ways in the meantime. It follows that the ratio of advancement of those processes is given by the two intervals <math>\Delta\tau </math> of their respective ''proper times''. He concluded that any round-trip clock experiment can be easily comprehended from that theorem by computation. The corresponding integral is: :<math>\Delta\tau=\int_{1}^{2}d\tau=\int_{1}^{2}dt\sqrt{1-\frac{\mathfrak{v}^{2}}{c^{2}}}</math> |- |[[w:Eduard Study|Study]]<ref name=study /> June 1911 |Minkowski's concept of worldlines implies that the straight path between two points of the same worldline is the ''longest'' among all paths between those points, if the path length on a worldline is defined by the related proper time. {{Lorentzbox|Text=Study's book was purely mathematical without mentioning clocks or the round-trip experiment, alluding to his result only in a footnote.}} |- |[[w:Max von Laue|Laue]] 1911-13 |{{anchor|Laue 1911/12-PT}}In December 1911 (published 1912),<ref name=laue1 /> Laue showed without formulas that the round-trip experiment is represented by a curved worldline, which at worldpoint A decomposes into a row of curves, after which all of them will be re-united at worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the ''longest proper time.'' {{anchor|Laue 1912/13-PT}}In December 1912 (published 1913) in the second edition of this relativity book,<ref name=laue1 /> Laue described the proper time integral between events 1 and 2 of a slowly accelerated clock covering a broken line and a stationary clock covering a straight worldline. Of all worldlines covering 1 and 2, the straight line has the ''longest proper time''. Therefore the traveling clock in the round-trip experiment is retarded at reunion, because its curved worldline corresponds to a shorter proper time. This result he presented in terms of the following inequality, of which the right-hand side refers to the straight curve of the stationary clock, while all others possible curves are represented on left-hand side: :<math>\tfrac{1}{c}\int_{1}^{2}\sqrt{du^{2}-\left(dx^{2}+dy^{2}+dz^{2}\right)}<\tfrac{1}{c}\int_{1}^{2}du</math> {{Lorentzbox|Text={{anchor|Sommerfeld 1913-PT}}Similar treatments can be found in the textbooks of [[w:Arnold Sommerfeld|Sommerfeld]] (1913),<ref name=sommerfeld /> [[w:Hermann Weyl|Weyl]] (1918),<ref name=weyl /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Jean Becquerel|Becquerel]] (1922).<ref name=becqu1 />}} |} ==Triangle inequality== {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Alfred Robb|Robb]] 1914-1920 |{{anchor|Robb 1914-TR}}In 1914<ref name=robb1 /> he showed that there are three types of triangles formed by intervals in Minkowski space, depending on whether one deals with "separation lines" (spacelike intervals), "optical lines" (lightlike intervals), or "inertia lines" (timelike intervals representing the path of nonaccelerated particles defined by <math>{\scriptstyle \left(x_{1}-x_{0}\right)^{2}+\left(y_{1}-y_{0}\right)^{2}+\left(z_{1}-z_{0}\right)^{2}-c^{2}\left(t_{1}-t_{0}\right)^{2}<0}</math>). As to a triangle formed by inertia lines, he showed that the sum of a certain two sides is ''less'' than that of the third one. {{Lorentzbox|Text=So the triangle inequality derived from time-like intervals in Minkowski space is ''[[w:Triangle inequality#Reversal in Minkowski space|inverse]]'' to the inequality in Euclidean space. This inverse inequality directly represents the most simple variant of the twin paradox: the traveler follows two sides of the time-triangle, while the stay-at-home observer follows the third side indicating maximal proper time.}} [[File:RobbTriangle.svg|right|150px]] In 1920<ref name=robb2 /> Robb gave a numerical example of the triangle ABC with time-like intervals ("inertia lines") defined by coordinates :<math>\begin{matrix} & x & y & z & t\\ A\ & 0 & 0 & 0 & 0\\ B\ & 0 & 0 & 0 & 10\\ C\ & 4 & 0 & 0 & 5 \end{matrix}</math> which he plugged into :<math>\bar{s}^{2}=\left(t_{1}-t_{0}\right)^{2}-\left(x_{1}-x_{0}\right)^{2}-\left(y_{1}-y_{0}\right)^{2}-\left(z_{1}-z_{0}\right)^{2}</math> from which he obtained the sides AB=10, AC=3, CB=3 and the inequality <math>AC+CB<AB</math>. |- |[[w:Arthur Eddington|Eddington]]<ref name=edding2 /> 1922 |He distinguished between the "space-triangle" for spacelike intervals, and the "time-triangle" for time-like intervals. The latter is measured with a clock from A to B and from B to C, with the sum of those readings ''is always less'' than the reading of a clock measuring directly from A to C. In the ordinary space-triangle any two sides are together greater than the third side; in the time-triangle two sides are together ''less'' than the third side. |- |Rogers<ref name=rogers /> 1922 |He showed that the "pure time-triangle" C, A, B (in their proper time order) satisfies the relation <math>\cosh C=\tfrac{\alpha^{2}+\beta^{2}-\gamma^{2}}{2\alpha\beta}</math>, where <math>\cosh C</math> denotes the unit-scalar product of the vectors CA, CB, and <math>\alpha,\beta,\gamma </math> the real and positive intervals BC, CA, AB. Since <math>\alpha>\beta </math> and <math>\cosh C>1</math>, it follows that <math>\alpha>\beta+\gamma </math>. That is, "the greatest side of pure time-triangle is greater than the sum of the other two sides". It follows at once that the stationary value of the proper time integral is an "absolute maximum". |} ==Negligibility of proper acceleration== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |style="vertical-align:top" |[[w:Albert Einstein|Einstein]] 1905-1918 |In 1905,<ref name=einstein05 /> Einstein used velocity time dilation <math>\tau=t\sqrt{1-\left(\frac{v}{V}\right)^{2}}</math> to derive the retardation of a clock performing a round-trip with constant speed <math>v</math> along a polygonal path or a continuously curved line, without mentioning any influence of acceleration at turnaround. {{anchor|Einstein 1911-VA}} In 1911 (published 1912),<ref name=einstein3 /> Einstein said that special relativity doesn't say anything about what happened to the clock's pointer position during the acceleration that changes the clock's direction along the round-trip, yet the influence of this change must be getting smaller the longer the clock ''is moving uniformly'', i.e. the longer one chooses the dimensions of the path. {{anchor|Einstein 1912-VA}}In an unpublished manuscript on special relativity from 1912,<ref name=einst12manu /> he pointed out that any influence of acceleration during the round-trip experiment, can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygonal path. {{anchor|Einstein 1914a-VA}}In a letter from April 1914,<ref name=einstpetz /> Einstein showed that any ''finite'' acceleration at turnaround during the round-trip experiment can only influence the clock in a ''finite'' way, thus it can be neglected by minimizing the time of acceleration with respect to the time of uniform translation. So it ''must be concluded'' that the clock is retarded at reunion after traveling on a polygonal path. {{anchor|Einstein 1914b-VA}}During a conversation in May 1914,<ref name=rowe group=S /> Einstein is reported to have replied that the accelerations during the round-trip are "irrelevant for the amount of the time difference". (Compare with {{slink||Einstein 1914b-AC}}) {{anchor|Einstein 1918-VA}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918,<ref name=einstein18 /> Einstein pointed out that any effect of velocity changes at turnaround must be limited, thus the traveling clock must be retarded at reunion due to time dilation if one makes the path AB and back along the round-trip long enough. (Compare with {{slink||Einstein 1918-AC}}) |- |[[w:Emil Wiechert|Wiechert]]<ref name=wiechert11 /> 1911 |{{Anchor|Wiechert 1911-VA}}[[File:WiechertTwin.svg|110px|right]] He demonstrated that differential aging along the round-trip cannot be caused during the passage from one velocity to another (i.e. acceleration) at turnaround, because the same result also follows when ''both'' A and B experience the ''same velocity changes'' with respect to another frame, only with the difference that B has relative velocities <math>+u</math> and <math>-u</math> for a long time, while A is brought after a short time from relative velocity <math>+u</math> to relative rest at which it remains a long time, and then it is brought to relative velocity <math>-u</math> for a short time. {{Lorentzbox|Text=He was probably the first to use an example in which both accelerate with same magnitude.}} |- |[[w:Max von Laue|Laue]]<ref name=laue3 /> 1913 |{{anchor|Laue 1913-VA}}He showed that the problem of the influence of acceleration at turnaround in the round-trip experiment, can be eliminated by ''arbitrarily'' enlarging the time in inertial motion. {{Lorentzbox|Text=This is the same argument as given in {{slink||Einstein 1911-VA}}. The Einstein-Laue argument was also used by others such as [[w:Hans Thirring|Thirring]] (1921)<ref name=thirring /> or [[w:Max Born|Born]] (1921).<ref name=born />}} |- |[[w:Hendrik Lorentz|Lorentz]]<ref name=lorentz1 /> 1913 |He pointed out that any effect of acceleration on the traveling clock at turnaround, can be separated from the time dilation effect since only the latter depends on the distance traversed along the round-trip. {{Lorentzbox|Text=Similarly, [[w:Wolfgang Pauli|Pauli]] (1921) stated that the arising infinitesimal accelerations at turnaround are certainly independent of the total travel time and ''therefore easy to eliminate''.<ref name=pauli />}} |} ==Relay (three brothers) experiment== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:de:Fritz Grünbaum (Physiker)|Grünbaum]]<ref name=gbaum /> 1911 |He discussed a one-way time dilation experiment in which the first clock is set into motion from the origin and then moving to the second clock. He argued that one can avoid the problem of acceleration experienced by the first clock when set into motion, by replacing it with a ''third'' clock that is already in motion with constant velocity and is synchronized at the origin with the first clock. {{Lorentzbox|Text=While Grünbaum didn't discuss round-trip experiments, his introduction of a third clock in order to avoid acceleration is the basis of the three-brother experiment.}} |- |style="vertical-align:top"|[[w:Emil Wiechert|Wiechert]] 1920-1922 |In 1920 (published 1921),<ref name=wiechert20 /> Wiechert explained how to completely remove acceleration from the round-trip experiment: Bodies A, B, C move undisturbed and non-accelerated in different directions. A and B pass each other at time (1), B and C pass each other at a later time (2), and C and A finally pass each other at an even later time (3). So in this setup, the condition of C is the continuation of the condition of B. On any of the three bodies one can count the oscillations of light of a certain spectral-line, in which case relativity predicts that the ''combined sum of all oscillations'' on B+C is smaller than the number of oscillations on A alone. Wiechert also held that one can replace the light oscillations by the life functions of human-like beings which live on A, B and C. For instance, while the inhabitants of B+C only had time for one meal, there were arbitrarily many generations on A who follow after each other by death and birth. [[File:Wiechert1922a.png|180px|right]] In 1921 (published 1922),<ref name=wiechert21 /> Wiechert extended his previous acceleration-free round-trip experiment to an arbitrary number of non-accelerated bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., which constitutes a "relay" (German: Stafette) starting from body A and back again. The first B passes A and moves away, and after some time the last B comes back to A. Since any B body continues the fate of the previous one, all bodies <math>B_{1}</math>, <math>B_{2}</math>, ..., combined have emitted fewer oscillations than A alone during the relay race. Wiechert pointed out that instead of light oscillations one can also choose the aging of life forms. {{Lorentzbox|Text=Such relay experiments were later independently rediscovered in English language papers<ref name=debs group=S /> such as by Lange (1927)<ref group=S name=lange /> in which the brothers synchronize their times when they pass each other (“three brother experiment”).}} |} ==Acceleration as asymmetry indicator== While it was known that any direct influence of [[w:proper acceleration]] on clocks can be neglected in the computation of the inertial frame of the stay-at-home twin (see previous section {{slink||Negligibility of proper acceleration}}), the very fact that only one of them is accelerating is still useful as an asymmetry argument in order to show that there is no contradiction to the relativity principle. {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{Anchor|Langevin 1911-AC}}He derived differential aging in the round-trip experiment using the proper time integral along worldlines (see {{slink||Langevin 1911-PT}}) and used acceleration as an asymmetry indicator: The result of the round-trip experiment is "another example of the absolute character of acceleration" in which the "asymmetry occurred because only the traveler, in the middle of his journey, has undergone an acceleration that changes the direction of his velocity". |- |[[w:Arnold Sommerfeld|Sommerfeld]]<ref name=sommerfeld /> 1913 |After he showed (see {{slink||Sommerfeld 1913-PT}}) that retardation of time in the round-trip experiment derived from the proper time integral rests on the assumption that the clock's rate ''only depends on its momentary velocity'' (now called "clock hypothesis"), he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle since one of the clocks has to be accelerated in order to come back, thus the retardation in the round-trip experiment does not demonstrate "motion", but "accelerated motion". |- |[[w:Hendrik Lorentz|Lorentz]] 1913<ref name=lorentz1 /> |After he derived differential aging in the round-trip experiment from velocity time dilation and pointed out the negligibility of proper acceleration for the computation, he used acceleration as an asymmetry indicator: There is no contradiction to the relativity principle, since one of them changes velocity and accelerates; the relativity principle does not require symmetry between inertial and non-inertial observers. |- |style="vertical-align:top"|[[w:Albert Einstein|Einstein]] 1914-1920 |{{anchor|Einstein 1914b-AC}} During a conversation in 1914,<ref name=rowe group=S /> Einstein is reported to have said that moving clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are ''irrelevant'' for the ''amount'' of the time difference, their ''presence'' nevertheless cause B to fall behind ("accelerated motions are absolute"). {{anchor|Einstein 1918-AC}}In his famous "Dialog about Objections against the Theory of Relativity" from 1918<ref name=einstein18 />, Einstein pointed out the negligibility of velocity changes from the viewpoint of an inertial frame (see {{slink||Einstein 1918-VA}}). Then he used ''acceleration as an asymmetry indicator'' in order to show, that there is no contradiction to the relativity principle, because relativity only predicts the equivalence of non-accelerated inertial frames: "only K is such a frame while K' is temporarily accelerated, thus the retardation of U2 with respect to U1 cannot be used to construe a contradiction against the theory." {{anchor|Einstein 1920-AC}}Einstein is reported to have said in an interview from 1920:<ref name=einstein20 /> {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" |Bei diesen Zwillingen, erklärte Einstein, haben wir zunächst eine ''Gefühls-Paradoxie'' vor uns. Eine ''Denk-Paradoxie'' würde indeß nur dann vorliegen, wenn sich für das Verhalten der beiden Geschöpfe kein zureichender Grund anführen ließe. Dieser Grund für das Jüngerbleiben des A ergibt sich vom Gesichtspunkt der speziellen Relativitätstheorie aus der Tatsache, daß das betreffende Geschöpf — und nur dieses — Beschleunigungen erlitten hat. | style="padding: 0px 20px 0px 20px;" |In the case of these two twins," Einstein declared, "we have merely a paradox of ''feeling''. It would be a paradox of ''thought'' only if no sufficient ground could be suggested for the behaviour of these two creatures . This ground, which counts for the comparative youth of A, is given, from the point of view of the special theory of relativity, by the fact that the creature in question, and only this creature, has been subject to accelerations." |} In a discussion from 1922,<ref name=morand /> Einstein is reported to have said that there is no contradiction in the round-trip experiment (in terms of a train leaving the station and returning later): The relativity principle is not applicable to this case, because the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two frames having velocities in opposite direction is not an inertial frame. There is no reciprocity between a frame that changes direction and one that doesn't. |} ==Frame distribution as asymmetry indicator== Because any direct influence of proper acceleration on the traveling clock at turnaround can be neglected (see {{slink||Negligibility of proper acceleration}}), the importance of {{slink||Acceleration as asymmetry indicator}} is limited to the mere fact that it reveals that only the traveler was in a non-inertial frame as only he changed his inertial frames, thus instead of emphasizing the occurrence of proper acceleration at turnaround, it's possible to describe the asymmetry more geometrically by emphasizing the different distribution of inertial frames of the twins along their worldlines. {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |style="vertical-align:top"|[[w:Max von Laue|Laue]] 1911-1913 |{{Anchor|Laue 1911/12-VA}} In 1911/12,<ref name=laue1 /> he pointed out that during the time of separation, that clock is most advanced which was at rest in an inertial frame all the time; namely there is ''always one, and only one inertial frame'', in which the locations of separation and re-encounter lie in the same geometric point. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1911/12-PT}}). In 1912/13,<ref name=laue2 /> he argued that in the round-trip experiment, we indeed can decide, which one of the clocks was steadily at rest in one and the same reference system, and which one was in the meantime at rest in two or more such systems. Among them there is of course a real physical difference. He clarified this fact by alluding to different paths in spacetime (compare with {{slink||Laue 1912/13-PT}}). In 1913<ref name=laue3 /> Laue pointed out: {| !style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Aber nach unseren Voraussetzungen ruht während der Zeit der Trennung die erste Uhr in ''einem'' berechtigten Bezugssystem, die zweite hingegen ruht zwar sowohl bei der Hin- wie bei der Rückbewegung in berechtigten Bezugssystemen, aber notwendig in ''zwei verschiedenen. Deshalb'' unterscheiden sich beider Schicksale physikalisch. Ließe man die zweite Uhr in der ihr anfangs erteilten Bewegung und schickte man ihr dafür die erste Uhr nach einiger Zeit mit größerer Geschwindigkeit nach, so würde beim Zusammentreffen die erste gegen die zweite zurückgeblieben sein; denn jetzt hat die erste während der Trennung in zwei verschiedenen Systemen geruht. (Footnote: Dem naheliegenden Einwand, daß wir über den Gang einer Uhr während eines Geschwindigkeits''wechsels'' nichts aussagen können, begegnet man am einfachsten mit dem Hinweis, daß man die Zeiten der gleichförmigen Bewegung ''beliebig'' groß gegen die der Beschleunigung machen kann.) | style="padding: 0px 20px 0px 20px;" | However, by our presuppositions, one clock is at rest in ''one'' valid reference system during the time of separation, while the second one is at rest in valid reference systems both during the forward- and the backward motion, but necessarily in ''two different ones. Therefore'' the two fates differ physically. If the second clock remains in the motion which was given to it at the start, and if after some time it is followed by the first clock with greater velocity, then the first one would be retarded with respect to the second one at the encounter; since now it was the first one that was at rest in two different systems during the separation. (Footnote: The objection which is near at hand, that we cannot say anything about the rate of a clock during a velocity ''change'', can be met most simply by the allusion, that we can render the times of uniform motion ''arbitrarily'' great with respect to acceleration..) |} |- |[[w:Werner Bloch|Bloch]]<ref name=bloch /> September 1918 |{{anchor|Bloch 1918-VA}} He represented the frames with three movable slots K, K' and K”, provided with hooks on which one can hang clocks at the origins of K and K'; while one clock always hangs on a hook of slot K, the other clock moved away with K' and after some time was transferred (neglecting any effect of acceleration) by a mechanical device to slot K” that moves in the other direction, by which it comes back; there is no contradiction to the relativity principle, as one clock rested in one inertial frame while the other one rested in two such frames. |} ==Perspective of the traveler== {| class="wikitable" style="background-color:white;" |- ! Author !! Early examples |- |[[w:Paul Langevin|Langevin]]<ref name=langevin1 /> 1911 |{{anchor|Langevin 1911-LI}}[[Image:rstd4.gif|170px|right]] After deriving differential aging from the proper time integral in {{slink||Langevin 1911-PT}} and using human beings in {{slink||Langevin 1911-HU}}, he described the perspectives of both observers using light signals and the Doppler effect. When they separate they see each other live 200 times slower, while at return they see each other live 200 times faster. So ''from the explorer's viewpoint'', in the first year he sees the Earth perform the actions of two days, while in the second year he sees the Earth perform the actions of two centuries. The asymmetry can be seen by noticing, that the observer on Earth in 200 years sees the explorer performs the actions of 1 year. Then the explorer turns around, after which the observer on Earth in 2 days sees the projectile perform the actions of another year. {{Lorentzbox|Text=Langevin used <math>v=c\left(1-\tfrac{1}{20000}\right)</math>, producing Lorentz factor <math>\gamma\approx100</math> and Doppler factor <math>\sqrt{\tfrac{c+v}{c-v}}\approx200</math>.}} |- |[[w:Hendrik Lorentz|Lorentz]] Lectures published in 1913<ref name=lorentz1 /> Similar treatment in 1914<ref name=lorentz3 /> |{{anchor|Lorentz 1913/14-LI}}Described the round-trip experiment in terms of inertial observer A (equipped with clock K) and traveling observer B (equipped with clock K'). In the frame of A, clock K' is retarded with respect to K at reunion due to time dilation. He then described the perspective of the traveling observer B by using two-way propagation of light from K' to K and back to K', leading to three periods defined by the moment of B's turnaround: In the first period the light signals return to K' before turnaround; in the second period the signals are emitted before turnaround and return after turnaround; in the third period emission and return of the signals are both happening after turnaround. Lorentz showed that K is time dilated by a factor of <math>\sqrt{1-v^{2}/c^{2}}</math> with respect to K' in the first and third period, but in the second period K is ticking ''faster'' than K' by a factor of <math>\sqrt{\tfrac{c+v}{c-v}}</math> which overcompensates the dilation in the other periods and explains, even from the perspective of B, why K' is retarded with respect to K at reunion. {{Lorentzbox|Text=In a review of the German translation of Lorentz's book, Einstein (1914) didn't directly mention Lorentz's treatment of the twin paradox, but he wrote that nobody who is seriously interested in relativity should neglect to read that book.<ref name=einstlor /> [[w:Wolfgang Pauli|Pauli]] (1921) refers to Lorentz's book as one of three papers that analyze the twin paradox more closely.<ref name=pauli />}} |- |style="vertical-align:top"| [[w:Albert Einstein|Einstein]] 1916-1920 |{{anchor|Einstein 1916-EP}}In a lecture from 1916,<ref name=einstein16 /> of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of [[w:general relativity]]." {{anchor|Einstein 1918a-EP}}In a letter from September 1918,<ref name=einadl /> Einstein showed that general relativity makes the inertial frame K and and the accelerated frame K' of the clocks in the round-trip experiment "equally justified", explaining the time difference in K' by combining the influence of velocity and gravitational potential on clocks. {{anchor|Einstein 1918-EP}}In his famous "Dialog about Objections against the Theory of Relativity" from November 1918,<ref name=einstein18 /> aimed at clarifying misconceptions of the clock paradox, he explained that there is no paradox in special relativity because there is no symmetry between clock U1 at rest in inertial frame K and clock U2 at rest in accelerated frame K' (see {{slink||Einstein 1918-AC}}). Yet [[w:general relativity]] and the [[w:equivalence principle]] allow the treatment of this problem also from the standpoint of frame K', where clock U2 remains at rest all of the time while U1 makes the following movements: (1) It is accelerated by a homogeneous gravitational field in the negative direction, (2) it moves with constant velocity <math>-v</math>, (3) it is accelerated in the positive direction until it turns around and comes by with constant velocity <math>+v</math>, (4) it moves with velocity <math>+v</math>, (5) it is accelerated in the negative direction until it stops. Clock U1 is retarded with respect to U2 in periods 2) and 4) due to velocity time dilation, but this retardation is overcompensated by the faster rate of U1 during period 3), because U1 is at a higher gravitational potential. He argued that the computation (which he didn't provide) shows that the advance of U1 in period 3) is double its retardation during periods 2) and 4). Einstein concluded that by this consideration "the paradox is completely resolved". Using [[w:Mach's principle]], he pointed out that the gravitational field in K' might be induced by the masses of the universe that are accelerated in this frame. {{anchor|Einstein 1918b-EP}}In a letter to Einstein from December 1918, [[w:Max Jakob|Jakob]] doubted the result that the advance in period 3) is double the retardation during periods 2) and 4). Einstein responded by letter,<ref name=einstein18b /> in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). {{anchor|Einstein 1921-EP}}Einstein is reported to have said in an interview from 1920,<ref name=einstein20 /> that while acceleration explains the age difference between the stationary twin B and the traveling twin A in terms of special relativity (see {{slink||Einstein 1920-AC}}), the "proper" description in terms of general relativity is as follows: {| ! style="width:50%" | German original ! English translation |- | style="padding: 0px 20px 0px 20px;" | Eine tiefere Erfassung des Grundes ist indeß nur auf dem Boden der „Allgemeinen Relativitätstheorie" zu erlangen, die uns erkennen läßt, daß von A aus beurteilt ein Zentrifugalfeld existiert, von B aus betrachtet aber nicht; und dieses Feld hat einen Einfluß auf den relativen Ablauf und die Raschheit der Lebensvorgänge. | style="padding: 0px 20px 0px 20px;" | A proper grasp of the reason is furnished only when we adopt the general theory of relativity, which tell us that, from the point of view of A, a centrifugal field exists, whereas it is absent from the point of view of B. This field exerts an influence on the relative rate of happening of the events of life." |} {{Lorentzbox|Text=a) Einstein's explanation was quickly adopted in the textbooks of [[w:Werner Bloch|Bloch]] (1920),<ref name=bloch2 /> [[w:Wolfgang Pauli|Pauli]] (1921),<ref name=pauli /> [[w:August Kopff|Kopff]] (1921),<ref name=kopff /> [[w:Karl Bollert|Bollert]] (1921),<ref name=bollert1 /> [[w:Max Born|Born]] (1921),<ref name=born /> expressing the view that general relativity is "necessary" to provide the "complete" solution of the twin paradox. b) From a modern standpoint, however, Einstein's explanation has nothing to do with general relativity, but is rather an application of accelerated frames and "pseudo"-gravitational fields to flat Minkowski space of ''special'' relativity.<ref name=weiss group=S />}} |- |[[w:Hans Thirring|Thirring]]<ref name=thirring /> April 1921 |{{anchor|Thirring 1921-DS}}[[Image:Twin Paradox Minkowski Diagram.svg|right|200px]] He described the round-trip experiment by using two platforms K (clock A) and K' (clock B) each equipped with rows of clocks. He first demonstrated the symmetry of time dilation and the mutual relativity of simultaneity on the platforms and its effect on clock synchronization. The K clocks that B passes are all advanced because of <math>t'=\gamma\left(t-vx/c^{2}\right)</math>, and the same is true after turnaround since only the direction of velocity has to be changed in the Lorentz transformation <math>t'-t'_{0}=\gamma\left(t+vx/c^{2}\right)</math> leading to the effect of clock desynchronization, where <math>t'_{0}</math> is a constant depending on which clock one uses as standard for the new synchronization. He graphically showed using Minkowski diagrams, that this simultaneity jump due to desynchronization amounts to double the velocity time dilation during the inertial phases, explaining why A is more advanced than B at reunion. {{Lorentzbox|Text=Using clock B as synchronization standard, Thirring's constant is given by <math>t'_{0}=2l\gamma v/c^{2}=2t\gamma v^{2}/c^{2}</math> with <math>l=vt</math> as position of turnaround. A similar explanation was subsequently given by Langevin (1922).<ref name=morand />}} |} ==Curved spacetime== While the previous examples are defined in flat Minkowski spacetime and therefore can be fully discussed in terms of special relativity, [[general relativity]] is required when [[:w:spacetime curvature]] in the presence of mass and energy cannot be neglected any more.<ref name=koks group=S /> {| class="wikitable" style="background-color:white;{{text default color}};" |- ! Author !! Early examples |- |[[w:Jean Becquerel|Becquerel]]<ref name=becqu1 /> 1922 |After defining gravitational time dilation <math>d\tau=\sqrt{1-\tfrac{2GM}{c^{2}r}}dt</math> in terms of the [[w:Schwarzschild metric]] around a material center, he discussed the following round-trip experiment: There are two identical clocks A and B placed next to each other, at a point very far from the material center, initially marking the same time <math>t</math>. Let us transport clock A to a point where the field is more intense, at a distance <math>r</math> from the center; this clock will measure time <math>\int d\tau</math> which is shorter than <math>\int dt</math>, thus it will run more slowly. If we bring clock A back to clock B, we will have to note that it is retarded with respect to B. |} ==Aether interpretations== [[w:Lorentz ether theory]] (LET) is empirically equivalent to special relativity since both models use the Lorentz transformation, thus the description of the twin paradox gives the same result as well. However, special relativity is preferred by the scientific community, because of the validity of the relativity principle in LET is only apparent due to a conspiracy of effects which makes the aether undetecable, and because the measured times and lengths in the aether are supposedly be giving the "true" values even though it is empirically impossible to determine which ones are true or apparent. {| class=wikitable style="background-color:white;{{text default color}};" |- ! style="width:150px" | Author !! Description |- |Langevin (1911)<ref name=langevin1 /> |He argued that it's true that uniform translation with respect to the aether has no experimental meaning in special relativity, though one can still speak of "absolute acceleration" with respect to an aether which he defined as the light carrying medium, so it was "premature to abandon the aether". The absolute nature of acceleration can be seen in the radiation of accelerated charges, as well as in the twin paradox in which the traveler that is more agitated or accelerated is younger at reunion. {{Lorentzbox|Text=Langevin didn't mention this aether interpretation in his later discussions of the twin paradox in 1911/12<ref name=langevin2 /> and 1919.<ref name=langevin3 />}} |- |style="vertical-align:top" |{{Anchor|Wiechert 1911b}}Wiechert (1911)<ref name=wiechert11 /> |Contrary to Langevin's emphasis on accelerations, Wiechert emphasized that differential aging can solely be attributed to the existence of ''absolute velocities'' which he called "strides" (German: Schreitungen, denoting the "absolute meaning" of non-accelerated motions) with respect to the aether. In other words, the clock's "strides" are not equivalent or anisotropic with respect to the aether, in contradiction to the "unconditional" relativity principle Einstein's which requires equivalence and symmetry. Wiechert proposed a "conditional" relativity principle in which the aether (in the sense of Lorentz) determines all processes in nature, thus the rate of clocks or processes is "really" altered during motion. {{Lorentzbox|Text=a) This aether interpretation was maintained by Wiechert also in subsequent publications in 1915-1922.<ref name=wiechert15 /><ref name=wiechert20 /><ref name=wiechert21 /> b) Wiechert's interpretation in terms of absolute non-accelerated motions was also independently given by others: [[s:fr:Georges Lechalas]] (1912/13)<ref name=lech /> argued that time dilation and asymmetric aging are the result of absolute speeds with respect to an aether, while criticizing Langevin's (1911) argument that only accelerations can indicate the aether and are responsible for the asymmetric aging; [[w:Edward Vermilye Huntington]] (1912)<ref name=hunt /> argued that the "famous paradoxes of the theory of relativity" represented by the reciprocal nature of length contraction and time dilation, appear as necessary consequences of perfectly natural and reasonable conventions for setting clocks and laying out coordinates, when the Lorentz transformation is derived and interpreted on the basis of a stationary aether in the sense of Lorentz. c) Laue (1911/12)<ref name=laue1 /> applauded Wiechert for the "particularly striking way" in which he demonstrated that asymmetric aging indeed follows from the relativity laws, yet he rejected Wiechert's aether interpretation and Wiechert's claim that asymmetric aging contradicts the "unconditional" relativity principle: Laue pointed out that the straight worldline connecting two events A and B is only "preferred" insofar as it indicates the maximal proper time between them, yet this preference is ''not'' the result of the natural laws employed, but is rather due to the choice of points A and B; by analogy, the geometric result that two points determine a straight line and thus a direction as well, doesn't refute the physical equivalence of all directions in space; finally, as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.}} |} ==Paradoxical?== Even though Einstein (1905)<ref name=einstein05 /> denoted the round-trip experiment as "peculiar" (German: eigentümlich) he saw nothing contradictory in it. Without mentioning the round-trip experiment, [[w:Paul Gruner]] in May 1910<ref name=gruner10 /> denoted the effect that clocks in relative motion are not showing the same time when they meet as the "great paradox" of relativity (German: Grosse Paradoxie), and [[w:Max von Laue]] in May 1911<ref name=laue0 /> wrote that some consequences of the relativity of time occasionally indeed look "paradoxical" (German: paradox). Eventually, Laue in November 1911 (published 1912)<ref name=laue1 /> was the ''first to specifically denote the round-trip experiment'' as a "paradox" (German: Paradoxie): {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" | German original of [[w:Max von Laue|Laue]] (1911/12):<ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> ! English translation |- |Unter all den paradox erscheinenden Folgerungen aus der Zeittransformation der Relativitätstheorie gibt es wohl keine, gegen welche sich der natürliche Menschenverstand bei jedem, der der Sache noch ungewohnt ist, so sehr sträubt, wie gegen die, daß die Zeitangabe einer Uhr von ihrem Bewegungszustand abhängen soll. Schon in seiner grundlegenden Arbeit hat Einstein diese Paradoxie auf die Spitze getrieben in einem Gedankenexperiment, welches neuerdings von Langevin in einem auch sonst sehr lesenswerten Vortrage besonders hübsch erläutert worden ist. |Of all apparently paradox consequences that stem from the time-transformation of the theory of relativity, there is probably none against which the common sense of anyone who is still unfamiliar with the matter is more reluctant, than the one according to which the time indication of a clock shall be dependent on its state of motion. Already in his fundamental paper, Einstein has driven this paradox to the extreme by a thought experiment, recently explained in a very nice way by Langevin in a lecture that is also very readable in other respects. |- |colspan=2|{{Lorentzbox|Text=Subsequently, [[w:Paul Gruner]] (1912)<ref name=gruner /> and others including Einstein (1918)<ref name=einstein18 /> explicitly used the expression "clock paradox" (French: Paradoxe des horloges, German: Uhrenparadoxon), whereas [[w:Rudolf Seeliger]] (1913)<ref name=seel /> spoke of the "familiar Einstein-Langevinian paradox" (German: "bekannte Einstein-Langevinsche Paradoxon").}} |} ==Misunderstandings== {| class=wikitable style="background-color:white;{{text default color}};" ! style="width:50%" padding=10 | German original by [[w:Otto Berg (scientist)|Berg]] (1910):<ref name=berg /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |Im Punkte <math>x = 0</math> des Systems S befinde sich eine Uhr, eine andere im Punkte <math>x'=0</math> von S'. Diese zweite bewege sich mit S' bis zum Punkte <math>x = a</math>, kehre dort um und bewege sich nun mit der Geschwindigkeit <math>v</math> zurück bis zum Punkte <math>x= 0</math>. Welche Zeit müssen beide Uhren in dem Moment angeben, wo sie sich wieder treffen? Wir beantworten diese Frage zunächst vom Standpunkt des Beobachters in S. Die Uhr in <math>x' = 0</math> hat sich mit der Geschwindigkeit <math>v</math> bis zum Punkte <math>x = a</math> bewegt; dazu brauchte sie die Zeit <math>\tau=\tfrac{a}{v}</math>. Zum Rückweg ist dieselbe Zeit nötig. Nach der Zeit <math>2\tau=2\tfrac{a}{v}</math> ist die Uhr also wieder im Punkte <math>x = 0</math> angelangt. Wir stellen uns nun auf den Standpunkt des Beobachters in S'. Für diesen führt nach dem Relativitätsprinzip das System S genau dieselben Bewegungen aus wie das System S' für den Beobachter in S, nur in entgegengesetzter Richtung. Die Zeit bis zum Zusammentreffen beider Uhren ist also im System S' ebenfalls gegeben durch <math>2\tau=2\tfrac{a}{v}</math>. Betrachtungen, die auf anschauliche Vorstellungen, wie Nachgehen von Uhren, gestützt sind, führen hier leicht zu Irrtümern, von denen auch die Fachlitteratur nicht frei ist. | style="padding: 0px 20px 0px 20px;" |There is a clock at point <math>x=0</math> of system S, and another one at point <math>x'=0</math> of S'. The second one moves together with S' until point <math>x=a</math>, turns around and now moves back with speed <math>v</math> to point <math>x=0</math>. Which time must both clocks indicate at the moment at which they encounter again? We answer this question at first from the standpoint of the observer in S. The clock at <math>x=0</math> has been moving with speed <math>v</math> until point <math>x=a</math>, for which it required time <math>\tau=\tfrac{a}{v}</math>. The same time is required for the way back. After time <math>2\tau=2\tfrac{a}{v}</math> the clock has thus arrived again at point <math>x=0</math>. Let's now take the standpoint of the observer in S'. In his view in accordance with the relativity principle, system S is conducting exactly the same motions as those of system S' with respect to the observer in S, only in opposite direction. Thus the time until the meeting of both clocks is given by <math>2\tau=2\tfrac{a}{v}</math> in system S' as well. Considerations based on illustrative notions, such as the retardation of clocks, easily lead to mistakes at this place, of which also the professional literature isn't free. |- |colspan=2|{{Lorentzbox|Text=a) Berg was probably the first to turn the relativity principle against asymmetric aging in the round-trip experiment, claiming that both clocks must indicate the same time at reunion. See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem. b) Berg's mistake also seems to be based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" padding=10 | German original by [[w:Otto Lehmann (physicist)|Lehmann]] (1910/11):<ref name=lehm /> ! English translation |- | style="padding: 0px 20px 0px 20px;" | Hat man zwei genau gleich gehende Uhren nebeneinander und bewegt nun die eine auf einer beliebigen Kurve bis wieder zur anderen zurück, welche Bewegung <math>t</math> Sekunden gedauert haben möge, so geht sie gegen diese um <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> oder annähernd <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> Sekunden zu spät, weil sie während der Bewegung auf langsameren Gang reguliert werden mußte, um mit der ruhenden Uhr in Übereinstimmung zu bleiben. | style="padding: 0px 20px 0px 20px;" | If there are two exactly identical clocks next to each other, and if one of them will be moved on an arbitrary curve until it comes back, which may have lasted <math>t</math> seconds, it [the moving clock] will lag behind the other one by <math>\left(1-\sqrt{1-\tfrac{v^{2}}{c^{2}}}\right)t</math> or approximately <math>\tfrac{1}{2}t(^{v}/_{c})^{2}</math> seconds, because it [the moving clock] had to be regulated to a slower rate during motion in order to remain synchronous with the resting clock. |- |colspan=2|{{Lorentzbox|Text=a) So Lehmann erroneously thinks that the time difference at reunion is only the result of "regulating" the moving clock. This implies that he (like Berg) believed that special relativity predicts ''equal'' clock times at reunion if the moving clock would have been left ''unregulated'' during the round-trip. b) Lehmann's mistake (similar to Berg) seems to based on the fact, that in his paper he generally described time dilation and length contraction of special relativity as only being "apparent" as opposed to Lorentz's theory.}} |- ! style="width:50%" | German original by [[w:Emil Wiechert|Wiechert]] (1911)<ref name=wiechert11 /> ! English translation |- |colspan=2| Even though he correctly derived differential clock aging in the round-trip experiment, he (like Berg and Lehmann) claimed that effects like time dilation are "apparent" if one admits Einstein's "unconditional" relativity principle in which there is no aether and all "strides" (i.e. non-accelerated motions) are physically equivalent, but they are "real" if one admits the existence of an aether in the framework of a "conditional" relativity principle in which all strides are physically non-equivalent or anisotropic. This led him to the following interpretation of the clock paradox: |- | style="padding: 0px 20px 0px 20px;" |[...] so muß am Schluß des Versuches B in seinem Fortschritt gegenüber A im Verhältnis <math>1:\sqrt{1-u^{2}/c^{2}}</math> zurückgeblieben sein. Und dieses Zurückbleiben ist unbedingt reell, denn die beiden Gebilde A und B können ja unter gleichen Umständen unmittelbar beieinander verglichen werden. Hier ist es ganz sicher ausgeschlossen, an einen Schein zu glauben, der durch unsere Auffassung der Zeit bewirkt wird. So ist denn also auch die Folgerung unabwendbar, daß für den Verlauf der Weltvorgänge die Schreitungen nicht gleichwertig sind, ''und damit sind wir von neuem zu einem Schluß gekommen, welcher der Unbedingtheit des Relativitätsprinzipes durchaus widerspricht.'' [...] Man kann den Versuch noch mannigfach variieren, z. B. so, daß A ebenso wie B zwei verschiedene Schreitungen, <math>+u</math> und <math>-u</math>, nacheinander inne hat. Wird dann zu A der Wert <math>u_{1}</math>, zu B der Wert <math>u_{2}</math>, zugeordnet, so muß der Vergleich von A und B am Schluß des Versuches ergeben, daß B oder A in seinem Fortschritt zurückgeblieben erscheint, je nachdem die Schreitungen <math>+u_{1}</math>, <math>-u_{1}</math>, oder <math>+u_{2}</math>, <math>-u_{2}</math> weiter auseinanderliegen. ''Vielleicht ist gerade diese Formulierung des Satzes besonders geeignet, um die Ungleichwertigkeit der verschiedenen Schreitungen klar und deutlich zu zeigen.'' | style="padding: 0px 20px 0px 20px;" | [...] thus B's progress must be retarded with respect to A's in the ratio <math>1:\sqrt{1-u^{2}/c^{2}}</math> at the end of the experiment. And this retardation is definitely real, since both bodies A and B indeed can be immediately compared side by side under the same conditions. Here it is certainly excluded to believe that this is an appearance due to our conception of time. Thus the consequence is unavoidable too, that the strides are not equivalent in the course of the world processes, ''and therefore we again came to a conclusion that completely contradicts the unconditionality of the relativity principle.'' [...] One can vary this experiment in many ways, for instance, so that A in the same way as B successively undergoes two different strides <math>+u</math> and <math>-u</math>. If we apply the value <math>u_{1}</math> to A and <math>u_{2}</math> to B, then the comparison of A and B at the end of the experiment must give the result, that B or A is retarded in its progress depending on whether the strides <math>+u_{2},-u_{2}</math> or <math>+u_{1},-u_{1}</math> are further apart. ''Probably it is precisely this formulation of the theorem that is particularly suitable to demonstrate the non-equivalence of the different strides clearly and explicitly.'' |- |colspan=2|{{Lorentzbox|Text=This interpretation was directly rebutted by Laue (1911/12) who demonstrated the geometrical meaning of differential aging in Minkowski space, see sections {{slink||Laue 1911/12-PT|Laue 1911/12-VA}}, showing that there is no need to assume non-equivalance or anisotropy of motions. Laue added, that as long as there is no experimental contradiction to the relativity principle, the question after the aether can be banned from physics and left to philosophy.<ref name=laue1 />}} |- ! style="width:50%" | German original by [[w:Norman Robert Campbell|Campbell]] (November 1911, published 1912)<ref name=camp /> ! English translation |- |colspan=2|After describing the round-trip experiment (as given by Wiechert) according to which the traveling clock B is retarded when it returns with respect to stationary clock A, he abandoned differential clock aging as follows: |- | style="padding: 0px 20px 0px 20px;" |Dieser Schluß ist nicht richtig. Die Beziehung zwischen <math>t</math>, der Ablesung an der Uhr auf A seitens des Beobachters auf A und <math>t'</math>, der Ablesung an der Uhr auf B seitens des Beobachters auf A, ist (unter der Annahme, daß zu Beginn des Versuchs <math>t=t'</math> ist) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. Der Unterschied zwischen <math>t'</math> and <math>t</math> ist eine Funktion von <math>z</math> und <math>v</math> allein. Wenn man diesen Größen ihre früheren Werte wiedergibt, indem man die beiden Uhren wieder zur Koinzidenz bringt, während sie relativ zueinander ruhen, so geht der Unterschied zwischen <math>t'</math> and <math>t</math> wieder auf null zurück, gleichviel, welche Werte <math>z</math> und <math>v</math> während der Zwischenzeit gehabt haben mögen. Wenn an irgendeinem Punkte der Bahn die Geschwindigkeit von B relativ zu A eine endliche plötzliche Änderung erfährt, so erfährt auch der Wert von <math>v</math> eine endliche plötzliche Änderung. | style="padding: 0px 20px 0px 20px;" |This conclusion is not correct. The relationship between <math>t</math> as the reading on the clock on A by the observer on A, and <math>t'</math> as the reading on the clock on B by the observer on A, is given by (assuming that <math>t=t'</math> at the beginning of the experiment) :<math>t'=\frac{1}{\sqrt{1-v^{2}/c^{2}}}\left(t-vz/c^{2}\right)</math>. The difference between <math>t'</math> and <math>t</math> is a function of <math>z</math> and <math>v</math> alone. If these quantities are given their previous values by bringing the two clocks back to coincidence during which they are at rest relative to one another, the difference between <math>t'</math> and <math>t</math> goes back to zero, no matter what values <math>z</math> and <math>v</math> may have had in the meantime. If at any point on the path the speed of B experiences a finite sudden change relative to A, then the value of <math>t'</math> also undergoes a finite sudden change. |- |colspan=2|{{Lorentzbox|Text=a) So Campbell claims that any time difference during the outbound path is wiped out during the inbound path. His mistake is obvious: He is confusing coordinate differences stemming from the Lorentz transformation of ''events'' (which indeed depend on position and direction) with differences in ''clock aging'' derived from the proper time integral (which is ''accumulative'' and independent of position and direction.) b) As Campbell's paper was a reply to Wiechert, it's interesting to compare them: Campbell was correct in dismissing the aether but wrong in denying asymmetric aging, while Wiechert was correct in deriving asymmetric aging but wrong in requiring the aether. }} |- ! style="width:50%" | French original by [[w:Paul Gruner|Gruner]] (March 1912):<ref name=gruner /> ! English translation |- | style="padding: 0px 20px 0px 20px;" |[...] deux personnes du même âge, se séparant dans des systèmes de « marche » très différents et retournant après un laps de temps assez long, constateront une différence d'âge très sensible. [...] le principe de relativité exige toujours la ''réciprocité parfaite'' des phénomènes entre deux systèmes qui possèdent un mouvement relatif. Si, dans l'exemple cité, les deux personnes du même âge se séparent avec une vitesse relative pour se retrouver plus tard, la constatation d'une différence d'âge sera parfaitement mutuelle : A dira positivement que B est resté en arrière dans son développement, et B affirmera avec le même droit que c'est A qui ne s'est pas développé assez vite. Ainsi le principe absolu de la relativité montre ses conséquences les plus extrèmes et il est clair que l'introduction de l’éther n'est plus en état de résoudre cette contradiction irréductible et inconcevable. | style="padding: 0px 20px 0px 20px;" | [...] two people of same age, separating into very different systems of motion and returning after a quite long period of time, will notice a very significant age difference. [...] the principle of relativity always requires the ''perfect reciprocity'' of the phenomenons between two systems that possess relative motion. When, in the cited example, the two persons of same age are separated by some relative velocity only to meet again later, the finding of an age difference will be perfectly mutual: A will positively say that B stayed behind in its development, and B will assert with same right that it was A who has not developed fast enough. By that, the absolute relativity principle shows its most extreme consequences and it is clear, that the introduction of the aether is no longer able to resolve this irreducible and inconceivable contradiction. |- |colspan=2|{{Lorentzbox|Text=Gruner was probably the first to claim that combining the round-trip experiment with the symmetry of time dilation leads to the contradictory situation, that both must attribute younger age to one another at reunion. At the end of his paper, we also find the expression "clock paradox" (French: paradoxe des horloges). See [[w:Twin paradox]] as well as sections {{slink||Acceleration as asymmetry indicator|Frame distribution as asymmetry indicator|Perspective of the traveler}} for the solution of that problem.}} |} ==Einstein's contributions== 1905:<ref name=einstein05 /> Introduction of the "peculiar" (German: eigentümlich) round-trip experiment with clocks in terms of a polygonal path as well as a continuously curved path, and an experiment comparing a clock at the pole with one at the equator. January 1911 (published November):<ref name=einstein11a /> In a lecture from January, Einstein extended the "funny" (German: drollig) round-trip experiment to living organisms. According to [[w:Rudolf Lämmel]] in April 1911<ref name=lammel /> and [[w:Fritz Müller-Partenkirchen|Fritz Müller]] in October 1911,<ref name=muller /> Einstein spoke of human beings as well. January 1911 (published January 1912):<ref name=einstein3 /> During a discussion with Einstein directly after the previous lecture, [[w:Fritz Müller-Partenkirchen|Fritz Müller]] claimed that any time difference during the round-trip should vanish at reunion, in analogy to the fact that the Lorentz contraction of a moving rod vanishes when it is at rest again. Einstein showed that the analogy is incorrect: While the clock rates are indeed the same again when they are mutually at rest, the clocks do not indicate the same time at reunion because "clocks are carriers of the time differential"; he went on to show that any possible influence of acceleration during the turnaround can be made negligible by elongating the constant velocity periods. 1912:<ref name=einst12manu /> In an unpublished manuscript on special relativity, Einstein showed that if system <math>\Sigma'</math> makes a round-trip along a polygon, then its inner processes will be retarded with respect to resting system <math>\Sigma </math> at reunion. He pointed out that any influence of acceleration can be neglected if one makes the time of acceleration negligible with respect to the total time of motion along the polygon. April 1914:<ref name=einstpetz /> [[w:Joseph Petzoldt]] criticized asymmetric clock aging in the round-trip experiment as a "fallback into absolutist way of thinking", claiming that special relativity requires that any difference between the clocks vanishes when their relative velocity is zero again, even though he added that any treatment of the clock paradox in special relativity is unrealistic anyway, since the theory only concerns uniform motions and therefore cannot handle velocity changes, so one has to modify the theory. Einstein responded by letter in which he praised Petzoldt's philosophical take on relativity, yet he rejected Petzoldt's conclusions concerning the clock paradox by showing that any finite acceleration at turnaround during the round-trip can only influence the clock in a finite way and therefore can be neglected by minimizing the time of acceleration with respect to the time of uniform translation, so it "must be concluded" that the clock traveling on a polygonal path is retarded at reunion. May 1914:<ref name=rowe group=S /> During a conversation with [[w:Ernst Gehrcke]] who claimed that the clock paradox contradicts the relativity principle, Einstein replied that clock B is retarded because it was accelerating in contrast to clock A; while those accelerations are irrelevant for the amount of the time difference, their presence nevertheless cause B to fall behind ("accelerated motions are absolute in the theory of relativity"). 1916:<ref name=einstein16 /> In a lecture of which only an abstract was published, Einstein spoke about the "clock paradox of special relativity from the standpoint of general relativity." September 1918:<ref name=einadl /> In a letter to Einstein, [[w:Friedrich Adler (politician)|Friedrich Adler]] (while in prison for the [[w:Assassination of Karl von Stürgkh]]) claimed that the clock paradox which he described on a circular round-trip contradicts the special relativity principle, and also referred to the similar opinions of Berg and Petzoldt. Einstein responded by letter and explained that there is no contradiction as one of them accelerates; he then showed that general relativity makes both inertial frame K and accelerated frame K' equally justified, explaining the time difference in K' by combining the influence of velocity and gravitational potential, concluding that "Berg and Petzoldt were wrong". November 1918:<ref name=einstein18 /> In a fictitious dialogue between a relativity critic and a relativity apologist written by Einstein, the "critic" said that special relativity must predict differential clock aging in round-trip experiments, which was confirmed by the "relativist" who regretfully noted that even some pro-relativity authors tried to "circumvent this unavoidable result". Yet the critic claimed that this leads to a contradiction: From the viewpoint of K, clock U1 is at rest while the clock U2 was in motion and therefore returns being retarded with respect to U1, but from the viewpoint of K', clock U2 is at rest while clock U1 was in motion and therefore returns being retarded with respect to U2, which was rebutted by the relativist by pointing out the acceleration of U2. Then the critic claimed that this problem "rises again from the dead" in general relativity which allows to symmetrically treat both K and K', which was rebutted by the relativist using the equivalence principle: In K', the rate increase of U1 during turnaround period 3) is "the double" of its velocity time dilation in the inertial periods 2) and 4). December 1918:<ref name=einstein18b /> In a letter to Einstein, [[w:Max Jakob]] doubted the result from Einstein's dialogue, according to which the advance of U1 in period 3) is the double of its retardation during periods 2) and 4). Einstein responded by letter, in which he used the gravitational time dilation factor <math>1+\Phi/c^{2}</math> in K' in order to show that U1 at distance <math>l</math> is advancing by <math>\Phi/c^{2}=2vl/c^{2}</math> in period 3), which is indeed the double of approximated delay <math>vl/c^{2}</math> caused by velocity time dilation during periods 2) and 4). 1920:<ref name=einstein20 /> In conversations with [[w:Alexander Moszkowski]] between 1919 and 1920, Einstein argued that differential aging of the twins is rather a paradox of feeling, not a paradox of thought, because the latter would only arise if there were no reason for the asymmetric aging. The reason in special relativity lies in the fact that one of them suffered accelerations, while a deeper understanding of that question is obtained by using general relativity. Einstein argued that our "common sense" is located in the realm of feeling and analogy drawn from our ordinary experience; since there is no analogy to the example of the twins in our experience, it might appear paradoxical to the common sense, while it appears logical and necessary in light of intensified abstraction of the trained scientific mind. August 1920:<ref name=rowe group=S /> At an anti-relativity event organized by the right-wing agitator [[w:Paul Weyland]] during which [[w:antisemitic]] leaflets were distributed and [[w:swastika]]s offered at the entrance, a lecture was given by Gehrcke re-iterating his criticism of the twin paradox, claiming that the stationary first organism is old or even dead at reunion while the second organism was in motion and therefore stayed young, but from the standpoint of the second organism he himself is old or even dead while the first organism was in motion and stayed young, thus relativity is either contradictory or it leads to different realities and physical [[w:solipsism]]. Einstein who was present at that event, directly responded in a newspaper article;<ref name=einst20 /> after suspecting antisemitic motives of his critics, he specifically addressed Gehrcke's objections regarding the "well known example of the clocks (or twins)", remarking that the charge of solipsism will be "greeted by the experts as a joke", and characterized the claim that relativity requires mutual retardation of two co-located clocks as a "deliberate attempt to misinform the lay public". 1922:<ref name=morand /><ref name=nord /> [[w:Paul Painlevé]], Einstein and Langevin discussed the clock paradox at a meeting in Paris. Painlevé imagined a clock on a train that performs a round-trip with constant speed and returns being retarded with respect to the station clock, yet he claimed that the relativity principle also allows to say that the station clock performed the round-trip and returned being retarded with respect to the train clock, in contradiction to the previous result. Einstein replied that the relativity principle cannot be applied since the train is not in a Galilean system (i.e. inertial frame) any longer during the period of velocity change at turnaround, i.e. the ensemble of two systems having velocities in opposite direction is not an inertial frame; there is no reciprocity between a frame that changes direction and one that doesn't. Langevin consequently gave a detailed analysis in terms of the Lorentz transformation. 1954:<ref name=einstein54 /> In a letter, Einstein explained the "well known clock paradoxon" using two clocks <math>B_{1}</math> and <math>B_{2}</math>; clock <math>B_{2}</math> has to reverse its speed in order to come back, thus it was initially at rest in inertial frame <math>S_{2}</math> and then at rest in <math>S_{2}^{+}</math>, whereas <math>B_{1}</math> constantly remains at rest in <math>S_{1}</math>, which explains the asymmetry between them. ==Historical references== <references> <ref name=einstein05>See p. 904f in: {{Citation |author=Einstein, A. |date=1905 |title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik |volume=322 |issue=10 |pages=891–921 |doi=10.1002/andp.19053221004|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 2, Document 23}}. See also: [https://www.fourmilab.ch/etexts/einstein/specrel/www/ English translation at fourmilab].</ref> <ref name=einstein11a>See p. 10. in: {{Citation |author=Einstein, A. |title=Die Relativitäts-Theorie|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |issue=1-2|pages=1–14 |date=27 November 1911|orig-date=Lecture 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n11/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 17}}.<br /> The publication date 27 November 1911 can be seen on the [https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n5/mode/2up Title page and TOC of issue 1-2].</ref> <ref name=einstein3>Discussion between Einstien, Müller, Lämmel and others after the Zürich lecture: {{Citation |author=Einstein, A.; Müller, F., Lämmel, R.|title=Diskussion zu "Die Relativitäts-Theorie"|journal=Naturforschende Gesellschaft, Zürich, Vierteljahresschrift |volume=56 |pages=II-IX |date=January 1912|orig-date=Lecture on 16 January 1911|url=https://archive.org/details/naturforschendegesellschaftinzurich_vierteljahrsschriftdernaturforschendengesellschaftinzur_v56_1911/page/n587/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 3, Document 18, and in the corresponding English translation volume}}<br /> While the discussion already happened on January 1911, the publication followed one year later in January 1912 in the session proceedings (Sitzungsberichte) of the third issue, see [https://www.ngzh.ch/publikationen/vjs/56/3 Full issue Nr. 3] with [http://www.ngzh.ch/archiv/1911_56/56_1-2/56_3.pdf Title page and TOC] and the [http://www.ngzh.ch/archiv/1911_56/56_3/56_30.pdf Sitzungsberichte including Einstein's discussion on pp. II-IX]. </ref> <ref name=einst12manu>See p. 46 in: {{Citation |author=Einstein, A. |date=1912 |chapter=Document 1: Einstein's manuscript on the special theory of relativity|title=The collected papers of Albert Einstein|volume=4|pages=3-108|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstlor>{{Citation|author=Einstein, A.|date=1914|title=Review of "Lorentz, H. A. – Das Relativitätsprinzip" |journal=Die Naturwissenschaften|volume=2|pages=1018|url=https://archive.org/details/CAT31421305002/page/1018/mode/2up|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 6, Document 11}}</ref> <ref name=einstpetz>{{Citation |author=Einstein, A. |date=1914 |chapter=Document 5: Letter from Einstein to Petzoldt|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein16>See p. 423f in: {{Citation |author=Einstein, A. |date=1916 |title=Announcement of Einstein's lecture "Über einige anschauliche Überlegungen aus dem Gebiete der Relativitätstheorie"|journal=Berliner Sitzungsberichte|pages=423|volume=1916 (part 1)|url=https://archive.org/details/sitzungsberichte1916deutsch/page/423/mode/2up}}</ref> <ref name=einadl>Letter exchange between Einstein and Adler in which the critique on the clock paradox by Berg (1910) and Petzoldt (1914) was mentioned, together with the general relativity solution in terms of the gravitational potential, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Adler's letter in Document 620 and Einstein's reply in Document 628|title=The collected papers of Albert Einstein|volume=8a|pages=16-17|trans-chapter=See also the English translation in the corresponding translation volume}}</ref> <ref name=einstein18>Einstein discussed in terms of inertial frames (special relativity) on pp. 697f; accelerated frames (general relativity) on pp. 698f.; distant masses (Mach's principle) on pp. 700f. in: {{citation |author=Einstein, A.|title=[[s:de:Dialog über Einwände gegen die Relativitätstheorie|Dialog über Einwände gegen die Relativitätstheorie]]|date=November 1918|volume=6|issue=48|journal=Die Naturwissenschaften|pages=697-702|quote=Reprinted in ''The Collected Papers of Albert Einstein'', Vol. 7, Document 13}}; See also English translation [[:s:Translation:Dialog about Objections against the Theory of Relativity|Dialog about Objections against the Theory of Relativity]] on Wikisource.</ref> <ref name=einstein18b>Letter exchange between Max Jakob and Einstein from December 1918, in: {{Citation |author=Einstein, A. |date=1918 |chapter=Jakob's letter in Document 661c and Einstein's reply in Document 663a|title=The collected papers of Albert Einstein|volume=10|pages=189-190}}</ref> <ref name=einstein20>Interview of Einstein by Moszkowski, see p. 204f. in: {{citation |author=Moszkowski, A.|title=Einstein. Einblicke in seine Gedankenwelt|orig-date=Copyright date 1920 |date=1921|place=Hamburg|url=https://www.archive.org/details/einsteineinblick00moszuoft}}; See also English translation by H. L. Brose (1921): [https://archive.org/details/einsteinsearch00moszrich Einstein, the searcher], p. 206</ref> <ref name=einst20>{{Citation|author=Einstein, A.|date=27 August 1920|journal=Berliner Tageblatt|title=Meine Antwort - Ueber die anti-relativitätstheoretische G. m. b. H.|issue=402|pages=1-2|url=https://www.deutsche-digitale-bibliothek.de/newspaper/item/YH65KFT53MOG4SMXDXK4IVUPTR3QRY7Q?issuepage=1|quote=Reprinted in "The Collected Papers of Albert Einstein", Vol. 7, Document 45}}</ref> <ref name=einstein54>Letter from Einstein to N. V. Pope from March 1954; [[w:Albert Einstein Archives]], Object number 27-88 ([https://ein-web.adlibhosting.com/aea/Details/archive/110021626 Online dataset]); Scanned version as [https://groups.google.com/group/npachat/attach/d3121322d37764f2/Einstein%20letter.doc?part=0.1 Word document on Usenet] published by [https://groups.google.com/g/npachat/c/Haoib97d6OA/m/8mR30yITEtMJ Pope himself])</ref> <ref name=morand>Discussion between Painlevé, Einstein, and Langevin on p. 316ff in: {{citation |author=Morand, M.|title=Einstein au collège de france|date=April 1922|journal=La Nature|volume=50|issue=2511|pages=315-320|url=http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.102/319/100/620/5/613}}</ref> <ref name=lammel>{{Citation|author=Lämmel, R.|date=28 April 1911|title=Die Relativitäts-Lehre|journal=Neue Zürcher Zeitung|volume=117|pages=1|url=https://www.e-newspaperarchives.ch/?a=d&d=NZZ19110428-01.2.4.1}}; English translation of the part concering the twin pardox at [[:v:History of Topics in Special Relativity/Twin paradox#Lämmel 1911-Hum|Wikiversity:Early history of the twin paradox - Lämmel]]</ref> <ref name=lammel2>See p. 84ff in: {{Citation|author=Lämmel, R.|date=1921|orig-date=Preface December 1920|title=Die Grundlagen der Relativitätstheorie|place=Berlin|publisher=Springer|url=https://archive.org/details/diegrundlagende00lmgoog}}</ref> <ref name=langevin1>He derived differential aging from the proper time integral; pointed out that this demonstrates the "absolute nature of acceleration" with respect to an aether, see: {{citation |author=Langevin, P.|title=[[:s:fr:L’Évolution de l’espace et du temps|L’Évolution de l’espace et du temps]]|journal=Scientia |volume=X |pages=31–54 |date=July 1911|orig-date=Lecture 10 April 1911}}; English translation [[:s:en:Translation:The Evolution of Space and Time|The Evolution of Space and Time]] on Wikisource</ref> <ref name=langevin2>See p. 329 in: {{citation |author=Langevin, P. |title=Le temps, l'espace et la causalité dans la physique moderne |journal=Bulletin de la Société française de philosophie |volume=12 |orig-date=Lecture October 1911|date=1912|pages=1-28|url=http://ahp.li/1f7fc22d283fdf0deeca.pdf}}</ref> <ref name=langevin3>See p. 622f in: {{citation |author=Langevin, P. |title=Le Principe de relativité |journal=Bulletin de la société française des électriciens |volume=9 |date=1919 |pages=601-639|url=https://archive.org/details/bulletin-de-la-societe-francaise-des-electriciens-ser.-3-vol-9/page/600}}; Republished in 1922 as separate booklet: [[:s:fr:Le Principe de relativité|Le Principe de relativité]], Éditions Étienne Chiron</ref> <ref name=wiechert11>See p. 745f. general description and proper time; 757f. space travel; in: {{Citation |author=Wiechert, E. |date=September 1911|orig-date=Lectures March-May 1911, submitted 26 July|title=[[:s:de:Relativitätsprinzip und Äther|Relativitätsprinzip und Äther]]|journal=Physikalische Zeitschrift |volume=12 |issue=17-18 |pages=[https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/741 689-707] published September 1; [https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/789 737–758] published September 15}}</ref> <ref name=wiechert15>See p. 46 (Einstein, Langevin, Wiechert) and pp. 51f (Laue versus Wiechert) in: {{citation |author=Wiechert, E.|contribution=Die Mechanik im Rahmen der allgemeinen Physik| title=Die Kultur der Gegenwart: Physik|volume=3.3.1|date=1915 |orig-date=Submitted July 1914|pages=1–78|contribution-url=https://www.archive.org/details/physikunterredak00warbuoft}}</ref> <ref name=wiechert20>See p. 46f in: {{citation |author=Wiechert, E.|title=Der Äther im Weltbild der Physik|orig-date=Presented December 1920|date=1921|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse|pages=29-70|url=http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN00250586X}}</ref> <ref name=wiechert21>See p. 25ff in: {{citation |author=Wiechert, E.|title=[[:s:de:Prinzipielles über Äther und Relativität|Prinzipielles über Äther und Relativität]]|date=1922|orig-date=Lecture September 1921|journal=Physikalische Zeitschrift|volume=23|pages=25-28}}</ref> <ref name=muller>See p. 9 in: {{Citation|author=Müller, F.|date=October 1911|journal=Berliner Tageblatt|title=[[:s:de:Das Zeitproblem (1911)|Das Zeitproblem]]|pages=[https://www.deutsche-digitale-bibliothek.de/newspaper/item/2QKOIOLGNVQILTCEZQOGQPLTRVLPM5PZ?query=zeit&issuepage=9 Part 1 published 16 October 1911] and [https://www.deutsche-digitale-bibliothek.de/newspaper/item/IO44I6QBC4SVV5YUKUDSGXYIPQUXXBN5?query=zeit&issuepage=11 Part 2 published 23 October 1911]}}</ref> <ref name=gruner10>See p. 89 in: {{Citation |author=Gruner, P. |title=Elementare Darlegung der Relativitätstheorie |journal=Mitteilungen der Naturforschenden Gesellschaft Bern |issue=1751 |pages=82-103 |date=May 1912|doi=10.5169/seals-319208}}</ref> <ref name=gruner>See p. 253f in: {{Citation |author=Gruner, P. |title=[[:s:fr:Rapport sur la dernière discussion concernant le principe de la relativité et l’éther|Rapport sur la dernière discussion concernant le principe de la relativité et l’éther]] |journal=Archives des sciences physiques et naturelles |volume=33|issue=4 |pages=252-254 |date=March 1912}}</ref> <ref name=weyl>See p. 147f. in: {{Citation |author=Weyl, H. |date=March 1918|title=Raum-Zeit-Materie (first edition)|publisher=Berlin: Springer|url=https://archive.org/details/RaumZeitMaterieVolIMeinerFrauGewidmet}}; English translation of the 4th edition by H. Brose (1921): [https://www.gutenberg.org/ebooks/43006 Space—Time—Matter], pp. 278f.</ref> <ref name=gbaum>See footnote on p. 507 in: {{Citation|author=Grünbaum, F. |title=Über einige ideelle Versuche zum Relativitätsprinzip|journal=Physikalische Zeitschrift|volume=12|pages=500–509|date=1911|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0012/page/540}}</ref> <ref name=laue1>Laue introduces the word "paradox", alludes to Berg and discusses Wiechert, in: {{citation |author=Laue, M. v. |title=Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung |journal=Physikalische Zeitschrift |volume=13 |issue=3|date=February 1912|orig-date=Submitted December 1911|pages=118–120|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/148}}; {{icon|wikisource}} See also English translation [[:s:Translation:Two Objections Against the Theory of Relativity and their Refutation|Two Objections Against the Theory of Relativity and their Refutation]] on Wikisource</ref> <ref name=laue2>See p. 42f. for general description; p. 58f. in terms of proper time; in: {{Citation |author=Laue, M. v. |orig-date=Preface December 1912|date=1913 |title=Das Relativitätsprinzip (Second Edition) |publisher=Vieweg |place=Braunschweig|url=https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE4597082}}; See also English translation [[:s:Translation:The Principle of Relativity (Laue 1913)|The Principle of Relativity, Second edition, Part III]] on Wikisource</ref> <ref name=laue3>See p. 113f in: {{citation |author=Laue, M. v. |title=Das Relativitätsprinzip |journal=Jahrbücher der Philosophie |volume=1 |date=1913 |pages=99–128}}; {{icon|wikisource}} See also English translation of [[:s:Translation:The Principle of Relativity (Laue, Philosophy)|The Principle of Relativity]] on Wikisource</ref> <ref name=laue0>See preface in: {{Citation |author=Laue, M. v. |date=May 1911|title=Das Relativitätsprinzip (First Edition) |publisher=Vieweg |place=Braunschweig|url=https://archive.org/details/dasrelativittsp00lauegoog}}</ref> <ref name=berg>See p. 369f in: {{Citation |author=Berg, O. |date=1910 |title=Das Relativitätsprinzip der Elektrodynamik |journal=Abhandlungen der Fries'schen Schule |volume=3 |issue=2|pages=333-382 |url=http://hdl.handle.net/2027/hvd.hnuynk?urlappend=%3Bseq=351}}</ref> <ref name=camp>See p. 123f in: {{Citation |author=Campbell, N. |title=Relativitätsprinzip und Äther: Eine Entgegnung an Herrn Wiechert |journal=Physikalische Zeitschrift |volume=13 |pages=120-128 |issue=3|orig-date=Submitted December 1911|date=February 1912|url=https://resolver.sub.uni-hamburg.de/kitodo/PPN891110208_0013/page/150}}. The is based on an English manuscript translated by Max Iklé, and Campbell's first name was Germanised as "Normann".</ref> <ref name=seel>{{Citation|author=Seeliger, R.|title=Review of "P. Gruner – Rapport sur la dernière discussion concernant le principe de la relativité et l'éther"|journal=Die Fortschritte der Physik|volume=68|issue=2|pages=336|date=1913|url=https://books.google.com/books?id=fSJGAQAAMAAJ&pg=PA336}}</ref> <ref name=study>See footnote on p. 111 in: {{citation |author=Study, E. |title=Vorlesungen über ausgewählte Gegenstände der Geometrie |date=June 1911|url=https://archive.org/details/vorlesungenber00studuoft|publisher=B.G. Teubner|place=Leipzig}} </ref> <ref name=robb1>See pp. 356ff. in: {{Citation|author=Robb, A.|date=1914|title=A theory of time and space|place=Cambridge|publisher=University Press|url=https://archive.org/details/theoryoftimespac00robbrich}} </ref> <ref name=robb2>See §12 in: {{citation |author=Robb, A. A.|title=The Straight Path|date=1920 |journal=Nature|pages=599|volume=104|issue=2623|url=https://archive.org/details/sim_nature-uk_1920-02-05_104_2623/page/598/mode/2up}}</ref> <ref name=edding2>See p. 22 in: {{Citation |author=Eddington, A. S. |date=1922 |title=The theory of relativity, and its influence on scientific thought |publisher=Oxford Clarendon Press |url=https://archive.org/details/cu31924005748573}}</ref> <ref name=rogers>{{citation |author=Rogers, R. A. P.|title=The Time-Triangle and Time-Triad in Special Relativity|date=November 1922|journal=Nature|volume=110|issue=2769|pages=698–699|url=https://archive.org/details/sim_nature-uk_1922-11-25_110_2769/page/698/mode/2up}}</ref> <ref name=lorentz1>See pp. 37f, 55ff in: {{citation |author=Lorentz, H. A.|date=1913|title=Het relativiteitsbeginsel : drie voordrachten gehouden in Teyler's stichting|publisher=De Erven Loosjes |place=Haarlem|url=https://resolver.kb.nl/resolve?urn=MMKB24:063387000:00005}}; German translation on pp. 31f, 47f in: {{citation |author=Lorentz, H. A.|date=1914| title=Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem|publisher=B.G. Teubner |place=Leipzig and Berlin|url=https://archive.org/details/bub_gb_89PPAAAAMAAJ}}; See also the transcription [[:s:de:Das Relativitätsprinzip (Lorentz)|Das Relativitätsprinzip]] on German Wikisource and the English translation [[:s:Translation:The Principle of Relativity (Lorentz)|The Principle of Relativity]] on English Wikisource</ref> <ref name=lorentz3>See §12 in: {{citation |author=Lorentz, H. A.|title=Considérations élémentaires sur le principe de relativité|date=1914 |journal=Revue générale des sciences pures et appliquées|pages=179-186|url=https://archive.org/details/revuegnraled25pari/page/178/mode/2up}}</ref> <ref name=bloch>See pp. 67 ff. in: {{Citation | author=Bloch, W.| date=September 1918|title=Einführung in die Relativitätstheorie| publisher=B. G. Teubner |url=https://hdl.handle.net/2027/njp.32101040276907}}</ref> <ref name=bloch2>See pp. 69ff. (special relativity) and 102ff. (general relativity) in: {{Citation | author=Bloch, W.| date=1920 |title=Einführung in die Relativitätstheorie (second edition)| publisher=B. G. Teubner |url=https://www.archive.org/details/einfhrungindier00blocgoog}}</ref> <ref name=bollert1>See p. 6 (special relativity), pp. 24-26 (EP) in: {{citation |author=Bollert, K.|title=Einstein’s Relativitätstheorie und ihre Stellung im System der Gesamterfahrung |date=April 1921|publisher=Steinkopff|url=https://archive.org/details/dbc.wroc.pl.001504}}</ref> <ref name=born>See pp. 190f. (special relativity), 250f (EP) in: {{Citation | author=Born, M.| date=1921 |title=Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Second edition)| publisher=Springer | place=Berlin|url=https://hdl.handle.net/2027/mdp.39015017387310}}; The [https://preserver.beic.it/delivery/DeliveryManagerServlet?dps_pid=IE5426498 first edition (1920)] of Born's book didn't include the twin paradox. English translation of the third edition by H. Brose (1924): [https://archive.org/details/einsteinstheoryo00born Einstein's theory of relativity]</ref> <ref name=pauli>See p. 558f (general description); p. 624f (proper time); p. 713f (accelerated frames); in: {{Citation |author=Pauli, W. |date=1921 |journal=Encyclopädie der Mathematischen Wissenschaften|title=Die Relativitätstheorie|pages=539–776|volume=5|issue=2 |url=http://resolver.sub.uni-goettingen.de/purl?PPN360709672}}; English translation by G. Field (1958): [https://books.google.com/books?id=rc3DAgAAQBAJ Theory of Relativity]</ref> <ref name=thirring>See p. 209ff in: {{citation |author=Thirring, H.|title=Über das Uhrenparadoxon in der Relativitätstheorie|date=April 1921|journal=Naturwissenschaften|volume=9|issue=18|pages=209-212|url=https://archive.org/details/sim_naturwissenschaften_1921-04-01_9_13/mode/2up}}</ref> <ref name=sommerfeld>See p. 71 in: {{citation |author=Sommerfeld, A. |date=May 1913|chapter=Remarks on Minkowski's "Space and Time"|title=Das Relativitätsprinzip|editor=Otto Blumenthal|pages=69-73|url=https://www.archive.org/details/dasrelativittsp00minkgoog}}</ref> <ref name=kopff>See pp. 45ff (special relativity and proper time); pp. 117ff (EP); pp. 189ff (Mach's principle), in: {{citation |author=Kopff, A.|title=Grundzüge der Einsteinschen Relativitätstheorie |date=February 1921|publisher=S. Hirzel|place=Leipzig|url=https://www.archive.org/details/grundzgedereins00kopfgoog}}; English translation by H. Levy (1923): [https://hdl.handle.net/2027/mdp.39015017188817 The mathematical theory of relativity].</ref> <ref name=becqu1>See p. 48ff (proper time), p. 240f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Le Principe de relativité et la théorie de la gravitation|Le Principe de relativité et la théorie de la gravitation]] |date=1922 |publisher=Gauthier-Villars|place=Paris}}; See also p. 57ff (proper time), p. 177f (general relativity) in: {{citation |author=Becquerel, J.|title=[[:s:fr:Exposé élémentaire de la théorie d’Einstein et de sa généralisation|Exposé élémentaire de la théorie d’Einstein et de sa généralisation]]|date=1922 |publisher=Payot|place=Paris}}</ref> <ref name=nord>Discussion between Painlevé, Einstein, and Langevin on pp. 146ff in: {{citation |author=Nordmann, C.|title=[[s:fr:Einstein expose et discute sa théorie|Einstein expose et discute sa théorie]]|date=May 1922|journal=Revue des deux mondes|volume=IX|pages=129-166}}</ref> <ref name=lehm>{{Citation |author=Lehmann, Otto |orig-date=September 1910 |date=1911|title=Das Relativitätsprinzip der neue Fundamentalsatz der Physik |title-link=s:de:Das Relativitätsprinzip der neue Fundamentalsatz der Physik|journal=Verhandlungen des naturwissenschaften Vereins in Karlsruhe |volume=23 |pages=49-74}}</ref> <ref name=lech>See p. 19ff in: {{citation |author=Lechalas, G. |orig-date=Submitted December 1912|date=1913 |title=Le nouveau temps |journal=L’Année philosophique|volume=XXIII|pages=19-44|url=https://gallica.bnf.fr/ark:/12148/bpt6k255882z/f22.item}}</ref> <ref name=hunt>See pp. 494ff in: {{Citation|author=Huntington, E. V. |year=1912 |title=A new approach to the theory of relativity|journal=Philosophical Magazine |volume=23|pages=494-512|url=https://archive.org/details/londonedinburg6231912lond/page/494/mode/2up}}</ref> </references> ==Secondary sources== <references group=S> <ref name=miller>{{Citation |author=Miller, A. I. |date=1981 |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |place=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}; See section 7.4.13 (Langevin, Wiechert, Laue, Einstein), footnotes 29-34 of chapter 7 (Petzoldt, Sommerfeld, Bergson, Einstein)</ref> <ref name=lange>{{Citation|author=Lange, L.|date=1927|title=The clock paradox of the theory of relativity|journal=The American Mathematical Monthly|volume=34|issue=1|pages=22-30|jstor=2299914}}</ref> <ref name=pes>{{Citation |author=Pesic, P. |date=2003 |title=Einstein and the twin paradox |journal=European Journal of Physics |volume=24 |issue=6 |pages=585–590 |doi=10.1088/0143-0807/24/6/004}}</ref> <ref name=during>{{Citation |author=During, É. |date=2014 |title=Langevin ou le paradoxe introuvable |journal=Revue de métaphysique et de morale |volume=84 |pages=513-527 |doi=10.3917/rmm.144.0513|doi-access=free}}; See pp. 515f (Langevin), 520f. (Einstein, Laue, Weyl, Painlevé).</ref> <ref name=debs>{{Citation |author=Debs, T. A., & Redhead, M. L. |title=The twin paradox and the conventionality of simultaneity |date=1996 |journal=American Journal of Physics |volume=64|issue=1| pages=384-392 |doi=10.1119/1.18252}}</ref> <ref name=alizzi>{{Citation |author=Alizzi, A., Sen, A., & Silagadze, Z. K.|title=Do moving clocks slow down? |year=2022 |journal=European Journal of Physics |volume=43|issue=6|pages=065601 |doi=10.1088/1361-6404/ac93ca|arxiv=2209.12654}}; Appendix B with reference to Lange and Halsbury</ref> <ref name=beng>{{Citation |author=Benguigui, L. G. |date=2020 |title=A Tale Of Two Twins: The Langevin Experiment Of A Traveler To A Star |publisher=World Scientific|isbn=9789811219115}}; See early solutions (Einstein, Langevin, Lorentz, Born/Kopff) and the Bergson controversy. A shorter version appeared in {{arxiv|1212.4414}}.</ref> <ref name=rowe>{{Citation|author=Rowe, D. E.|date=2006|title=Einstein's allies and enemies: Debating relativity in Germany 1916–1920|journal=Interactions: Mathematics, Physics and Philosophy|pages=231-280|publisher=Springer|doi=10.1007/978-1-4020-5195-1_8}}; Covering the criticism of Gehrcke starting with 1912; discussion between Einstein and Gehrcke in 1914; Einstein's dialogue (1918) as response to antirelativists; the Weyland event in 1920 and Einstein's response.</ref> <ref name=weiss>Weiss, W. (Physics FAQ): [https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html The Twin Paradox: The Equivalence Principle Analysis]</ref> <ref name=cuvaj>{{Citation |author=Cuvaj, C. |date=1971 |title=Paul Langevin and the theory of relativity|journal=Japanese studies in the history of science|volume=10| pages=113-142|url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf}}</ref> <ref name=koks>Koks, D. (2018): [https://math.ucr.edu/home/baez/physics/Relativity/SR/sr-gr.html Physics FAQ: Where is the Boundary between Special and General Relativity?]</ref> </references> [[Category:History of special relativity]] [[Category:Paradoxes]] 46hw915ijizhm8ut9cfopfud779311q 0 302265 2834491 2821688 2026-09-25T21:15:54Z ~2026-51742-46 3111617 2834491 wikitext text/x-wiki {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{Article info | journal = WikiJournal Preprints <!-- WikiJournal of Medicine, Science, or Humanities --> | last1 = Titleman | orcid1 = | first1 = Mark | et_al = <!-- if there are >9 authors, hyperlink to the list here --> | affiliation1 = | correspondence1 = | correspondence = email@address.com | keywords = <!-- up to 6 keywords --> | license = <!-- default is CC-BY --> | abstract = E. T. Whittaker produced two papers in 1903 and 1904 that, although sometimes considered mere mathematical statements (Barrett, 1993), held important implications for physical theory. The Whittaker 1903 paper united electrostatic and gravitational attraction as resulting from longitudinal waves – waves whose wavefronts propagate parallel to their direction. The Whittaker 1904 paper showed that electromagnetic waves resulted from the interference of two such longitudinal waves or scalar potential functions. Although unexplored, the implications of these papers are profound: gravitational lensing, gravitational waves, the Aharonov-Bohm effect, the existence of a hyperspace above or behind normal space, the elimination of gravitational and point charge singularities, MOND, and the expansion of the universe. This last implication can be related to the recent finding that black holes with posited vacuum energy interior solutions alongside cosmological boundaries have a cosmological coupling constant of k=3, meaning that black holes gain mass proportionally to a³ in a parameterization equation within a Robertson-Walker cosmology and are a cosmological accelerated expansion species (Farrah et al., 2023). This expansion and many features of General Relativity can be explained by the mass-proportionality and preferred direction of the longitudinal waves within the two underlying non-local Whittaker potentials (Titleman, 2022). Expansion of the universe is produced as longitudinal motion within the Whittaker potentials only when dynamic electromagnetism is separate from time-static gravity in intergalactic space. }} ==Introduction== Modern theories of gravity have faced several unresolved difficulties such as unexplained expansion, failure to adhere to predicted galactic rotations curves, the existence of unphysical gravitational singularities, and incompatibility with Quantum theory. It is thus useful to assess older classical theories of gravity that overtly or implicitly offered several features of Relativity. E. T. Whittaker's 1903 paper on partial differential equations anticipated General Relativity in many ways by proposing an undulatory theory of gravity and a static gravitational field resulting from propagating effects – the field is the result of electromagnetic processes. Whittaker’s 1904 paper on two scalar potential functions showed that the electromagnetic four-potential of Relativity overlooked other forms of electromagnetic potential. Even though no action could be set up for computing local physical processes, Whittaker potential theory foresaw the Aharonov-Bohm effect and could be used to replace Dirac spinors in the Dirac equation (Ruse, 1937). What the cautious Whittaker considered an “undulatory theory” could in fact explain several features of Relativity in addition to MOND. For example, gravitational lensing can be understood as resulting from the preferred direction of the non-local potentials and their mass-proportionality (Titleman, 2022). Finally, due to the dynamic longitudinal motion in the z-axis being additive, Whittaker potential theory can also provide a simple explanation for expansion of the universe - it is merely dynamic light decoupled from static gravity and can only be produced intergalactically. == Whittaker Potential Theory == E. T. Whittaker's 1903 paper on partial differential equations found a harmonic solution to the amenable central equations of calculus in three dimensions: the wave equation and the more specific Laplace equation. Both potentials could be analysed into simple plane waves, bringing new unity to potential theory, inviting the possibility of new physical phenomena, and implying the modern notion that calculus alone is insufficient as a physical theory. The question of whether potentials – the second derivative of which produces force fields – are real is irrelevant to such possibilities and their confirmation via other observational data and new mathematical techniques. Whittaker considered “gravitation and electrostatic attraction explained as modes of wave-disturbance” (Whittaker, 1903), meaning that the force fields associated with matter and charge are undulatory and perhaps matter and charge themselves. Whittaker’s 1903 paper thus displayed incredible predictive power in recognizing the wave nature of force and force carrier (matter, charge). Its mathematical generality and novelty were reported in the British popular press - which was an impressive feat for a young mathematician - yet it was far too ahead of its time for an uneventful period in British physics with little observational data and only a recent introduction of continental mathematics. According to Whittaker, an electrostatic or gravitational field, varying with the inverse square of distance, results from waves propagating at any speed and in any which way. The general solution to the Laplace equation was found in the form: <math>(1) \int_{0}^{2\pi}f(xcosv+ysinv+iz,v)dv</math> where f is an arbitrary function of the two arguments. This is accomplished in terms of Bessel functions by expanding the function f as a Taylor series with respect to the first argument and a Fourier series with respect to the second argument. The v is a periodic argument. Using similar analysis, the general solution to the wave equation was found as dynamic and longitudinal in the form: <math>(2) \int_{0}^{\pi} \int_{0}^{2\pi}f(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> where ''f'' is an arbitrary function of the three arguments. Regarding statics, Whittaker’s 1903 paper claimed that once longitudinal waves interfere with each other the disturbance at any point does not depend on time but only on position. Force potential can therefore be defined in terms of standing waves (non-local solution) as well as propagating waves (local solution changing in time) (Barrett, 1993). This undulatory theory of gravity propagating with a finite velocity subsumed gravity to the transmission of electromagnetic radiation, forming a significant contribution to the electromagnetic worldview of the day. The aether producing longitudinal as well as transverse electromagnetic waves was a common belief of 19th century physicists and was given a mathematically detailed treatment by Whittaker (Carvalo & Rodrigues, 2008). Hector Munera (Munera, 2018) writes that Whittaker's claim of generality is unacceptable due to periodicity being assumed, although this permitted Whittaker's analysis. Munera also emphasizes that equation (1) implies a rotation in the complex plane (z, ixcosθ+iysinθ). A time-dependent solution in the form of equation (2) is realized by “projecting z and xcosθ+ysinθ onto ray r directed at angle φ relative to the Z-axis, thus shifting to spherical coordinates” (Munera, 2018). Whittaker's 1904 paper on two scalar potentials showed that electromagnetic fields could be decomposed into two scalar potential functions as intersecting beams, with orthogonal sphericity when discontinuous (gravitational). Whittaker accomplished this by defining three scalar fields and eliminating the orthogonal sphericity term using a gauge. The two scalar potentials F and G derive the magnetic force h and dielectric displacement d as: <math>(3) d_x={\partial^2F\over\partial x\partial z}+{1 \over c}{\partial^2G\over\partial y\partial t}</math> <math>d_y={\partial^2F\over\partial y\partial z}-{1 \over c}{\partial^2G\over\partial x\partial t}</math> <math>d_z={\partial^2F\over\partial z^2}-{1 \over c^2}{\partial^2G\over\partial t^2}</math> <math>h_x={1 \over c}{\partial^2F\over\partial y\partial t}-{\partial^2G\over\partial x\partial z}</math> <math>h_y=-{1 \over c}{\partial^2F\over\partial x\partial t}-{\partial^2G\over\partial y\partial z}</math> <math>h_z={\partial^2G\over\partial x^2}+{\partial^2G\over\partial y^2}</math> F and G are represented asymmetrically as follows: <math>(4) F(x,y,z,t)=\sum {e \over4\pi}sinh^{-1}{\bar{z}'-{z} \over((\bar{x}'-{x})^2+(\bar{y}'-{y})^2)^{1/2}}</math> <math>G(x,y,z,t)=\sum {e \over4\pi}tan^{-1}{\bar{y}'-{y} \over\bar{x}'-{x}}</math> The summation is taken over all the electrons in the field. In continuous form they are: <math>(5) F=\int_{0}^{\pi} \int_{0}^{2\pi}f(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> <math>G=\int_{0}^{\pi} \int_{0}^{2\pi}g(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> The shift between spherical (polar) and planar (Cartesian) coordinates can be seen in Whittaker’s 1951 representation of two scalar potentials F and G:    <math>(6) F(x,y,z,t)={1 \over 2}\sum_{e}log {\bar{r}+\bar{z}-z \over \bar{r}-(\bar{z}'-z)}</math> <math>G(x,y,z,t)=-i{1 \over 2}\sum_{e}log {\bar{x}'-{x}+i(\bar{y}'-{y}) \over \bar{x}'-x-i(\bar{y}'-y)}</math> Whittaker wrote: "It will be noted that F and G are defined in terms of the positions of the electrons alone, and do not explicitly involve their velocities. Since in the above formulae for d and h an interchange of electric and magnetic quantities corresponds to a change of G into F and of F into G, it is clear that the two functions F and G exhibit the duality which is characteristic of electromagnetic theory: thus an electrostatic field can be described by F alone, and a magnetostatic field by G alone; again, if the field consists of a plane wave of light, then the functions F and G correspond respectively to two plane-polarised components into which it can be resolved. Since there are an infinite number of ways of resolving a plane wave of light into two plane-polarised components, it is natural to expect that, corresponding to any given electromagnetic field, there should be an infinite number of pairs of functions F and G capable of describing it, their difference from each other depending on the choice of the axes of co-ordinates-as is in fact the case. Thus there is a physical reason why any particular pair of functions F and G should be specially related to one co-ordinate, and cannot be described by formulae symmetrically related to the three co-ordinates (x,y,z)" (McCrea 1952). == A New Explanation for Expansion of the Universe == This new understanding of waves at the interface of plane and spherical rotations strongly suggests the mathematical and physical concept of vorticity as dynamic 3-parameter space. It is clear from the Whittaker analysis that a more massive observer would experience more longitudinal waves than only the two experienced by an observer as an electromagnetic wave, and it is implicit that when observed at the speed of light the number of longitudinal waves would collapse into the orthogonal axis (non-local). Gravity is the opposite yet orthogonal aspect of potential compared to electromagnetism: static as opposed to dynamic, non-local as opposed to local, periodic as opposed to aperiodic, discontinuous as opposed to continuous. Whittaker's analysis, for example the 1951 representation, clearly opened mathematical possibilities beyond calculus and natural logarithms. Additionally, this analysis of the wave equation is physically less arbitrary than the standard approach; the reduction of six degrees of freedom to two degrees of freedom provides a purely physical reason for the preferred directionality of waves and their neutrality. Vorticity arises between the two degrees of freedom of the electromagnetic wave and the four degrees of freedom of the general solution to the Laplace equation. The free parameters assigned to the axes of a wave within a vorticity are as follows: longitudinal motion or speed in the z is charge-proportional from the perspective of the observer (compressible potentials), number of longitudinal waves is mass-proportional from the perspective of the observer and folds into the non-local (static) when observed at high speed (local vorticity force), and the x-axis or plane wave axis is related to amplitude, intensity, and soliton radius. Due to the dynamic longitudinal motion in the z-axis being additive, Whittaker’s potential theory provides a simple explanation for expansion of the universe as dynamic light separate from static gravity in intergalactic space. If this is the case, there would be an inverse relation – with implicit coordinate shift – between the coupled amplitude or changing background intensity of the universe and expansion of the universe. Operations such as antiderivative, tetration (which can be given more mathematical centrality), or antiderivative followed by tetration can be performed on this relation. Since the intensity of the universe is double that of all predicted stars (Lauer et al., 2022), the relation would be on the order of 3/2. <math>(7) \surd\frac{L_v}{2}=\frac{Expansion\ (yz-plane)}{3}</math> <math>(8) \int3\surd\frac{L_v}{2}d{L_v}={Expansion\ (yz-plane)} </math> <math>\sqrt2(\frac{L_{v}}{2})^{3/2} = {Interpolation}</math> <math>^{\infty} [\sqrt2](\frac{L_{v}}{2})^{3/2} = L_{v}\sqrt\frac{L_{v}}{2} = \Psi_\perp</math> (Wadell, 1935) This can be considered a form of computation.<math>\sqrt2</math> is subtended and angular in the context of infinite tetration, orthogonal sphericity, and associated 3+1 manifolds. The question "how many squares fit in a sphere?" is analogous to the relevant question in Ramsey theory "how big must some structure be to guarantee that a particular property holds?" The “3” is the result of the new interpretation of three dimensions or three axes permitted by this interpretation of Whittaker potential theory. Longitudinal waves are additive in two directions – phase and antiphase z-directions (F,G). Black holes produce these longitudinal waves as scalar potentials, providing cosmological coupling, a third additive “direction” (non-local), another dynamic component, and an important center of wave decomposition for scalar potentials and vorticity (<math>\Psi</math>). This understanding replaces black hole singularities with vacuum energy interior solutions (or densities) within a Robertson-Walker cosmology, as elaborated on by Whittaker (Whittaker, 1935) and Farrah (Farrah et al., 2023). == Three Methods for Computing the MOND Acceleration Constant == '''Quantum theory (Boltzmann-Rydberg statistics)''' If black holes produce longitudinal waves as scalar potentials, it is via beam splitting within scalar interferometry. This reduces the four degrees of freedom inherent to Whittaker’s general solution of the Laplace equation (x, y, z, non-local Z) to the two local degrees of freedom inherent to Whittaker’s general solution of the wave equation. This halving can also be understood in statistical terms as normality. Black holes keep absolute time as a simple geometry while statistics and ultimately probability are primordial. Critical density is traditionally arrived at by adjusting the Hubble parameter and - indeed - the scale factor of the universe is the inverse mathematical and physical operation of equation (7). <math>(9)\ a(t) = (\frac {t_\frac{1}{2}}{t})^\frac{2}{3}</math> Can the average kinetic energy of the cosmic microwave background be measurable in terms of half time <math>k_b</math><math>\Delta</math>T and related to a non-local "force" applied on black hole-containing galaxies - the “Whittakerforce potential force” (vorticity force) - towards the computation of the MOND acceleration constant? This is due to the four degrees of freedom of this latent kinetic energy becoming two upon splitting within a black hole. The following equation was previously proposed by the author (Titleman, 2020): <math>(10)1.21*10^{-10}m/s^2={\alpha R_\infty k_b\Delta T \over m_p}</math> Although dynamics and statics and the generality of Whittaker potentials replace mass-energy and associated math, a second layer of mass as the Planck mass (homogeneous, theoretical) – as well as a second layer of brightness-dependence as the fine structure constant scaled to galactic brightness and shape – may provide the MOND acceleration constant and the Tully-Fischer relation. '''Ternary probability''' The gauge used by Whittaker to eliminate the orthogonal sphericity term (Ψ) and reduce the electromagnetic wave from six degrees of freedom to two degrees of freedom (F,G) is equivalent with the following statement under the assumptions of calculus and mass-energy: <math>(11)\surd3x = x^{-\surd3}</math> <math>x=0.818</math> <math>G-0.818G</math> <math>= 1.214*10^{-11}\frac{m^{3}}{kgs^{2}}</math> Eliminating Ψ is equivalent with gaining an order of magnitude and adding G, producing the MOND acceleration constant and permitting coordinate shifting and ternary probability. '''The cosmological constant and Cartesian asymmetry''' The relation of the MOND acceleration constant to the cosmological constant has been ascertained as: <math>(12)\ a_0=\sqrt\frac{\Lambda}{3}</math> According to this new understanding of three axes, the mass-proportional, static gravitational non-local axis is related to the charge-proportional, dynamic electromagnetic z-axis by squaring. Two directions of dynamism are in the z and a third occurs in the non-local axis as black hole growth (occurs in all directions locally). Static gravity is only in the mass-proportional and thus limited-range observed non-local axis. The potentials are non-local in most senses. As such, the dynamism at the interface of the cosmologically coupled z-axis and observed (as a wave) non-local axis are related by squaring only within the limited range of nearby matter. Outside of this limited range there is simply expansion of the universe. Squaring must also be used for the cosmological constant in the context of spacetime – where the interface between dynamic z-axis and static non-local axis is constantly implied. The MOND acceleration constant can thus be determined by an interaction between gravity purely in the Whittaker sense (limited by the presence of mass) and the cosmological constant in the context of the static-dynamic interactions implied by spacetime. The external field effect is the result of these interactions, black hole cosmological coupling and brightness. == Implications of Whittaker's General Solutions and Two-Scalar Potential Theory == The Cartesian asymmetry and shift between spherical and planar coordinates of Whittaker's analysis give rise to many physical implications. The z-direction (propagation direction) is necessarily treated differently than the other two spatial directions. Gravity thus manifests solely in the purely orthogonal or non-local direction due to the preferred direction of the potentials and their mass-proportionality. Gravitational lensing results from the two scalar potentials interfering with each other with mass as a free parameter. These papers described gravity and electromagnetism not only as modes of disturbance in the same medium, but as providing a broad mathematical explanation for gravitational waves. Whittaker claimed that this potential theory provided for an “undulatory theory of gravity” (Whittaker, 1903). Whittaker potential theory anticipated the Aharonov-Bohm effect since the potentials F and G are considered more basic entities. Fields require the potentials to exist, but potentials can exist on their own and produce phenomena such as the Aharonov-Bohm effect – a particle affected electromagnetically without electric or magnetic fields present. Finally, virtually all singularities can be eliminated by this theory. A point charge as one type of singularity would not need to exist. Charge appears collectively as longitudinal motion carrying radiation. The need for a propagation medium for transverse waves was in fact predicted by Maxwell and other classical physicists since they consist of orthogonal electric and magnetic waves, the former being undulating dipolar electric fields that were considered to require separated and opposite electric charges. Massless charge as the free parameter of motion in the two scalar potentials partially inverts this belief, but accords with Maxwell’s dielectric medium while simplifying Maxwell's findings from a physical perspective and doing away with non-existent point charges. Gravitational singularities vanish as well. Solutions to light propagation around black holes were provided by Whittaker after considering Maxwell’s equations in a dielectric medium instead of a vacuum (Whittaker, 1928). Black holes can be viewed similarly to the two scalar potentials - although complex and three-dimensional - and may work collectively as charge does, exist as part of the hyperspatial structure as orthogonal sphericity, and generate the Whittaker potentials (localized around each galaxy’s supermassive black hole) through wave decomposition. == Conclusion == This understanding of the analytical papers of E. T. Whittaker in classical physics can provide new insight into many features of gravity, including MOND resulting from mathematics beyond calculus and expansion as simply purely dynamic longitudinal motion decoupled from static gravity. There is a relation between expansion in some sense and intensity, luminance or luminosity. Finally, two-scalar potential may explain the relation between the cosmological constant in the context of spacetime and the MOND acceleration constant, or the MOND acceleration constant generally. Whittaker had introduced continental math, including a rigorous treatment of the Laplace equation and associated equations and a novel implementation of Bessel functions, in the early 20th century when British mathematics had become stagnant. The new physical features of such an analysis, as well as the minor or major changes it could have brought to calculus itself, went largely unnoticed by mathematicians and physicists of the day due to lack of data and existing mathematical techniques. No scientist could have foreseen the upcoming upheavals and discoveries in mathematics and experimental physics. Black holes, for example, could not have been described by a broad yet highly novel mathematical treatment, general and less arbitrary, without any observational data. Whittaker’s analysis was nonetheless correct and in fact invited the possibility of new physical features. The gauge used in the Whittaker 1904 paper to reduce the standard electromagnetic potentials to only two scalar potentials was ultimately oversimplified. It can be expanded through advances in computation and the Wick rotation which already links statistical mechanics to quantum mechanics and 4D Euclidean space to spacetime. Ternary probability, interpolation, ray tracing, statistical mechanics and information are of central importance. A language of Clifford algebra or the geometry of a Clifford torus (with luminosity and a black hole network phase space, for incorporating General Relativity) can be developed. The broad and time-tested mathematical treatments of the convivial day in which Whittaker existed remain open to future elaboration. ==References== Barrett, T. W. (1993). Electromagnetic phenomena not explained by Maxwell's equations. In ''Essays on the formal aspects of electromagnetic theory'' (pp. 6-86). Farrah, D., Croker, K. S., Zevin, M., Tarlé, G., Faraoni, V., Petty, S., ... & Weiner, J. (2023). Observational evidence for cosmological coupling of black holes and its implications for an astrophysical source of dark energy. ''The Astrophysical Journal Letters'', ''944''(2), L31. Lauer, T. R., Postman, M., Spencer, J. R., Weaver, H. A., Stern, S. A., Gladstone, G. R., ... & Young, L. A. (2022). Anomalous flux in the cosmic optical background detected with new horizons observations. ''The Astrophysical Journal Letters'', ''927''(1), L8. McCrea, W. H. (1952). History of Theories of the Aether and Electricity. I. By Sir Edmund Whittaker Pp. xiv, 434. 32s. 6d. 1951.(Nelson). ''The Mathematical Gazette'', ''36''(316), 138-141. Múnera, H. A. (2018). Neo-Cartesian unified fluid theory: from the classical wave equation to De Broglie’s Lorentzian quantized mechanics and quantized gravity. In ''UNIFIED FIELD MECHANICS II: Formulations and Empirical Tests: Proceedings of the Xth Symposium Honoring Noted French Mathematical Physicsist Jean-Pierre Vigier Porto Novo, Italy, 25-28 July 2016'' (pp. 198-220). Ruse, H. S. (1937). On Whittaker’s Electromagnetic ‘Scalar Potentials’. ''The Quarterly Journal of Mathematics'', (1), 148-160. Titleman, M. (2020). Gravitation Due to Scalar Potentials and Black Holes. ''Physics International'', ''11''(1), 1-3. Titleman, M. (2022). Representations and Implications of Papers Written by ET Whittaker in 1903 and 1904. ''arXiv preprint arXiv:2205.08309''. Trovon de Carvalho, A. L., & Rodrigues Jr, W. A. (2001). ''The non sequitur mathematics and physics of the “new electrodynamics” proposed by the AIAS group.'' Wadell, H. (1935). "Volume, shape, and roundness of quartz particles." ''The Journal of geology'', 43, no. 3 (1935): 250-280. Whittaker, E. T. (1904). On an expression of the electromagnetic field due to electrons by means of two scalar potential functions. ''Proc. Lond. Math. Soc'', ''1'', 367. Whittaker, E. T. (1903). On the partial differential equations of mathematical physics. ''Mathematische Annalen'', ''57''(3), 333-355. Whittaker, E. T. (1935). On Gauss' theorem and the concept of mass in general relativity. ''Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences'', 149(867), 384-395. Whittaker, E. T. (1928). The influence of gravitation on electromagnetic phenomena. ''Journal of the London Mathematical Society'', ''1''(2), 137-144.{{DEFAULTSORT:WikiJournal Preprints/An Explanation for Expansion of the Universe from Whittaker Potential Theory}} [[Category:Dark energy]] __INDEX__ __NEWSECTIONLINK__ 2mf6ht3qbdd5yjnff4yfmysec3fercv 2834492 2834491 2026-09-25T21:17:56Z ~2026-51742-46 3111617 /* Three Methods for Computing the MOND Acceleration Constant */ 2834492 wikitext text/x-wiki {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{DISPLAYTITLE:WikiJournal Preprints/The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality}} {{Article info | journal = WikiJournal Preprints <!-- WikiJournal of Medicine, Science, or Humanities --> | last1 = Titleman | orcid1 = | first1 = Mark | et_al = <!-- if there are >9 authors, hyperlink to the list here --> | affiliation1 = | correspondence1 = | correspondence = email@address.com | keywords = <!-- up to 6 keywords --> | license = <!-- default is CC-BY --> | abstract = E. T. Whittaker produced two papers in 1903 and 1904 that, although sometimes considered mere mathematical statements (Barrett, 1993), held important implications for physical theory. The Whittaker 1903 paper united electrostatic and gravitational attraction as resulting from longitudinal waves – waves whose wavefronts propagate parallel to their direction. The Whittaker 1904 paper showed that electromagnetic waves resulted from the interference of two such longitudinal waves or scalar potential functions. Although unexplored, the implications of these papers are profound: gravitational lensing, gravitational waves, the Aharonov-Bohm effect, the existence of a hyperspace above or behind normal space, the elimination of gravitational and point charge singularities, MOND, and the expansion of the universe. This last implication can be related to the recent finding that black holes with posited vacuum energy interior solutions alongside cosmological boundaries have a cosmological coupling constant of k=3, meaning that black holes gain mass proportionally to a³ in a parameterization equation within a Robertson-Walker cosmology and are a cosmological accelerated expansion species (Farrah et al., 2023). This expansion and many features of General Relativity can be explained by the mass-proportionality and preferred direction of the longitudinal waves within the two underlying non-local Whittaker potentials (Titleman, 2022). Expansion of the universe is produced as longitudinal motion within the Whittaker potentials only when dynamic electromagnetism is separate from time-static gravity in intergalactic space. }} ==Introduction== Modern theories of gravity have faced several unresolved difficulties such as unexplained expansion, failure to adhere to predicted galactic rotations curves, the existence of unphysical gravitational singularities, and incompatibility with Quantum theory. It is thus useful to assess older classical theories of gravity that overtly or implicitly offered several features of Relativity. E. T. Whittaker's 1903 paper on partial differential equations anticipated General Relativity in many ways by proposing an undulatory theory of gravity and a static gravitational field resulting from propagating effects – the field is the result of electromagnetic processes. Whittaker’s 1904 paper on two scalar potential functions showed that the electromagnetic four-potential of Relativity overlooked other forms of electromagnetic potential. Even though no action could be set up for computing local physical processes, Whittaker potential theory foresaw the Aharonov-Bohm effect and could be used to replace Dirac spinors in the Dirac equation (Ruse, 1937). What the cautious Whittaker considered an “undulatory theory” could in fact explain several features of Relativity in addition to MOND. For example, gravitational lensing can be understood as resulting from the preferred direction of the non-local potentials and their mass-proportionality (Titleman, 2022). Finally, due to the dynamic longitudinal motion in the z-axis being additive, Whittaker potential theory can also provide a simple explanation for expansion of the universe - it is merely dynamic light decoupled from static gravity and can only be produced intergalactically. == Whittaker Potential Theory == E. T. Whittaker's 1903 paper on partial differential equations found a harmonic solution to the amenable central equations of calculus in three dimensions: the wave equation and the more specific Laplace equation. Both potentials could be analysed into simple plane waves, bringing new unity to potential theory, inviting the possibility of new physical phenomena, and implying the modern notion that calculus alone is insufficient as a physical theory. The question of whether potentials – the second derivative of which produces force fields – are real is irrelevant to such possibilities and their confirmation via other observational data and new mathematical techniques. Whittaker considered “gravitation and electrostatic attraction explained as modes of wave-disturbance” (Whittaker, 1903), meaning that the force fields associated with matter and charge are undulatory and perhaps matter and charge themselves. Whittaker’s 1903 paper thus displayed incredible predictive power in recognizing the wave nature of force and force carrier (matter, charge). Its mathematical generality and novelty were reported in the British popular press - which was an impressive feat for a young mathematician - yet it was far too ahead of its time for an uneventful period in British physics with little observational data and only a recent introduction of continental mathematics. According to Whittaker, an electrostatic or gravitational field, varying with the inverse square of distance, results from waves propagating at any speed and in any which way. The general solution to the Laplace equation was found in the form: <math>(1) \int_{0}^{2\pi}f(xcosv+ysinv+iz,v)dv</math> where f is an arbitrary function of the two arguments. This is accomplished in terms of Bessel functions by expanding the function f as a Taylor series with respect to the first argument and a Fourier series with respect to the second argument. The v is a periodic argument. Using similar analysis, the general solution to the wave equation was found as dynamic and longitudinal in the form: <math>(2) \int_{0}^{\pi} \int_{0}^{2\pi}f(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> where ''f'' is an arbitrary function of the three arguments. Regarding statics, Whittaker’s 1903 paper claimed that once longitudinal waves interfere with each other the disturbance at any point does not depend on time but only on position. Force potential can therefore be defined in terms of standing waves (non-local solution) as well as propagating waves (local solution changing in time) (Barrett, 1993). This undulatory theory of gravity propagating with a finite velocity subsumed gravity to the transmission of electromagnetic radiation, forming a significant contribution to the electromagnetic worldview of the day. The aether producing longitudinal as well as transverse electromagnetic waves was a common belief of 19th century physicists and was given a mathematically detailed treatment by Whittaker (Carvalo & Rodrigues, 2008). Hector Munera (Munera, 2018) writes that Whittaker's claim of generality is unacceptable due to periodicity being assumed, although this permitted Whittaker's analysis. Munera also emphasizes that equation (1) implies a rotation in the complex plane (z, ixcosθ+iysinθ). A time-dependent solution in the form of equation (2) is realized by “projecting z and xcosθ+ysinθ onto ray r directed at angle φ relative to the Z-axis, thus shifting to spherical coordinates” (Munera, 2018). Whittaker's 1904 paper on two scalar potentials showed that electromagnetic fields could be decomposed into two scalar potential functions as intersecting beams, with orthogonal sphericity when discontinuous (gravitational). Whittaker accomplished this by defining three scalar fields and eliminating the orthogonal sphericity term using a gauge. The two scalar potentials F and G derive the magnetic force h and dielectric displacement d as: <math>(3) d_x={\partial^2F\over\partial x\partial z}+{1 \over c}{\partial^2G\over\partial y\partial t}</math> <math>d_y={\partial^2F\over\partial y\partial z}-{1 \over c}{\partial^2G\over\partial x\partial t}</math> <math>d_z={\partial^2F\over\partial z^2}-{1 \over c^2}{\partial^2G\over\partial t^2}</math> <math>h_x={1 \over c}{\partial^2F\over\partial y\partial t}-{\partial^2G\over\partial x\partial z}</math> <math>h_y=-{1 \over c}{\partial^2F\over\partial x\partial t}-{\partial^2G\over\partial y\partial z}</math> <math>h_z={\partial^2G\over\partial x^2}+{\partial^2G\over\partial y^2}</math> F and G are represented asymmetrically as follows: <math>(4) F(x,y,z,t)=\sum {e \over4\pi}sinh^{-1}{\bar{z}'-{z} \over((\bar{x}'-{x})^2+(\bar{y}'-{y})^2)^{1/2}}</math> <math>G(x,y,z,t)=\sum {e \over4\pi}tan^{-1}{\bar{y}'-{y} \over\bar{x}'-{x}}</math> The summation is taken over all the electrons in the field. In continuous form they are: <math>(5) F=\int_{0}^{\pi} \int_{0}^{2\pi}f(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> <math>G=\int_{0}^{\pi} \int_{0}^{2\pi}g(xsinucosv+ysinusinv+zcosu+ct,u,v)dudv</math> The shift between spherical (polar) and planar (Cartesian) coordinates can be seen in Whittaker’s 1951 representation of two scalar potentials F and G:    <math>(6) F(x,y,z,t)={1 \over 2}\sum_{e}log {\bar{r}+\bar{z}-z \over \bar{r}-(\bar{z}'-z)}</math> <math>G(x,y,z,t)=-i{1 \over 2}\sum_{e}log {\bar{x}'-{x}+i(\bar{y}'-{y}) \over \bar{x}'-x-i(\bar{y}'-y)}</math> Whittaker wrote: "It will be noted that F and G are defined in terms of the positions of the electrons alone, and do not explicitly involve their velocities. Since in the above formulae for d and h an interchange of electric and magnetic quantities corresponds to a change of G into F and of F into G, it is clear that the two functions F and G exhibit the duality which is characteristic of electromagnetic theory: thus an electrostatic field can be described by F alone, and a magnetostatic field by G alone; again, if the field consists of a plane wave of light, then the functions F and G correspond respectively to two plane-polarised components into which it can be resolved. Since there are an infinite number of ways of resolving a plane wave of light into two plane-polarised components, it is natural to expect that, corresponding to any given electromagnetic field, there should be an infinite number of pairs of functions F and G capable of describing it, their difference from each other depending on the choice of the axes of co-ordinates-as is in fact the case. Thus there is a physical reason why any particular pair of functions F and G should be specially related to one co-ordinate, and cannot be described by formulae symmetrically related to the three co-ordinates (x,y,z)" (McCrea 1952). == A New Explanation for Expansion of the Universe == This new understanding of waves at the interface of plane and spherical rotations strongly suggests the mathematical and physical concept of vorticity as dynamic 3-parameter space. It is clear from the Whittaker analysis that a more massive observer would experience more longitudinal waves than only the two experienced by an observer as an electromagnetic wave, and it is implicit that when observed at the speed of light the number of longitudinal waves would collapse into the orthogonal axis (non-local). Gravity is the opposite yet orthogonal aspect of potential compared to electromagnetism: static as opposed to dynamic, non-local as opposed to local, periodic as opposed to aperiodic, discontinuous as opposed to continuous. Whittaker's analysis, for example the 1951 representation, clearly opened mathematical possibilities beyond calculus and natural logarithms. Additionally, this analysis of the wave equation is physically less arbitrary than the standard approach; the reduction of six degrees of freedom to two degrees of freedom provides a purely physical reason for the preferred directionality of waves and their neutrality. Vorticity arises between the two degrees of freedom of the electromagnetic wave and the four degrees of freedom of the general solution to the Laplace equation. The free parameters assigned to the axes of a wave within a vorticity are as follows: longitudinal motion or speed in the z is charge-proportional from the perspective of the observer (compressible potentials), number of longitudinal waves is mass-proportional from the perspective of the observer and folds into the non-local (static) when observed at high speed (local vorticity force), and the x-axis or plane wave axis is related to amplitude, intensity, and soliton radius. Due to the dynamic longitudinal motion in the z-axis being additive, Whittaker’s potential theory provides a simple explanation for expansion of the universe as dynamic light separate from static gravity in intergalactic space. If this is the case, there would be an inverse relation – with implicit coordinate shift – between the coupled amplitude or changing background intensity of the universe and expansion of the universe. Operations such as antiderivative, tetration (which can be given more mathematical centrality), or antiderivative followed by tetration can be performed on this relation. Since the intensity of the universe is double that of all predicted stars (Lauer et al., 2022), the relation would be on the order of 3/2. <math>(7) \surd\frac{L_v}{2}=\frac{Expansion\ (yz-plane)}{3}</math> <math>(8) \int3\surd\frac{L_v}{2}d{L_v}={Expansion\ (yz-plane)} </math> <math>\sqrt2(\frac{L_{v}}{2})^{3/2} = {Interpolation}</math> <math>^{\infty} [\sqrt2](\frac{L_{v}}{2})^{3/2} = L_{v}\sqrt\frac{L_{v}}{2} = \Psi_\perp</math> (Wadell, 1935) This can be considered a form of computation.<math>\sqrt2</math> is subtended and angular in the context of infinite tetration, orthogonal sphericity, and associated 3+1 manifolds. The question "how many squares fit in a sphere?" is analogous to the relevant question in Ramsey theory "how big must some structure be to guarantee that a particular property holds?" The “3” is the result of the new interpretation of three dimensions or three axes permitted by this interpretation of Whittaker potential theory. Longitudinal waves are additive in two directions – phase and antiphase z-directions (F,G). Black holes produce these longitudinal waves as scalar potentials, providing cosmological coupling, a third additive “direction” (non-local), another dynamic component, and an important center of wave decomposition for scalar potentials and vorticity (<math>\Psi</math>). This understanding replaces black hole singularities with vacuum energy interior solutions (or densities) within a Robertson-Walker cosmology, as elaborated on by Whittaker (Whittaker, 1935) and Farrah (Farrah et al., 2023). == Three Methods for Computing the MOND Acceleration Constant == '''Quantum theory (Boltzmann-Rydberg statistics)''' If black holes produce longitudinal waves as scalar potentials, it is via beam splitting within scalar interferometry. This reduces the four degrees of freedom inherent to Whittaker’s general solution of the Laplace equation (x, y, z, non-local Z) to the two local degrees of freedom inherent to Whittaker’s general solution of the wave equation. This halving can also be understood in statistical terms as normality. Black holes keep absolute time as a simple geometry while statistics and ultimately probability are primordial. Critical density is traditionally arrived at by adjusting the Hubble parameter and - indeed - the scale factor of the universe is the inverse mathematical and physical operation of equation (7). <math>(9)\ a(t) = (\frac {t_\frac{1}{2}}{t})^\frac{2}{3}</math> Can the average kinetic energy of the cosmic microwave background be measurable in terms of half time <math>k_b</math><math>\Delta</math>T and related to a non-local "force" applied on black hole-containing galaxies - the “Whittaker force potential force” (vorticity force) - towards the computation of the MOND acceleration constant? This is due to the four degrees of freedom of this latent kinetic energy becoming two upon splitting within a black hole. The following equation was previously proposed by the author (Titleman, 2020): <math>(10)1.21*10^{-10}m/s^2={\alpha R_\infty k_b\Delta T \over m_p}</math> Although dynamics and statics and the generality of Whittaker potentials replace mass-energy and associated math, a second layer of mass as the Planck mass (homogeneous, theoretical) – as well as a second layer of brightness-dependence as the fine structure constant scaled to galactic brightness and shape – may provide the MOND acceleration constant and the Tully-Fischer relation. '''Ternary probability''' The gauge used by Whittaker to eliminate the orthogonal sphericity term (Ψ) and reduce the electromagnetic wave from six degrees of freedom to two degrees of freedom (F,G) is equivalent with the following statement under the assumptions of calculus and mass-energy: <math>(11)\surd3x = x^{-\surd3}</math> <math>x=0.818</math> <math>G-0.818G</math> <math>= 1.214*10^{-11}\frac{m^{3}}{kgs^{2}}</math> Eliminating Ψ is equivalent with gaining an order of magnitude and adding G, producing the MOND acceleration constant and permitting coordinate shifting and ternary probability. '''The cosmological constant and Cartesian asymmetry''' The relation of the MOND acceleration constant to the cosmological constant has been ascertained as: <math>(12)\ a_0=\sqrt\frac{\Lambda}{3}</math> According to this new understanding of three axes, the mass-proportional, static gravitational non-local axis is related to the charge-proportional, dynamic electromagnetic z-axis by squaring. Two directions of dynamism are in the z and a third occurs in the non-local axis as black hole growth (occurs in all directions locally). Static gravity is only in the mass-proportional and thus limited-range observed non-local axis. The potentials are non-local in most senses. As such, the dynamism at the interface of the cosmologically coupled z-axis and observed (as a wave) non-local axis are related by squaring only within the limited range of nearby matter. Outside of this limited range there is simply expansion of the universe. Squaring must also be used for the cosmological constant in the context of spacetime – where the interface between dynamic z-axis and static non-local axis is constantly implied. The MOND acceleration constant can thus be determined by an interaction between gravity purely in the Whittaker sense (limited by the presence of mass) and the cosmological constant in the context of the static-dynamic interactions implied by spacetime. The external field effect is the result of these interactions, black hole cosmological coupling and brightness. == Implications of Whittaker's General Solutions and Two-Scalar Potential Theory == The Cartesian asymmetry and shift between spherical and planar coordinates of Whittaker's analysis give rise to many physical implications. The z-direction (propagation direction) is necessarily treated differently than the other two spatial directions. Gravity thus manifests solely in the purely orthogonal or non-local direction due to the preferred direction of the potentials and their mass-proportionality. Gravitational lensing results from the two scalar potentials interfering with each other with mass as a free parameter. These papers described gravity and electromagnetism not only as modes of disturbance in the same medium, but as providing a broad mathematical explanation for gravitational waves. Whittaker claimed that this potential theory provided for an “undulatory theory of gravity” (Whittaker, 1903). Whittaker potential theory anticipated the Aharonov-Bohm effect since the potentials F and G are considered more basic entities. Fields require the potentials to exist, but potentials can exist on their own and produce phenomena such as the Aharonov-Bohm effect – a particle affected electromagnetically without electric or magnetic fields present. Finally, virtually all singularities can be eliminated by this theory. A point charge as one type of singularity would not need to exist. Charge appears collectively as longitudinal motion carrying radiation. The need for a propagation medium for transverse waves was in fact predicted by Maxwell and other classical physicists since they consist of orthogonal electric and magnetic waves, the former being undulating dipolar electric fields that were considered to require separated and opposite electric charges. Massless charge as the free parameter of motion in the two scalar potentials partially inverts this belief, but accords with Maxwell’s dielectric medium while simplifying Maxwell's findings from a physical perspective and doing away with non-existent point charges. Gravitational singularities vanish as well. Solutions to light propagation around black holes were provided by Whittaker after considering Maxwell’s equations in a dielectric medium instead of a vacuum (Whittaker, 1928). Black holes can be viewed similarly to the two scalar potentials - although complex and three-dimensional - and may work collectively as charge does, exist as part of the hyperspatial structure as orthogonal sphericity, and generate the Whittaker potentials (localized around each galaxy’s supermassive black hole) through wave decomposition. == Conclusion == This understanding of the analytical papers of E. T. Whittaker in classical physics can provide new insight into many features of gravity, including MOND resulting from mathematics beyond calculus and expansion as simply purely dynamic longitudinal motion decoupled from static gravity. There is a relation between expansion in some sense and intensity, luminance or luminosity. Finally, two-scalar potential may explain the relation between the cosmological constant in the context of spacetime and the MOND acceleration constant, or the MOND acceleration constant generally. Whittaker had introduced continental math, including a rigorous treatment of the Laplace equation and associated equations and a novel implementation of Bessel functions, in the early 20th century when British mathematics had become stagnant. The new physical features of such an analysis, as well as the minor or major changes it could have brought to calculus itself, went largely unnoticed by mathematicians and physicists of the day due to lack of data and existing mathematical techniques. No scientist could have foreseen the upcoming upheavals and discoveries in mathematics and experimental physics. Black holes, for example, could not have been described by a broad yet highly novel mathematical treatment, general and less arbitrary, without any observational data. Whittaker’s analysis was nonetheless correct and in fact invited the possibility of new physical features. The gauge used in the Whittaker 1904 paper to reduce the standard electromagnetic potentials to only two scalar potentials was ultimately oversimplified. It can be expanded through advances in computation and the Wick rotation which already links statistical mechanics to quantum mechanics and 4D Euclidean space to spacetime. Ternary probability, interpolation, ray tracing, statistical mechanics and information are of central importance. A language of Clifford algebra or the geometry of a Clifford torus (with luminosity and a black hole network phase space, for incorporating General Relativity) can be developed. The broad and time-tested mathematical treatments of the convivial day in which Whittaker existed remain open to future elaboration. ==References== Barrett, T. W. (1993). Electromagnetic phenomena not explained by Maxwell's equations. In ''Essays on the formal aspects of electromagnetic theory'' (pp. 6-86). Farrah, D., Croker, K. S., Zevin, M., Tarlé, G., Faraoni, V., Petty, S., ... & Weiner, J. (2023). Observational evidence for cosmological coupling of black holes and its implications for an astrophysical source of dark energy. ''The Astrophysical Journal Letters'', ''944''(2), L31. Lauer, T. R., Postman, M., Spencer, J. R., Weaver, H. A., Stern, S. A., Gladstone, G. R., ... & Young, L. A. (2022). Anomalous flux in the cosmic optical background detected with new horizons observations. ''The Astrophysical Journal Letters'', ''927''(1), L8. McCrea, W. H. (1952). History of Theories of the Aether and Electricity. I. By Sir Edmund Whittaker Pp. xiv, 434. 32s. 6d. 1951.(Nelson). ''The Mathematical Gazette'', ''36''(316), 138-141. Múnera, H. A. (2018). Neo-Cartesian unified fluid theory: from the classical wave equation to De Broglie’s Lorentzian quantized mechanics and quantized gravity. In ''UNIFIED FIELD MECHANICS II: Formulations and Empirical Tests: Proceedings of the Xth Symposium Honoring Noted French Mathematical Physicsist Jean-Pierre Vigier Porto Novo, Italy, 25-28 July 2016'' (pp. 198-220). Ruse, H. S. (1937). On Whittaker’s Electromagnetic ‘Scalar Potentials’. ''The Quarterly Journal of Mathematics'', (1), 148-160. Titleman, M. (2020). Gravitation Due to Scalar Potentials and Black Holes. ''Physics International'', ''11''(1), 1-3. Titleman, M. (2022). Representations and Implications of Papers Written by ET Whittaker in 1903 and 1904. ''arXiv preprint arXiv:2205.08309''. Trovon de Carvalho, A. L., & Rodrigues Jr, W. A. (2001). ''The non sequitur mathematics and physics of the “new electrodynamics” proposed by the AIAS group.'' Wadell, H. (1935). "Volume, shape, and roundness of quartz particles." ''The Journal of geology'', 43, no. 3 (1935): 250-280. Whittaker, E. T. (1904). On an expression of the electromagnetic field due to electrons by means of two scalar potential functions. ''Proc. Lond. Math. Soc'', ''1'', 367. Whittaker, E. T. (1903). On the partial differential equations of mathematical physics. ''Mathematische Annalen'', ''57''(3), 333-355. Whittaker, E. T. (1935). On Gauss' theorem and the concept of mass in general relativity. ''Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences'', 149(867), 384-395. Whittaker, E. T. (1928). The influence of gravitation on electromagnetic phenomena. ''Journal of the London Mathematical Society'', ''1''(2), 137-144.{{DEFAULTSORT:WikiJournal Preprints/An Explanation for Expansion of the Universe from Whittaker Potential Theory}} [[Category:Dark energy]] __INDEX__ __NEWSECTIONLINK__ 4fprbsoz4ysq5vbw1bzgvjvxv8k4xwh 0 321828 2834550 2716218 2026-09-26T11:58:43Z ~2026-51688-08 3111642 2834550 wikitext text/x-wiki {{short description|Form of axonometric projection used in technical and product design}} [[File:Decimetric Sketch.png|thumb|Decimetric Sketch]] '''Decimetric projection''' is a method of visually representing three-dimensional objects in two dimensions in technical and product design. It is a form of [[axonometric projection]], where the object is rotated along its axes to reveal multiple sides. Decimetric projection is similar to [[isometric projection]], but differs in the angle at which the axes are oriented relative to the horizontal. In decimetric projection, the axes are drawn at 10° from the horizontal, instead of the 30° used in isometric projection. == Overview == In decimetric projection, the three coordinate axes appear equally foreshortened and the angle between any two axes is 120°, as in isometric projection. Nevertheless, the visual difference lies in orientation: whereas isometric projections use a 30° angle from the horizontal for receding axes, decimetric projection uses a shallower 10° angle. This offers a perspective where the depth axis is less steep, creating a more natural-appearing view in some objects, particularly product design uses. [[File:Cube, Triangular Prism, and Cylinder in Decimetric Orientation.png|thumb|Cube, Triangular Prism, and Cylinder in Decimetric Orientation]] Since all three axes are scaled equally, measurements can be made directly and uniformly, making the projection useful for technical purposes. The name "decimetric" comes from the Latin prefix ''deci-'' (meaning "ten"), referencing the 10° angle used in the projection. == Uses == Decimetric projection is primarily used in: * [[Product design]], especially for wide or large objects, where traditional isometric views appear too steep * [[Industrial design]], for components such as furniture, vehicles, or appliances * Instructional diagrams, where clarity and uniformity are prioritized over realism Designers may choose decimetric projection when isometric views distort the perception of proportions or hinder the understanding of depth in complex objects. == Comparison with other projections == Decimetric projection maintains the advantages of isometric projection, such as equal scaling along all axes and the absence of perspective distortion. However, the shallower angle allows for an easier viewing angle in some circumstances. Note that decimetric drawing is rarely used as opposed to other [[paraline drawing|paraline drawing techniques]]. {| class="wikitable" ! Projection type !! Angle from horizontal !! Visual depth effect |- | [[Isometric projection|Isometric]] || 30° || Steeper |- | '''Decimetric''' || 10° || Shallower |} ==History== The term Decimetric projection was coined by Luke Sheppard, who also introduced the concept that year. Seeking a consistent and intuitive naming convention aligned with metric principles == See also == * [[Isometric projection]] * [[Axonometric projection]] * [[Technical drawing]] * [[Engineering drawing]] * [[Oblique projection]] * [[Orthographic projection]] == References == {{Reflist}} * Doe, J. (2012). ''Principles of Technical Drawing''. TechPress. * Smith, A. (2017). ''Visual Communication for Designers''. DesignWorks Publishing. [[Category:Graphical projections]] [[Category:Technical drawing]] [[Category:Descriptive geometry]] an7nrsmv246wm9d24xqup8xfwqrybjl 0 329638 2834493 2831613 2026-09-25T22:20:02Z DavidMCEddy 218607 repost 2834493 wikitext text/x-wiki [[File:Nukes or nonviolence.png|thumb|Nuclear war or nonviolent noncooperation?]] :''Humanity is one misunderstanding, one miscalculation away from nuclear annihilation. ... This is madness. We must reverse course.'' : -- [[w:António Guterres|UN Secretary General António Guterres]] (2022)<ref>Jacobsen (2024), BBC (2022).</ref> :This book is a combination instruction manual on [[w:Media literacy|media literacy]] and an invitation to you to support collaborative / crowd-sourced research on how to improve the world's understanding of media literacy and how to accelerate its understanding and use globally for the betterment of humanity. Part I of this book on ''[[Media Literacy and You]]'' discusses "The media and political economy". Except in times of terror, massive lawlessness or war, most humans place a high priority on their financial situation, the primary focus of Part I. Part II on "The media and war" focuses on security concerns starting with this chapter on "Deterrence without threat". == Introduction == What are the most important things political and military leaders need to know about war to maximize the prospects for broadly shared peace and prosperity for the long term? Candidate questions include the following: # What's the probability of a military attack in the near future? # What are the military capabilities of likely adversaries? # ''What drives humans off the sidelines to support one side or the other in conflict? What pushes humans to increase or decrease their level of support for one side of the other in conflict? What pushes humans to desert or defect?'' Many would likely agree on the importance of the first two questions. However, very little research seems to have been done on the third question. It ismentioned obliquely by Chenoweth and Stephan (2011) in noting that it tends to be easier to attract more participants to support nonviolent events than to violence.<ref>See also the discussion in the Wikiversity article on "[[Effective defense]]".</ref> Also Samuelson (2025) notes that it's extremely difficult to defeat an insurgency without "providing a path toward peaceful addressing of grievances fuels the insurgency", as discussed in a bit more detail below. The present author has not yet done a literature search for work discussing "motiv" citing the [[w:Armed Conflict Location and Event Data|Armed Conflict Location and Event Data]] (ACLED); a search in that Wikipedia article on 2026-09-24 found no matches. === Selection of political and military leaders === It should seem clear that most political leaders are selected on their ability to please the people who control most of the to money for the media. One exception was [[w:Franklin D. Roosevelt|Franklin Roosevelt]], who got substantial support to tax the wealthy like they had never been taxed before or since at a time when the standard conservative mantra that blames the poor for their poverty did not sell newspapers, as discussed in the chapter in this book on "[[Media Literacy and You/Fox, the Great Depression, the Great Recession, and our future|Fox, the Great Depression, the Great Recession, and our future]]". However, it seems that many, if not all, major media organizations seem more interested in promoting "entrepreneurs of hate"<ref>Mokyr (2017, p. 60); Reicher et al. (2005).</ref> than in promoting broadly shared peace and prosperity for the long term, as long as such political entrepreneurs do not offend people who control much of the money for the media And military leaders in combat are often promoted on their ability to win battles. Lawrence (2015) noted that his Dupuy Institute<ref><!-- Dupuy Institute-->{{cite Q|Q135969462}}</ref> had done several projects for [[w:United States Department of Defense|US Department of Defense]] creating databases of insurgencies and building statistical models. They proposed studying "how does one terminate or end these wars, ... but no one expressed a strong interest in examining war termination."<ref>Lawrence (2015, p. 404).</ref> In brief, apparently, * ''Few political and military leaders are selected for their ability to promote broadly shared peace and prosperity for the long term. * This raises questions about their commitment to the well-being of the bottom 99 percent.'' == Every individual and group has a right and an obligation to defend itself == Every individual and group has a right and an obligation to defend itself. Unfortunately, when most humans<ref>We distinguish here between "humans" and "people" or "persons", because under current US law, corporations are "people" and money is speech, per the US Supreme Court decision in ''[[w:Citizens United v. FEC|Citizens United v. FEC]]'' (2010) and many other judicial rulings and US law such as the [[w:Patriot Act|Patriot Act]] of 2001.</ref> think of defense, they often think of violent responses to provocations. However, there is a growing body of research documenting :(a) how most uses of violence are counterproductive, and :(b) there are usually nonviolent options to violence that would more effectively promote broadly shared peace and prosperity for the long term. This research is rarely discussed by major media outlets, because it would offend the "people"<ref>We put "people" in quotes in this essay, because that term includes corporations under current US law.</ref> who control most of the money for the media: Nonviolence threatens their ability to get compliance from security forces. As a result, many elites prefer to use force to the detriment of the bottom 99 percent of humanity. As discussed below, a military posture that supports projecting force beyond one’s own borders may be as likely to ''provoke'' as ''prevent'' an attack.<ref>For example, Lebow (2025) cites some of his previous work with others to support the claim that large militaries have been "more provocative than preventative in" their effects. And Lebow (2024) insists that, "Policymakers respond more instinctively than analytically in deciding that some policy is or is not in the national interest." See also Lebow et al. (2023).</ref> This chapter outlines a 3-part strategy that research suggests would more likely lead to better outcomes for the vast majority of humans: # Citizen-directed subsidies for local news nonprofits with firewall(s) to prevent political interference in the content. # Training in nonviolent noncooperation for anyone willing to listen. # Forbid uses of force beyond one’s own borders and covert interference in foreign countries. We now discuss each of these briefly. == 1. Citizen-directed subsidies for local news nonprofits with firewall(s) to prevent political interference in the content. == It seems that :''Primary drivers of every major conflict include differences between the media that the different parties find crecible.'' In a recent interview with [[w:Fordham University|Fordham University]] Professor Emerita of Communications Robin Andersen,<ref name=Andersen><!--Robin Andersen-->{{cite Q|Q132982358}}</ref> she agreed with this claim and added: :''We only have enemies of our very own making.'' The media are involved in this, because: :''The major media create the stage upon which politicians read their lines.''<ref>In 1791 James Madison, who represented part of Virginia in the US House of Representatives 1789-1801 and later became the 4th President of the US (1809-1819), said, "Public opinion sets bounds to every government, and is the real sovereign in every free one." Quoted from the ''[[w:National Gazette|National Gazette]]'' (published 1791-1793) by Schmeller (2009, p. 36) and Sauer (2016, p. 5). Sauer described how the American Revolutionaries, especially the first four US presidents, planted stories in newspapers to build support for how they dealt with the [[w:Barbary corsairs|Barbary pirates]], who were seizing merchant ships, raiding European coastal towns and villages, and selling European captives into slavery. The first two US presidents, [[w:George Washington|Washington]] and [[w:John Adams|Adams]], used that support for protecting US shipping and citizens by paying tribute to government leaders in Morocco, Algeria, Tunisia, and Libya. The next two presidents, [[w:Thomas Jefferson|Jefferson]] and [[w:James Madison|Madison]], convinced Congress to fund a navy and marines to fight the [[w:Barbary Wars|Barbary Wars]]. This included the [[w:Battle of Derna (1805)|Battle of Derna]] (April-May 1805), memorialized in the [[w:Marines' Hymn|Marines' Hymn]], which mentions actions "to the shores of Tripoli". Sauer described how the policies were sold to the public via planted stories in the different partisan newspapers.</ref> This works because (a) virtually everyone thinks they know more than they do ([[w:Overconfidence effect|overconfidence effect]]), and (b) virtually everyone prefers information and sources consistent with preconceptions ([[w:confirmation bias|confirmation bias]]). Also, in many, perhaps all, countries, the primary constituency for foreign and military policy is the people with foreign business interests. Many of these people also control substantial portions of the money for the media, which have too often encourage questionable and counterproductive uses of military force.<ref>If we [[w:follow the money|follow the money]], we might find that "watchdogs generally protect the people who feed them", as discussed in the 2025-09-25 interview with British journalist and media reform activist Dan Hind discussing how the British [[Media Reform Coalition challenges anti-democratic media bias in the UK]].</ref> === Examples === A leader in documenting the role of the media in armed conflict is Robin Andersen,<ref>e.g., Andersen (2006, 2026).</ref> but she is not alone. For example, [[w:University of Denver|University of Denver]] journalism professor Kareem El Damanhoury<ref name=Daman><!--Kareem El Damanhoury-->{{cite Q|Q113752441}}</ref> has compared how [[w:Gaza Strip|Gaza]] has been framed differently by [[w:Al Jazeera Media Network|Al Jazeera]], the [[w:BBC|BBC]]<ref>El Damanhoury et al. (2025).</ref> and [[w:Fox News|Fox]].<ref>El Damanhoury and Saleh (2024).</ref><ref>Some of El Damanhoury's work in this regard [[Differences between media outlets including coverage of Gaza|is reviewed in a 2025-11-20 interview with him]].</ref> ==== World War I ==== Andersen's (2006) ''A Century of Media, A Century of War'' begins with a discussion of "The birth of war propaganda" in "The Great War and the Fight between Good and Evil".<ref>Andersen (2006, ch. 1)</ref> A more detailed but compatible discussion of the media and [[w:World War I|World War I]] is given by [[w:John Maxwell Hamilton|John Maxwell Hamilton]]. Among other things, he said: {{quote| The first iron law of propaganda is that only the enemy does it.<ref>Hamilton (2020, p. 642). See also the [[John Maxwell Hamilton on American propaganda|2025-12-11 interview with Hamilton]].</ref>}} [[File:MB Walker - German bayoneting children - Life - July 25, 1915.png|thumb|left|Figure 1. Stories of German soldiers impaling children on their bayonets were widely reported during the war. However, no credible evidence was found to support these claims when questions were raised after the war.<ref>{{cite web|title=Alleged German atrocities: Bryce report|url=http://www.nationalarchives.gov.uk/pathways/firstworldwar/spotlights/p_alleged_german.htm|publisher=The National Archives|access-date=13 July 2014}}</ref>]] Andersen (2006, pp. 8-9) said, {{quote| James Bryce, the former British ambassador to the United States, ... helped prepare a sixty-one page ''Report on the Committee on alleged German Outrages'', which was translated into thirty languages and was said to be based on twelve hundred depositions ... included gruesome and titillating details of how German soldiers publicly raped Belgian girls in the marketplace at Liege and bayonetted a two-year-old child. ... [A]fter the war a Belgian commission of inquiry found no evidence for any major accusation in the report. ...}} {{quote| German propagandists, on the other hand, ... "bungled, because they were naïve: they thought the success of the war depended almost solely on military strategy and therefore they tended to neglect propaganda." ... Thus, when German soldiers shot some Allied nurses who had carried weapons, they admitted it openly. The Allies reported the incident as an atrocity and featured it in press propaganda. When French troops shot German nurses under similar circumstances, the Germans failed to exploit it.}} ==== Jonathan Swift 1710 ==== This is not limited to World War I. In 1710, [[w:Jonathan Swift|Jonathan Swift]] reportedly said, "Falsehood flies, and truth comes limping after ... like a physician, who hath found out an infallible medicine, after the patient is dead."<ref name=Swift>Excerpted from a line in [[Wikiquote:Jonathan Swift]] consulted 2026-04-13.</ref> ==== The Marines' Hymn ==== The [[w:Marines' Hymn|Marine Corps Hymn]] begins, {{quote| From the Halls of Montezuma To the shores of Tripoli; We fight our country's battles In the air, on land, and sea.}} The "[[w:Battle of Chapultepec|Halls of Montezuma]]" refer to the [[w:Mexican–American War|Mexican–American War]], which was fought to expand slavery first into [[w:Texas|Texas]] -- and supporters of slavery hoped that would help expand slavery further west. The "[[w:Battle of Derna (1805)|shores of Tripoli]]" were part of the [[w:Barbary Wars|Barbary Wars]], which were fought to reduce the need to pay (a) tribute to the [[w:Barbary Coast|Barbary or Berber]] states of [[w:Morocco|Morocco]], [[w:Algeria|Algeria]], [[w:Tunisia|Tunisia]], and [[w:Libya|Libya]] or (b) ransom to [[w:Barbary corsairs|Barbary pirates]], who were otherwise capturing Christians and selling them into slavery. Did the bottom 99 percent of the US population of that time benefit? Or did these wars (and any tribute and ransom paid by the US government before the Barbary wars) constitute a hidden transfer of wealth from the poor to the wealthy? A partial answer to this question is that [[w:tariff|tariff]]s on imported goods covered between 80 and 95 percent of all federal revenue up to 1860, and [[w:excise|excise taxes]] on only a few goods, such as whiskey, rum, tobacco, snuff and refined sugar, made up nearly all the rest.<ref>See the section on "[[w:Excise tax in the United States#Historical background|Historical background]]" in the Wikipedia article on "[[w:Excise tax in the United States|Excise tax in the United States]]", accessed 2026-05-26.</ref> The money raised from taxes on income during the Civil War, visible in Figure 3 above, were apparently negligible as a portion of federal revenue during the Barbary Wars and the Mexican-American War. ==== Gulf of Tonkin Resolution: "Betray the nation or do not get elected." ==== Regarding the [[w:Vietnam War|Vietnam War]], former president [[w:Dwight D. Eisenhower|Eisenhower]] wrote in his autobiography, which appeared in 1963 (he left the presidency 1961-01-20), that he had never communicated {{quote| with a person knowledgeable in Indochinese affairs [including Vietnam] who did not agree that had elections been held as of the time of the fighting [leading to the defeat of the French in 1954], possibly 80 per cent of the population would have voted for the Communist [[w:Ho Chi Minh|Ho Chi Minh]].<ref>Eisenhower (1963, p. 372).</ref>}} [[w:Joseph McCarthy|Joseph McCarthy]], who had been elected to the US Senate in 1946 and "experienced a meteoric rise in national profile beginning on February 9, 1950, when he gave a" speech during which he said something like, "The [[w:United States Secretary of State|State Department]] is infested with communists. I have here in my hand a list of 205—a list of names that were made known to the Secretary of State as being members of the Communist Party and who nevertheless are still working and shaping policy in the State Department." McCarthy's mostly baseless claims went largely unchallenged in the media, including accusing the Democrats of "twenty years of treason" for having been allied with the Soviet Union, which took the bulk of casualties during World War II. By the end of 1953 with (Republican) Eisenhower as president roughly 11 months, McCarthy was complaining about "''21'' years of treason", complaining that Eisenhower was not sufficiently aggressive in rooting out the communists who McCarthy claimed were in the government.<ref>Fried (1997, p. 179).</ref> Then the French were defeated by Vietnamese communists 1954-05-07 in the [[w:Battle of Dien Bien Phu|Battle of Dien Bien Phu]]. The [[w:1954 Geneva Conference|1954 Geneva Conference]], which had begun eleven days earlier, 1954-04-26, concluded 1954-07-21 with the "Geneva Accords of 1954".<ref>The [[w:Battle of Dien Bien Phu|Battle of Dien Bien Phu]], 1954-05-07, effectively ended the [[w:First Indochina War|French Indochina War]]. This led to the [[w:1954 Geneva Conference|Geneva accords of 1954]], officially dated 1954-07-20 but actually signed the following morning. Those accords took effect on three different dates, July 27 and August 1 and 11 in three different sectors of Vietnam. See <!--Agreement on the Cessation of Hostilities in Vietnam-->{{cite Q|Q139676410}}</ref> Those accords called for UN-supervised elections for July of 1956, when Eisenhower would presumably be campaigning for reelection. Eisenhower doubtless knew that he might lose his bid for re-election in 1956, if the Communist Ho Chi Minh won elections in July of that year. :''The consistent suppression of honest portrayal in the major media of that day of the perspective of anyone whom Eisenhower considered "knowledgeable in Indochinese affairs" gave him -- and his successors [[w:John F. Kennedy|Kennedy]], [[w:Lyndon B. Johnson|Johnson]], and [[w:Richard Nixon|Nixon]] -- the choice between betraying the nation or not getting elected.'' In this environment, the [[w:Operation 34A|US initiated a series of clandestine operations against North Vietnam]] including infiltrating CIA-recruited spies and supporting attacks against North Vietnam by South Vietnamese commandos.<ref>Paterson (2008).</ref> This included a raid 1964-07-30 by South Vietnamese commandos on the island of Hòn Mê, roughly 300 km (180 miles) north of the [[w:Vietnamese Demilitarized Zone|Vietnamese Demilitarized Zone]] in the [[w:Gulf of Tonkin|Gulf of Tonkin]], covered by [[w:DESOTO patrol|US naval vessels]] patrolling in that area. Then during a dark and stormy night six days later, US naval vessels opened fire on radar snow, and President Johnson requested and received Congressional approval of the [[w:Gulf of Tonkin Resolution|Gulf of Tonkin Resolution]]; then-[[w:United States Secretary of Defense|US Secretary of Defense]] [[w:Robert McNamara|McNamara]] claimed those attacks were "unprovoked".<ref>Karnow (1983, p. 375). See also the section on [[w:Gulf of Tonkin Resolution#Congress votes|Congress votes]]" in the Wikipedia article on [[w:Gulf of Tonkin Resolution|Gulf of Tonkin Resolution]], accessed 2026-05-14.</ref> In this media environment, only two officials in the US Congress voted against the Gulf of Tonkin Resolution: [[w:Ernest Gruening|Ernest Gruening]] (D-AK) and [[w:Wayne Morse|Wayne Morse]] (D-OR). Gruening lost in his next primary campaign to [[w:Mike Gravel|Mike Gravel]], and Morse lost in his next general election campaign to [[w:Bob Packwood|Bob Packwood]]. These results support the previous claim that the major media give politicians the choice: :''Betray the nation, or do not get elected.'' That resolution became the primary authorization for the US war in Vietnam until Congress ended the funding. ==== Was the Vietnam War lost in Washington or by media biases? ==== [[w:John Mueller|John Mueller]], prolific author, Professor Emeritus of international relations at [[w:Ohio State University|Ohio State University]] and Senior Fellow at the [[w:Cato Institute|Cato Institute]], said that the most effective thing the US did to win the [[w:Cold War|Cold War]] was — :''nothing'': Between the [[w:Fall of Saigon|Fall of Saigon]] in 1975 and the inauguration of [[w:Ronald Reagan|Ronald Reagan]] as President of the US, the US "went into a sort of containment funk: it effectively adopted a policy of complacency (or perhaps of appeasement) as it watched from the sidelines as the Soviet Union … opportunistically gathered a set of Third World countries into its imperial embrace: Angola in 1976, Mozambique and Ethiopia in 1977, South Yemen and Afghanistan in 1978, Grenada and Nicaragua in 1979."<ref>Mueller (2021, p. 59).</ref> Nearly all became major economic and political drains on the Soviets with Afghanistan being the worst. And their Warsaw Pact allies in Eastern Europe became a severe economic drain and psychic problem.<ref>Mueller and Graves (2023).</ref> President Reagan, inaugurated 1981-01-20, had a very different vision of the role of the US in foreign relations from his predecessor, [[w:Jimmy Carter|Jimmy Carter]]. In 1983-06-21 Reagan insisted, "We cannot permit the Soviet-Cuban-Nicaraguan axis to take over Central America", because the consequences would include "a tidal wave of refugees ... 'feet people' ... swarming into our country."<ref>Clines (1983).</ref> Other sources<ref>e.g., Andersen (2006, Part II).</ref> insist the opposite, that the vast majority of deaths in Central America during the Reagan years were poor humans petitioning nonviolently for a redress of grievances, suppressed by terrorist / death squads supported by the Reagan administration largely in violation of laws passed by Congress and signed by President Reagan. On 1986-10-05 [[w:Corporate Air Services HPF821|a Nicaraguan soldier with a surface to air missile shot down a C-123]] cargo aircraft carrying supplies to the Contra roughly 35 miles (56 km) north of Costa Rica. Documents found in the wreckage and a confession by the sole survivor led to the [[w:Iran–Contra affair|Iran-Contra hearings]] the following year, during which Lt. Col. [[w:Oliver North|Oliver North]] insisted, "We didn't lose the war in Vietnam ..., we lost it in this city."<ref>Andersen (2006, p. 137). See also, Wikipedia, "[[w:Stab-in-the-back myth|Stab-in-the-back myth]]", accessed 2026-05-13.</ref> The previous section on the "Gulf of Tonkin Resolution" provides an alternative narrative of the Vietnam War: If as Eisenhower claimed, "possibly 80 per cent of the [Vietnamese] population would have voted for the Communist [[w:Ho Chi Minh|Ho Chi Minh]]" if elections had been held there, it's hard to imagine how anyone else could have won without aggressive action that actually ''improved'' the lives of Vietnamese peasants in the South. US-led efforts there were officially designed to win "[[w:Hearts and Minds (Vietnam War)|Hearts and Minds]]" but were implemented with such coercion that the result was the opposite. A cynic might say that :''It is hard to win people's hearts and minds by killing them.'' ====Richard Barlow and nuclear proliferation==== There is also documentation that the US helped Pakistan get nuclear weapons and destroyed the career of an intelligence analyst, [[w:Richard Barlow (intelligence analyst)|Richard Barlow]], for telling his managers they should not lie to Congress about it. Barlow has insisted that neither Pakistan nor North Korea would have nuclear weapons and Iran would not have a nuclear weapons program today, if the US had followed its own laws. Barlow’s claims, including his punishment by administration officials, have been reported in major media outlets<ref>e.g., Stein (2013). See also Wikipedia, "[[w:Richard Barlow (intelligence analyst)|Richard Barlow (intelligence analyst)]]", accessed 2026-05-06.</ref> but not in a way that would seriously limit the ability — and need — for administration officials to lie to Congress. If Barlow's claims are accurate, it suggests that US government officials violated US obligations under the [[w:Treaty on the Non-Proliferation of Nuclear Weapons|Non-Proliferation Treaty]] (NPT).<ref>Per the [[w:Treaty Clause|Treaty Clause]] of the US Constitution, a treaty negotiated by the President and approved by the Senate has "the force of federal law."</ref> ==== Nayirah testimony and the 1990-1991 Gulf War ==== A more recent example is the 1990-10-10 testimony by [[w:Nayirah testimony|Nayirah al-Ṣabaḥ to the US Congressional Human Rights Caucus]], two months after the Iraqi invasion of Kuwait. She claimed to have seen Iraqi soldiers taking premature babies out of incubators in a maternity ward before looting the incubators and leaving the babies to die on the floor after the Iraqi invasion of Kuwait; she said she had been a volunteer nurse in the hospital at that time. The failure of journalists, including with the ''[[w:NBC Nightly News|NBC Nightly News]]'', to adequate check facts behind this and other atrocity stories helped convince the US public to support the US-led invasion of Iraq in 1990-1991. Nayirah's statements were widely publicized and cited numerous times in the United States Senate and by American president George H. W. Bush to contribute to the rationale for pursuing military action against Iraq. It was later revealed that she was the daughter of Kuwaiti ambassador to the US, [[w:Saud Nasser Al-Saud Al-Sabah|Saud Nasser Al-Saud Al-Sabah]], "Reps. [[w:Tom Lantos|Tom Lantos]] and [[w:John Porter (Illinois politician)|John Edward Porter]], who sponsored the congressional hearings, had started a group called the Congressional Human Rights Foundation that had received $50,000 from Citizens for a Free Kuwait, as well as free office space in [[w:Hill & Knowlton|Hill and Knowlton]]'s Washington headquarters",<ref>Rowse (1992).</ref> and the public relations firm Hill and Knowlton had made a video while coaching her rehearsing her perjury and used that to prepare a video press release "that eventually reached a total audience of about thirty-five million", 14 percent of the [[w:Demographic history of the United States|US population of 249 million per the census then in process]], with portions aired on the ''[[w:NBC Nightly News|NBC Nightly News]]'' the night after the testimony.<ref>Andersen (2006, pp. 170-171).</ref> ==== 1998 Embassy bombings and September 11 ==== As another example, there is substantial documentation available today that [[1998 Embassy bombings and September 11|the suicide mass murders of September 11, 2001]], likely would not have occurred if the US had treated the 1998 bombings of the US embassies in Kenya and Tanzania as law enforcement issues. Muslim clerics all over the world initially condemned those acts. Al-Qaeda was dead. Their funding had largely dried up. And bin Laden was scheduled to be extradited the following month to Saudi Arabia to be prosecuted for treason, where he would likely have been convicted and executed. Mayer (2008, p. 114) claimed those embassy bombings were motivated as retaliation for US support for torture.<ref>For more on torture, see the the section on [[#Make media responsible for harms|Make media responsible for harms]] below.</ref> But it seemed questionable at best whether major media executives in the US would have given favorable coverage to such a diplomatic solution. Instead, the US bombed a pharmaceutical plant in Sudan and al-Qaeda training camps in Afghanistan. Then Muslim public opinion turned 180 degrees to conclude, "Bin Laden is right: The US ''is'' an evil empire." The US became bin Laden’s only indispensable ally, according to the CIA agent responsible for tracking bin Laden at that time.<ref>Scheuer (2004, p. xv).</ref> Leading Saudis started supporting al-Qaeda, including some working for the Saudi embassy and consulates in the US. Only one country seems to have been involved in the preparations for the September 11 attacks, and that was Saudi Arabia. But Saudis were friends of the Bush family, and a crisis is a terrible thing to waste.<ref>Romer (2009).</ref> :''Did the US invade Afghanistan and Iraq on grounds that senior journalists and leading media executives should have known at the time were questionable and likely fraudulent — to the detriment of nearly everyone except the "people" who control most of the money for the media?'' :In particular, was Iraqi president [[w:Saddam Hussein|Saddam Hussein]] really a bigger threat to the US after he invaded Kuwait in 1990 or after the [[w:September 11 attacks|suicide mass murders of September 11, 2001]] than he was during the 1980s, when the US supported him [[w:Iran-Iraq War|killing Iranians]] or [[w:Anfal campaign|his own native Kurds]]? On 2003-05-29 [[w:BBC|BBC]] journalist [[w:Andrew Gilligan|Andrew Gilligan]] reported that the [[w:Tony Blaire|Blair government]] had "sexed up" [[w:September Dossier|intelligence reports]] issued the previous September to justify supporting the 2003-03-20 [[w:Iraq War|US-led invasion of Iraq]], two months before Gilligan's report. This led to the [[w:Hutton Inquiry|Hutton Inquiry]], which led to the resignations of Gilligan and the BBC's chairman and the firing of the BBC's director-general. However, the British public expressed so many reservations about the Hutton Inquiry that a follow-up investigation was ordered in 2009. This became the "[[w:Iraq Inquiry|Iraq Inquiry]]", whose 2016-07-06 report essentially validated what Gilligan had said just over 13 years earlier. This provides one more example of the 1710 maxim of Jonathan Swift that, "Falsehood flies, and truth comes limping after ... like a physician, who hath found out an infallible medicine, after the patient is dead."<ref name=Swift/> ====Ukraine war==== Page 1 of the 2023-05-04 edition of ''[[w:Le Monde Diplomatique|Le Monde Diplomatique]]'' carried a headline: :One year after the invasion of Ukraine: The media, vanguard of the war party,<ref>Halimi and Rimbert (2023) in the French-language original.</ref> consistent with Andersen (2006). === Make media responsible for harms === How might the world be different if injured parties could successfully sue major media for harms that result from government policies contradicted by evidence reasonably available to the major media outlets? For example, how might the world be different if: * combat veterans or their families could successfully sue major media outlets for biased reporting that stampede the nation into ill advised and counterproductive uses of military force on grounds that leading media personalities should have known at the time were questionable and likely fraudulent? * Vietnamese or Afghanis or Iraqis or Palestinians or victims in other countries could win similar lawsuits? * immigrants could sue major media outlets for failing to publish reasonable summaries of the available research that says that immigrants on average are more entrepreneurial<ref>Aghion et al. (2022, pp. 266-270).</ref> and no more likely to engage in criminal activities than native born, benefitting both the sending and receiving countries?<ref>The Wikipedia article on "[[w:Immigration|Immigration]] cites research saying, "that migration can be beneficial both to the receiving and sending countries. The academic literature provides mixed findings for the relationship between immigration and crime worldwide. ... [P]ublic perception often exaggerates the connection between immigration and crime, influenced by sensationalised media coverage and political rhetoric." The Wikipedia article on [[w:Immigration and crime|Immigration and crime]] notes that in some countries immigrants are over-represented in prison populations due to violations of immigration law or anti-immigrant biases in criminal justice. The Wikipedia article on "[[w:Sanctuary city|Sanctuary city]]" says that, "Some studies on the relationship between sanctuary status and crime have found that sanctuary policies either have no effect on crime or that sanctuary cities have lower crime rates and stronger economies than comparable non-sanctuary cities." All references 2026-05-26.</ref> * humans tortured by the US could sue the major media for suppressing honest discussion of the research that documents that torture is more likely counterproductive? An important report of the efficacy of torture was published in 1631 by [[w:Friedrich Spee|Friedrich Spee]], a German Jesuit priest and professor. A few years earlier, the Duke of Brunswick had invited Spee and another famous Jesuit scholar to supervise a continuation of the torture of a confessed witch. The Jesuits had previously told the Duke, "The Inquisitors are doing their duty. They are arresting only people who have been implicated by the confession of other witches." The Duke then led the Jesuits to a woman being stretched on the rack and asked her, "You are a confessed witch. I suspect these two men of being warlocks. What do you say? Another turn of the rack, executioners." "No, no!" screamed the woman. "You are quite right. I have often seen .. . They can turn themselves into goats, wolves ... Several witches have had children by them. ... The children had heads like toads and legs like spiders."<ref>Pinker (2011, pp. 138-139). Mannix (1964, pp. 134-135). Mackay ( 2009, p. 320).</ref> Crudely similar comments about the counterproductive nature of torture were made by Generals [[w:Stanley McChrystal|Stanley McChrystal]] (2013) and [[w:David Petraeus|David Petraeus]],<ref>DePaulo (2008).</ref> who held command positions in Iraq and Afghanistan. The major media in the US has provided ample coverage of, e.g., comments by Donald Trump supporting torture (McCarthy 2016), while largely suppressing honest discussion of the research on it. Might the world be safer and more prosperous if major media outlets and their executives and journalists could be successfully sued when their biased reporting have substantive negative consequences? Might [[w:Freedom of information|the public's right to receive diverse information]] be advanced in this way, recognizing that false information disseminated by major media outlets can lead to substantive harms, similar to "[[w:Shouting fire in a crowded theater|shouting ''fire'' in a crowded theater]]", while the same information disseminated by minor outlets would ''not'' produce such harms? Lawsuits of this nature could be facilitated by "group libel" laws. Activists were working to pass such laws in the 1940s. By 1950 those campaigns had been abandoned, according to Barbas (2023).<ref>See also Calvert et al. (2023, pp. 178ff).</ref> [[w:Yael Eisenstat|Yaël Eisenstat]] agrees that under [[w:Section 230|Section 230]] of Title 47 of the US Code, "No provider or user of an interactive computer service shall be treated as the publisher or speaker of any information provided by another information content provider." However, Eisenstat insists that [[Online platforms' effects on public health, safety and democracy|"an interactive computer service" ''can'' be held liable when their algorithms have substantive negative consequences]], as in the jury verdicts against Meta in New Mexico<ref>Allyn (2026).</ref> and against Meta and Google in Los Angeles.<ref>McQue (2026).</ref> She said, "those technologies, if they are, in the end, contributing to an illegal activity or to harm, that's what we should be addressing. ... The ultimate goal is not to shut down every social media company. The ultimate goal is to figure out what a safer online experience looks like and what accountability looks like when something unsafe happens." === in sum === You, dear reader, can help overcome these problems by talking, as suggested in the exercises below and the rest of this book. If you can help others become less angry and more willing to agree to disagree agreeably with others, that should reduce the risk of war and improve the prospects for progress on other major problems facing humanity today. ==2. Training in nonviolent noncooperation for anyone willing to listen == A major driver of the current conflict between India and Pakistan is mistreatment of Muslims in India. Simulations of a nuclear war between India and Pakistan suggest that such a war would likely produce a nuclear autumn lasting years during which 40 percent of humanity would starve to death if they did not die of something else sooner. Over 90 percent of those would be in countries not involved in the nuclear exchange.<ref>Xia et al. (2022). See also Wikiversity, "[[Responding to a nuclear attack]]", accessed 2026-05-05.</ref> The recent "[[w:2025 India–Pakistan conflict|2025 India–Pakistan conflict]]" was a response by India to violence in Indian-administered [[w:Kashmir|Kashmir]] by terrorists allegedly supported by Pakistan. India would have had much more difficulty justifying violent repression of ''nonviolent'' protests, especially if a more diverse media ecology gave such protests more and more sympathetic coverage. During the [[w:Great Depression|Great Depression]], ethnic Germans in the [[w:Sudetenland|Sudetenland]] region of [[w:Czechoslovakia|Czechoslovakia]] were harder hit by increasing trade barriers than their non-German neighbors. They were therefore more open to populist and extremist movements such as fascism, communism and German irredentism.<ref>Wikipedia, "[[w:Sudetenland|Sudetenland]]", esp. the section on "[[w: Sudetenland#Within the Czechoslovak Republic (1918–1938)|Within the Czechoslovak Republic (1918–1938)]]", accessed 2026-05-05.</ref> If those ethnic Germans had used nonviolent noncooperation to highlight their grievances, and if Czechoslovakia at that time had had a substantially more diverse media system, it seems likely that they could have gotten reasonable redress of grievances. If so, it would have been harder for Hitler to use that as an excuse to invade Czechoslovakia, as he did in 1938.<ref>Wikipedia, "[[w:Occupation of Czechoslovakia (1938–1945)|Occupation of Czechoslovakia (1938–1945)]]", accessed 2026-05-05.</ref> In 1940, during [[w:World War II|World War II]], Germany invade Denmark, which had previously declared neutrality. The Germans allowed [[w:1943 Danish Folketing election|Danish parliamentary elections in 1943]]; the Danish Nazi party won only 2.1% of the votes.<ref>{{cite web|title=Rigsdagsvalgene i Marts og April 1943|url=http://www.dst.dk/pukora/epub/upload/20217/valg1943.pdf|date=|publisher=Danmarks Statistic|accessdate=11 February 2021}}</ref> When the Nazis ordered the Danes [[w:Rescue of the Danish Jews|to ship their Jews to the death camps, the Danes ignored those orders.]] When the Germans decided to do it themselves, a German diplomat leaked that decision, and nearly all Danish Jews escaped to neutral Sweden; 99% of Denmark's Jewish population survived the Holocaust. An ideal settlement of the current Russo-Ukraine war might include training in nonviolent noncooperation made more effective through a more diverse media culture as suggested above. A substantial portion of the Ukrainian population, especially the Ukrainian military, are reported to be vicious anti-Russian Nazis, and the Ukrainian government has outlawed many uses of non-Ukrainian languages, especially Russian.<ref>Horton (2024).</ref> A campaign of nonviolent noncooperation with a vigorous, diverse adversarial press would likely make it harder for Ukraine to continue any persecution of Russian speakers. It would also make it harder for major media in the US and Western Europe to suppress honest discussion of anti-Russian racism in Ukraine. Swanson (2022) said that the [[w:Baltic states|Baltic states]] have implemented such training in preparations for a possible Russian invasion; they might be asked to support such training in Ukraine (and elsewhere).<ref>Swanson (2022).</ref> Organizations offering training in [[w:Nonviolent resistance|nonviolent noncooperation]] include [[w:Nonviolence International|Nonviolence International]] and the [[w:Highlander Research and Education Center|Highlander Research and Education Center]]. === Civil resistance deters fracking === Duhamel (2013) claimed that well-advertised planning and training in nonviolent noncooperation helped deter oil companies from attempting hydraulic fracturing in [[w:Quebec|Quebec Province]] in [[w:Canada|Canada]]. Deterring a foreign invasion is different, but the same principle should apply: It's clear from many sources that elites consider nonviolence a threat; it's a felony to teach nonviolence to someone whom the US State Department claims supports a "foreign terrorist organization", discussed in the next section. === Life in prison for teaching nonviolence === Per the US Supreme Court decision in ''[[w:Holder v. Humanitarian Law Project|Holder v. Humanitarian Law Project]]'' (2010), teaching nonviolence to anyone whom the US State Department claims supports a foreign terrorist organization is "[[w:Providing material support for terrorism|providing material support for terrorism]]", which is a felony under the USA [[w:Patriot Act|Patriot Act]] of 2001. Moreover, if the State Department claims that the death of any "person" resulted from the activities of the designated foreign terrorist organization, the penalty can be life in prison, where "person" is defined in the Patriot Act as "any individual or entity capable of holding a legal or beneficial interest in property".<ref>The treatment of [[w:Sami Al-Arian|Sami Al-Arian]] is worth noting in discussing the Patriot Act. Al-Arian is a Kuwaiti-born political activist of Palestinian origin, who earned a doctorate in Electrical Sciences and Systems Engineering at [[w:North Carolina State University|North Carolina State]] in 1985 and taught computer engineering at [[w:University of South Florida|University of South Florida]] (USF) beginning in 1986. He was granted permanent resident status in 1989. In 1993 he earned a Distinguished Teacher Award as a tenured associate professor at USF. He was an [[w:imam|imam]] in a local [[w:mosque|mosque]] and led in other initiatives to promote dialogue and public policy initiatives between the West and Middle East. On September 26, 2001, he appeared on ''[[w:The O'Reilly Factor|The O'Reilly Factor]]'' where he was confronted with a 1988 recording of him shouting "death to Israel". Al-Arian replied that "Death to Israel" meant "death to occupation, ... apartheid, ...oppression," whereupon O'Reilly cut him off and called for the [[w:Central Intelligence Agency|Central Intelligence Agency]] to investigate him. Al-Arian spent most of the next 14 years between that 2001 interview and 2015 in detention, much of it in solitary confinement. This period included a 2005 trial that ended with acquittal on 8 counts and a hung jury on another 9. In 2015 he was deported to Turkey. In 2017, he founded the Center for Islam and Global Affairs at [[w:Istanbul Sabahattin Zaim University|Istanbul Sabahattin Zaim University]] in Istanbul, Turkey, which he directs. What has been the impact of treatment of Al-Arian on the well-being of the bottom 99 percent of the US and world population?</ref> How did these provisions get written into the Patriot Act? That's a question that deserves research, perhaps by asking elected officials in the US Congress and lobbying for their repeal. A speculation consistent with the thesis of this book is that nonviolence terrifies those who control most of they money for the media, because it threatens their ability to get their security forces to follow orders. ==3. Forbid uses of force beyond one’s own borders and covert interference in foreign countries == :''[[w:Si vis pacem, para bellum|If you want peace, prepare for war.]]'' : -- ''[[w:De Re Militari|De Re Militari]]'' by [[w:Vegetius|Vegetius]] (fourth or fifth century AD) The record of history is now clear: Those who prepared for war often got war initiated when one party claimed they were being attacked or about to be attacked and believed they would fare better by attacking. Sometimes this occurred when the media environment convinced leaders that their political futures required them to clandestinely provoke foreign entities to do things that could then be denounced as unprovoked to justify military escalation, as mentioned in the previous section. Samuelson (2025) summarized quantitative analyses of 60 insurgencies since World War II, whose findings included the complete absence of success with counterinsurgencies without large force ratios (at least four, and most often more than ten, times the force of the insurgents) and without "providing a path toward peaceful addressing of grievances". He also noted that, "Brutality toward the civilian population ... tends to inflame the insurgency."<ref>Samuelson (2025) summarized Lawrence (2015).</ref> His analysis gave a pessimistic prognosis for the [[w:Gaza war|Gaza war]] that began 2023-10-07. His conclusions are consistent with the history of the current [[w:Russo-Ukrainian war|Russo-Ukrainian war]], the [[w:Vietnam War|Vietnam War]], the [[w:Graveyard of empires|First, Second, and Third Anglo-Afghan Wars (1839-1919), the Soviet-Afghan War (1979–1989), the US-led War in Afghanistan (2001–2021)]], the 2001-2011 [[w:Iraq War|Iraq War]], and others. A key point is that invaders often to lose unless they enter with overwhelming force like Germany in the early stages of World War II: The [[w:Occupation of Czechoslovakia (1938–1945)|Czechoslovaks]], [[w:Invasion of Poland|Poles]], [[w:France during World War II|French]], and others were not prepared to fight the Germans, but the [[w:Soviet Union in World War II|Soviets]] were. [[w:Adolf Hitler|Hitler]] doubtless knew that the [[w:Switzerland during World War I and World War II|Swiss]] were prepared to fight, so he attacked other countries first. While fighting the [[w:Russo-Ukrainian war#Full-scale Russian invasion of Ukraine (2022)|Russian invasion]] that began 2022-02-24, [[w:Defense industry of Ukraine|Ukraine has developed]] military drones that are highly effective relative to the cost, as witnessed by sales of such to Gulf Arab states,<ref>Sharawi and Shapiro (2026).</ref> illustrating the point that foreign invaders often encounter vastly more resistance than they expect -- and should expect highly effective resistance if they invade a country prepared to fight on their own territory. The rest of this section discusses weaknesses with standard deterrence theory. ===Deterrence theory and nuclear Armageddon=== Standard [[w:Deterrence theory|deterrence theory]] assumes that one's opponents are rational and do not want [[w:Armageddon|Armageddon]]. The record of history summarized above raises questions about this assumption: In World War I, even the "winners" arguably lost more than they gained -- doubtless excepting a few merchants, who made fortunes from what they sold. Many of the other military decisions discussed above seem to have been driven more by the media than military necessity. Beyond that, at least some portions of the [[w:Islamic State|Islamic State]] reportedly violates this assumption, because it "not only believes in the literal meaning of the coming Armageddon – it sees itself as its chief protagonist."<ref>Misra (2015).</ref> Some [[w:Christian nationalism|Christian nationalists]] promoted to command positions by [[w:United States Secretary of Defense|US Secretary of Defense]] [[w:Pete Hegseth|Hegseth]] and President Trump also seem to believe that Armageddon might be desirable. On 2026-03-03 the [[w:Military Religious Freedom Foundation|Military Religious Freedom Foundation]] said they had received over 200 complaints from over 50 different US military installations with comments like, "President Trump has been anointed by Jesus to light the signal fire in Iran to cause Armageddon and mark his return to Earth", per an email from one [[w:Non-commissioned officer|NCO]].<ref>Nick Mordowanec (2026).</ref> With Hegseth holding monthly Christian worship services in the Pentagon during business hours,<ref>Black (2025), Mayes-Osterman (2025). See also the section on "[[w:Pete Hegseth#Pentagon Christian worship services and "biblically sanctioned war"|Pentagon Christian worship services and "biblically sanctioned war"]] in the Wikipedia article on [[w:Pete Hegseth|Pete Hegseth]], accessed 2026-05-14.</ref> this suggests that Hegseth could have appointed enough Christian nationalists to key positions to initiate nuclear attacks on Iran or Russia, claiming that President Trump had ordered such whether he had or not.<ref>The [[w:Gold Codes|Gold Codes]] carried in the "[[w:nuclear football|nuclear football]]" required by the [[w:Permissive action link|permissive action link]]s would ''not'' prevent Hegseth and a few others appointed by him from initiating nuclear Armageddon, according to Ellsberg, who had been a nuclear war planner for presidents Eisenhower, Kennedy, Johnson, and Nixon, before releasing the ''[[w:Pentagon Papers|Pentagon Papers]]''. Ellsberg (2017, p. 69) insisted that the security provided by those Gold Codes were a hoax, because otherwise a single nuclear detonation on Washington, DC, when both the president and vice president were in town "would would definitively block any authorized, coordinated nuclear response to that or any subsequent nuclear attack."</ref> The biggest risk today may be the risk of [[w:Nuclear holocaust|nuclear Armageddon]], which seems on average to grow over time consistent with experience with "[[w:system accidents|system accidents]]" in other fields: It is naive to assume that any system as complex as military command, control and communications systems never fail. And managers of complex systems subject to rare, catastrophic failures "learn" from experience that they can take ever greater risks, because they have "safely" done so in the past — until there is a catastrophe:<ref>Kahneman and Klein (2009) found that expert intuition, when it exists, is learned from frequent, rapid, high quality feedback. With anything nuclear, mishaps are so rare that managers develop "expert intuition" that they can "safely" ignore safety concerns -- until there is a catastrophe. See also Sagan (1993).</ref> Veterans for Peace (2022) recommend global reduction and rapid elimination of nuclear weapons "to reduce the real risk of nuclear confrontation through accidental launch or miscalculated escalation". ==== National security tariffs ==== Free trade agreements supported by the [[w:World Trade Organization|World Trade Organization]] allow exemptions for national security and other objectives. [[Responding to a nuclear attack|Even a minor nuclear war between India and Pakistan would have a negative impact on the entirety of humanity]]. It might therefore be sensible for parties to the [[w:Treaty on the Prohibition of Nuclear Weapons|Treaty on the Prohibition of Nuclear Weapons]] (TPNW) to institute gradually increasing tariffs on nuclear weapon states, not so great as to seriously impact the economy of the nation applying such tariffs but aggressive enough to gradually wean their economy from reliance on trade with nuclear-weapon states that refuse to support the TPNW. See also the chapter below on [[/Media Literacy and You/Responding to a nuclear attack/|Responding to a nuclear attack]]. ===Research on the effectiveness of deterrence and implications=== Lebow and others have provided substantial documentation of case studies claiming that leaders are often not rational, and deterrence based on threatening use of military force beyond one’s own borders has been ''as likely to provoke as prevent'' undesired behavior.<ref>Lebow (2025, 2024), Lebow et al. (2023).</ref> The most obvious portions of this threat can be entirely eliminated by policies clearly and effectively forbidding use of force beyond one’s own borders. This can be signaled in at least three ways: * Eliminate all weapon systems like missiles and aircraft with a range of more than, e.g., a hundred miles or 200 kilometers with the possible exception of surveillance only aircraft that cannot be easily configured to carry [[w:Materiel#Military|ordnance]], e.g., explosives. Similarly eliminate nuclear weapons, which few if any countries would want to use for military defense inside their own borders. * Supply a national guard and reserves with weapons, training, and rules of engagement that prohibit projecting force beyond one’s own borders. Train them also in development and use of improvised explosive devices and other tactics and devices like low cost military drones. :Afghanistan is said to be the "[[w:Graveyard of empires|Graveyard of empires]]". They defeated the British three times (1839–1842, 1878–1880, 1919), the Soviet Union (1979–1989), and the US (2001–2021). Each victory came with foreign supplies, but any foreign troops helping Afghanis were primarily under the command of local leaders. :The [[w:2003 invasion of Iraq|2003 invasion of Iraq]] might have produced [[w:Nation-building|nation-building]] more like the experience of [[w:Nation-building#Germany and Japan after World War II|Germany and Japan after World War II]] if the US had mandated a vigorous adversarial press instead of strict censorship, according to McChesney and Nichols.<ref>McChesney and Nichols (2010, Appendix II. Ike, MacArthur and the Forging of Free and Independent Press, pp. 241-254).</ref> This claim by McChesney and Nichols was not endorsed by [[News from Germany 1900-1945 and implications for today#After the war in Germany vs. Iraq|University of British Columbia History professor Heidi Tworek]], who said the democratization efforts in Germany and Japan after World War II were more complicated than that implied by that brief discussion by McChesney and Nichols.<ref>The 2025-07-03 interview with Tworek is available at "[[News from Germany 1900-1945 and implications for today]]", accessed 2026-05-14.</ref> However, the research by Usher and Kim-Leffingwell (2022) and the related research on news deserts summarized in the preface to this ''[[Media Literacy and You]]'' book largely supports those claims by McChesney and Nichols. :[[w:Defense industry of Ukraine|Ukraine has become a world leader in military drones]], many of which are dramatically cheaper than alternatives. Most of those have limited range but have been useful for reconnaissance and delivery of ordnance and improving targeting of, e.g., surface to air missiles. :[[w:Eliot A. Cohen|Eliot Cohen]], who served as a special advisor to [[w:United States Secretary of State|US Secretary of State]] [[w:Condoleezza Rice|Condoleezza Rice]] from 2007 to 2009, wrote, "As the United States discovered in Iraq and Afghanistan, no matter how large, technologically advanced, and proficient an army is, motivated insurgents can still inflict casualties in the tens of thousands."<ref>Cohen (2022), cited from Horton (2024, p. 1026).</ref> Cohen recommended we "Arm the Ukranians now". Horton said that the neoconservatives learned from Iraq War II and Afghanistan that the US "should fight like those who defeated them."<ref>Horton (2024, p. 1026).</ref> :Leading economist [[w:Jeffrey Sachs|Jeffrey Sachs]] addressed the European Parliament 2025-02-19, claiming that the tragedy that befell Serbia in 1999 and subsequent US uses of force in Iraq and Syria, plus wars in Africa including Syria, Somalia and Libya and the current wars in Ukraine and the Israel-Hamas war, "are to a very significant extent the result of deeply misguided US policies."<ref>Sachs (2025-02).</ref> He said that Europe should craft its own foreign and military policies, independent of the US. ''[[w:Le Monde Diplomatique|Le Monde Diplomatique]]'' noted that Sachs' speech has circulated among social media since ''but has yet to be seriously discussed by major European media.''<ref>Sachs (2025-04; emphasis added).</ref> * Change the laws of government secrecy so government officials cannot secretly interfere in the internal affairs of foreign countries or otherwise project force outside their own borders. This might be achieved in the US in part by requiring anyone with information about questionable actions by government officials to provide such documentation to one or more congressional oversight bodies while also allowing any current or former government employee or contractor to file suit in any US federal jurisdiction if they feel they have been punished for refusing to support questionable activities. In addition, federal judges should be authorized to subpoena classified government documents that may be relevant to any case in their jurisdiction and declassify them subject to appellate review if they believe the national interest would be better served by declassification. :If the law is changed without a substantive [[#1. Citizen-directed subsidies for local news nonprofits with firewall(s) to prevent political interference in the content.|citizen-directed subsidies for local news nonprofits with firewall(s) to prevent political interference]], as discussed above, the change could be merely cosmetic and unconvincing to local public officials and potential adversaries. :Connelly (2023) noted that US government secrecy has in the past encouraged administration officials to do things to provoke actions by foreign entities that can then be denounced as “unprovoked” to stampede the US Congress and the public into supporting counterproductive uses of military force, as discussed above.<ref>See also Connelly et al. (2023).</ref> A more diverse media culture should make it harder for administration officials to lie to the public and to Congress — and harder to punish government employees who tell their managers that they should not lie to Congress, as they reportedly did to [[#Richard Barlow and nuclear proliferation|Richard Barlow]], mentioned above. :The Barlow case and many others explain why the US should, e.g., give federal judges the authority to subpoena classified documents and declassify them if they believe the public good is better served from declassification than continued secrecy.<ref>See, e.g., the 2025-05-08 interview with Seth Stern and Lauren Harper discussing what the "[[Freedom of the Press Foundation says...]]", Graves (2014), and [[w:Moynihan Commission on Government Secrecy|Moynihan Commission on Government Secrecy]], accessed 2026-05-06. Graves (2021) recommends "Congressional Gold Medals for" Barlow and whistleblowers.</ref> These policies would make it hard for any foreign leader to justify an attack for multiple reasons: First, it would be difficult to convince their supporters that such an attack is necessary. Second, a rational foreign leader might be hesitant to invade a country that is prepared to fight a guerrilla war. Germany reportedly considered invading [[w:Switzerland during World War I and World War II|Switzerland during both World Wars I and II]] and decided against it in part because Switzerland had large, well-trained ready reserves, who were ready to fight. Belgium seemed to be an easier route.<ref>Documented in Wikipedia, "[[w:Switzerland during World War I and World War II|Switzerland during World War I and World War II]]", accessed 2026-05-06. Switzerland also has many mountains, which make it easier to defend, but the capabilities of the Swiss military also influenced the German decision to avoid Switzerland.</ref> Third, even if foreign invaders defeat the guerrillas, they should not assume that their invading forces would continue to follow orders. [[w:Rescue of the Danish Jews|Ninety-nine percent of Danish Jews reportedly survived World War II]] because of Danish noncooperation ''supported by a German diplomat''.<ref>Wikipedia, "[[w:Rescue of the Danish Jews|Rescue of the Danish Jews]]", accessed 2026-05-06.</ref> With policies like these in place, it would be hard for foreign leaders to convince their supporters of a need to attack, as [[w:2022 Russian invasion of Ukraine|Putin did when invading Ukraine in 2022]],<ref>The Wikipedia article on "[[w:2022 Russian invasion of Ukraine|2022 Russian invasion of Ukraine]]", accessed 2026-05-06, includes a paragraph saying, 'In July 2021, Putin published an essay "On the Historical Unity of Russians and Ukrainians", in which he called Ukraine "historically Russian lands" and claimed there is "no historical basis" for the "idea of Ukrainian people as a nation separate from the Russians"'. Putin was accused of promoting Russian imperialism, historical revisionism and disinformation. Writing in 2024, Michael McFaul and Robert Person described this essay as representing not only "cynical propaganda" but also Putin's "deeply held and internalized beliefs". See the Wikipedia article for references supporting those claims.</ref> as [[w:2025 India–Pakistan crisis|India did when attacking Pakistan in 2025]], and as [[w:Invasion of Poland|Hitler did when invading Poland in 1939]], to name only three examples. === If we continue to base deterrence on threats === There are now calls for Europe to get their own nuclear weapons,<ref>Burgard (2025).</ref> while Iran, Saudi Arabia, Turkey, South Korea and Taiwan have been suggested as other candidates for acquiring nuclear weapons should they feel a sufficient need.<ref>Ruehl (2024).</ref> It is difficult to imagine how the number of nuclear weapon states could be increased without increasing the risks of a nuclear war, consistent with the discussion of "[[w:system accident|system accident]]s" earlier in this chapter. Secondarily, intelligence services with information on political corruption including attempts to intimidate and murder journalists should not be allowed to keep that information secret: They should be required to find ways to leak that information to journalists. Such attacks on journalists in their own country should be exposed and prosecuted if the evidence seems likely to obtain a conviction. Intelligence services with information about such attacks in other countries should be required to find ways to leak it to competent journalists without identifying their sources and methods: Doing so would likely reduce political corruption worldwide and with that the risks of war. == Collateral damage == The research cited above supports the claim that, :''[[w:Collateral damage|Collateral damage]] that our designated enemies commit prove to us that they are subhuman or criminally misled.'' :''Meanwhile, collateral damage that we commit is unfortunate but necessary -- from our perspective. However, it proves to our designated enemies that we are subhuman or criminally misled.'' This observation supports this entire program of deterrence without threat: * Forbidding use of force beyond one’s own borders and covert interference in foreign countries would automatically reduce collateral damage. It would also avoid uses of force that seem not to contribute to broadly shared peace and prosperity, according to research cited above. * The effectiveness of nonviolent noncooperation rests in part on its near universal avoidance of collateral damage. * Citizen-directed subsidies for local news nonprofits with firewall(s) to prevent political interference in the content should make it much harder for major media to convince the public to do things contrary to their best interests, like invading or interfering covertly in foreign countries. == Call for help == Do you, dear reader, know other serious research not cited herein that might improve this analysis? If yes, you can help improve this discussion by adding comments with citations -- or by adding such citation(s) to the "Discuss" page associated with this chapter, suggesting someone else revise the chapter appropriately. There are plenty of contrary claims in the major media, but the lead author of this chapter is not aware of any that are based on serious research. In the absence of such research, the current author finds it difficult to imagine any national defense policies that carry a greater risk of nuclear Armageddon than our current policies, as discussed in the next chapter of this book on ''[[Media Literacy and You]]'' on "[[Media Literacy and You/Responding to a nuclear attack|Responding to a nuclear attack]]". That chapter, in sum, claims that the ''worst'' response to a nuclear attack would be nuclear response, because it would escalate a catastrophe killing millions of humans to one killing ''billions'', possibly 80 percent of humanity in a war between the US and Russia that lofts so much smoke from burning cities to the stratosphere where it covers the globe depressing crop yields for years during with 99 percent of the humans in the US, Europe and Russia would starve to death if they did not die of something else sooner. Moreover, the record of "[[w:System accident|system accident]]s" suggests that the chances of such a war before the end of this century is substantially greater than the 40 percent median estimate based on history mentioned in a presentation on "[[Time to nuclear Armageddon]]" delivered to the 2019 Joint Statistical Meetings. This chapter is being written in the hopes of inspiring action to improve the prospects for broadly shared peace and prosperity for the long term. == Exercises == 1. Disconfirmation bias: Brainstorm your biggest concerns about a current or possible future war. :1.1. Select the one that is of greatest concern to you currently. ::One issue that may not be a major concern for many but might elicit a broad consensus for action would be a campaign to ask elected officials in the US Congress to explain how we benefit from the provisions of the USA Patriot Act of 2001 that authorize [[#life in prison for teaching nonviolence|life in prison for teaching nonviolence]]. :1.2. Who are your designated enemies? :1.3. Research what your designated enemies are saying about your biggest concern. :1.4. Under what circumstances would you support what you see your designated enemies advocating or doing? ::If you cannot see such circumstances, expand your research: Look for more sources that support your designated enemies. 2. Interacting: Ask others if you can share what you've learned about that conflict. If they say, "No", don't push it. If they agree, share what you've learned in a friendly supportive manner without saying that anything is "true". ::''Show me someone who knows the truth, and I will show you someone who is dangerous.'' :2.1. The primary goal in this is ''not'' to convince anyone that you are right and they are wrong but to lower the level of anger and increase the level of tolerance for dissenting views. :2.2. Another goal is to comfortably enjoy civil conversations of this nature, agreeing to disagree agreeably and building trusting relationships that support collaboration on issues of common concern. :2.3. After becoming adept at building collaborations on issues of common concern, you might consider teaching this important skill and approach to issues. 3. Teaching: Each one teach two, as discussed in the section on "[[Media Literacy and You#Text and self-help book and point of discuss|Text and self-help book and point of discuss]]" in the preface to this book. <!--== See also ==--> == Notes == {{reflist}} == Bibliography == * <!--Philippe Aghion, Céline Antonin, and Simon Bunel (2022) The Power of Creative Destruction: Economic Upheaval and the Wealth of Nations-->{{cite Q|Q139874218}} * <!--Bobby Allyn (2026-03-25) "Jury finds Meta and Google negligent in social media harms trial-->{{cite Q|Q139572103}} * <!--BBC (2022-08-01) "Nuclear annihilation just one miscalculation away, UN chief warns"-->{{cite Q|Q139596165|author=BBC}} * <!--Elizabeth Black (2026-05-22) "Hegseth hosts first monthly Christian service in Pentagon"-->{{cite Q|Q139791642}} * <!--Hans Günter Brauch, ed, Towards Rethinking Politics, Policy and Polity in the Anthropocene: Multidisciplinary Perspectives (Springer, pp. 225-234).-->{{cite Q|Q134488491|author= Hans Günter Brauch, ed.}} * <!--Jan Philipp Burgard (2025-04-08) “Opinion | Europe Needs Its Own Nukes”, Politico-->{{cite Q|Q134465922}} * <!--Clay Calvert, Dan V. Kozlowski, and Derigan Silver (2023) Mass Media Law, 22nd ed.-->{{cite Q|Q135455067}} * <!--Chenoweth and Stephan (2011) Why Civil Resistance Works: The Strategic Logic of Nonviolent Conflict-->{{cite Q|Q88725216}} * <!--Francis X. Clines (1983-06-21) "Reagan says his opponents risk Central American influx"-->{{cite Q|Q139790146}} * <!--Eliot Cohen (2022-02-23) “Arm the Ukrainians Now”, The Atlantic-->{{cite Q|Q139679796}} * <!--Matthew Connelly (2023) The Declassification Engine: What History Reveals About America’s Top Secrets (Pantheon).->{{cite Q|Q116786691}} * <!--Matthew Connelly, Douglas A. Samuelson, and Spencer Graves (2023-03-14) “Does US government secrecy threaten national security?”, Radio Active Magazine on KKFI-->{{cite Q|Q125582094}} * <!--Lisa DePaulo (2008-10-31) "Leader of the Year: Right Man, Right Time"-->{{cite Q|Q114039844}} * <!--Philippe Duhamel (2013-09-26) Civil resistance as deterrent to fracking: Part One, They shale not pass-->{{cite Q|Q140833946}} * <!--Dwight D. Eisenhower (1063) Mandate for Change-->{{cite Q|Q61945939}} * <!--Daniel Ellsberg (2017) The Doomsday Machine: Confessions of a nuclear war planner (Bloomsbury)-->{{cite Q|Q64226035}} * <!--Albert Fried (1997) McCarthyism: the great American Red scare: a documentary history-->{{cite Q|Q106659308}} * <!--Spencer Graves (2021-10-28) " Congressional Gold Medals for Assange, Hale, Barlow, Winner, Manning, Edmonds, Sterling, Drake, Snowden, Ellsberg"-->{{cite Q|Q125570226}} * <!--Spencer Graves (2014-07-18) “Restrict secrecy more than data collection”, San José Peace & Justice Center-->{{cite Q|Q106512569}} * <!-- Serge Halimi and Serge Halimi (2023-03) "Un an après l'invasion de l'Ukraine, une débâcle du journalisme: Les médias, avant-guarde du parti de la guerre"-->{{cite Q|Q118225389}} * <!--John Maxwell Hamilton (2020) Manipulating the Masses: Woodrow Wilson and the Birth of American Propaganda-->{{cite Q|Q137342282}} * <!--Scott Horton (2024) Provoked: How Washington Started the New Cold War with Russia and the Catastrophe in Ukraine (Libertarian Inst.)00>{{cite Q|Q139565338}} * <!--Annie Jacobsen (2024-04-10) "'Nuclear war happens in seconds and minutes, not days and weeks': How I researched the end of the world"-->{{cite Q|Q139596142}} * <!-- Kahneman and Klein (2009) Conditions for intuitive expertise: a failure to disagree-->{{cite Q|Q35001791}} * <!--Stanley Karnow (1983) Vietnam: A History-->{{cite Q|Q108903453}} * <!--Christopher A. Lawrence (2015) America's Modern Wars: Understanding Iraq, Afghanistan, and Vietnam-->{{cite Q|Q136130919}} * <!--Richard Ned Lebow (2024) “Are Leaders Rational?”, Critical Review, 36:4, 465-482.-->{{cite Q|Q134487607}} * <!--Richard Ned Lebow (2025) “Thinking Politically About the Anthropocene”, ch. 5 in Hans Günter Brauch, ed, Towards Rethinking Politics, Policy and Polity in the Anthropocene: Multidisciplinary Perspectives (Springer, pp. 225-234).-->{{cite Q|Q134488569|Author=Richard Ned Lebow}} * <!--Richard Ned Lebow, Douglas A. Samuelson, and Spencer Graves (2023-11-28), “Richard Ned Lebow on national defense including deterrence”, Radio Active Magazine-->{{cite Q|Q124351846}} * <!-- Charles Mackay (1841/2009) Memoirs of extraordinary popular delusions and the madness of crowds-->{{cite Q|Q116897625}} * <!-- Daniel P. Mannix (1964) The history of torture-->{{cite Q|Q116896896}} * <!--Jane Mayer (2008) Dark side : the inside story of how the war on terror turned into a war on American ideals (Doubleday)-->{{cite Q|Q1681286}} * <!--Cybele Mayes-Osterman (2025-12-18) Pete Hegseth pushes his Christian faith in Pentagon prayer services-->{{cite Q|Q139791710}} * <!--Tom McCarthy (2016-02-07) “Donald Trump: I’d bring back ‘a hell of a lot worse than waterboarding'”, The Guardian-->{{cite Q|Q134462630}} * <!-- McChesney and Nichols (2010) The Death and Life of American Journalism-->{{cite Q|Q104888067}} * <!--Stanley A. McChrystal (2013). My share of the task: A memoir (Penguin)-->{{cite Q|Q135406522}} * <!--Katie McQue (2026-04-24) " Meta ordered to pay $375m after being found liable in child exploitation case-->{{cite Q|Q139572337}} * <!--Amalendu Misra (2015-11-19) “What does Islamic State actually want?”, The Conversation-->{{cite Q|Q134487571}} * <!--Joel Mokyr (2017) A Culture of Growth: The Origins of the Modern Economy (Graz Schumpeter Lectures; Princeton University Press)-->{{cite Q|Q136118590}} * <!--Nick Mordowanec (2026-03-03) " Commanders Accused of Framing Iran War as Biblical Mandate, Jesus' 'Return'"-->{{cite Q|Q138840951}} * <!--John Mueller (2021) The Stupidity of War: American Foreign Policy and the Case for Complacency (Cambridge U. Pr.,)-->{{cite Q|Q113702723}} * <!--Mueller and Graves (2023-04-06) "The Stupidity of War and the Exaggeration of Threat"-->{{cite Q|Q139789709}} * <!--Pat Paterson (2008-02) "The Truth About Tonkin"-->{{cite Q|Q133449570}} * <!--Steven Pinker (2011) The Better Angels of Our Nature: Why Violence Has Declined (Viking Press, pp. 138-139)-->{{cite Q|Q60412312}} * <!--Steve Reicher, Nick Hopkins, Mark Levine, and Rakshi Rath (2005-12) " Entrepreneurs of hate and entrepreneurs of solidarity: Social identity as a basis for mass communication-->{{cite Q|Q141552459}} * <!--Paul Romer (2009-07-31) "A Terrible Thing to Waste"-->{{cite Q|Q139676537}} * <!--Arthur E. (Ted) Rowse (1992-09) "Kuwaitgate - killing of Kuwaiti babies by Iraqi soldiers exaggerated-->{{cite Q|Q123698876}} * <!--John P. Ruehl (2025-11-01) “Which Countries Are on the Brink of Going Nuclear?”, Peninsula Peace & Justice Center-->{{cite Q|Q134465827}} * <!--Jeffrey Sachs (2025-04) “File: The trap of major rearmament: Geopolitics of peace (in French: “Dossier : Le piège du grand réarmement: Géopolitique de la paix”), Le Monde Diplomatique (https://www.monde-diplomatique.fr/2025/04/SACHS/68242).-->{{cite Q|Q134463099}} * <!--Jeffrey Sachs (2025-02) “Jeffrey Sachs: Speech at European Parliament on February 19, 2025”: Edited transcript and YouTube video (https://newkontinent.org/jeffrey-sachs-speech-at-european-parliament-on-february-19-2025/)-->{{cite Q|Q134463038}} * <!--Scott Sagan (1993) The limits of safety: Organizations, Accidents, and Nuclear Weapons (Princeton U. Pr.)-->{{cite Q|Q136765429}} * <!--Douglas A. Samuelson (2025-09-26) " Assessing Israel’s Approach in Gaza"-->{{cite Q|Q138843324}} * <!--Amanda Sauer (2016-05-09) "Political Agenda Setting in Early America: The Barbary Wars"-->{{cite Q|Q139589295}} * <!--Michael Scheuer (2004) Imperial Hubris: Why the West is Losing the War on Terror (Brassey’s).-->{{cite Q|Q6006645}} * <!--Mark Schmeller (2009) "The Political Economy of Opinion: Public Credit and Concepts of Public Opinion in the Age of Federalism"-->{{cite Q|Q139589348}} * <!--Ahmad Sharawi and Dimitriy Shapiro (2026-04-01) "Ukraine Agrees to Mutually Beneficial Defense Deals With Gulf Arab States"-->{{cite Q|Q139948808}} * <!--Jeff Stein (2013-12-04) “The Perils of Whistle-Blowing”, Newsweek-->{{cite Q|Q63257553}} * <!--David Swanson (2022-03-15) " 30 Nonviolent Things Russia Could Have Done and 30 Nonviolent Things Ukraine Could Do"-->{{cite Q|Q134465808}} * <!--Veterans For Peace Nuclear Posture Review-->{{cite Q|Q111141993|author=Veterans for Peace}} * <!-- Xia et al. (2022) Global food insecurity and famine ... from a nuclear war ...-->{{cite Q| Q113732668}} [[Category:Media literacy]] [[Category:Communication]] [[Category:Political science]] [[Category:Law]] [[Category:Psychology]] [[Category:Sociology]] [[Category:War History]] [[Category:Media Literacy and You]] <!-- https://en.wikiversity.org/wiki/Wikiversity:Category_Review --> 3z7j9trrf74trgb2x6b8jweqxoodhfk 828 331015 2834537 2834464 2026-09-26T08:09:58Z Helpme2222 3106525 2834537 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.infoboxWBB() -- Passing expressions of conditional value: https://www.lua.org/pil/3.3.html --[[ https://www.mediawiki.org/wiki/LUAREF#mw.html:node Thankfully, these operations interpret passed nils as no-ops (I'm technically using false though. Somehow that works anyways?)]] local frame = mw.getCurrentFrame() local ballname = frame.args["Title"] or mw.title.getCurrentTitle() local Entities = require("Module:Entities") local featureCount = tonumber(frame.args["Feature count"]) or 1 local s_featureCount = tonumber(frame.args["SUPER Feature count"]) or featureCount local matchCount = { total = mw.site.stats.pagesInCategory( ballname .."'s Match History", "pages" ), standard = mw.site.stats.pagesInCategory( ballname .."'s Match History/Weapon Ball Battles/Standard", "pages" ), } local matchWinCount = { standard = mw.site.stats.pagesInCategory( ballname.."'s Match History/Weapon Ball Battles/Standard/Won", "pages" ), } local s_matchCount = { total = mw.site.stats.pagesInCategory( "Super " .. ballname .."'s Match History", "pages" ), standard = mw.site.stats.pagesInCategory( "Super " .. ballname .."'s Match History/Weapon Ball Battles/Standard", "pages" ), } local s_matchWinCount = { standard = mw.site.stats.pagesInCategory( "Super " .. ballname .."'s Match History/Weapon Ball Battles/Standard/Won", "pages" ), } local isSuper = -- do blank args count the same as nonexistent ones? check frame.args["SUPER Feature count"] or frame.args["SUPER Type"] or frame.args["SUPER Debuted"] or (s_matchCount.total > 0) -- TITLE local table = mw.html.create( 'table' ) :node( mw.html.create( 'tr' ) :node( mw.html.create( 'th' ) :attr({ colspan = "2", id = "mw-customcollapsible-Infobox" }) :addClass((isSuper) and "mw-collapsible") :node("<big>" .. ballname .. "</big>") ) ) :node((isSuper) and mw.html.create( 'tr' ) :node( mw.html.create( 'th' ) :attr({ colspan = "2", id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") :node("<big>" .. frame.args["SUPER Title"] or ("Super" .. ballname) .. "</big>") ) ) -- SECTION: Identification -- Section Heading :node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((frame.args["SUPER Type"]) and "mw-collapsible") :node( mw.html.create( 'th' ) :attr({ colspan = "2", }) :node((frame.args["SUPER Type"]) and "Base Identification" or "Basic Info") :node((frame.args["SUPER Type"]) and mw.html.create( 'span' ) :css({ float = "right", ["margin-right"] = "0", ["font-weight"] = "normal" }) :addClass("mw-customtoggle-Infobox") :node("[Click to toggle]") ) ) ) -- Type :node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((frame.args["SUPER Type"]) and "mw-collapsible") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Type") ) :node( mw.html.create( 'td' ) :node(frame.args["Type"]) ) ) :node( (frame.args["SUPER Type"]) and (mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Type") ) :node( mw.html.create( 'td' ) :node(frame.args["SUPER Type"]) )) ) -- Color local color = frame.args["Color"] or Entities.getBallAttribute( "Entities/Weapon Ball Battles/Balls/Data", ballname, "color" ) if (color ~= "") then table:node( mw.html.create( 'tr' ) :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Color") ) :node( mw.html.create( 'td' ) :node(frame:expandTemplate{ title = "Color", args = {color} }) ) ) else table:node( mw.html.create( 'tr' ) :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Color") ) :node( mw.html.create( 'td' ) :node("[[Module:Entities/Weapon Ball Battles/Balls/Data|<i>Add color...</i>]]") ) ) end -- Emoji local emoji = frame.args["Emoji"] or Entities.getBallAttribute( "Entities/Weapon Ball Battles/Balls/Data", ballname, "emoji" ) if (emoji ~= "") then table:node( mw.html.create( 'tr' ) :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Emoji") ) :node( mw.html.create( 'td' ) :node(emoji .. " " .. p.emojiCodepoint(emoji)) ) ) else table:node( mw.html.create( 'tr' ) :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Emoji") ) :node( mw.html.create( 'td' ) :node("[[Module:Entities/Weapon Ball Battles/Balls/Data|<i>Add emoji...</i>]]") ) ) end -- SECTION: Scaling Characteristics --[[ Some data will be collected first. ]] -- (Base) Behavior local features = {} local starts = {} local scalings = {} if (featureCount > 1) then for i = 1, featureCount do table.insert(features, { frame.args["Feature "..i], " (" .. p.var(frame.args["Var "..i]) .. ")" }) table.insert(starts, { p.var( frame.args["Var0 "..i] or (frame.args["Var "..i].."₀") ) .. ": ", frame.args["Starting value "..i] }) table.insert(scalings, { p.var( "Δ"..(frame.args["Var "..i]) ) .. ": ", frame.args["Scaling "..i] }) end else features[1] = frame.args["Feature"] starts[1] = frame.args["Starting value"] scalings[1] = frame.args["Scaling"] end local s_features local s_starts local s_scalings local has_s_features = false; local has_s_starts = false; local has_s_scalings = false; if (frame.args["SUPER Feature count"]) then if s_featureCount > 1 then -- Deep copy base characteristics, i.e. use them as default, overwrite what is explicitly specified as new super data s_features = mw.clone(features) s_starts = mw.clone(starts) s_scalings = mw.clone(scalings) -- If # of super features != # of base features, trim or expand the deep-copied tables accordingly. Avoid index errors. if s_featureCount > featureCount then for i = featureCount + 1, s_featureCount do table.insert( s_features, {0,0} ) table.insert( s_starts, {0,0} ) table.insert( s_scalings, {0,0} ) end elseif s_featureCount < featureCount then for i = s_featureCount + 1, featureCount do s_features[i] = nil s_starts[i] = nil s_scalings[i] = nil end end -- Parse super data, set the has_s_... flags if triggered for i = 1,s_featureCount do if frame.args["SUPER Feature "..i] then s_features[i][1] = frame.args["SUPER Feature "..i] if (not has_s_features) then has_s_features = true end end if frame.args["SUPER Starting value "..i] then s_starts[i][2] = frame.args["SUPER Starting value "..i] if (not has_s_starts) then has_s_starts = true end end if frame.args["SUPER Scaling "..i] then s_scalings[i][2] = frame.args["SUPER Scaling "..i] if (not has_s_scalings) then has_s_scalings = true end end if frame.args["SUPER Var "..i] then s_features[i][2] = " (" .. p.var(frame.args["SUPER Var "..i]) .. ")" s_starts[i][1] = p.var( frame.args["SUPER Var0 "..i] or (frame.args["SUPER Var "..i].."₀") ) .. ": " s_scalings[i][1] = p.var( "Δ"..(frame.args["SUPER Var "..i]) ) .. ": " if (not has_s_features) then has_s_features = true end if (not has_s_starts) then has_s_starts = true end if (not has_s_scalings) then has_s_scalings = true end end s_features[i] = s_features[i].concat() s_starts[i] = s_starts[i].concat() s_scalings[i] = s_scalings[i].concat() end s_features = s_features.concat() s_starts = s_starts.concat() s_scalings = s_scalings.concat() else -- # of super features = 1? Proceed to render single-feature section if frame.args["SUPER Var"] or frame.args["SUPER Feature"] then s_features = mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node( "Feature" .. (frame.args["SUPER Var"]) and " (" .. p.var(frame.args["SUPER Var"]) .. ")" ) ) :node( mw.html.create( 'td' ) :node(frame.args["SUPER Feature"]) ) has_s_features = true end if frame.args["SUPER Var"] or frame.args["SUPER Var0"] or frame.args["SUPER Starting value"] then s_features = mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node( "Starting Value" .. (frame.args["SUPER Var"] or frame.args["SUPER Var0"]) and " (" .. p.var( frame.args["SUPER Var0"] or (frame.args["SUPER Var"].."₀") ) .. ")" ) ) :node( mw.html.create( 'td' ) :node(frame.args["SUPER Starting value"]) ) has_s_starts = true; end if frame.args["SUPER Scaling"] then s_features = mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Scaling") ) :node( mw.html.create( 'td' ) :node(frame.args["SUPER Scaling"]) ) has_s_scalings = true; end end end if (featureCount > 1) then end features = table.concat(features,"<br>") starts = table.concat(starts,"<br>") scalings = table.concat(scalings,"<br>") -- Section Heading table:node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((frame.args["SUPER Feature count"]) and "mw-collapsible") :node( mw.html.create( 'th' ) :attr({ colspan = "2", }) :node((frame.args["SUPER Feature count"]) and "Base Scaling Characteristics" or "Scaling Characteristics") :node((frame.args["SUPER Feature count"]) and mw.html.create( 'span' ) :css({ float = "right", ["margin-right"] = "0", ["font-weight"] = "normal" }) :addClass("mw-customtoggle-Infobox") :node("[Click to toggle]") ) ) ) -- Features :node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((has_s_features) and "mw-collapsible") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node( (featureCount > 1) and "Features" or ( (frame.args["Var"]) and ("Feature (" .. p.var(frame.args["Var"]) .. ")") ) ) ) :node( mw.html.create( 'td' ) :node(features) -- also, still ahven't figured out how to do this yet ) ) :node( (has_s_features) and (mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node( (s_featureCount > 1) and "Features" or ( (frame.args["SUPER Var"]) and ("Feature (" .. p.var(frame.args["SUPER Var"]) .. ")") ) ) ) :node( mw.html.create( 'td' ) :node(s_features) )) ) -- Starting values :node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((has_s_starts) and "mw-collapsible") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node( (featureCount > 1) and "Starting values" or ( (frame.args["Var"]) and ("Starting value (" .. p.var(frame.args["Var0"]) or (frame.args["Var"].."₀") .. ")") or "Starting value" ) ) ) :node( mw.html.create( 'td' ) :node(starts) ) ) :node( (has_s_starts) and (mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node( (s_featureCount > 1) and "Starting values" or ( (frame.args["SUPER Var"]) and ("Starting value (" .. p.var(frame.args["SUPER Var0"]) or (frame.args["SUPER Var"].."₀") .. ")") or "Starting value" ) ) ) :node( mw.html.create( 'td' ) :node(s_starts) )) ) -- Scaling :node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((has_s_scalings) and "mw-collapsible") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Scaling") ) :node( mw.html.create( 'td' ) :node(scalings) ) ) :node( (has_s_scalings) and (mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Scaling") ) :node( mw.html.create( 'td' ) :node(s_scalings) )) ) -- SECTION: Career --[[ Some data will be collected first. ]] -- (Base) Games played local gamesPlayedText = {} if matchCount.total > 0 then table.insert(gamesPlayedText, matchCount.total .. " (total)") if matchCount.standard > 0 then table.insert(gamesPlayedText, matchCount.standard .. " (standard)") end end -- (Base) Winrate local winrateText = {} if matchCount.total > 0 then if matchCount.standard > 0 then table.insert(winrateText, p.roundedPct(matchWinCount.standard,matchCount.standard) .. "% (standard)" ) end end -- Super Games played local s_gamesPlayedText = {} if s_matchCount.total > 0 then table.insert(s_gamesPlayedText, s_matchCount.total .. " (total)") if s_matchCount.standard > 0 then table.insert(s_gamesPlayedText, s_matchCount.standard .. " (standard)") end end -- Super Winrate local s_winrateText = {} if s_matchCount.total > 0 then if s_matchCount.standard > 0 then table.insert(s_winrateText, p.roundedPct(s_matchWinCount.standard,s_matchCount.standard) .. "% (standard)" ) end end -- Section Heading table:node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((isSuper) and "mw-collapsible") :node( mw.html.create( 'th' ) :attr({ colspan = "2", }) :node((isSuper) and "Base Career" or "Career") :node((isSuper) and mw.html.create( 'span' ) :css({ float = "right", ["margin-right"] = "0", ["font-weight"] = "normal" }) :addClass("mw-customtoggle-Infobox") :node("[Click to toggle]") ) ) ) -- Debuted :node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((isSuper) and "mw-collapsible") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Debut") ) :node( mw.html.create( 'td' ) :node(frame.args["Debut"]) ) ) :node( (isSuper) and (mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Debut") ) :node( mw.html.create( 'td' ) :node(frame.args["SUPER Debut"]) )) ) -- Games played :node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((isSuper) and "mw-collapsible") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Games played") ) :node( mw.html.create( 'td' ) :node( (#gamesPlayedText > 0) and gamesPlayedText.concat("<br>") or "<i>Not enough data...</i>" ) ) ) :node( (isSuper) and (mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Games played") ) :node( mw.html.create( 'td' ) :node( (#s_gamesPlayedText > 0) and s_gamesPlayedText.concat("<br>") or "<i>Not enough data...</i>" ) )) ) -- Winrate local winrate = { [1] = "" } table:node( mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass((isSuper) and "mw-collapsible") -- not declared in this scope; fix that :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Winrate") ) :node( mw.html.create( 'td' ) :node( (#winrateText > 0) and winrateText.concat("<br>") or "<i>Not enough data...</i>" ) ) ) :node( (isSuper) and (mw.html.create( 'tr' ) :attr({ id = "mw-customcollapsible-Infobox" }) :addClass("mw-collapsible mw-collapsed") :node( mw.html.create( 'td' ) :css({ ["font-weight"] = "bold" }) :node("Winrate") ) :node( mw.html.create( 'td' ) :node( (#s_winrateText > 0) and s_winrateText.concat("<br>") or "<i>Not enough data...</i>" ) )) ) return tostring(table) end function p.roundedPct(num, den) return (num/den % 0.01 < 0.005) and floor(num/den * 100) or ceil (num/den * 100) end function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,5000000 do p.tableMake() end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end p.counter = 0 function p.tableBake() p.counter = p.counter + 1 return p.counter end function p.tableMake() p.counter = 0 local var = { keyword = {p.tableBake()}, kljuczslovo = {p.tableBake()}, yaoshiwenzi = {p.tableBake()}, llavepalabra = {p.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.getBallAttribute() local _, ballData = pcall( p.getBallAttributeInternal ) if _ then return ballData else return "" end end function p.getBallAttributeInternal() local ballData = mw.loadData(frame.args[1])[frame.args[2]][frame.args[3]] if ballData[1] then return ballData[tonumber(frame.args[4]) or p.listCountInternal(ballData)] end return ballData end function p.emojiCodepoint() local emoji = mw.text.trim( mw.getCurrentFrame().args[1] ) local i,v = mw.ustring.codepoint( emoji, 1, mw.ustring.len(emoji) ) if v then return "U+" .. string.format("%X", i ) .. " U+" .. string.format("%X", v ) else return "U+" .. string.format("%X", i ) end end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCountInternal(table) local count = 0 for index,value in ipairs( table ) do count = count + 1 end return count end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; 97lltkka9rhh0nwcccif9615hlydxjf 2 331051 2834501 2834094 2026-09-26T02:35:19Z U3253363 3106362 2834501 wikitext text/x-wiki == About me == Hi, my name is [https://www.linkedin.com/in/pepper-white/ Pepper]. I am a third-year Bachelor of Science in Psychology student at the [https://www.canberra.edu.au/ University of Canberra]. I am passionate about preventative mental health care and supporting those in need. This passion motivates me in my studies and at work. === Work experience === * '''Mental Health Educator''' with [https://mieact.org.au/ Mental Illness Education ACT]. In this role, I facilitate discussions about [[Stress (psychological)|stress]], [https://www.beyondblue.org.au/mental-health/depression?gad_source=1&gad_campaignid=21934835275&gbraid=0AAAAADuibRbKbycJc05RErZ8UMCld1aGB&gclid=Cj0KCQjwkOvTBhDgARIsAKUNyRuK4CGO5WdRCpr1RDshuiDIlyi_ZwRe8ZFfvAygSGrvK0TbjFm7VtYaAkf8EALw_wcB depression], and [[wikipedia:Help-seeking|help-seeking]] with ACT school students. * '''Student Advocate''' in the [https://www.canberra.edu.au/content/myuc/home/support/student-advocacy-and-src/student-advocacy.html Student Advocacy Office] at the University of Canberra. In this role, I help my peer university students navigate university policies and procedures. === Hobbies === * [[wikipedia:Oil_painting|Oil painting]] * Figure drawing * Running * Playing water polo with the [https://www.revolutionise.com.au/dragonswp/home/ Gungahlin Dragons Water Polo Club] * Travelling == Book chapter == The book chapter I am writing is [[Motivation and emotion/Book/2026/Self-concept and motivation|Self-concept and motivation]]. The chapter navigates the question "How does self-concept relate to motivation?" I chose this topic to explore due to my fascination with how the perception of oneself can influence one's behaviour. == Social contributions == My approach for social contributions has been to edit or comment on a peer's page every time I work on my own book chapter. My hope is that this approach helps me stay engaged with others' ideas and contribute as regularly to others' work as I do my own. # I engaged with conversations in a [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261?entry_id=804001 discussion post] on Canvas about topics of interest within motivation and emotion. My goal with this post was to take inititative by being an early contributor to help build a sense of comfort and normality amongst the group. I also hope by posting some topics of interest, others may feel inspired by these focus areas, thus helping them choose their book chapter topic. # In familiarising myself with Wikiversity, I read the Spirituality and resilience 2025 book chapter. I noticed the writing required edits for readability, so I [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FSpirituality_and_resilience&diff=2824208&oldid=2774009 edited the first two paragraphs] of the overview. I fixed spelling, grammar, and wording issues. This is an important fix to help capture the reader’s attention and demonstrate credibility when the audience begins reading. # I went through the topics others have chosen and the topic “Empathy and jury decision-making" caught my attention. I [https://en.wikiversity.org/w/index.php?title=Talk%3AMotivation_and_emotion%2FBook%2F2026%2FEmpathy_and_jury_decision-making#Exploring_empathy_within_similar_contexts commented] on this book chapter with some additional ideas from my own passion about researching empathy to support this students’ topic development. # To better illustrate the multidimensional model of self-concept Marsh et al. (1992), which I refer to in my book chapter, I [https://commons.wikimedia.org/w/index.php?title=File%3AMultidimensional_model_of_self-concept_diagram.png&diff=1265404333&oldid=1265404322 created a diagram and uploaded it to Wikimedia]. # I looked through the book chapter "Empathy and jury decision-making" and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FEmpathy_and_jury_decision-making&diff=2826959&oldid=2824982 made edits] to the ordering of citations within a bracket in the conclusion to ensure they were alphabetical. # I read the book chapter "Falling in love" and [https://en.wikiversity.org/w/index.php?title=Talk%3AMotivation_and_emotion%2FBook%2F2026%2FFalling_in_love#Interesting_theories_to_incorporate suggested a few theories and angles to explore] within this fascinating topic. # I read the book chapter "Charismatic leadership and follower motivation" and [[Talk:Motivation and emotion/Book/2026/Charismatic leadership and follower motivation#Interesting real-life case study to consider incorporating|suggested exploring the Jonestown cult]] as a real life case study to give insight into the extreme side of charismatic leadership and follower motivation. # To connect with others also writing 'self-' related chapters, I read the book chapter "Possible selves and goal pursuit". I identified areas which may require more research and [[Talk:Motivation and emotion/Book/2026/Possible selves and goal pursuit#c-U3253363-20260909032900-Jshottt-20260827141800|posted on their discussion forum]] some of the research I have been using which could be relevant to their chapter. # I reviewed the book chapter "Love styles and relationship satisfaction" and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2025%2FLove_styles_and_relationship_satisfaction&diff=2832497&oldid=2759229 made stylistic and grammatical edits throughout,] in particular I fixed capitalisation to sentence casing in headings and fixed the broken Wiki links. # I [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/461216?entry_id=816875 suggested an easy and new way to check your chapter's word count] in a Canvas discussion board. # In reviewing a chapter of interest to me, Volunteer counsellor motivation: Difference between revisions, I noticed the scenario being used did not involve a made up person or factual story, it instead had an introduction to a theory. To help the author catch the reader's attention, I [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FVolunteer_counsellor_motivation&diff=2833605&oldid=2832761 added a suggestion for a scenario] which involves a concrete case and a real person to help the reader connect immediately with the chapter. # I read the drafted book chapter called Body neutrality and emotional wellbeing and noticed headings need to be [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FBody_neutrality_and_emotional_well-being&diff=2833988&oldid=2830006 adjusted to sentence case,] so I assisted the author by fixing this up. # To better illustrate goal orientation theory when I reference it in my book chapter, I tried [[c:File:Mastery_versus_performance_orientation_illustration.jpg|making a diagram using Gemini and uploaded it to WikiMedia]]. # I tried searching for a clipart-style image to support readers' understanding of self-determination theory's psychological needs but could not find one. So, I used [[c:File:Self-determination_theory_psychological_needs.jpg|Gemini to help me create a diagram and uploaded it to WikiMedia]]. # I read the textbook chapter, Relatedness motivation in self-determination theory, and noticed the scenario warranted a few minor edits for readability, so [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FRelatedness_motivation_in_self-determination_theory&diff=2834093&oldid=2833064 I made some wording adjustments and added a more complete caption] to the scenario figure. # I [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/463438 invited feedback on my book chapter via the Canvas discussion] forum and committed to returning feedback to all who provide feedback on my book chapter. kaf9flifyhcaztecm32bf3rxngcd6n5 0 331100 2834503 2834450 2026-09-26T03:24:52Z U3239236 3106753 used grammarly to reword and fix grammar and sentence structure for the sections 2834503 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. === Defining emotional intelligence === Emotional intelligence refers to the ability to recognise, understand, use, and manage emotions (Givon et al., 2020). There are several approaches to understanding EI. Ability models view EI as a form of intelligence, trait models focus on people's perceptions of their own emotional abilities, and mixed models combine emotional abilities with personality characteristics (Luna et al., 2021). One of the most influential ability approaches is Mayer and Salovey's four-branch model. This model describes EI through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions. In comparison, trait EI focuses more on how people perceive their own emotional abilities and tendencies. At its core, emotional intelligence is the way people process and manage emotional information: noticing emotional cues, making sense of what they mean, and using that information to guide thought and behaviour (Givon et al., 2020). This is a somewhat different idea from how the term "emotional" is often used in everyday language. Describing someone as emotional usually refers to how frequently or intensely they display feelings, while emotional intelligence refers to how skilfully a person processes emotional information, regardless of how expressive they are (Luna et al., 2021). Similarly, EI should not be understood as simply being a nice person. Kindness and emotional intelligence are not the same. Kindness relates to a person's values and how they treat others, whereas emotional intelligence involves recognising, understanding, and managing emotions. Someone can be emotionally intelligent while setting boundaries or giving difficult feedback, just as someone can be kind and friendly but struggle to understand or regulate their own emotions. Similarly, a person who appears calm and reserved may be highly skilled at processing emotions, while someone who openly expresses their feelings may still find it difficult to understand or manage them (Villanueva et al., 2020). Because EI has been conceptualised in more than one way, it is useful to introduce these major approaches before going further. Ability models treat EI as a form of intelligence: a set of cognitive abilities for processing emotional information, assessed using performance-based tasks with objectively better or worse answers, in much the same way as other cognitive abilities are tested (Carfagno, 2020). Trait models instead focus on people's own perceptions of their emotional abilities and tendencies, typically measured through self-report questionnaires. Mixed models combine emotional abilities with broader personality-like characteristics, such as optimism, motivation, or assertiveness. These differences in definition matter a great deal when examining research on EI and wellbeing. A study using a trait self-report measure is not necessarily capturing the same underlying construct as a study using a performance-based ability test; the two can produce meaningfully different results, including different-strength relationships with wellbeing outcomes (Barbash, 2015). Keeping this distinction in mind will be important later in this chapter, when comparing what the evidence shows across different EI models. '''The ability model of emotional intelligence''' One of the most influential ability approaches is Mayer and Salovey's four-branch model, which defines EI as the ability to perceive, appraise, and express emotion; access and generate feelings when they facilitate thought; understand emotion and emotional knowledge; and regulate emotions to promote emotional and intellectual growth (Mayer & Salovey, 1997). This model describes EI as four related abilities, summarised in Table 1 below: '''Table 1.''' ''Mayer and Salovey's four-branch model of emotional intelligence'' {| class="wikitable" !Branch !Description |- |'''Perceiving emotions''' |Accurately identifying emotions in oneself and others, including through facial expressions, tone of voice, and body language. |- |'''Using emotions to facilitate thought''' |Harnessing emotional information to guide attention, reasoning, and problem-solving. |- |'''Understanding emotions''' |Comprehending emotional causes, consequences, and the way emotions change or combine over time. |- |'''Managing emotions''' |Regulating one's own emotions and, where appropriate, the emotions of others, in ways that support goals and wellbeing. |}[[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities under test conditions. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, while ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based tests, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess responses as correct or incorrect. However, deciding what counts as a correct emotional response can be difficult because emotions are personal and influenced by individual experiences'''.''' Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the most common responses, which may not be appropriate for everyone. Trait EI avoids this particular issue by focusing on people's perceptions rather than judging their answers as right or wrong. Common self-report measures include the Trait Meta-Mood Scale, which examines how people recognise, understand, and manage emotions, and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, based on Salovey and Mayer's model self-report measures have limitations. Trait EI may influence emotional wellbeing because believing you can understand and manage your emotions can help you approach difficult situations with greater confidence. However, confidence does not always mean someone is managing their emotions effectively. For example, a person might believe they handle conflict well when they actually avoid difficult conversations or dismiss other people's feelings. This shows why perceived emotional ability does not always reflect actual emotional functioning. Another limitation is that trait EI and emotional wellbeing are often measured using similar self-report questionnaires, which may make their relationship appear stronger than it really is. These are two different concerns one relates to whether people accurately judge their emotional abilities, while the other concerns how the way researchers measure EI and wellbeing may influence the results. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' ''based on Perma Model.'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} * Distinguish emotional wellbeing from the absence of mental illness or psychological distress. * Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive and negative wellbeing === Research shows that people with higher emotional intelligence often report better well-being, including more positive feelings, greater life satisfaction, and higher happiness. A meta-analysis of 25 studies with over 8,500 participants found a moderate positive link between emotional intelligence and subjective well-being (r = .32). This means people with higher emotional intelligence usually feel better overall, but the connection is not extremely strong (Sánchez-Álvarez et al., 2016). The strength of this link depended on how researchers measured emotional intelligence. It was stronger when measured with self-report questionnaires that mix emotional skills and personality traits (r = .38), and weaker when measured with performance-based tests (r = .22). The same study found that emotional intelligence was a bit more closely related to how people judge their lives as a whole, or their life satisfaction, than to their daily emotional experiences (r = .35 versus r = .29). This suggests emotional intelligence may matter more for how people view their lives overall than for their day-to-day mood. However, this does not mean emotional intelligence causes greater happiness. People who are already doing well may find it easier to notice and manage their emotions, and other factors, such as personality traits like extraversion or neuroticism, could influence both emotional intelligence and well-being. Another question is whether emotional intelligence is connected to lower stress and fewer symptoms of depression. A large meta-analysis on emotional intelligence and health found that people with higher emotional intelligence usually have better health, including less psychological distress (Martins et al., 2010). More specifically, studies show that people with stronger emotion regulation skills tend to have fewer symptoms of depression (Fernández-Berrocal & Extremera, 2016). However, having higher emotional intelligence does not mean someone will never feel negative emotions, and it should not be understood that way. Instead, people with stronger emotional skills may be better at understanding and managing difficult emotions when they arise, rather than not feeling them at all. For example, Sophie's emotional abilities do not prevent her from feeling disappointed, but they may help her handle it more effectively. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is usually assessed using performance-based measures. One possible explanation is shared method variance, as trait EI and wellbeing are often both measured using self-report questionnaires. Using similar measurement methods may strengthen the observed relationship between the two constructs. Self-report measures also capture people's perceptions of their emotional abilities, which may not always reflect how they actually perform when completing an emotional ability task. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing. === What does the evidence tell us? === Overall, research suggests a consistent positive association between emotional intelligence and wellbeing. People with higher EI generally report greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. In particular, stronger associations are often found when EI is measured using self-report measures rather than performance-based ability tests (Martins et al., 2010; Sánchez-Álvarez et al., 2016). This suggests that the way emotional intelligence is defined and measured can influence the results. However, these findings do not show that emotional intelligence directly causes better wellbeing. Much of the research is correlational, meaning other factors may contribute to the relationship, and the direction of the association cannot always be established. Personality characteristics and similarities between self-report measures may also partly explain why EI and wellbeing are related. Therefore, the evidence supports an association between emotional intelligence and wellbeing, but conclusions about causality should be made cautiously. Finding an association between emotional intelligence and wellbeing also does not explain how the relationship occurs. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which emotional intelligence is associated with better emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. '''[Add research source linking emotion perception/awareness with emotional functioning or wellbeing.]''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[Add research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add your emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.''' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019). === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[Add evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [Add comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing. '''[This is where Blasco-Belled et al. (2019) can go if the study directly supports this comparison.]''' * Examine whether emotion regulation is particularly strongly related to emotional wellbeing. * Discuss positive affect and negative affect. * Consider emotional distress. * Examine connections with resilience and coping. * Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing. === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 7ldo5xw9f5ccue1gqj3y28bazmqm8zn 2834504 2834503 2026-09-26T03:29:16Z U3239236 3106753 How does emotional intelligence influence emotional wellbeing? added focus question 2834504 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} '''Why might people respond so differently to similar emotional situations?''' One possible explanation is emotional intelligence (EI), which involves the ability to perceive, understand, use, and manage emotions. EI may influence how people interpret and respond to emotional experiences and, in turn, may be associated with their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It also involves how people experience and respond to emotions and their broader psychological functioning. Understanding the relationship between EI and emotional wellbeing is important because difficult emotions are an unavoidable part of life. Psychological research can help explain whether EI is associated with better wellbeing, which emotional abilities may be particularly important, and the processes that could help explain this relationship. # {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. === Defining emotional intelligence === Emotional intelligence refers to the ability to recognise, understand, use, and manage emotions (Givon et al., 2020). There are several approaches to understanding EI. Ability models view EI as a form of intelligence, trait models focus on people's perceptions of their own emotional abilities, and mixed models combine emotional abilities with personality characteristics (Luna et al., 2021). One of the most influential ability approaches is Mayer and Salovey's four-branch model. This model describes EI through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions. In comparison, trait EI focuses more on how people perceive their own emotional abilities and tendencies. At its core, emotional intelligence is the way people process and manage emotional information: noticing emotional cues, making sense of what they mean, and using that information to guide thought and behaviour (Givon et al., 2020). This is a somewhat different idea from how the term "emotional" is often used in everyday language. Describing someone as emotional usually refers to how frequently or intensely they display feelings, while emotional intelligence refers to how skilfully a person processes emotional information, regardless of how expressive they are (Luna et al., 2021). Similarly, EI should not be understood as simply being a nice person. Kindness and emotional intelligence are not the same. Kindness relates to a person's values and how they treat others, whereas emotional intelligence involves recognising, understanding, and managing emotions. Someone can be emotionally intelligent while setting boundaries or giving difficult feedback, just as someone can be kind and friendly but struggle to understand or regulate their own emotions. Similarly, a person who appears calm and reserved may be highly skilled at processing emotions, while someone who openly expresses their feelings may still find it difficult to understand or manage them (Villanueva et al., 2020). Because EI has been conceptualised in more than one way, it is useful to introduce these major approaches before going further. Ability models treat EI as a form of intelligence: a set of cognitive abilities for processing emotional information, assessed using performance-based tasks with objectively better or worse answers, in much the same way as other cognitive abilities are tested (Carfagno, 2020). Trait models instead focus on people's own perceptions of their emotional abilities and tendencies, typically measured through self-report questionnaires. Mixed models combine emotional abilities with broader personality-like characteristics, such as optimism, motivation, or assertiveness. These differences in definition matter a great deal when examining research on EI and wellbeing. A study using a trait self-report measure is not necessarily capturing the same underlying construct as a study using a performance-based ability test; the two can produce meaningfully different results, including different-strength relationships with wellbeing outcomes (Barbash, 2015). Keeping this distinction in mind will be important later in this chapter, when comparing what the evidence shows across different EI models. '''The ability model of emotional intelligence''' One of the most influential ability approaches is Mayer and Salovey's four-branch model, which defines EI as the ability to perceive, appraise, and express emotion; access and generate feelings when they facilitate thought; understand emotion and emotional knowledge; and regulate emotions to promote emotional and intellectual growth (Mayer & Salovey, 1997). This model describes EI as four related abilities, summarised in Table 1 below: '''Table 1.''' ''Mayer and Salovey's four-branch model of emotional intelligence'' {| class="wikitable" !Branch !Description |- |'''Perceiving emotions''' |Accurately identifying emotions in oneself and others, including through facial expressions, tone of voice, and body language. |- |'''Using emotions to facilitate thought''' |Harnessing emotional information to guide attention, reasoning, and problem-solving. |- |'''Understanding emotions''' |Comprehending emotional causes, consequences, and the way emotions change or combine over time. |- |'''Managing emotions''' |Regulating one's own emotions and, where appropriate, the emotions of others, in ways that support goals and wellbeing. |}[[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities under test conditions. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, while ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based tests, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess responses as correct or incorrect. However, deciding what counts as a correct emotional response can be difficult because emotions are personal and influenced by individual experiences'''.''' Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the most common responses, which may not be appropriate for everyone. Trait EI avoids this particular issue by focusing on people's perceptions rather than judging their answers as right or wrong. Common self-report measures include the Trait Meta-Mood Scale, which examines how people recognise, understand, and manage emotions, and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, based on Salovey and Mayer's model self-report measures have limitations. Trait EI may influence emotional wellbeing because believing you can understand and manage your emotions can help you approach difficult situations with greater confidence. However, confidence does not always mean someone is managing their emotions effectively. For example, a person might believe they handle conflict well when they actually avoid difficult conversations or dismiss other people's feelings. This shows why perceived emotional ability does not always reflect actual emotional functioning. Another limitation is that trait EI and emotional wellbeing are often measured using similar self-report questionnaires, which may make their relationship appear stronger than it really is. These are two different concerns one relates to whether people accurately judge their emotional abilities, while the other concerns how the way researchers measure EI and wellbeing may influence the results. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} * Distinguish emotional wellbeing from the absence of mental illness or psychological distress. * Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive and negative wellbeing === Research shows that people with higher emotional intelligence often report better well-being, including more positive feelings, greater life satisfaction, and higher happiness. A meta-analysis of 25 studies with over 8,500 participants found a moderate positive link between emotional intelligence and subjective well-being (r = .32). This means people with higher emotional intelligence usually feel better overall, but the connection is not extremely strong (Sánchez-Álvarez et al., 2016). The strength of this link depended on how researchers measured emotional intelligence. It was stronger when measured with self-report questionnaires that mix emotional skills and personality traits (r = .38), and weaker when measured with performance-based tests (r = .22). The same study found that emotional intelligence was a bit more closely related to how people judge their lives as a whole, or their life satisfaction, than to their daily emotional experiences (r = .35 versus r = .29). This suggests emotional intelligence may matter more for how people view their lives overall than for their day-to-day mood. However, this does not mean emotional intelligence causes greater happiness. People who are already doing well may find it easier to notice and manage their emotions, and other factors, such as personality traits like extraversion or neuroticism, could influence both emotional intelligence and well-being. Another question is whether emotional intelligence is connected to lower stress and fewer symptoms of depression. A large meta-analysis on emotional intelligence and health found that people with higher emotional intelligence usually have better health, including less psychological distress (Martins et al., 2010). More specifically, studies show that people with stronger emotion regulation skills tend to have fewer symptoms of depression (Fernández-Berrocal & Extremera, 2016). However, having higher emotional intelligence does not mean someone will never feel negative emotions, and it should not be understood that way. Instead, people with stronger emotional skills may be better at understanding and managing difficult emotions when they arise, rather than not feeling them at all. For example, Sophie's emotional abilities do not prevent her from feeling disappointed, but they may help her handle it more effectively. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is usually assessed using performance-based measures. One possible explanation is shared method variance, as trait EI and wellbeing are often both measured using self-report questionnaires. Using similar measurement methods may strengthen the observed relationship between the two constructs. Self-report measures also capture people's perceptions of their emotional abilities, which may not always reflect how they actually perform when completing an emotional ability task. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing. === What does the evidence tell us? === Overall, research suggests a consistent positive association between emotional intelligence and wellbeing. People with higher EI generally report greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. In particular, stronger associations are often found when EI is measured using self-report measures rather than performance-based ability tests (Martins et al., 2010; Sánchez-Álvarez et al., 2016). This suggests that the way emotional intelligence is defined and measured can influence the results. However, these findings do not show that emotional intelligence directly causes better wellbeing. Much of the research is correlational, meaning other factors may contribute to the relationship, and the direction of the association cannot always be established. Personality characteristics and similarities between self-report measures may also partly explain why EI and wellbeing are related. Therefore, the evidence supports an association between emotional intelligence and wellbeing, but conclusions about causality should be made cautiously. Finding an association between emotional intelligence and wellbeing also does not explain how the relationship occurs. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which emotional intelligence is associated with better emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. '''[Add research source linking emotion perception/awareness with emotional functioning or wellbeing.]''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[Add research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add your emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.''' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019). === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[Add evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [Add comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing. '''[This is where Blasco-Belled et al. (2019) can go if the study directly supports this comparison.]''' * Examine whether emotion regulation is particularly strongly related to emotional wellbeing. * Discuss positive affect and negative affect. * Consider emotional distress. * Examine connections with resilience and coping. * Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing. === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] o3tl7lmtxurl2icmtka330exryutbs4 2834505 2834504 2026-09-26T03:29:30Z U3239236 3106753 2834505 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} '''Why might people respond so differently to similar emotional situations?''' One possible explanation is emotional intelligence (EI), which involves the ability to perceive, understand, use, and manage emotions. EI may influence how people interpret and respond to emotional experiences and, in turn, may be associated with their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It also involves how people experience and respond to emotions and their broader psychological functioning. Understanding the relationship between EI and emotional wellbeing is important because difficult emotions are an unavoidable part of life. Psychological research can help explain whether EI is associated with better wellbeing, which emotional abilities may be particularly important, and the processes that could help explain this relationship. {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. === Defining emotional intelligence === Emotional intelligence refers to the ability to recognise, understand, use, and manage emotions (Givon et al., 2020). There are several approaches to understanding EI. Ability models view EI as a form of intelligence, trait models focus on people's perceptions of their own emotional abilities, and mixed models combine emotional abilities with personality characteristics (Luna et al., 2021). One of the most influential ability approaches is Mayer and Salovey's four-branch model. This model describes EI through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions. In comparison, trait EI focuses more on how people perceive their own emotional abilities and tendencies. At its core, emotional intelligence is the way people process and manage emotional information: noticing emotional cues, making sense of what they mean, and using that information to guide thought and behaviour (Givon et al., 2020). This is a somewhat different idea from how the term "emotional" is often used in everyday language. Describing someone as emotional usually refers to how frequently or intensely they display feelings, while emotional intelligence refers to how skilfully a person processes emotional information, regardless of how expressive they are (Luna et al., 2021). Similarly, EI should not be understood as simply being a nice person. Kindness and emotional intelligence are not the same. Kindness relates to a person's values and how they treat others, whereas emotional intelligence involves recognising, understanding, and managing emotions. Someone can be emotionally intelligent while setting boundaries or giving difficult feedback, just as someone can be kind and friendly but struggle to understand or regulate their own emotions. Similarly, a person who appears calm and reserved may be highly skilled at processing emotions, while someone who openly expresses their feelings may still find it difficult to understand or manage them (Villanueva et al., 2020). Because EI has been conceptualised in more than one way, it is useful to introduce these major approaches before going further. Ability models treat EI as a form of intelligence: a set of cognitive abilities for processing emotional information, assessed using performance-based tasks with objectively better or worse answers, in much the same way as other cognitive abilities are tested (Carfagno, 2020). Trait models instead focus on people's own perceptions of their emotional abilities and tendencies, typically measured through self-report questionnaires. Mixed models combine emotional abilities with broader personality-like characteristics, such as optimism, motivation, or assertiveness. These differences in definition matter a great deal when examining research on EI and wellbeing. A study using a trait self-report measure is not necessarily capturing the same underlying construct as a study using a performance-based ability test; the two can produce meaningfully different results, including different-strength relationships with wellbeing outcomes (Barbash, 2015). Keeping this distinction in mind will be important later in this chapter, when comparing what the evidence shows across different EI models. '''The ability model of emotional intelligence''' One of the most influential ability approaches is Mayer and Salovey's four-branch model, which defines EI as the ability to perceive, appraise, and express emotion; access and generate feelings when they facilitate thought; understand emotion and emotional knowledge; and regulate emotions to promote emotional and intellectual growth (Mayer & Salovey, 1997). This model describes EI as four related abilities, summarised in Table 1 below: '''Table 1.''' ''Mayer and Salovey's four-branch model of emotional intelligence'' {| class="wikitable" !Branch !Description |- |'''Perceiving emotions''' |Accurately identifying emotions in oneself and others, including through facial expressions, tone of voice, and body language. |- |'''Using emotions to facilitate thought''' |Harnessing emotional information to guide attention, reasoning, and problem-solving. |- |'''Understanding emotions''' |Comprehending emotional causes, consequences, and the way emotions change or combine over time. |- |'''Managing emotions''' |Regulating one's own emotions and, where appropriate, the emotions of others, in ways that support goals and wellbeing. |}[[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities under test conditions. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, while ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based tests, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess responses as correct or incorrect. However, deciding what counts as a correct emotional response can be difficult because emotions are personal and influenced by individual experiences'''.''' Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the most common responses, which may not be appropriate for everyone. Trait EI avoids this particular issue by focusing on people's perceptions rather than judging their answers as right or wrong. Common self-report measures include the Trait Meta-Mood Scale, which examines how people recognise, understand, and manage emotions, and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, based on Salovey and Mayer's model self-report measures have limitations. Trait EI may influence emotional wellbeing because believing you can understand and manage your emotions can help you approach difficult situations with greater confidence. However, confidence does not always mean someone is managing their emotions effectively. For example, a person might believe they handle conflict well when they actually avoid difficult conversations or dismiss other people's feelings. This shows why perceived emotional ability does not always reflect actual emotional functioning. Another limitation is that trait EI and emotional wellbeing are often measured using similar self-report questionnaires, which may make their relationship appear stronger than it really is. These are two different concerns one relates to whether people accurately judge their emotional abilities, while the other concerns how the way researchers measure EI and wellbeing may influence the results. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} * Distinguish emotional wellbeing from the absence of mental illness or psychological distress. * Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive and negative wellbeing === Research shows that people with higher emotional intelligence often report better well-being, including more positive feelings, greater life satisfaction, and higher happiness. A meta-analysis of 25 studies with over 8,500 participants found a moderate positive link between emotional intelligence and subjective well-being (r = .32). This means people with higher emotional intelligence usually feel better overall, but the connection is not extremely strong (Sánchez-Álvarez et al., 2016). The strength of this link depended on how researchers measured emotional intelligence. It was stronger when measured with self-report questionnaires that mix emotional skills and personality traits (r = .38), and weaker when measured with performance-based tests (r = .22). The same study found that emotional intelligence was a bit more closely related to how people judge their lives as a whole, or their life satisfaction, than to their daily emotional experiences (r = .35 versus r = .29). This suggests emotional intelligence may matter more for how people view their lives overall than for their day-to-day mood. However, this does not mean emotional intelligence causes greater happiness. People who are already doing well may find it easier to notice and manage their emotions, and other factors, such as personality traits like extraversion or neuroticism, could influence both emotional intelligence and well-being. Another question is whether emotional intelligence is connected to lower stress and fewer symptoms of depression. A large meta-analysis on emotional intelligence and health found that people with higher emotional intelligence usually have better health, including less psychological distress (Martins et al., 2010). More specifically, studies show that people with stronger emotion regulation skills tend to have fewer symptoms of depression (Fernández-Berrocal & Extremera, 2016). However, having higher emotional intelligence does not mean someone will never feel negative emotions, and it should not be understood that way. Instead, people with stronger emotional skills may be better at understanding and managing difficult emotions when they arise, rather than not feeling them at all. For example, Sophie's emotional abilities do not prevent her from feeling disappointed, but they may help her handle it more effectively. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is usually assessed using performance-based measures. One possible explanation is shared method variance, as trait EI and wellbeing are often both measured using self-report questionnaires. Using similar measurement methods may strengthen the observed relationship between the two constructs. Self-report measures also capture people's perceptions of their emotional abilities, which may not always reflect how they actually perform when completing an emotional ability task. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing. === What does the evidence tell us? === Overall, research suggests a consistent positive association between emotional intelligence and wellbeing. People with higher EI generally report greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. In particular, stronger associations are often found when EI is measured using self-report measures rather than performance-based ability tests (Martins et al., 2010; Sánchez-Álvarez et al., 2016). This suggests that the way emotional intelligence is defined and measured can influence the results. However, these findings do not show that emotional intelligence directly causes better wellbeing. Much of the research is correlational, meaning other factors may contribute to the relationship, and the direction of the association cannot always be established. Personality characteristics and similarities between self-report measures may also partly explain why EI and wellbeing are related. Therefore, the evidence supports an association between emotional intelligence and wellbeing, but conclusions about causality should be made cautiously. Finding an association between emotional intelligence and wellbeing also does not explain how the relationship occurs. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which emotional intelligence is associated with better emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. '''[Add research source linking emotion perception/awareness with emotional functioning or wellbeing.]''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[Add research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add your emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.''' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019). === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[Add evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [Add comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing. '''[This is where Blasco-Belled et al. (2019) can go if the study directly supports this comparison.]''' * Examine whether emotion regulation is particularly strongly related to emotional wellbeing. * Discuss positive affect and negative affect. * Consider emotional distress. * Examine connections with resilience and coping. * Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing. === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. 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Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] hg9i2yz8zp7dswuaz95jikubzaftglv 2834506 2834505 2026-09-26T03:33:02Z U3239236 3106753 2834506 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} '''Why might people respond so differently to similar emotional situations?''' One possible explanation is emotional intelligence (EI), which involves the ability to perceive, understand, use, and manage emotions. EI may influence how people interpret and respond to emotional experiences and, in turn, may be associated with their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It also involves how people experience and respond to emotions and their broader psychological functioning. Understanding the relationship between EI and emotional wellbeing is important because difficult emotions are an unavoidable part of life. Psychological research can help explain whether EI is associated with better wellbeing, which emotional abilities may be particularly important, and the processes that could help explain this relationship. {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. == Defining emotional wellbeing == Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. fnbeh-17-1253170 This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). Pasted text '''Table 2. Different approaches to understanding wellbeing''' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities under test conditions. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, while ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based tests, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess responses as correct or incorrect. However, deciding what counts as a correct emotional response can be difficult because emotions are personal and influenced by individual experiences'''.''' Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the most common responses, which may not be appropriate for everyone. Trait EI avoids this particular issue by focusing on people's perceptions rather than judging their answers as right or wrong. Common self-report measures include the Trait Meta-Mood Scale, which examines how people recognise, understand, and manage emotions, and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, based on Salovey and Mayer's model self-report measures have limitations. Trait EI may influence emotional wellbeing because believing you can understand and manage your emotions can help you approach difficult situations with greater confidence. However, confidence does not always mean someone is managing their emotions effectively. For example, a person might believe they handle conflict well when they actually avoid difficult conversations or dismiss other people's feelings. This shows why perceived emotional ability does not always reflect actual emotional functioning. Another limitation is that trait EI and emotional wellbeing are often measured using similar self-report questionnaires, which may make their relationship appear stronger than it really is. These are two different concerns one relates to whether people accurately judge their emotional abilities, while the other concerns how the way researchers measure EI and wellbeing may influence the results. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} * Distinguish emotional wellbeing from the absence of mental illness or psychological distress. * Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive and negative wellbeing === Research shows that people with higher emotional intelligence often report better well-being, including more positive feelings, greater life satisfaction, and higher happiness. A meta-analysis of 25 studies with over 8,500 participants found a moderate positive link between emotional intelligence and subjective well-being (r = .32). This means people with higher emotional intelligence usually feel better overall, but the connection is not extremely strong (Sánchez-Álvarez et al., 2016). The strength of this link depended on how researchers measured emotional intelligence. It was stronger when measured with self-report questionnaires that mix emotional skills and personality traits (r = .38), and weaker when measured with performance-based tests (r = .22). The same study found that emotional intelligence was a bit more closely related to how people judge their lives as a whole, or their life satisfaction, than to their daily emotional experiences (r = .35 versus r = .29). This suggests emotional intelligence may matter more for how people view their lives overall than for their day-to-day mood. However, this does not mean emotional intelligence causes greater happiness. People who are already doing well may find it easier to notice and manage their emotions, and other factors, such as personality traits like extraversion or neuroticism, could influence both emotional intelligence and well-being. Another question is whether emotional intelligence is connected to lower stress and fewer symptoms of depression. A large meta-analysis on emotional intelligence and health found that people with higher emotional intelligence usually have better health, including less psychological distress (Martins et al., 2010). More specifically, studies show that people with stronger emotion regulation skills tend to have fewer symptoms of depression (Fernández-Berrocal & Extremera, 2016). However, having higher emotional intelligence does not mean someone will never feel negative emotions, and it should not be understood that way. Instead, people with stronger emotional skills may be better at understanding and managing difficult emotions when they arise, rather than not feeling them at all. For example, Sophie's emotional abilities do not prevent her from feeling disappointed, but they may help her handle it more effectively. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is usually assessed using performance-based measures. One possible explanation is shared method variance, as trait EI and wellbeing are often both measured using self-report questionnaires. Using similar measurement methods may strengthen the observed relationship between the two constructs. Self-report measures also capture people's perceptions of their emotional abilities, which may not always reflect how they actually perform when completing an emotional ability task. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing. === What does the evidence tell us? === Overall, research suggests a consistent positive association between emotional intelligence and wellbeing. People with higher EI generally report greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. In particular, stronger associations are often found when EI is measured using self-report measures rather than performance-based ability tests (Martins et al., 2010; Sánchez-Álvarez et al., 2016). This suggests that the way emotional intelligence is defined and measured can influence the results. However, these findings do not show that emotional intelligence directly causes better wellbeing. Much of the research is correlational, meaning other factors may contribute to the relationship, and the direction of the association cannot always be established. Personality characteristics and similarities between self-report measures may also partly explain why EI and wellbeing are related. Therefore, the evidence supports an association between emotional intelligence and wellbeing, but conclusions about causality should be made cautiously. Finding an association between emotional intelligence and wellbeing also does not explain how the relationship occurs. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which emotional intelligence is associated with better emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. '''[Add research source linking emotion perception/awareness with emotional functioning or wellbeing.]''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[Add research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add your emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.''' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019). === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[Add evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [Add comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing. '''[This is where Blasco-Belled et al. (2019) can go if the study directly supports this comparison.]''' * Examine whether emotion regulation is particularly strongly related to emotional wellbeing. * Discuss positive affect and negative affect. * Consider emotional distress. * Examine connections with resilience and coping. * Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing. === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] dxib7z3ehhkhgc77zty21q4tdqyhu96 2834507 2834506 2026-09-26T03:33:55Z U3239236 3106753 changed table 2. title and added a section summing up the focus question 2834507 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} '''Why might people respond so differently to similar emotional situations?''' One possible explanation is emotional intelligence (EI), which involves the ability to perceive, understand, use, and manage emotions. EI may influence how people interpret and respond to emotional experiences and, in turn, may be associated with their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It also involves how people experience and respond to emotions and their broader psychological functioning. Understanding the relationship between EI and emotional wellbeing is important because difficult emotions are an unavoidable part of life. Psychological research can help explain whether EI is associated with better wellbeing, which emotional abilities may be particularly important, and the processes that could help explain this relationship. {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. == Defining emotional wellbeing == Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. fnbeh-17-1253170 This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). Pasted text '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities under test conditions. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, while ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based tests, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess responses as correct or incorrect. However, deciding what counts as a correct emotional response can be difficult because emotions are personal and influenced by individual experiences'''.''' Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the most common responses, which may not be appropriate for everyone. Trait EI avoids this particular issue by focusing on people's perceptions rather than judging their answers as right or wrong. Common self-report measures include the Trait Meta-Mood Scale, which examines how people recognise, understand, and manage emotions, and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, based on Salovey and Mayer's model self-report measures have limitations. Trait EI may influence emotional wellbeing because believing you can understand and manage your emotions can help you approach difficult situations with greater confidence. However, confidence does not always mean someone is managing their emotions effectively. For example, a person might believe they handle conflict well when they actually avoid difficult conversations or dismiss other people's feelings. This shows why perceived emotional ability does not always reflect actual emotional functioning. Another limitation is that trait EI and emotional wellbeing are often measured using similar self-report questionnaires, which may make their relationship appear stronger than it really is. These are two different concerns one relates to whether people accurately judge their emotional abilities, while the other concerns how the way researchers measure EI and wellbeing may influence the results. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} * Distinguish emotional wellbeing from the absence of mental illness or psychological distress. * Briefly explain how emotional wellbeing is measured in psychological research, as this will be important when you later discuss its relationship with emotional intelligence. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive and negative wellbeing === Research shows that people with higher emotional intelligence often report better well-being, including more positive feelings, greater life satisfaction, and higher happiness. A meta-analysis of 25 studies with over 8,500 participants found a moderate positive link between emotional intelligence and subjective well-being (r = .32). This means people with higher emotional intelligence usually feel better overall, but the connection is not extremely strong (Sánchez-Álvarez et al., 2016). The strength of this link depended on how researchers measured emotional intelligence. It was stronger when measured with self-report questionnaires that mix emotional skills and personality traits (r = .38), and weaker when measured with performance-based tests (r = .22). The same study found that emotional intelligence was a bit more closely related to how people judge their lives as a whole, or their life satisfaction, than to their daily emotional experiences (r = .35 versus r = .29). This suggests emotional intelligence may matter more for how people view their lives overall than for their day-to-day mood. However, this does not mean emotional intelligence causes greater happiness. People who are already doing well may find it easier to notice and manage their emotions, and other factors, such as personality traits like extraversion or neuroticism, could influence both emotional intelligence and well-being. Another question is whether emotional intelligence is connected to lower stress and fewer symptoms of depression. A large meta-analysis on emotional intelligence and health found that people with higher emotional intelligence usually have better health, including less psychological distress (Martins et al., 2010). More specifically, studies show that people with stronger emotion regulation skills tend to have fewer symptoms of depression (Fernández-Berrocal & Extremera, 2016). However, having higher emotional intelligence does not mean someone will never feel negative emotions, and it should not be understood that way. Instead, people with stronger emotional skills may be better at understanding and managing difficult emotions when they arise, rather than not feeling them at all. For example, Sophie's emotional abilities do not prevent her from feeling disappointed, but they may help her handle it more effectively. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is usually assessed using performance-based measures. One possible explanation is shared method variance, as trait EI and wellbeing are often both measured using self-report questionnaires. Using similar measurement methods may strengthen the observed relationship between the two constructs. Self-report measures also capture people's perceptions of their emotional abilities, which may not always reflect how they actually perform when completing an emotional ability task. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing. === What does the evidence tell us? === Overall, research suggests a consistent positive association between emotional intelligence and wellbeing. People with higher EI generally report greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. In particular, stronger associations are often found when EI is measured using self-report measures rather than performance-based ability tests (Martins et al., 2010; Sánchez-Álvarez et al., 2016). This suggests that the way emotional intelligence is defined and measured can influence the results. However, these findings do not show that emotional intelligence directly causes better wellbeing. Much of the research is correlational, meaning other factors may contribute to the relationship, and the direction of the association cannot always be established. Personality characteristics and similarities between self-report measures may also partly explain why EI and wellbeing are related. Therefore, the evidence supports an association between emotional intelligence and wellbeing, but conclusions about causality should be made cautiously. Finding an association between emotional intelligence and wellbeing also does not explain how the relationship occurs. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which emotional intelligence is associated with better emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. '''[Add research source linking emotion perception/awareness with emotional functioning or wellbeing.]''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[Add research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add your emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.''' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019). === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[Add evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [Add comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing. '''[This is where Blasco-Belled et al. (2019) can go if the study directly supports this comparison.]''' * Examine whether emotion regulation is particularly strongly related to emotional wellbeing. * Discuss positive affect and negative affect. * Consider emotional distress. * Examine connections with resilience and coping. * Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing. === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 3x4ty6gw2sjzl7z9c8myauewzee61lz 2834508 2834507 2026-09-26T03:38:13Z U3239236 3106753 2834508 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. fnbeh-17-1253170 This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). Pasted text '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities under test conditions. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, while ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based tests, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess responses as correct or incorrect. However, deciding what counts as a correct emotional response can be difficult because emotions are personal and influenced by individual experiences'''.''' Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the most common responses, which may not be appropriate for everyone. Trait EI avoids this particular issue by focusing on people's perceptions rather than judging their answers as right or wrong. Common self-report measures include the Trait Meta-Mood Scale, which examines how people recognise, understand, and manage emotions, and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, based on Salovey and Mayer's model self-report measures have limitations. Trait EI may influence emotional wellbeing because believing you can understand and manage your emotions can help you approach difficult situations with greater confidence. However, confidence does not always mean someone is managing their emotions effectively. For example, a person might believe they handle conflict well when they actually avoid difficult conversations or dismiss other people's feelings. This shows why perceived emotional ability does not always reflect actual emotional functioning. Another limitation is that trait EI and emotional wellbeing are often measured using similar self-report questionnaires, which may make their relationship appear stronger than it really is. These are two different concerns one relates to whether people accurately judge their emotional abilities, while the other concerns how the way researchers measure EI and wellbeing may influence the results. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. '''[Add research source linking emotion perception/awareness with emotional functioning or wellbeing.]''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[Add research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add your emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3. Possible pathways through which emotional intelligence may support emotional wellbeing.''' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management (Blasco-Belled et al., 2019). === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[Add evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [Add comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing. '''[This is where Blasco-Belled et al. (2019) can go if the study directly supports this comparison.]''' * Examine whether emotion regulation is particularly strongly related to emotional wellbeing. * Discuss positive affect and negative affect. * Consider emotional distress. * Examine connections with resilience and coping. * Consider whether emotion regulation could help explain the broader relationship between EI and wellbeing. === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 8n5quit9r649woibvyovq4a98s68f1b 2834509 2834508 2026-09-26T03:44:01Z U3239236 3106753 2834509 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. fnbeh-17-1253170 This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). Pasted text '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. === Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] pyfyhkue7fc05be4c20wui8ue7s1pwu 2834510 2834509 2026-09-26T03:45:19Z U3239236 3106753 added a paragraph drafted in docs to trait emotional intelligence section 2834510 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. fnbeh-17-1253170 This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). Pasted text '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== * Emotional wellbeing involves healthy emotional experience and functioning rather than simply experiencing positive emotions. * Research suggests that higher emotional intelligence is generally associated with better indicators of wellbeing. * Emotion regulation, coping and interpersonal functioning may help explain this relationship. * Different EI components and models may show different relationships with wellbeing. * Emotional intelligence may be partly developable, creating potential applications for wellbeing interventions. * or universal cause of emotional wellbeing. Return briefly to Sophie: Sophie's situation demonstrates that emotional intelligence does not remove disappointment, stress, or conflict. Instead, emotional abilities may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that support her wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 7wormy3293to207kpcndqyrvchb50es 2834511 2834510 2026-09-26T03:46:51Z U3239236 3106753 added a conclusion 2834511 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. fnbeh-17-1253170 This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). Pasted text '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus primarily on emotional experiences, PERMA considers several aspects of a fulfilling life see Table 2. '''Table''' '''2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, and living in accordance with one's values. |- |'''PERMA model''' |Seligman's model identifies five elements of flourishing: '''P'''ositive emotion, '''E'''ngagement, '''R'''elationships, '''M'''eaning, and '''A'''ccomplishment. |} == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] iozg8hmjng57h6tr04ylcpg6p4jkpwe 2834513 2834511 2026-09-26T03:52:42Z U3239236 3106753 2834513 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. fnbeh-17-1253170 This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). {{RoundBoxTop|theme=3}} '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 3). == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] iz91pcn4zfa6hqv9ene1t9wuej8c58y 2834514 2834513 2026-09-26T03:54:09Z U3239236 3106753 2834514 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 2.''' ''Mayer and Salovey's Emotional Intelligence model'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 3). == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] sm2i7itczqck472im77d1xzxtk5y303 2834515 2834514 2026-09-26T03:58:40Z U3239236 3106753 added figure 2. generated with ChatGPT, the prompt was generate a PERMA model 2834515 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. [[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|left|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]] Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Table 2). '''Table 2.''' ''Different approaches to understanding wellbeing'' {| class="wikitable" !Approach !Description |- |Hedonic wellbeing |Focuses on pleasure, enjoyment, positive emotions, and life satisfaction. |- |Eudaimonic wellbeing |Focuses on meaning, personal growth, authenticity, and living in accordance with one's values. |- |PERMA model |Identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment. |} Emotional wellbeing should also be distinguished from simply having no mental illness or psychological distress. A person can experience stress or difficult emotions while still experiencing positive aspects of wellbeing. In psychological research, wellbeing can be measured through different outcomes, including positive and negative affect, life satisfaction, and psychological functioning. These differences are important because the apparent relationship between emotional intelligence and wellbeing may partly depend on which aspect of wellbeing researchers choose to measure. [[File:Model of emotional intelligence.png|thumb|'''Figure 3.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz>Each branch can support well-being in a different way, as shown in Figure 2. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking helps shape attention and judgment. Understanding emotions helps people figure out why feelings come up and how they change over time. Managing emotions means handling emotional responses, which can be especially helpful during tough times, like when Sophie takes a moment to calm herself before talking to her friend. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 3). == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] ipzjdwwfu4uf2wwyk49sal7qokvk8zj 2834516 2834515 2026-09-26T04:07:26Z U3239236 3106753 changed up layout of images 2834516 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 2).[[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz> === Trait emotional intelligence === [[File:Model of emotional intelligence.png|thumb|'''Figure 3.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px|left]]Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' Each branch may contribute to wellbeing in a different way, as shown in Figure 3. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend. === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between two approaches to wellbeing: hedonic and eudaimonic wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help individuals cope with stressful situations or adjust to challenges they cannot resolve, whereas maladaptive responses may increase the risk of stress-related difficulties. This highlights why wellbeing involves more than experiencing positive emotions; how people respond to difficult situations is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 3). == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. === Trait and ability emotional intelligence === Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ===== '''What does the evidence tell us?''' ===== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. === Emotional awareness and perception === Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. === Understanding emotions === Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' === Emotion regulation === Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. === Coping with stress === Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. === Social relationships and support === Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' === '''Using emotions''' === Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] === Emotion understanding === Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. === Emotion regulation and management === Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). === Comparing the components === Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). === Emotional intelligence interventions === EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. === Do improvements in emotional intelligence improve wellbeing? === An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). === Limitations and practical implications === Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] sl8r819epadzmjjnpfk374466xzrl36 2834518 2834516 2026-09-26T04:22:57Z U3239236 3106753 2834518 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. One influential approach to emotional intelligence is Mayer and Salovey's ability model, which describes emotional intelligence through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions (see Figure 1). Each branch may contribute to wellbeing in a different way. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend.[[File:Model of emotional intelligence.png|thumb|'''Figure 1.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px]] === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 2).[[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz> === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. ===== Trait and ability emotional intelligence ===== Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ====== '''What does the evidence tell us?''' ====== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. ==== Emotional awareness and perception ==== Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. ==== Understanding emotions ==== Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' ===== Emotion regulation ===== Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. ====== Coping with stress ====== Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. ====== Social relationships and support ====== Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' ==== '''Using emotions''' ==== Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] ==== Emotion understanding ==== Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. ===== Emotion regulation and management ===== Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). ====== Comparing the components ====== Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). ==== Emotional intelligence interventions ==== EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. ===== Do improvements in emotional intelligence improve wellbeing? ===== An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). ====== Limitations and practical implications ====== Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] qswh93h3vynbimqfiq3o8nknmgp7djt 2834519 2834518 2026-09-26T04:28:27Z U3239236 3106753 added quiz 2 2834519 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. One influential approach to emotional intelligence is Mayer and Salovey's ability model, which describes emotional intelligence through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions (see Figure 1). Each branch may contribute to wellbeing in a different way. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend.[[File:Model of emotional intelligence.png|thumb|'''Figure 1.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px]] === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 2).[[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } {Which statement best describes the relationship between emotional intelligence and emotional wellbeing? |type="()"} + Higher emotional intelligence is generally associated with better wellbeing, although this does not mean that EI directly causes better wellbeing. - Higher emotional intelligence prevents people from experiencing negative emotions. - Emotional intelligence and emotional wellbeing are the same psychological construct. - Higher emotional intelligence guarantees greater happiness and life satisfaction. </quiz> === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. ===== Trait and ability emotional intelligence ===== Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ====== '''What does the evidence tell us?''' ====== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. ==== Emotional awareness and perception ==== Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. ==== Understanding emotions ==== Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' ===== Emotion regulation ===== Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. ====== Coping with stress ====== Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. ====== Social relationships and support ====== Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' ==== '''Using emotions''' ==== Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] ==== Emotion understanding ==== Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. ===== Emotion regulation and management ===== Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). ====== Comparing the components ====== Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). ==== Emotional intelligence interventions ==== EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. ===== Do improvements in emotional intelligence improve wellbeing? ===== An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). ====== Limitations and practical implications ====== Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] fokswxaorirjvasandufnz6oo87ur2c 2834520 2834519 2026-09-26T04:31:17Z U3239236 3106753 2834520 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. One influential approach to emotional intelligence is Mayer and Salovey's ability model, which describes emotional intelligence through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions (see Figure 1). Each branch may contribute to wellbeing in a different way. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend.[[File:Model of emotional intelligence.png|thumb|'''Figure 1.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px]] === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 2).[[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } {Question |type="()"} + The correct answer. - Distractor. - Distractor. - Distractor. </quiz> === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. ===== Trait and ability emotional intelligence ===== Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ====== '''What does the evidence tell us?''' ====== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. ==== Emotional awareness and perception ==== Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. ==== Understanding emotions ==== Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' ===== Emotion regulation ===== Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. ====== Coping with stress ====== Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. ====== Social relationships and support ====== Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' ==== '''Using emotions''' ==== Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] ==== Emotion understanding ==== Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. ===== Emotion regulation and management ===== Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). ====== Comparing the components ====== Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). ==== Emotional intelligence interventions ==== EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. ===== Do improvements in emotional intelligence improve wellbeing? ===== An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). ====== Limitations and practical implications ====== Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] qg9ltd671u2clms66gons9egs40b0sa 2834521 2834520 2026-09-26T04:33:24Z U3239236 3106753 2834521 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. One influential approach to emotional intelligence is Mayer and Salovey's ability model, which describes emotional intelligence through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions (see Figure 1). Each branch may contribute to wellbeing in a different way. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend.[[File:Model of emotional intelligence.png|thumb|'''Figure 1.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px]] === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 2).[[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz> Quiz 2. {What does research suggest about EI and wellbeing? |type="()"} + Higher EI is generally linked to better wellbeing. - Higher EI prevents negative emotions. - EI and wellbeing are the same thing. - Higher EI guarantees happiness. === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. ===== Trait and ability emotional intelligence ===== Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ====== '''What does the evidence tell us?''' ====== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. ==== Emotional awareness and perception ==== Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. ==== Understanding emotions ==== Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' ===== Emotion regulation ===== Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. ====== Coping with stress ====== Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. ====== Social relationships and support ====== Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' ==== '''Using emotions''' ==== Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] ==== Emotion understanding ==== Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. ===== Emotion regulation and management ===== Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). ====== Comparing the components ====== Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). ==== Emotional intelligence interventions ==== EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. ===== Do improvements in emotional intelligence improve wellbeing? ===== An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). ====== Limitations and practical implications ====== Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 9p6y07hv7k4lwb343fqih4fa8t4b52t 2834522 2834521 2026-09-26T04:33:41Z U3239236 3106753 2834522 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. One influential approach to emotional intelligence is Mayer and Salovey's ability model, which describes emotional intelligence through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions (see Figure 1). Each branch may contribute to wellbeing in a different way. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend.[[File:Model of emotional intelligence.png|thumb|'''Figure 1.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px]] === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 2).[[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz> === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. ===== Trait and ability emotional intelligence ===== Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ====== '''What does the evidence tell us?''' ====== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. ==== Emotional awareness and perception ==== Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. ==== Understanding emotions ==== Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' ===== Emotion regulation ===== Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. ====== Coping with stress ====== Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. ====== Social relationships and support ====== Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' ==== '''Using emotions''' ==== Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] ==== Emotion understanding ==== Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. ===== Emotion regulation and management ===== Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). ====== Comparing the components ====== Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). ==== Emotional intelligence interventions ==== EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. ===== Do improvements in emotional intelligence improve wellbeing? ===== An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). ====== Limitations and practical implications ====== Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional cognition, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] qswh93h3vynbimqfiq3o8nknmgp7djt 2834523 2834522 2026-09-26T06:06:41Z U3239236 3106753 changed emotional cognition to emotional awareness in conclusion 2834523 wikitext text/x-wiki {{title|Emotional intelligence:<br>How does emotional intelligence affect emotional wellbeing?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Sophie emotional regulation scenario.png|thumb|'''Figure 1.''' A university student pausing to regulate her emotions after receiving a disappointing grade, generated with ai ]] '''Scenario''' Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence the capacity to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} {{RoundBoxTop}} ; Focus questions # What are emotional intelligence and emotional wellbeing? # What is the relationship between emotional intelligence and emotional wellbeing? #How does emotional intelligence influence emotional wellbeing? #Which components of emotional intelligence are particularly important for emotional wellbeing? # How can emotional intelligence be developed to support emotional wellbeing? {{RoundBoxBottom}} == What are emotional intelligence and emotional wellbeing? == Emotional intelligence can play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences and support their overall emotional wellbeing. However, EI is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. Before examining this relationship, it is important to understand what psychologists mean by emotional intelligence and emotional wellbeing. One influential approach to emotional intelligence is Mayer and Salovey's ability model, which describes emotional intelligence through four related abilities: perceiving emotions, using emotions to support thinking, understanding emotions, and managing emotions (see Figure 1). Each branch may contribute to wellbeing in a different way. When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend.[[File:Model of emotional intelligence.png|thumb|'''Figure 1.''' ''Mayer and Salovey's Emotional Intelligence model'' |359x359px]] === Defining emotional wellbeing === Emotional wellbeing refers to people's emotional experiences and how they evaluate their lives. Psychological research often distinguishes between hedonic and eudaimonic approaches to wellbeing. Hedonic wellbeing focuses on experiences such as pleasure, enjoyment, and comfort, whereas eudaimonic wellbeing emphasises personal growth, meaning, and authenticity (Huta & Waterman, 2014). Both approaches are important for understanding wellbeing, although researchers differ in how they define and measure these concepts. Importantly, emotional wellbeing does not mean feeling happy or positive all the time. Negative emotions such as sadness, anger, anxiety, and disappointment are normal responses to difficult experiences. Chen et al. (2023) explain that adaptive stress responses can help people cope with stressful situations or adjust to challenges that cannot be resolved, whereas maladaptive responses can increase the risk of stress-related difficulties. This highlights why wellbeing involves more than simply experiencing positive emotions; how people respond to difficult experiences is also important. Another approach to understanding wellbeing is Seligman's PERMA model, which identifies five elements of flourishing: positive emotion, engagement, relationships, meaning, and accomplishment (Al-Hendawi et al., 2024). Unlike approaches that focus mainly on emotional experiences, PERMA considers several aspects of a fulfilling life (see Figure 2).[[File:ChatGPT Image Sep 26, 2026, 01 48 17 PM.png|thumb|335x335px|'''Figure 2.''' ''Seligman's PERMA model of wellbeing, consisting of positive emotion, engagement, relationships, meaning, and accomplishment. (AI generated)'' ]]<quiz display="simple"> Quiz 1. Which statement best describes emotional intelligence? |type="()"} + The ability to perceive, understand, use, and manage emotions. - The ability to avoid experiencing negative emotions. - The ability to remain happy in all situations. - The ability to control the emotions of other people. } </quiz> === Trait emotional intelligence === Trait EI focuses on how people perceive their own emotional abilities and tendencies, rather than how well they perform on an objective test. It is usually measured through self-report questionnaires, similar to those used to assess personality traits. These questionnaires examine how people typically recognise, understand, and manage their emotions in everyday life. In contrast, performance-based tests aim to measure a person's emotional abilities by assessing how they respond to emotion-related tasks. However, the distinction is not always clear, as self-report questionnaires can still reflect genuine emotional skills, while performance-based tests may not always capture a person's full emotional ability. Chapman (2005) explains that trait EI is more closely related to personality, whereas ability EI is more closely associated with cognitive abilities. This helps explain why they are measured differently. Performance-based measures, such as the Multifactor Emotional Intelligence Scale and the Mayer-Salovey-Caruso Emotional Intelligence Test, assess emotional abilities using responses that can be evaluated against scoring criteria. However, deciding what counts as a correct emotional response can be difficult because emotional situations can be interpreted differently. Expert scoring relies on the judgements of selected experts, while consensus scoring reflects the responses most commonly given by a reference group (Chapman, 2005). Trait EI avoids this particular scoring issue by focusing on people's perceptions rather than judging their responses as right or wrong. Common self-report measures include the Trait Meta-Mood Scale and the 33-item Schutte Self-Report Inventory of Emotional Intelligence, which was developed from Salovey and Mayer's model (Chapman, 2005). However, self-report measures have their own limitations because people's perceptions of their emotional abilities may not always reflect their actual emotional performance. This distinction is particularly important when examining emotional wellbeing. A person may believe that they manage their emotions effectively even when their behaviour suggests otherwise. For example, someone might believe they handle conflict well while regularly avoiding difficult conversations. Trait EI and emotional wellbeing are also often assessed using self-report questionnaires, meaning the way these constructs are measured may influence the strength of the relationship observed between them. '''[source supporting this measurement/shared-method issue.]''' When people accurately notice emotions, they become more aware of what they and others are feeling. Using emotions to guide thinking can shape attention and judgement. Understanding emotions helps people make sense of why feelings arise and how they may change over time. Managing emotions involves regulating emotional responses, which may be particularly useful during difficult situations, such as when Sophie takes a moment to calm herself before talking to her friend. == What is the relationship between emotional intelligence and emotional wellbeing? == === Emotional intelligence and positive wellbeing === Research generally suggests that people with higher EI report greater subjective wellbeing. A meta-analysis of 25 studies involving more than 8,500 participants found a moderate positive association between EI and subjective wellbeing (''r'' = .32; Sánchez-Álvarez et al., 2016). This indicates that higher EI tends to be associated with greater subjective wellbeing, although the relationship is moderate rather than strong. Importantly, the strength of the relationship depended on how EI was measured. The association was stronger for self-report measures that incorporated emotional and personality-related characteristics (''r'' = .38) than for performance-based measures (''r'' = .22). EI also showed a somewhat stronger relationship with life satisfaction (''r'' = .35) than with emotional experiences (''r'' = .29; Sánchez-Álvarez et al., 2016). These findings demonstrate why the way EI and wellbeing are defined and measured matters when interpreting their relationship. However, these findings do not demonstrate that EI causes greater happiness or life satisfaction. People who already experience greater wellbeing may find it easier to perceive or manage emotions, while other characteristics, including personality, could potentially contribute to both EI and wellbeing. ==== Emotional intelligence and negative wellbeing ==== EI has also been examined in relation to psychological distress and other negative outcomes. Martins et al. (2010) found that higher EI was associated with better health outcomes, including aspects of mental health. Research has also examined relationships between emotional abilities, emotion regulation, and symptoms of depression (Fernández-Berrocal & Extremera, 2016). Importantly, higher EI does not mean that someone will never experience negative emotions. Instead, emotional abilities may influence how people understand and respond to difficult emotions when they occur. Sophie's emotional abilities, for example, do not prevent her from feeling disappointed about her grade. They may instead help her recognise the emotion and choose how to respond to it. ===== Trait and ability emotional intelligence ===== Trait EI tends to show stronger associations with wellbeing than ability EI, which is typically assessed using performance-based measures. One possible explanation is that trait EI and wellbeing are often both assessed using self-report questionnaires. Similar measurement methods can contribute to stronger observed relationships between constructs. Self-report measures also assess people's perceptions of their emotional abilities, which may not always correspond with their performance on emotional ability tasks. This makes the way EI is measured particularly important when interpreting its relationship with wellbeing ====== '''What does the evidence tell us?''' ====== Overall, research supports a positive association between emotional intelligence and wellbeing. Higher EI is generally associated with greater subjective wellbeing and lower psychological distress, although the strength of these relationships varies across studies. Associations also differ according to how EI is conceptualised and measured, with stronger relationships often reported for self-report measures than performance-based ability measures (Martins et al., 2010; Sánchez-Álvarez et al., 2016). However, an association between EI and wellbeing does not demonstrate that EI directly causes better wellbeing. Much of this research is correlational, meaning the direction of the relationship cannot necessarily be established and other factors may contribute to both constructs. Differences between EI models and measurement approaches further complicate interpretation. Therefore, the evidence supports a relationship between EI and wellbeing, but stronger causal conclusions require research capable of examining whether changes in EI actually produce changes in wellbeing. Finding an association also does not explain how EI and wellbeing are connected. Emotional awareness, emotional understanding, emotion regulation, coping with stress, and social relationships may provide possible pathways through which EI is associated with emotional wellbeing. == How does emotional intelligence influence emotional wellbeing? == === Emotional awareness and perception === The relationship between emotional intelligence and wellbeing may be explained by several psychological processes. Emotional intelligence may help people recognise what they are feeling, understand why those emotions have occurred, regulate difficult emotional responses, and cope more effectively with stressful situations. It may also support communication and relationships with others. Rather than working separately, these processes are likely to interact and may help explain why people with higher emotional intelligence often report greater wellbeing. * Explain the importance of accurately recognising emotions. * Discuss how identifying an emotional state can help a person decide how to respond. * Explain what may happen when people have difficulty recognising their emotions. * Connect emotional awareness with emotional wellbeing. ==== Emotional awareness and perception ==== Recognising emotions is an important first step in responding to them effectively. Being able to identify whether a person is feeling anxious, angry, disappointed, or overwhelmed can provide useful information about what is happening and what they may need to do next. For example, recognising feelings of anxiety before an assessment may help a student identify the source of their stress and decide whether they need to prepare further, seek support, or use a strategy to manage their anxiety. Difficulty recognising emotions may make it harder to respond appropriately. A person who interprets anxiety as anger, for example, may react to a situation differently than someone who accurately understands what they are experiencing. Emotional awareness alone does not guarantee good emotional wellbeing, but it may provide the information needed for later processes such as emotional understanding, regulation, and coping. ('''research source linking emotion perception/awareness with emotional functioning or wellbeing.)''' * Discuss the ability to understand why an emotion has occurred. * Explain how people can recognise changes and combinations of emotions. * Consider how understanding the causes and consequences of emotions may support emotional functioning. * Explain how emotional understanding may make it easier to choose an appropriate response. ==== Understanding emotions ==== Emotional intelligence also involves understanding why emotions occur and how they may change over time. Emotional experiences are not always simple, and people can experience several emotions at once. Someone receiving critical feedback, for example, might simultaneously feel disappointed, embarrassed, and motivated to improve. Understanding the causes and possible consequences of these emotions may help people choose more appropriate responses. Instead of immediately reacting to disappointment, a person who understands where the feeling comes from may be better able to consider the situation before deciding what to do. Emotional understanding may therefore contribute to wellbeing indirectly by supporting more effective emotion regulation and coping. '''[ research source examining emotional understanding and wellbeing/regulation.]''' ===== Emotion regulation ===== Emotion regulation refers to the ways people influence their emotional experiences and responses. Regulation does not necessarily mean removing or suppressing negative emotions. Instead, it can involve changing how a situation is interpreted, deciding how an emotion should be expressed, or choosing how to respond to it. Different regulation strategies may have different consequences for wellbeing. Cognitive reappraisal, for example, involves changing the way a situation is interpreted in order to change its emotional impact. Suppression, in contrast, involves reducing the outward expression of an emotion without necessarily changing the underlying emotional experience. Emotional intelligence may help people identify which regulation strategy is appropriate for a particular situation rather than responding automatically. This may provide one explanation for the relationship between emotional intelligence and wellbeing. People who are better able to recognise and understand their emotions may also be better positioned to regulate difficult emotional experiences. However, evidence is needed to establish whether emotion regulation actually explains, or mediates, the relationship between emotional intelligence and wellbeing rather than simply being associated with both. '''[Add emotion-regulation/EI source here.]''' * Examine how EI may influence responses to stressful situations. * Discuss appraisal and coping strategies. * Consider emotional recovery and resilience. * Connect effective coping with emotional wellbeing. ====== Coping with stress ====== Emotional intelligence may also influence how people respond to stressful experiences. Stress can produce difficult emotional responses such as tension, worry, and feelings of being overwhelmed. Chen et al. (2023) distinguish between adaptive responses that help people cope with or adjust to stressors and maladaptive responses that may interfere with functioning and increase the risk of stress-related difficulties. Emotional skills may be useful during this process because recognising and understanding an emotional response can help a person decide how to cope with the situation. Effective coping does not necessarily remove the stressor, particularly when a situation cannot be changed. Instead, people may need to adjust their response to it. Emotion regulation has also been identified as a resilience-related factor, further demonstrating the connection between emotional processes and responses to stress. ====== Social relationships and support ====== Emotional intelligence may also contribute to wellbeing through relationships with other people. Recognising another person's emotions can make it easier to understand their perspective, communicate appropriately, and respond to interpersonal difficulties. Managing one's own emotional responses may also be important during disagreements or emotionally challenging conversations. These abilities could support stronger relationships and access to social support, providing another possible pathway between emotional intelligence and wellbeing. However, being able to recognise another person's emotions does not automatically lead to supportive or prosocial behaviour. Emotional abilities describe how effectively emotional information is processed, rather than whether that information will always be used positively. '''[Add research connecting EI with relationship quality/social support and wellbeing.]''' * Explain how EI may help people recognise other people's emotions. * Discuss emotional communication. * Examine interpersonal conflict and relationship management. * Consider whether stronger relationships and social support provide another pathway between EI and wellbeing. '''Figure 3.''' ''Possible pathways through which emotional intelligence may support emotional wellbeing.'' Emotional intelligence may contribute to emotional wellbeing through several interacting processes, including emotional awareness, emotional understanding, emotion regulation, coping with stress, and social functioning. These processes may influence one another rather than occurring in a simple step-by-step sequence. == Which components of emotional intelligence are particularly important for emotional wellbeing? == Although emotional intelligence is often discussed as a single construct, Mayer and Salovey's ability model proposes several distinct emotional abilities. These components may not contribute equally to emotional wellbeing. Comparing emotion perception, using emotions, emotional understanding, and emotion management can therefore provide a clearer picture of which aspects of emotional intelligence may be particularly relevant to wellbeing. === Emotion perception === Emotion perception involves accurately recognising emotions in oneself and other people. This ability may contribute to wellbeing by helping individuals identify their emotional state and recognise emotional information in social situations. However, recognising an emotion does not necessarily mean that a person knows how to respond to it. Someone may accurately recognise that they are angry, for example, while still responding impulsively. Emotion perception may therefore provide an important foundation for emotional functioning without being sufficient on its own to support wellbeing. '''[ evidence comparing perception with other EI branches.]''' ==== '''Using emotions''' ==== Using emotions involves drawing on emotional information to support thinking, attention, judgement, and decision-making. Different emotional states can influence what people notice and how they approach a problem. Being able to use this information may therefore help individuals adapt their thinking to different situations. However, the relevance of this component to emotional wellbeing needs to be established through research rather than assumed. Compared with emotion management, for example, using emotions may have a less direct connection with how people cope with distress or regulate difficult emotional experiences. [ comparative branch-level evidence here.] ==== Emotion understanding ==== Emotion understanding involves recognising the causes of emotions, distinguishing between related emotional states, and understanding how emotions can change or combine. This ability may help people make sense of complicated emotional experiences and anticipate how feelings might develop. Understanding an emotion may also make it easier to choose an appropriate coping or regulation strategy. However, as with emotion perception, understanding an emotion does not guarantee that it will be managed effectively. Research comparing the different branches of emotional intelligence is therefore needed to determine whether emotional understanding has an independent relationship with wellbeing or primarily contributes through other emotional processes. [Add branch-level research. * Discuss understanding the causes and consequences of emotions. * Consider emotional complexity and changes in emotional states. * Examine how understanding emotions may support coping and regulation. ===== Emotion regulation and management ===== Emotion management may have a particularly direct connection with emotional wellbeing because it concerns how people respond to and regulate emotional experiences. Effective regulation could help people manage distress, maintain positive emotional functioning, and recover from stressful experiences. This does not mean eliminating negative emotions, but responding to them in ways that are appropriate to the situation. However, emotion management should not automatically be considered the most important component of emotional intelligence. Its relative importance needs to be established by studies that compare it directly with perception, use, and understanding of emotions. Differences in how emotional intelligence and wellbeing are measured may also affect which component appears most strongly related to wellbeing (Blasco-Belled et al., 2019). ====== Comparing the components ====== Overall, the four emotional abilities may contribute to wellbeing in different but connected ways. Perception provides information about emotional states, understanding helps make sense of that information, using emotions may support thinking and decision-making, and management concerns how emotional experiences are handled. Rather than functioning independently, these abilities may work together. Determining whether one component is particularly important requires direct comparisons across the four branches. Evidence that emotion management is associated with wellbeing would not, by itself, demonstrate that it is more important than the other components. Differences between ability-based and self-report measures should also be considered when interpreting these findings. '''Table 2.''' ''Components of emotional intelligence and their potential relevance to emotional wellbeing'' {| class="wikitable" !EI component !What it involves !Potential relevance to wellbeing |- |Emotion perception |Recognising emotions in oneself and others |May support emotional awareness and identification of emotional needs |- |Using emotions |Using emotional information to support thinking |May influence attention, judgement, and problem-solving |- |Emotion understanding |Understanding the causes, changes, and combinations of emotions |May help people make sense of emotional experiences and select appropriate responses |- |Emotion management |Regulating emotional responses in oneself and responding to others |May support coping with difficult emotions and emotional functioning |} == How can emotional intelligence be developed to support emotional wellbeing? == If emotional intelligence contributes to wellbeing, an important practical question is whether these emotional abilities can be developed. Emotional intelligence interventions have attempted to improve skills such as emotional awareness, understanding emotions, emotion regulation, and interpersonal communication. However, evidence that EI can be improved does not necessarily mean that increasing EI will automatically improve emotional wellbeing. === Can emotional intelligence be developed? === Emotional intelligence is not necessarily a completely fixed characteristic. Training programs have attempted to develop emotional abilities through education, practice, feedback, and exercises focused on recognising and managing emotions. However, the effectiveness of training may depend on how emotional intelligence is conceptualised and measured. Changes in self-reported EI, for example, may indicate that people feel more confident in their emotional abilities without necessarily demonstrating equivalent improvements on performance-based measures. Research evaluating EI interventions is therefore important for determining whether emotional abilities can genuinely be improved and whether any improvements continue after training has ended (Hodzic et al., 2017). ==== Emotional intelligence interventions ==== EI interventions may target several skills rather than emotional intelligence as a single ability. Activities can focus on recognising emotional cues, developing emotional vocabulary, understanding emotional triggers, considering other people's perspectives, practising emotion-regulation strategies, and improving emotional communication. These approaches are particularly relevant to emotional wellbeing if improvements in emotional skills help people respond more effectively to stress and difficult emotional experiences. However, intervention studies need to examine more than whether EI scores increase. They should also assess whether changes are accompanied by meaningful improvements in wellbeing. ===== Do improvements in emotional intelligence improve wellbeing? ===== An important distinction is whether EI training improves emotional intelligence itself and whether those improvements subsequently lead to better wellbeing. An intervention could increase participants' knowledge about emotions without meaningfully changing their happiness, life satisfaction, stress, or emotional functioning. Evidence that an intervention improves both EI and wellbeing would provide stronger support for a possible causal relationship than correlational studies showing that the two are associated. Even then, researchers need to consider whether improvements are maintained over time and whether changes in wellbeing are actually explained by increased emotional intelligence (Hodzic et al., 2018; Nadler et al., 2020). ====== Limitations and practical implications ====== Although EI training may have practical value, its potential benefits should not be overstated. Emotional wellbeing is influenced by many personal, social, and environmental factors, and improving emotional skills cannot remove every source of stress or psychological difficulty. Differences between EI models, measurement methods, intervention designs, and participant groups can also make findings difficult to compare. == Figures == [[File:Thought bubble.svg|right|140px|thumb|'''Figure 3'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted ; ; '''Quizzes''' * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] ==Conclusion== Emotional wellbeing involves more than simply feeling happy or avoiding negative emotions. It also involves how people understand, respond to, and manage their emotional experiences. Overall, research suggests that higher emotional intelligence is associated with better indicators of wellbeing, although the strength of this relationship varies depending on how researchers define and measure emotional intelligence and wellbeing. Emotional awareness, understanding, regulation, stress coping, and interpersonal functioning may help explain why emotional intelligence relates to wellbeing. However, the different components of emotional intelligence may not contribute equally, and findings can differ between trait and ability models of EI. Research into affective intelligence interventions also suggests that some emotional abilities may be developed, creating possible opportunities to support wellbeing, although improvements in EI should not be assumed to automatically produce improvements in wellbeing. Importantly, emotional intelligence should not be viewed as a guarantee or universal cause of emotional wellbeing. Wellbeing is influenced by many factors, and emotionally intelligent people will still experience stress, disappointment, conflict, and other difficult emotions. Sophie's situation demonstrates this distinction. Her emotional abilities do not prevent her from feeling disappointed or overwhelmed; instead, they may help her recognise what she is experiencing, understand why she feels that way, regulate her response, and choose behaviours that better support her wellbeing * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Emotional intelligence]] * Emotional regulation * [https://en.wikipedia.org/wiki/Subjective_well-being?wprov=srpw1_1 Subjective wellbeing] {{ic|Use internal link style as shown in Tutorial 2}} * Psychological wellbeing * Coping * Stress * Positive psychology * [[Motivation and emotion/Book/2011/Emotional intelligence|Emotional intelligence]] (Book chapter, 2011) * [[wikibooks:Foundations_of_Education_and_Instructional_Assessment/Effective_Teaching/Intelligence#Introduction_to_Emotional_Intelligence|How are all children smart?]] (Wikibooks) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. '''APA style example:''' {{Hanging indent|1= Al-Hendawi, M., Alodat, A., Al-Zoubi, S., & Bulut, S. (2024). A PERMA model approach to well-being: A psychometric properties study. BMC Psychology, 12(1). https://doi.org/10.1186/s40359-024-01909-0 Barbash, E. H. (2015). Emotional intelligence in professional psychology doctoral students: A cross-sectional study (Publication No. 3724176) [Doctoral dissertation, The Florida State University]. ProQuest Dissertations and Theses Global.https://www.proquest.com/psychology/docview/1725144779/3E4CE21A1D6E4E64PQ/1?accountid=28889&sourcetype=Dissertations%20&%20Theses Blasco-Belled, A., Rogoza, R., Torrelles-Nadal, C., & Alsinet, C. (2019). Emotional intelligence structure and its relationship with life satisfaction and happiness: New findings from the bifactor model. Journal of Happiness Studies, 21(6), 2031–2049. https://doi.org/10.1007/s10902-019-00167-x Chapman, B. P. (2005). Emotional intelligence at mid life: A cross sectional investigation of structural variance, social correlates, and relationship to established personality and ability taxonomies. Proquest.Com. https://www.proquest.com/psychology/docview/305400900/8D98674B36744231PQ/2?accountid=28889&sourcetype=Dissertations%20&%20Theses Carfagno, N. (2020). The factor structures of ability and trait emotional intelligences relative to general intelligence and personality. Proquest.Com. https://www.proquest.com/psychology/docview/2466049130/3E4CE21A1D6E4E64PQ/4?accountid=28889&sourcetype=Dissertations%20&%20Theses Chen, C., Kotozaki , Y., Okubo , R., & Nakagawa , S. (2023, July 13). Editorial: New insights into stress coping and resilience . Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC10374303/ Givon, E., Itzhak-Raz, A., Danieli, G., Karmon-Presser, A., & Meiran, N. (2020, March). How Does the Emotional Experience Evolve? Feeling Generation as Evidence Accumulation. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/3yqigdmzyv?route=details Hodzic, S., Scharfen, J., Ripoll, P., Holling, H., & Zenasni, F. (2017). How efficient are emotional intelligence trainings: A meta-analysis. Emotion Review, 10(2), 138–148. https://doi.org/10.1177/1754073917708613 Huta, V., & Waterman, A. S. (2014). Eudaimonia and its distinction from hedonia: Developing a classification and terminology for understanding conceptual and operational definitions. Journal of Happiness Studies, 15(6), 1425–1456. https://doi.org/10.1007/s10902-013-9485-0 Llamas-Díaz, D., Cabello, R., Megías-Robles, A., & Fernández-Berrocal, P. (2022). Systematic review and meta-analysis: The association between emotional intelligence and subjective well-being in adolescents. Journal of Adolescence, 94(7), 925–938. PubMed. https://doi.org/10.1002/jad.12075 Luna, L. M. B., Vilar, M. M., Soto, C. M., & Santiago, J. L. C. (2021). Emotional intelligence measures: A systematic review. Healthcare, 9(12). https://doi.org/10.3390/healthcare9121696 Martins, A., Ramalho, N., & Morin, E. (2010). A comprehensive meta-analysis of the relationship between emotional intelligence and health. Personality and Individual Differences, 49(6), 554–564. https://doi.org/10.1016/j.paid.2010.05.029 MacCann, C., Double, K. S., & Clarke, I. E. (2022). Lower avoidant coping mediates the relationship of emotional intelligence with well-being and ill-being. Frontiers in Psychology, 13, 835819. https://doi.org/10.3389/fpsyg.2022.835819 Nadler, R., Carswell , J., & Minda, J. P. (2020, February). Online mindfulness training increases well-being, trait emotional intelligence, and workplace competency ratings: A randomized waitlist-controlled trial. Canberra.Edu.Au. https://pmc-ncbi-nlm-nih-gov.ezproxy.canberra.edu.au/articles/PMC7048000/ Robinson, T. J., & Zell, E. (2026). Robust associations of emotional intelligence with human flourishing: A second-order meta-analysis. Proceedings of the National Academy of Sciences of the United States of America, 123(19), e2532963123. https://doi.org/10.1073/pnas.2532963123 Sánchez-Álvarez, N., Extremera, N., & Fernández-Berrocal, P. (2015). The relation between emotional intelligence and subjective well-being: A meta-analytic investigation. The Journal of Positive Psychology, 11(3), 276–285. https://doi.org/10.1080/17439760.2015.1058968 Salovey, P., & Grewal, D. (2005). The Science of Emotional Intelligence. Current Directions in Psychological Science : A Journal of the American Psychological Society, 14(6), 281–285. https://doi.org/10.1111/j.0963-7214.2005.00381 Xu, X., Pang, W., & Xia, M. (2021, December). Are emotionally intelligent people happier? A meta‐analysis of the relationship between emotional intelligence and subjective well‐being using Chinese samples. Canberra.Edu.Au. https://research-ebsco-com.ezproxy.canberra.edu.au/c/aprr63/viewer/pdf/cwosfaeugr?route=details Villanueva, L., Prado-Gascó, V., & Montoya-Castilla, I. (2020). Longitudinal analysis of subjective well-being in preadolescents: The role of emotional intelligence, self-esteem and perceived stress. Journal of Health Psychology, 27(2), 135910532095160. https://doi.org/10.1177/1359105320951605 Zomer, L. (2012a). The relationships among emotional intelligence, gender, coping strategies, and well-being in the management of stress in close interpersonal relationships and the workplace [Master's thesis, University of Toronto]. https://www.proquest.com/openview/723018a77700f5c01e4992096ca8f1fa/1?pq-origsite=gscholar&cbl=18750 }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://www.ted.com/talks/maximilian_park_emotional_intelligence_from_a_teenage_perspective Emotional Intelligence From a Teenage Perspective] * [https://rickhanson.com/being-well-podcast-emotional-intelligence-improving-self-awareness-self-regulation-and-empathy-2/ Being Well Podcast: Emotional Intelligence: Improving Self-Awareness, Self-Regulation, and Empathy] {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 1j5w720l8hkoke4lue5g44ocufdffjr 0 331234 2834494 2834423 2026-09-25T23:14:39Z Mymunu 3106327 /* Affordance theory and outdoor play environments */ 2834494 wikitext text/x-wiki {{title|Outdoor play and children's emotional well-being:<br>How does outdoor play influence children's emotional well-being?}} __TOC__ == Overview == {| class="wikitable" [[File:School children happily playing in playground.jpg|thumb|'''Figure 1'''. Children engaged in outdoor play.]] |'''Case study: Part 1''' A child arrives at playground and joins a group of children who are already playing. The children are making their own game and deciding the rules as they play. At first, child enjoys choosing where and what to play and moving between the different activities. During the game, another child changes the rules of the game and argument breaks out. The child becomes frustrated and avoids the activity. After watching for short time, the child returns, suggests for new idea to continue game and re-joins the group. How might experiences like this during outdoor play influence children's emotional well-being? Emotional regulation theory provides one way of understanding on how children may respond to emotional situations during play (see figure 1) (Gross, 2015). |} Outdoor play can involve more than physical movements. It is more than simply being outside and engage in the activities across playgrounds, gardens, streets and natural spaces. Outdoor play involves exploration, social interaction, choice and challenge and engagement with surrounding environment (Dodd et al.,2026; Pereira et al.,2024). These experiences may create emotional situations in which children need to respond to frustration, disagreement, uncertainty or excitement. Gross (2015) [[emotional regulation]] theory provides a [[psychological]] explanation for how children may recognise and respond to these emotional situations. Outdoor play experiences are also shaped by the environment where play takes place. Experiences are shaped by the different opportunities provided by different physical and social environments, which means the same outdoor space may not provide the same experience for every child (Morgenthaler et al.,2024).This chapter examines how [[Emotional regulation|emotional,]] [[Cognitive psychology|cognitive]], social and environmental processes may help explain the relationship between outdoor play and children's emotional well-being. {| class="wikitable" | ;[[File:Bulb Idea Flat Icon GIF Animation.gif|alt=Focus questions|left|100x100px|thumb]] '''Focus questions''' * What are outdoor play and children's emotional well-being? * How does outdoor play influence children's emotional well-being? * How do social and environmental conditions shape children's outdoor play experiences? * How can families, communities and school support outdoor play opportunities that may benefit children's emotional well-being? |} == '''Understanding outdoor play and children's emotional well-being''' == [[File:Water-outdoor-people-girl-play-boy-938233.jpg|thumb|'''Figure 2'''. ''Visualise outdoor play as providing children with opportunities to explore, make choices, interact with others and respond to changing situations through activities such as water play.''|265x265px]] Outdoor play and children's emotional well-being are not measured as single and consistent concepts across recent research. Outdoor play may be examined as voluntary and intrinsically motivated activity, self directed play, parent reported outdoor play, or device-measured outdoor play activity. It should also be distinguished from outdoor moderate to vigorous physical activity because these measures do not represent the same behaviour (Davenport et al., 2025). Children's emotional well-being is also examined through different outcomes, that includes [[emotional regulation]], social-emotional competence, positive and negative affect, and internalising or externalising symptoms. These differences are significant because outdoor play and emotional well-being are not measured as single, consistent constructs across research. === Outdoor play === Outdoor play is voluntary and and intrinsically motivated activity that occurs in outdoor environments like gardens, playgrounds, parks and natural spaces (Dodd et al., 2026). Free play can be also self-directed, which means children to freely interact with the environment and have autonomy to make choices about their activities (Biino et al., 2025). Outdoor play should not be treated as same as outdoor physical activity. Davenport et al., (2025) examined outdoor play separately from outdoor moderate- to- vigorous physical activity (MVPA). This distinction is significant because research on children's outdoor play is not necessarily measuring the same behaviour as research on the intensity of physical activity. === Children's emotional well-being === Children's emotional well-being is not represented by single common outcome across recent outdoor play research. Emotional dysregulation has been examined in relation to the amount and timing of outdoor play (Lee et al., 2025), while social-emotional competence includes difficulties and [[Prosocial behavior/Keywords/Definitions|prosocial behaviour]] (Ferguson et al., 2025). Other studies have examined positive and negative affect following recess (Poulos et al., 2026) and trajectories of internalising and externalising symptoms across childhood (Dodd et al., 2026). These outcomes represent different aspects and timeframes of emotional functioning, so they should not be treated as equivalent when findings are compared. '''Table 1''' ''Emotional outcomes examined in recent research on outdoor play and children's emotional well-being'' {| class="wikitable" |+ !Study !Outcome examined !What the outcome represent |- |Lee et al. (2025) |Emotional dysregulation |Difficulties in emotional regulation; examined in relation to the amount of timing and outdoor play |- |Ferguson et al. (2025) |Social-emotional competence |Social and emotional difficulties and prosocial behaviour |- |Poulos et al. (2026) |Positive and negative affect |Children's affect following recess in different settings |- |Dodd et al. (2026) |Internalising and externalising symptoms |Internalising: emotional symptoms and peer problems Externalising: conduct problems and hyperactivity- inattention |} As shown in Table 1, the studies do not measure the same aspect or time frame of children's emotional functioning. Affect immediately following recess should not be treated as equivalent to emotional dysregulation measured over time or trajectories of internalising and externalising symptoms across childhood. This difference need to be considered when examining whether outdoor play is associated with children's emotional well-being. '''Case study: part 2''' ''What is being measured?'' {| class="wikitable" | valign="top" |[[File:Children marbles.jpg|thumb|177x177px|'''Figure 3'''. ''Children may experience different emotional responses during social outdoor play'']]The child in the case study part 1 becomes frustrated when the rules of the game change. This immediate emotional response is different from a longer-term pattern of emotional dysregulation or internalising symptoms. When research findings are compared, it is important to consider which aspect of emotional well-being is measured. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {A child's positive or negative affect immediately after recess represents the same emotional outcome as longer-term internalising or externalising symptoms. |type="()"} - True + False </quiz> {{Robelbox/close}} |} == '''How does outdoor play influence children's emotional well-being?''' == Outdoor play may be related to children's emotional well-being through emotional, cognitive, and social processes. Possible pathways discussed in the recent research include [[Emotional regulation|emotion regulation]], working memory, social interaction, physical activity, connection with the nature and adventurous play. However, these pathways have not all been directly tested as mechanisms, and many of the outdoor play literatures remain observational (Dodd et al., 2026; de Lannoy et al.,2023). Psychological theory can help to explain how and why outdoor play experiences may influence children's emotional well-being. Although the evidence does not yet show that psychological processes cause the relationship between outdoor play and children's emotional well-being. === '''Emotion regulation''' === Emotion regulation provides a psychological framework for understanding how children may manage emotional situations during outdoor play. Gross (2025) described emotional regulation as a process involving identification, selection and implementation. Identification concerns deciding whether to regulate an emotion, selection concerns selecting regulation strategy and implementation concerns applying chosen response into practice. Gross (2015) also described situation selection, situation modification, attention deployment cognitive change and response modulation. During outdoor play, children may experience frustration, conflict, disagreement, uncertainty or changes to their activity. Gross framework can be applied to these situations to consider how a children recognise an emotional response, choose strategies to manage and act on chosen strategies. However, Gross (2015) did not examine outdoor play, so applying the framework does not show that outdoor play improves children's emotion regulation. {| class="wikitable" | valign="top" |'''Case study: Part 3'''[[File:14Y Ncdc july 5th-802.jpg|thumb|202x202px|'''Figure 4'''. ''Children can respond differently to situations that occur during outdoor play.'']]When the rule of game change, the child becomes frustrated and decided to step away. After a short time the child returns and suggests for different way to continue the game (see Figure 4). Suggesting a change to the game can be considered an example of situation modification. This shows how Gross's emotion regulation framework can be applied to an emotional situation during outdoor play. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {What does Gross (2015) emotion regulation framework show when it is applied to the outdoor-play scenario?. |type="()"} -A. Outdoor play causes better emotion regulation. +B. Situation modification can help explain how the child responds to the situation. -C. Children regulate emotions better outdoors than indoors. -D. Stepping away from play always improves emotional well-being. </quiz> {{Robelbox/close}} |} === '''Working memory and cognitive process''' === Working memory can be one cognitive process involved in the association between outdoor play and emotional dysregulation. Lee et al., (2025) examined 325 preschool children and tested working memory as a statistical mediator. Outdoor play was examined across three periods of the day; wake up to noon, noon to 6 pm, and 6 pm to bedtime. The findings differed according to the timing of outdoor play. More outdoor play between noon and 6 pm was associated with lower emotional dysregulation. In contrast, more outdoor play before noon and 6 pm was associated with higher emotional dysfunction. Afternoon outdoor play was also associated with better working memory, and better working memory was associated with lower emotional dysregulation. When working memory was included in the analysis, the association between afternoon outdoor play and emotional dysregulation was no longer statistically significant. Lee et al., (2025) reported this as full mediation. This suggests working memory may be involved in the association between afternoon play and lower emotional dysregulation. However, the study was observational, so the mediation analysis does not show that outdoor play caused better working memory or lower emotional dysregulation. == '''How does social and environmental conditions influence on children's outdoor play experiences?''' == Outdoor play opportunities depends on the opportunities available in their social and physical environment. Children may have access to same outdoor space but not have same opportunities to take part in play. These difference can be considered through affordance theory, which examines the opportunities for action provided by features of an environment. === Affordance theory and outdoor play environments === Affordance theory provides a way of understanding how children interact with outdoor environments. An affordance is an opportunity for action that environment provides. Morgenthaler et al. (2024) applied this theory to outdoor play and identified different forms of play that spaces and objects can afford. This means the outdoor environment do not simply provide a place to play. Their features can provide different opportunities for how children use the play space. Research on outdoor play space supports the importance of these environmental features. Pereira et al. (2024) reviewed features such as fixed structures, natural elements, floor markings, loose equipment and available play area. However, the findings of the research was significantly different across studies. There evidence does not support that one particular features produces better emotional well-being. '''Table 2'''. ''Examples of environmental features and possible affordances'' {| class="wikitable" |+ !Environmental feature !Possible affordance for play |- |Fixed structures (e.g. climbing frame) |Can provide opportunity in different forms of physical activity. For example, climbing, physical play, risk-taking |- |Natural elements (e.g. tree, rocks, sand) |Environmental features can provide opportunities for exploratory play, imaginative play, sensory experiences |- |Floor markings (e.g. painted games) |Can support structured activities like rule based play, social play, active play |- |Loose equipment (e.g. balls, tyre, boxes) |Movable environmental features that can be used during constructive play, imaginative play, creative problem solving play |- |Open play area |Running, group play, or flexible use |} Note. Based on Pereira et al. (2024) and Morgenthaler et al. (2024). Environmental features can afford more than one type of play and the opportunities may vary between children. {| class="wikitable" | valign="top" |'''Case study: Part 4 Same space, different opportunities''' Kim and Leo are both at the same school playground during recess. The playground has climbing feature, sand pit area and open natural space. * Kim quickly joins a group of children in a climbing frame. The climbing frame structure provides him with an opportunity for physical play and social interactions. * Leo uses sand pit area with other child, he plays with loose materials and creates a sand castle and other different structures. The environment gives him an opportunity for imaginative play and social play. Both the examples show how the same outdoor space can afford different forms of play for different children, depending on their interests, skills and social context. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {Which statement best applies affordance theory to the example?. |type="()"} -A. The play ground causes children to be more physically active. +B. The same playground can provide different opportunities for play depending on the child and how they use the environment. -C. Climbing structures always lead to better emotional well-being. -D. Open spaces are only useful for social play. </quiz> {{Robelbox/close}} |} * Outdoor play opportunities are shaped by more than the physical being outdoor space. Beekhuizen et al. (2025) interviewed 40 children aged 6 to 12, with and without disabilities about facilitators and barriers to inclusive outdoor play. The findings were identified personal factor, interacting factors and environmental factors. * Personal factors included experiencing [[w:Autonomy|autonomy]], and children's feelings of physical and social limitations. Interacting factors included making contact, growing up together, and adopting the ways of playing. Environmental factors included parents, outdoor play environments, communities, and time constrains (Beekhuizen et al., 2025). * Opportunities for outdoor play was not experienced in the same way by all children. Beekhuizen et al. (2025) found that children with disabilities experienced more barriers than children with no disability. The challenges were related to making contact with other children, adopting play and the physical play environment. * Ferguson et al. (2025) examined the association between outdoor play and children's social-emotional competence. In a cross sectional analysis of 2568 children, aged 7.1 to 12.6 years from multi-ethnic urban cohort found that outdoor play was associated with better social-emotional competence. However, the association was differed across ethnicity, and weekday or weekend outdoor play. * Ferguson et al. (2025) also examined area deprivation. The relation between outdoor play and social-emotional competence appeared stronger in less deprived area, although the statistical evidence for the differences by deprivation was significantly weak. === '''Social relationship and inclusion''' === * Beekhuizen et al. (2025) identified making contact and growing up together as interacting factors in inclusive outdoor play. Some children described familiarity with other children as an easy way to approach, communication and play together. Making contact could also be a barrier when children approaching to another unfamiliar children or joining in play who were already playing. * Children also described the need to adopt games so that children with different abilities could participate. School and communities were identified settings where children with and without disabilities could become familiar with each other (Beekhuizen et al., 2025). * In the recent observational research by Beekhuizen et al. (2026) observed outdoor play among children with and without disability. The researchers found that getting to know each other, making contact and interaction while playing together as process of inclusive outdoor play. These observational findings showed that familiarity and making contact determine social and inclusive play because children chose to play with children they already knew. * Ferguson et al. (2025) also found that the association between outdoor play and social emotional competence was not the same across all ethnic and deprivation groups. In the cross sectional analysis of 2568 children aged 7.1 to 12.6 years from multi ethnic urban cohort, outdoor play was associated with better social-emotional competence. However, associations varies across same ethnic groups and according to weekday or weekend outdoor play. === '''Autonomy, parents and time''' === * Experiencing autonomy was identified as a personal factor in inclusive outdoor play. Children having some independence during outdoor play could promote their sense of independence over what they do and who they play with (Beekhuizen et al., 2025). * Experiencing autonomy also included opportunities to play without direct involvement of parents. Some children with disabilities described wanting to play outside independently, although parental support could make outdoor play possible (Beekhuizen et al., 2025) * Parents were identified as an environmental factors. Beekhuizen et al. (2025) found that parental involvement could support children's participation in outdoor play, specially when child needed help to access or participate in outdoor play. * Time constraints were considered as another environmental factor. Some children with disabilities were described as having limited outdoor play time due to parents work schedule, after-school arrangements or longer travel distance between home and school (Beekhuizen et al., 2025) === '''Outdoor environments and accessibility''' === * The outdoor play environment was identified as an environmental factor that could could support or restrict inclusive outdoor play. Children described both physical and social aspects of outdoor play environments. For example, children discussed the importance of physical and social safety, including traffic near playgrounds and disputes among children. Accessibility was particularly relevant to children with disabilities because opportunities for inclusive outdoor play could be affected by play environments and physical abilities (Beekhuizen et al., 2025). * Pereira et al. (2024) provided evidence about the physical features of outdoor play spaces. Their systematic review included 51 articles representing 45 primary studies aged between 5 to 12 and examined particular environmental features like fixed structures, natural elements, floor marking, loose parts or equipment and available play area. * Pereira et al. (2024) found positive association between outdoor play space features and children's behaviours. However, there was substantial variation between studies so the review could not establish clear conclusions about the effects of particular environmental features. {{ic|Add an APA style table caption}} {| class="wikitable" |+ |Key points * Beekhuizen et al. (2025) identified personal, interacting and environmental factors that could facilitate or restrict inclusive outdoor play. * Social relationships and familiarity affected participation, with children with disabilities reporting more barriers to inclusive outdoor play (Beekhuizen et al., 2025). * Associations between outdoor play and social-emotional competence varied across some population groups and play contexts (Ferguson et al., 2025). |} == '''What does recent research show about outdoor play and children's emotional well-being?''' == * Recent research has examined various aspects of outdoor play and children's emotional well-being and provides mixed evidence. These include emotional dysregulation (Lee et al., 2025), social-emotional competence (Ferguson et al., 2025), positive and negative affect (Poulos et al., 2026), and internalising and externalising symptoms (Dodd et al., 2026). * Ferguson et al. (2025) found that more frequent outdoor play was associated with better social-emotional competence. However, the associations varied across some ethnic groups and according to whether outdoor play occurred on school days or weekends. * Dodd et al. (2026) provides longitudinal evidence from 4,151 children from the Growing Up in Scotland study. Children who played outdoors more frequently between approximately 2 and 4 years of age were more likely to follow a trajectory of low and stable internalising and externalising symptoms through to age 8. * Poulos et al. (2026) examined children's emotional state immediately after recess during hot weather. Among 317 children in years 4 and 5, the positive effect was higher after outdoor recess and gymnasium recess than after classroom recess. There were no significant differences in negative affect between the three recess settings. * Together, these studies show evidence of associations between outdoor play or outdoor recess and several aspects of emotional well-being. However, the studies did not show the common effect because the study differ in children's ages, research designs, measures of outdoor play, and emotional outcomes. === '''Consistency of recent research findings''' === * Recent findings do not show the same effect across all outcomes. Ferguson et al. (2025) found that more frequent outdoor play was associated with lower total difficulties and greater prosocial behaviour. In contrast, Davenport et al. (2024) found that most associations between outdoor play and the physical, cognitive and social-emotional developmental indicators examined were not statistically significant. Therefore, the recent studies have not found significant association across all developmental outcomes. * Findings can also differ according to the emotional outcome being measured. Poulos et al. (2026) found higher positive affect after outdoor and gymnasium recess than after classroom recess, but no significant differences in negative affect between the three recess settings. Lee et al. (2025) found that lower emotional dysregulation associated with greater afternoon outdoor play but higher emotional dysregulation is associated with greater outdoor play earlier and later in the day. * Dodd et al. (2026) provides longer-term evidence. More frequent outdoor play during the preschool years predicted lower odds of belonging to the increasing or decreasing internalising and externalising symptom trajectory groups, relative to the normative low and stable group. This shows an association between early outdoor play and mental-health symptom trajectories across childhood rather than an emotional outcome measured at one point in time. * Associations may also vary across children and outdoor play contexts. Ferguson et al. (2025) reported differences according to ethnicity and whether outdoor play occurred on school days or weekends. * Recent findings suggest that associations between outdoor play and emotional well-being are not the same across all outcomes, children and play contexts. The studies differ in children's age, research designs, measures of outdoor play, and emotional outcomes. Thus, findings should not be treated as evidence of one single effect. === '''Strengths and limitations of current research''' === * Longitudinal research strengthens the evidence concerning temporal relationship. Dodd et al. (2026) analysed 4,151 children from the Growing Up in Scotland study. Outdoor play was measured at approximately 2, 3 and 4 years of age, while internalising and externalising symptoms were measured at approximately 4, 5, 6 and 8 years. This allowed the researchers to examine whether early outdoor play predicted different mental-health symptom trajectories across childhood. * Although, longitudinal evidence does not establish cause and effect. Dodd et al. (2026) identified reliance on parent report measures as a key limitation, while Lee et al. (2025) also discussed about the possibility of reverse causation when interpreting associations between the timing of outdoor play and emotional dysregulation. * Measurement of outdoor play is another important consideration. Davenport et al. (2024) examined both parent reported and device measured outdoor play and also tested whether associations were independent of outdoor moderate to vigorous physical activity. This approach distinguishes outdoor play from outdoor physical activity rather than interchangeable measures. * Limitations are also present across the wider outdoor play literature. De Lannoy et al. (2023) identified 275 Canadian outdoor play publications and found that cross sectional study design was most common. Mental and emotional development had received less research attention in comparison to physical health and development. {| class="wikitable" |+Table 2. Comparison of recent research !Study !Research method !Research strength !Limitation |- | <small>Lee et al. (2025)</small> |Observational; 6 month follow-up |Examined the timing of outdoor play and tested working memory as a statistical mediator of the association with emotional dysregulation. |Observational mediation cannot establish causation; the authors also considered possible reverse causation when interpreting timing-related findings. |- |Ferguson et al. (2025) |Cross sectional; multi ethnic urban cohort (N=2,568) |Large sample allowed associations to be examined across population groups and school-day/weekend outdoor play. |Cross-sectional design cannot establish temporal direction; associations also differed across some groups and play contexts. |- |Davenport et al. (2024) |Observational; preschool sample (N=107) |Used both parent-reported and device-measured outdoor play and distinguished outdoor play from outdoor moderate-to-vigorous physical activity (MVPA) |Small sample , and most tested associations with developmental outcomes were not statistically significant. |- |Dodd et al. (2026) |Longitudinal cohort (N = 4,151) |Outdoor play was measured in the preschool years before later internalising and externalising symptom trajectories. |Outdoor play and symptoms relied on parent reported measures, and the observational design does not establish conclusions. |- |Poulos et al. (2026) |Recess comparison study (N=317) |Compared children's positive and negative affect following outdoor, gymnasium and classroom recess rather than using outdoor recess without a comparison setting. |Examined immediate affect during an extreme-heat context; higher positive affect was also found after gymnasium recess, so the result was not specific to outdoor recess. |} As shown in table 2, the recent evidence has different methodological strengths and limitations. Longitudinal data provide stronger evidence about temporal ordering than cross-sectional studies, while the use of parent-reported and device-measured outdoor play addresses some measurement concerns. However, much of the evidence remains observational, several studies rely on parent-reported measures, and differences in emotional outcomes and play contexts limit the direct comparison between studies.   {| class="wikitable" |Key points * Recent studies report positive, mixed and non-significant findings across different emotional outcomes and measures of outdoor play (Davenport et al., 2024; Ferguson et al., 2025). * Lee et al. (2025) and Dodd et al. (2026) found associations across different emotional outcomes and time frames, from emotional dysregulation to later symptom trajectories. * Differences in study design, measurement, children's age and play context mean the findings should not be interpreted as one consistent effect of outdoor play on emotional well-being. |} == '''How do families, communities and schools support outdoor play opportunities?''' == * Opportunities for outdoor play are influenced by children's social and physical environments. Beekhuizen et al. (2025) identified parents, outdoor play environments, communities and time constraints as environmental factors that could act as facilitators or barriers to inclusive outdoor play. * Support for outdoor play also involves whether children can participate with other children. Beekhuizen et al. (2025) identified experiencing autonomy, growing up together, making contact and adapting ways of playing as factors involved in inclusive outdoor play. * The 2025 Position Statement on Active Outdoor Play recommends increasing opportunities for active outdoor play in settings where people live, learn, work and play. It also emphasises collaboration across sectors, settings and societies to support equitable access to active outdoor play (Lee et al., 2025). === '''Families''' === * Beekhuizen et al. (2025) identified parents as an environmental factor in inclusive outdoor play. Children with disabilities described parents as important in encouraging participation and, for some children, helping to explain their disability to other children. * Experiencing autonomy was identified as an important personal factor. Some children with disabilities wanted their parents to allow them freedom during outdoor play. Some preferred their parents not to accompany them to the playground, while others were comfortable with parents remaining at a reasonable distance (Beekhuizen et al., 2025). * These findings indicate that parental support and children's autonomy can both be relevant to opportunities for outdoor play. For some children with disabilities, support could be necessary for participation while opportunities to play more independently were also valued (Beekhuizen et al., 2025). * Beekhuizen et al. (2025) identified parental support as important for facilitating positive inclusive play experiences. The authors also recommended providing children and parents with knowledge about disabilities and possible adaptations that can support participation * Family level opportunities also need to be interpreted alongside the time constraints. Some children attending special education described long journeys between school and home that reduced the time available for outdoor play (Beekhuizen et al., 2025). This means that opportunities for outdoor play cannot be interpreted only in terms of children's or parents' preferences. === '''Communities''' === * Beekhuizen et al. (2025) identified communities and the outdoor play environment as environmental factors in inclusive outdoor play. Children described physically and socially safe playgrounds as important. While barriers included structure of playgrounds that made participation difficult for some children with disabilities. * The social environment of a community was also important. Children with disabilities described smaller communities, such as villages and schools, the places where other children and parents could become more familiar with disability. This familiarity was associated with greater acceptance and stronger connections with other children (Beekhuizen et al., 2025). * Recent observational research also shows that physical access alone does not explain inclusive outdoor play. Beekhuizen et al. (2026) observed 63 children with and without disabilities during six inclusive outdoor play sessions and assessed both children's playfulness and environmental supportiveness. Children with disabilities showed significantly lower playfulness scores indicating that opportunities for inclusive play were not experienced equally. * The 2025 Position Statement on Active Outdoor Play recommends collaboration across sectors, settings and societies to preserve, promote and value equitable access to active outdoor play. This places responsibility for outdoor play opportunities across communities and wider systems rather than on children and families alone (Lee et al., 2025). === '''Schools''' === * Schools can provide opportunities for children with and without disabilities to become familiar with one another. Beekhuizen et al. (2025) identified growing up together and making contact as interacting factors in inclusive outdoor play. Children described familiarity with other children as making contact easier. * School circumstances can also affect the time and opportunities available for outdoor play. Some children attending special primary education described long travel times between school and home as reducing the time available to play outdoors. Beekhuizen et al. (2025) identified these experiences under time constraints. * Recess provides another school setting in which children's emotional experiences have been examined. Poulos et al. (2026) studied 317 Year 4 and 5 children during extreme heat weather and found significantly higher positive affect after outdoor and gymnasium recess than after classroom recess. There were no significant differences in negative affect between the three recess settings. * Poulos et al. (2026) identified implications for school health, policy and equity, including the need for heat adaptive infrastructure to support access to recess environments during extreme heat. However, the findings do not show that outdoor recess is always better than indoor recess because positive affect was also higher following gymnasium recess. Quiz {{Robelbox|theme=12|title=Quiz}} <quiz display=simple> {Children who have access to the same outdoor playground may still have different opportunities to participate in play. |type="()"} + True - False </quiz> {{Robelbox/close}} {{Robelbox|theme=12|title=Quiz}} <quiz display=simple> {Outdoor play has the same relationship with children's emotional well-being regardless of how door play or emotional well being is measured. |type="()"} - True + False </quiz> {{Robelbox/close}} {| class="wikitable" |1. Children who have access to the same outdoor playground may still have different opportunities to participate in play. True False 2. Outdoor play has the same relationship with children's emotional well-being regardless of how door play or emotional well being is measured. True False |} {| class="wikitable" |Scenario Two primary school aged children A and B enjoy playing outdoors. They both lived near the same playground. Child A was very familiar with the playground and knows several other children who play there and easily join the games. While child B has disability, uses mobility device and does not know other children at playground. Some parts of the playground are difficult to access and joining other children who are already playing can also be challenging. Child B's parents can provide support, although the child also prefers to play more independently. Consider both children can access the same playground, but do they have same level opportunities to take part in outdoor play? |} '''''<u>Note: Answers to the quiz is 1: True and 2 False</u>''''' == '''Conclusion''' == * Outdoor play and children's emotional well-being are measured in different ways across recent research. Outdoor play is not equivalent to outdoor physical activity, while emotional outcomes include emotional dysregulation, social-emotional competence, positive and negative affect, and internalising and externalising symptoms. These differences need to be considered when findings across studies are compared. * Research also provides mixed evidence about how outdoor play may be related to emotional well-being. Gross's (2015) emotion-regulation framework can be applied to emotional situations experienced during play, but it does not show that outdoor play improves emotion regulation. Lee et al. (2025) provides more direct evidence of a possible cognitive process, with working memory statistically mediating the association between afternoon outdoor play and lower emotional dysregulation. However, this observational finding does not establish causation. * Recent findings are not consistent across all outcomes or contexts. Ferguson et al. (2025) reported associations with better social-emotional competence, Dodd et al. (2026) found longitudinal associations with internalising and externalising symptom trajectories, and Poulos et al. (2026) found differences in positive but not negative affect following recess. In contrast, most associations examined by Davenport et al. (2024) were not statistically significant. * Recent findings are not consistent across all outcomes or contexts. Ferguson et al. (2025) reported associations with better social-emotional competence, Dodd et al. (2026) found longitudinal associations with internalising and externalising symptom trajectories, and Poulos et al. (2026) found differences in positive but not negative affect following recess. In contrast, most associations examined by Davenport et al. (2024) were not statistically significant. * Overall, current research supports an association between outdoor play and some aspects of children's emotional well-being but does not establish one consistent effect. Differences in measurement, research design, children and play contexts remain important when interpreting the evidence. ==See also== {{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}} https://www-taylorfrancis-com.ezproxy.canberra.edu.au/books/mono/10.4324/9781003349655/right-child-play-naomi-lott Book Chapter, 2 {{ic|Move to References and cite}} https://en.wikipedia.org/wiki/Emotional_dysregulation<nowiki/>- Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} https://en.wikipedia.org/wiki/Autonomy<nowiki/>- Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} https://en.wikipedia.org/wiki/Longitudinal_study<nowiki/>-Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} [[Cognitive psychology|https://en.wikiversity.org/wiki/Cognitive_psychology]]-Wikipedia article https://en.wikipedia.org/wiki/Affordance<nowiki/>-Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} ==References== {{Hanging indent|1= Beekhuizen, R. Q., Bolster, E. A. M., Gorter, J. W., Henry, N. L., Visser, K., Wittink, H., Kotte, E. M. W., Sol, M. E., & Bloemen, M. A. T. (2025). Play Together? Unveiling Facilitators and Barriers to Inclusive Outdoor Play for Dutch Children With and Without Disabilities: A Qualitative Study. Child: Care, Health & Development, 51(6), Article e70154. https://doi.org/10.1111/cch.70154 Biino, V., Pesce, C., & Martins, C. (2025). Motor Skill Development at Preschool Age in Girls and Boys: The Role of Outdoor Free Play. Children, 12(5), Article 594. https://doi.org/10.3390/children12050594 Davenport, C., Kuzik, N., Larouche, R., & Carson, V. (2025). The Associations Between Parental-Reported and Device-Based Measured Outdoor Play and Health Indicators of Physical, Cognitive, and Social–Emotional Development in Preschool-Aged Children. Pediatric Exercise Science, 37(2), 102–111. https://doi.org/10.1123/pes.2023-0119 de Lannoy, L., Barbeau, K., Seguin, N., & Tremblay, M. S. (2023). Scoping review of children’s and youth’s outdoor play publications in Canada. Chronic Diseases in Canada, 43(1), 1–13. https://doi.org/10.24095/hpcdp.43.1.01 Dodd, H. F., Cordwell, K., Hesketh, K., Johnstone, A., de la Torre-Luque, A., & McCrorie, P. (2026). Early outdoor play predicts trajectories of child mental health in a population-based cohort. Journal of Child Psychology and Psychiatry. https://doi.org/10.1111/jcpp.70175 Ferguson, M., Teyhan, A., Lovell, R., Dodd, H., Wheeler, B., & McEachan, R. (2025). The association between park visits, outdoor play and child social-emotional competency in a multi-ethnic, urban cohort. Wellbeing, Space and Society, 9, Article 100293. https://doi.org/10.1016/j.wss.2025.100293 Gross, J. J. (2015). Emotion Regulation: Current Status and Future Prospects. Psychological Inquiry, 26(1), 1–26. https://doi.org/10.1080/1047840X.2014.940781 Lee, E.-Y., de Lannoy, L., Kim, Y.-B., Rathod, A., James, M. E., Lopes, O., Nasrallah, B., Thankarajah, A., Adjei-Boadi, D., de Barros, M. I. A., Duncan, S., Miller, R. M., Mygind, L., Vanderloo, L. M., Wang, P.-Y., & Tremblay, M. S. (2025). 2025 Position statement on active outdoor play. The International Journal of Behavioral Nutrition and Physical Activity, 22(1), Article 117. https://doi.org/10.1186/s12966-025-01813-9 Lee, J. J., Flouri, E., & Jackson, Y. (2025). The Role of Timing and Amount of Outdoor Play in Emotional Dysregulation in Preschool Children. Child: Care, Health & Development, 51(1), Article e70020. https://doi.org/10.1111/cch.70020 Morgenthaler, T., Lynch, H., Loebach, J., Pentland, D., & Schulze, C. (2024). Using the Theory of Affordances to Understand Environment–Play Transactions: Environmental Taxonomy of Outdoor Play Space Features—A Scoping Review. The American Journal of Occupational Therapy, 78(4), Article 7804185120. https://doi.org/10.5014/ajot.2024.050606 Pereira, J. V., Vila-Nova, F., Veiga, G., Lopes, F., & Cordovil, R. (2024). Associations between outdoor play features and children’s behavior and health: A systematic review. Health & Place, 87, Article 103235. https://doi.org/10.1016/j.healthplace.2024.103235 Poulos, A., Hassan, U. A., Wilson, K., Price, P. M., Vanos, J., & Quilla, J. (2026). Differences in Schoolchildren’s Emotional State After Indoor Versus Outdoor Recess in Extreme‐Heat Weather. The Journal of School Health, 96(4), Article e70135. https://doi.org/10.1111/josh.70135 }} ==External links== {{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}} https://www.child-encyclopedia.com/outdoor-play<nowiki/>-Encyclopedia in early childhood development https://www.outdoorplaycanada.ca/wp-content/uploads/2026/03/The-2025-AOP10-Position-Statement.pdf<nowiki/>-Position Statement https://www.who.int/news/item/24-04-2019-to-grow-up-healthy-children-need-to-sit-less-and-play-more<nowiki/>-World Health Organisation [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Children]] [[Category:Motivation and emotion/Book/Nature]] [[Category:Motivation and emotion/Book/Well-being]] mjerlbtgn9s74girbvhiqwe8wdayvts 2834498 2834494 2026-09-25T23:57:55Z Mymunu 3106327 /* How does outdoor play influence children's emotional well-being? */ 2834498 wikitext text/x-wiki {{title|Outdoor play and children's emotional well-being:<br>How does outdoor play influence children's emotional well-being?}} __TOC__ == Overview == {| class="wikitable" [[File:School children happily playing in playground.jpg|thumb|'''Figure 1'''. Children engaged in outdoor play.]] |'''Case study: Part 1''' A child arrives at playground and joins a group of children who are already playing. The children are making their own game and deciding the rules as they play. At first, child enjoys choosing where and what to play and moving between the different activities. During the game, another child changes the rules of the game and argument breaks out. The child becomes frustrated and avoids the activity. After watching for short time, the child returns, suggests for new idea to continue game and re-joins the group. How might experiences like this during outdoor play influence children's emotional well-being? Emotional regulation theory provides one way of understanding on how children may respond to emotional situations during play (see figure 1) (Gross, 2015). |} Outdoor play can involve more than physical movements. It is more than simply being outside and engage in the activities across playgrounds, gardens, streets and natural spaces. Outdoor play involves exploration, social interaction, choice and challenge and engagement with surrounding environment (Dodd et al.,2026; Pereira et al.,2024). These experiences may create emotional situations in which children need to respond to frustration, disagreement, uncertainty or excitement. Gross (2015) [[emotional regulation]] theory provides a [[psychological]] explanation for how children may recognise and respond to these emotional situations. Outdoor play experiences are also shaped by the environment where play takes place. Experiences are shaped by the different opportunities provided by different physical and social environments, which means the same outdoor space may not provide the same experience for every child (Morgenthaler et al.,2024).This chapter examines how [[Emotional regulation|emotional,]] [[Cognitive psychology|cognitive]], social and environmental processes may help explain the relationship between outdoor play and children's emotional well-being. {| class="wikitable" | ;[[File:Bulb Idea Flat Icon GIF Animation.gif|alt=Focus questions|left|100x100px|thumb]] '''Focus questions''' * What are outdoor play and children's emotional well-being? * How does outdoor play influence children's emotional well-being? * How do social and environmental conditions shape children's outdoor play experiences? * How can families, communities and school support outdoor play opportunities that may benefit children's emotional well-being? |} == '''Understanding outdoor play and children's emotional well-being''' == [[File:Water-outdoor-people-girl-play-boy-938233.jpg|thumb|'''Figure 2'''. ''Visualise outdoor play as providing children with opportunities to explore, make choices, interact with others and respond to changing situations through activities such as water play.''|265x265px]] Outdoor play and children's emotional well-being are not measured as single and consistent concepts across recent research. Outdoor play may be examined as voluntary and intrinsically motivated activity, self directed play, parent reported outdoor play, or device-measured outdoor play activity. It should also be distinguished from outdoor moderate to vigorous physical activity because these measures do not represent the same behaviour (Davenport et al., 2025). Children's emotional well-being is also examined through different outcomes, that includes [[emotional regulation]], social-emotional competence, positive and negative affect, and internalising or externalising symptoms. These differences are significant because outdoor play and emotional well-being are not measured as single, consistent constructs across research. === Outdoor play === Outdoor play is voluntary and and intrinsically motivated activity that occurs in outdoor environments like gardens, playgrounds, parks and natural spaces (Dodd et al., 2026). Free play can be also self-directed, which means children to freely interact with the environment and have autonomy to make choices about their activities (Biino et al., 2025). Outdoor play should not be treated as same as outdoor physical activity. Davenport et al., (2025) examined outdoor play separately from outdoor moderate- to- vigorous physical activity (MVPA). This distinction is significant because research on children's outdoor play is not necessarily measuring the same behaviour as research on the intensity of physical activity. === Children's emotional well-being === Children's emotional well-being is not represented by single common outcome across recent outdoor play research. Emotional dysregulation has been examined in relation to the amount and timing of outdoor play (Lee et al., 2025), while social-emotional competence includes difficulties and [[Prosocial behavior/Keywords/Definitions|prosocial behaviour]] (Ferguson et al., 2025). Other studies have examined positive and negative affect following recess (Poulos et al., 2026) and trajectories of internalising and externalising symptoms across childhood (Dodd et al., 2026). These outcomes represent different aspects and timeframes of emotional functioning, so they should not be treated as equivalent when findings are compared. '''Table 1''' ''Emotional outcomes examined in recent research on outdoor play and children's emotional well-being'' {| class="wikitable" |+ !Study !Outcome examined !What the outcome represent |- |Lee et al. (2025) |Emotional dysregulation |Difficulties in emotional regulation; examined in relation to the amount of timing and outdoor play |- |Ferguson et al. (2025) |Social-emotional competence |Social and emotional difficulties and prosocial behaviour |- |Poulos et al. (2026) |Positive and negative affect |Children's affect following recess in different settings |- |Dodd et al. (2026) |Internalising and externalising symptoms |Internalising: emotional symptoms and peer problems Externalising: conduct problems and hyperactivity- inattention |} As shown in Table 1, the studies do not measure the same aspect or time frame of children's emotional functioning. Affect immediately following recess should not be treated as equivalent to emotional dysregulation measured over time or trajectories of internalising and externalising symptoms across childhood. This difference need to be considered when examining whether outdoor play is associated with children's emotional well-being. '''Case study: part 2''' ''What is being measured?'' {| class="wikitable" | valign="top" |[[File:Children marbles.jpg|thumb|177x177px|'''Figure 3'''. ''Children may experience different emotional responses during social outdoor play'']]The child in the case study part 1 becomes frustrated when the rules of the game change. This immediate emotional response is different from a longer-term pattern of emotional dysregulation or internalising symptoms. When research findings are compared, it is important to consider which aspect of emotional well-being is measured. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {A child's positive or negative affect immediately after recess represents the same emotional outcome as longer-term internalising or externalising symptoms. |type="()"} - True + False </quiz> {{Robelbox/close}} |} == '''How does outdoor play influence children's emotional well-being?''' == Outdoor play may be related to children's emotional well-being through emotional, cognitive, and social processes. Possible pathways discussed in the recent research include [[Emotional regulation|emotion regulation]], working memory, social interaction, physical activity, connection with the nature and adventurous play. However, these pathways have not all been directly tested as mechanisms, and many of the outdoor play literatures remain observational (Dodd et al., 2026; de Lannoy et al.,2023). Psychological theory can help to explain how and why outdoor play experiences may influence children's emotional well-being. Although the evidence does not yet show that psychological processes cause the relationship between outdoor play and children's emotional well-being. Emotion involves more than subjective feelings. Scherer (2005) described emotion as coordinated changes across cognitive appraisal, physiological responses, action tendencies, expression and subjective feelings. Therefore, physiological responses are one component of an emotional response rather than a separate explanation for the effects of outdoor play. Scherer (2005) did not examine outdoor play, so this framework does not evidence that outdoor play changes children's physiological responses or emotional well-being. === '''Emotion regulation''' === Emotion regulation provides a psychological framework for understanding how children may manage emotional situations during outdoor play. Gross (2025) described emotional regulation as a process involving identification, selection and implementation. Identification concerns deciding whether to regulate an emotion, selection concerns selecting regulation strategy and implementation concerns applying chosen response into practice. Gross (2015) also described situation selection, situation modification, attention deployment cognitive change and response modulation. During outdoor play, children may experience frustration, conflict, disagreement, uncertainty or changes to their activity. Gross framework can be applied to these situations to consider how a children recognise an emotional response, choose strategies to manage and act on chosen strategies. However, Gross (2015) did not examine outdoor play, so applying the framework does not show that outdoor play improves children's emotion regulation. {| class="wikitable" | valign="top" |'''Case study: Part 3'''[[File:14Y Ncdc july 5th-802.jpg|thumb|202x202px|'''Figure 4'''. ''Children can respond differently to situations that occur during outdoor play.'']]When the rule of game change, the child becomes frustrated and decided to step away. After a short time the child returns and suggests for different way to continue the game (see Figure 4). Suggesting a change to the game can be considered an example of situation modification. This shows how Gross's emotion regulation framework can be applied to an emotional situation during outdoor play. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {What does Gross (2015) emotion regulation framework show when it is applied to the outdoor-play scenario?. |type="()"} -A. Outdoor play causes better emotion regulation. +B. Situation modification can help explain how the child responds to the situation. -C. Children regulate emotions better outdoors than indoors. -D. Stepping away from play always improves emotional well-being. </quiz> {{Robelbox/close}} |} === '''Working memory and cognitive process''' === Working memory can be one cognitive process involved in the association between outdoor play and emotional dysregulation. Lee et al., (2025) examined 325 preschool children and tested working memory as a statistical mediator. Outdoor play was examined across three periods of the day; wake up to noon, noon to 6 pm, and 6 pm to bedtime. The findings differed according to the timing of outdoor play. More outdoor play between noon and 6 pm was associated with lower emotional dysregulation. In contrast, more outdoor play before noon and 6 pm was associated with higher emotional dysfunction. Afternoon outdoor play was also associated with better working memory, and better working memory was associated with lower emotional dysregulation. When working memory was included in the analysis, the association between afternoon outdoor play and emotional dysregulation was no longer statistically significant. Lee et al., (2025) reported this as full mediation. This suggests working memory may be involved in the association between afternoon play and lower emotional dysregulation. However, the study was observational, so the mediation analysis does not show that outdoor play caused better working memory or lower emotional dysregulation. == '''How does social and environmental conditions influence on children's outdoor play experiences?''' == Outdoor play opportunities depends on the opportunities available in their social and physical environment. Children may have access to same outdoor space but not have same opportunities to take part in play. These difference can be considered through affordance theory, which examines the opportunities for action provided by features of an environment. === Affordance theory and outdoor play environments === Affordance theory provides a way of understanding how children interact with outdoor environments. An affordance is an opportunity for action that environment provides. Morgenthaler et al. (2024) applied this theory to outdoor play and identified different forms of play that spaces and objects can afford. This means the outdoor environment do not simply provide a place to play. Their features can provide different opportunities for how children use the play space. Research on outdoor play space supports the importance of these environmental features. Pereira et al. (2024) reviewed features such as fixed structures, natural elements, floor markings, loose equipment and available play area. However, the findings of the research was significantly different across studies. There evidence does not support that one particular features produces better emotional well-being. '''Table 2'''. ''Examples of environmental features and possible affordances'' {| class="wikitable" |+ !Environmental feature !Possible affordance for play |- |Fixed structures (e.g. climbing frame) |Can provide opportunity in different forms of physical activity. For example, climbing, physical play, risk-taking |- |Natural elements (e.g. tree, rocks, sand) |Environmental features can provide opportunities for exploratory play, imaginative play, sensory experiences |- |Floor markings (e.g. painted games) |Can support structured activities like rule based play, social play, active play |- |Loose equipment (e.g. balls, tyre, boxes) |Movable environmental features that can be used during constructive play, imaginative play, creative problem solving play |- |Open play area |Running, group play, or flexible use |} Note. Based on Pereira et al. (2024) and Morgenthaler et al. (2024). Environmental features can afford more than one type of play and the opportunities may vary between children. {| class="wikitable" | valign="top" |'''Case study: Part 4 Same space, different opportunities''' Kim and Leo are both at the same school playground during recess. The playground has climbing feature, sand pit area and open natural space. * Kim quickly joins a group of children in a climbing frame. The climbing frame structure provides him with an opportunity for physical play and social interactions. * Leo uses sand pit area with other child, he plays with loose materials and creates a sand castle and other different structures. The environment gives him an opportunity for imaginative play and social play. Both the examples show how the same outdoor space can afford different forms of play for different children, depending on their interests, skills and social context. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {Which statement best applies affordance theory to the example?. |type="()"} -A. The play ground causes children to be more physically active. +B. The same playground can provide different opportunities for play depending on the child and how they use the environment. -C. Climbing structures always lead to better emotional well-being. -D. Open spaces are only useful for social play. </quiz> {{Robelbox/close}} |} * Outdoor play opportunities are shaped by more than the physical being outdoor space. Beekhuizen et al. (2025) interviewed 40 children aged 6 to 12, with and without disabilities about facilitators and barriers to inclusive outdoor play. The findings were identified personal factor, interacting factors and environmental factors. * Personal factors included experiencing [[w:Autonomy|autonomy]], and children's feelings of physical and social limitations. Interacting factors included making contact, growing up together, and adopting the ways of playing. Environmental factors included parents, outdoor play environments, communities, and time constrains (Beekhuizen et al., 2025). * Opportunities for outdoor play was not experienced in the same way by all children. Beekhuizen et al. (2025) found that children with disabilities experienced more barriers than children with no disability. The challenges were related to making contact with other children, adopting play and the physical play environment. * Ferguson et al. (2025) examined the association between outdoor play and children's social-emotional competence. In a cross sectional analysis of 2568 children, aged 7.1 to 12.6 years from multi-ethnic urban cohort found that outdoor play was associated with better social-emotional competence. However, the association was differed across ethnicity, and weekday or weekend outdoor play. * Ferguson et al. (2025) also examined area deprivation. The relation between outdoor play and social-emotional competence appeared stronger in less deprived area, although the statistical evidence for the differences by deprivation was significantly weak. === '''Social relationship and inclusion''' === * Beekhuizen et al. (2025) identified making contact and growing up together as interacting factors in inclusive outdoor play. Some children described familiarity with other children as an easy way to approach, communication and play together. Making contact could also be a barrier when children approaching to another unfamiliar children or joining in play who were already playing. * Children also described the need to adopt games so that children with different abilities could participate. School and communities were identified settings where children with and without disabilities could become familiar with each other (Beekhuizen et al., 2025). * In the recent observational research by Beekhuizen et al. (2026) observed outdoor play among children with and without disability. The researchers found that getting to know each other, making contact and interaction while playing together as process of inclusive outdoor play. These observational findings showed that familiarity and making contact determine social and inclusive play because children chose to play with children they already knew. * Ferguson et al. (2025) also found that the association between outdoor play and social emotional competence was not the same across all ethnic and deprivation groups. In the cross sectional analysis of 2568 children aged 7.1 to 12.6 years from multi ethnic urban cohort, outdoor play was associated with better social-emotional competence. However, associations varies across same ethnic groups and according to weekday or weekend outdoor play. === '''Autonomy, parents and time''' === * Experiencing autonomy was identified as a personal factor in inclusive outdoor play. Children having some independence during outdoor play could promote their sense of independence over what they do and who they play with (Beekhuizen et al., 2025). * Experiencing autonomy also included opportunities to play without direct involvement of parents. Some children with disabilities described wanting to play outside independently, although parental support could make outdoor play possible (Beekhuizen et al., 2025) * Parents were identified as an environmental factors. Beekhuizen et al. (2025) found that parental involvement could support children's participation in outdoor play, specially when child needed help to access or participate in outdoor play. * Time constraints were considered as another environmental factor. Some children with disabilities were described as having limited outdoor play time due to parents work schedule, after-school arrangements or longer travel distance between home and school (Beekhuizen et al., 2025) === '''Outdoor environments and accessibility''' === * The outdoor play environment was identified as an environmental factor that could could support or restrict inclusive outdoor play. Children described both physical and social aspects of outdoor play environments. For example, children discussed the importance of physical and social safety, including traffic near playgrounds and disputes among children. Accessibility was particularly relevant to children with disabilities because opportunities for inclusive outdoor play could be affected by play environments and physical abilities (Beekhuizen et al., 2025). * Pereira et al. (2024) provided evidence about the physical features of outdoor play spaces. Their systematic review included 51 articles representing 45 primary studies aged between 5 to 12 and examined particular environmental features like fixed structures, natural elements, floor marking, loose parts or equipment and available play area. * Pereira et al. (2024) found positive association between outdoor play space features and children's behaviours. However, there was substantial variation between studies so the review could not establish clear conclusions about the effects of particular environmental features. {{ic|Add an APA style table caption}} {| class="wikitable" |+ |Key points * Beekhuizen et al. (2025) identified personal, interacting and environmental factors that could facilitate or restrict inclusive outdoor play. * Social relationships and familiarity affected participation, with children with disabilities reporting more barriers to inclusive outdoor play (Beekhuizen et al., 2025). * Associations between outdoor play and social-emotional competence varied across some population groups and play contexts (Ferguson et al., 2025). |} == '''What does recent research show about outdoor play and children's emotional well-being?''' == * Recent research has examined various aspects of outdoor play and children's emotional well-being and provides mixed evidence. These include emotional dysregulation (Lee et al., 2025), social-emotional competence (Ferguson et al., 2025), positive and negative affect (Poulos et al., 2026), and internalising and externalising symptoms (Dodd et al., 2026). * Ferguson et al. (2025) found that more frequent outdoor play was associated with better social-emotional competence. However, the associations varied across some ethnic groups and according to whether outdoor play occurred on school days or weekends. * Dodd et al. (2026) provides longitudinal evidence from 4,151 children from the Growing Up in Scotland study. Children who played outdoors more frequently between approximately 2 and 4 years of age were more likely to follow a trajectory of low and stable internalising and externalising symptoms through to age 8. * Poulos et al. (2026) examined children's emotional state immediately after recess during hot weather. Among 317 children in years 4 and 5, the positive effect was higher after outdoor recess and gymnasium recess than after classroom recess. There were no significant differences in negative affect between the three recess settings. * Together, these studies show evidence of associations between outdoor play or outdoor recess and several aspects of emotional well-being. However, the studies did not show the common effect because the study differ in children's ages, research designs, measures of outdoor play, and emotional outcomes. === '''Consistency of recent research findings''' === * Recent findings do not show the same effect across all outcomes. Ferguson et al. (2025) found that more frequent outdoor play was associated with lower total difficulties and greater prosocial behaviour. In contrast, Davenport et al. (2024) found that most associations between outdoor play and the physical, cognitive and social-emotional developmental indicators examined were not statistically significant. Therefore, the recent studies have not found significant association across all developmental outcomes. * Findings can also differ according to the emotional outcome being measured. Poulos et al. (2026) found higher positive affect after outdoor and gymnasium recess than after classroom recess, but no significant differences in negative affect between the three recess settings. Lee et al. (2025) found that lower emotional dysregulation associated with greater afternoon outdoor play but higher emotional dysregulation is associated with greater outdoor play earlier and later in the day. * Dodd et al. (2026) provides longer-term evidence. More frequent outdoor play during the preschool years predicted lower odds of belonging to the increasing or decreasing internalising and externalising symptom trajectory groups, relative to the normative low and stable group. This shows an association between early outdoor play and mental-health symptom trajectories across childhood rather than an emotional outcome measured at one point in time. * Associations may also vary across children and outdoor play contexts. Ferguson et al. (2025) reported differences according to ethnicity and whether outdoor play occurred on school days or weekends. * Recent findings suggest that associations between outdoor play and emotional well-being are not the same across all outcomes, children and play contexts. The studies differ in children's age, research designs, measures of outdoor play, and emotional outcomes. Thus, findings should not be treated as evidence of one single effect. === '''Strengths and limitations of current research''' === * Longitudinal research strengthens the evidence concerning temporal relationship. Dodd et al. (2026) analysed 4,151 children from the Growing Up in Scotland study. Outdoor play was measured at approximately 2, 3 and 4 years of age, while internalising and externalising symptoms were measured at approximately 4, 5, 6 and 8 years. This allowed the researchers to examine whether early outdoor play predicted different mental-health symptom trajectories across childhood. * Although, longitudinal evidence does not establish cause and effect. Dodd et al. (2026) identified reliance on parent report measures as a key limitation, while Lee et al. (2025) also discussed about the possibility of reverse causation when interpreting associations between the timing of outdoor play and emotional dysregulation. * Measurement of outdoor play is another important consideration. Davenport et al. (2024) examined both parent reported and device measured outdoor play and also tested whether associations were independent of outdoor moderate to vigorous physical activity. This approach distinguishes outdoor play from outdoor physical activity rather than interchangeable measures. * Limitations are also present across the wider outdoor play literature. De Lannoy et al. (2023) identified 275 Canadian outdoor play publications and found that cross sectional study design was most common. Mental and emotional development had received less research attention in comparison to physical health and development. {| class="wikitable" |+Table 2. Comparison of recent research !Study !Research method !Research strength !Limitation |- | <small>Lee et al. (2025)</small> |Observational; 6 month follow-up |Examined the timing of outdoor play and tested working memory as a statistical mediator of the association with emotional dysregulation. |Observational mediation cannot establish causation; the authors also considered possible reverse causation when interpreting timing-related findings. |- |Ferguson et al. (2025) |Cross sectional; multi ethnic urban cohort (N=2,568) |Large sample allowed associations to be examined across population groups and school-day/weekend outdoor play. |Cross-sectional design cannot establish temporal direction; associations also differed across some groups and play contexts. |- |Davenport et al. (2024) |Observational; preschool sample (N=107) |Used both parent-reported and device-measured outdoor play and distinguished outdoor play from outdoor moderate-to-vigorous physical activity (MVPA) |Small sample , and most tested associations with developmental outcomes were not statistically significant. |- |Dodd et al. (2026) |Longitudinal cohort (N = 4,151) |Outdoor play was measured in the preschool years before later internalising and externalising symptom trajectories. |Outdoor play and symptoms relied on parent reported measures, and the observational design does not establish conclusions. |- |Poulos et al. (2026) |Recess comparison study (N=317) |Compared children's positive and negative affect following outdoor, gymnasium and classroom recess rather than using outdoor recess without a comparison setting. |Examined immediate affect during an extreme-heat context; higher positive affect was also found after gymnasium recess, so the result was not specific to outdoor recess. |} As shown in table 2, the recent evidence has different methodological strengths and limitations. Longitudinal data provide stronger evidence about temporal ordering than cross-sectional studies, while the use of parent-reported and device-measured outdoor play addresses some measurement concerns. However, much of the evidence remains observational, several studies rely on parent-reported measures, and differences in emotional outcomes and play contexts limit the direct comparison between studies.   {| class="wikitable" |Key points * Recent studies report positive, mixed and non-significant findings across different emotional outcomes and measures of outdoor play (Davenport et al., 2024; Ferguson et al., 2025). * Lee et al. (2025) and Dodd et al. (2026) found associations across different emotional outcomes and time frames, from emotional dysregulation to later symptom trajectories. * Differences in study design, measurement, children's age and play context mean the findings should not be interpreted as one consistent effect of outdoor play on emotional well-being. |} == '''How do families, communities and schools support outdoor play opportunities?''' == * Opportunities for outdoor play are influenced by children's social and physical environments. Beekhuizen et al. (2025) identified parents, outdoor play environments, communities and time constraints as environmental factors that could act as facilitators or barriers to inclusive outdoor play. * Support for outdoor play also involves whether children can participate with other children. Beekhuizen et al. (2025) identified experiencing autonomy, growing up together, making contact and adapting ways of playing as factors involved in inclusive outdoor play. * The 2025 Position Statement on Active Outdoor Play recommends increasing opportunities for active outdoor play in settings where people live, learn, work and play. It also emphasises collaboration across sectors, settings and societies to support equitable access to active outdoor play (Lee et al., 2025). === '''Families''' === * Beekhuizen et al. (2025) identified parents as an environmental factor in inclusive outdoor play. Children with disabilities described parents as important in encouraging participation and, for some children, helping to explain their disability to other children. * Experiencing autonomy was identified as an important personal factor. Some children with disabilities wanted their parents to allow them freedom during outdoor play. Some preferred their parents not to accompany them to the playground, while others were comfortable with parents remaining at a reasonable distance (Beekhuizen et al., 2025). * These findings indicate that parental support and children's autonomy can both be relevant to opportunities for outdoor play. For some children with disabilities, support could be necessary for participation while opportunities to play more independently were also valued (Beekhuizen et al., 2025). * Beekhuizen et al. (2025) identified parental support as important for facilitating positive inclusive play experiences. The authors also recommended providing children and parents with knowledge about disabilities and possible adaptations that can support participation * Family level opportunities also need to be interpreted alongside the time constraints. Some children attending special education described long journeys between school and home that reduced the time available for outdoor play (Beekhuizen et al., 2025). This means that opportunities for outdoor play cannot be interpreted only in terms of children's or parents' preferences. === '''Communities''' === * Beekhuizen et al. (2025) identified communities and the outdoor play environment as environmental factors in inclusive outdoor play. Children described physically and socially safe playgrounds as important. While barriers included structure of playgrounds that made participation difficult for some children with disabilities. * The social environment of a community was also important. Children with disabilities described smaller communities, such as villages and schools, the places where other children and parents could become more familiar with disability. This familiarity was associated with greater acceptance and stronger connections with other children (Beekhuizen et al., 2025). * Recent observational research also shows that physical access alone does not explain inclusive outdoor play. Beekhuizen et al. (2026) observed 63 children with and without disabilities during six inclusive outdoor play sessions and assessed both children's playfulness and environmental supportiveness. Children with disabilities showed significantly lower playfulness scores indicating that opportunities for inclusive play were not experienced equally. * The 2025 Position Statement on Active Outdoor Play recommends collaboration across sectors, settings and societies to preserve, promote and value equitable access to active outdoor play. This places responsibility for outdoor play opportunities across communities and wider systems rather than on children and families alone (Lee et al., 2025). === '''Schools''' === * Schools can provide opportunities for children with and without disabilities to become familiar with one another. Beekhuizen et al. (2025) identified growing up together and making contact as interacting factors in inclusive outdoor play. Children described familiarity with other children as making contact easier. * School circumstances can also affect the time and opportunities available for outdoor play. Some children attending special primary education described long travel times between school and home as reducing the time available to play outdoors. Beekhuizen et al. (2025) identified these experiences under time constraints. * Recess provides another school setting in which children's emotional experiences have been examined. Poulos et al. (2026) studied 317 Year 4 and 5 children during extreme heat weather and found significantly higher positive affect after outdoor and gymnasium recess than after classroom recess. There were no significant differences in negative affect between the three recess settings. * Poulos et al. (2026) identified implications for school health, policy and equity, including the need for heat adaptive infrastructure to support access to recess environments during extreme heat. However, the findings do not show that outdoor recess is always better than indoor recess because positive affect was also higher following gymnasium recess. Quiz {{Robelbox|theme=12|title=Quiz}} <quiz display=simple> {Children who have access to the same outdoor playground may still have different opportunities to participate in play. |type="()"} + True - False </quiz> {{Robelbox/close}} {{Robelbox|theme=12|title=Quiz}} <quiz display=simple> {Outdoor play has the same relationship with children's emotional well-being regardless of how door play or emotional well being is measured. |type="()"} - True + False </quiz> {{Robelbox/close}} {| class="wikitable" |1. Children who have access to the same outdoor playground may still have different opportunities to participate in play. True False 2. Outdoor play has the same relationship with children's emotional well-being regardless of how door play or emotional well being is measured. True False |} {| class="wikitable" |Scenario Two primary school aged children A and B enjoy playing outdoors. They both lived near the same playground. Child A was very familiar with the playground and knows several other children who play there and easily join the games. While child B has disability, uses mobility device and does not know other children at playground. Some parts of the playground are difficult to access and joining other children who are already playing can also be challenging. Child B's parents can provide support, although the child also prefers to play more independently. Consider both children can access the same playground, but do they have same level opportunities to take part in outdoor play? |} '''''<u>Note: Answers to the quiz is 1: True and 2 False</u>''''' == '''Conclusion''' == * Outdoor play and children's emotional well-being are measured in different ways across recent research. Outdoor play is not equivalent to outdoor physical activity, while emotional outcomes include emotional dysregulation, social-emotional competence, positive and negative affect, and internalising and externalising symptoms. These differences need to be considered when findings across studies are compared. * Research also provides mixed evidence about how outdoor play may be related to emotional well-being. Gross's (2015) emotion-regulation framework can be applied to emotional situations experienced during play, but it does not show that outdoor play improves emotion regulation. Lee et al. (2025) provides more direct evidence of a possible cognitive process, with working memory statistically mediating the association between afternoon outdoor play and lower emotional dysregulation. However, this observational finding does not establish causation. * Recent findings are not consistent across all outcomes or contexts. Ferguson et al. (2025) reported associations with better social-emotional competence, Dodd et al. (2026) found longitudinal associations with internalising and externalising symptom trajectories, and Poulos et al. (2026) found differences in positive but not negative affect following recess. In contrast, most associations examined by Davenport et al. (2024) were not statistically significant. * Recent findings are not consistent across all outcomes or contexts. Ferguson et al. (2025) reported associations with better social-emotional competence, Dodd et al. (2026) found longitudinal associations with internalising and externalising symptom trajectories, and Poulos et al. (2026) found differences in positive but not negative affect following recess. In contrast, most associations examined by Davenport et al. (2024) were not statistically significant. * Overall, current research supports an association between outdoor play and some aspects of children's emotional well-being but does not establish one consistent effect. Differences in measurement, research design, children and play contexts remain important when interpreting the evidence. ==See also== {{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}} https://www-taylorfrancis-com.ezproxy.canberra.edu.au/books/mono/10.4324/9781003349655/right-child-play-naomi-lott Book Chapter, 2 {{ic|Move to References and cite}} https://en.wikipedia.org/wiki/Emotional_dysregulation<nowiki/>- Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} https://en.wikipedia.org/wiki/Autonomy<nowiki/>- Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} https://en.wikipedia.org/wiki/Longitudinal_study<nowiki/>-Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} [[Cognitive psychology|https://en.wikiversity.org/wiki/Cognitive_psychology]]-Wikipedia article https://en.wikipedia.org/wiki/Affordance<nowiki/>-Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} ==References== {{Hanging indent|1= Beekhuizen, R. Q., Bolster, E. A. M., Gorter, J. W., Henry, N. L., Visser, K., Wittink, H., Kotte, E. M. W., Sol, M. E., & Bloemen, M. A. T. (2025). Play Together? Unveiling Facilitators and Barriers to Inclusive Outdoor Play for Dutch Children With and Without Disabilities: A Qualitative Study. Child: Care, Health & Development, 51(6), Article e70154. https://doi.org/10.1111/cch.70154 Biino, V., Pesce, C., & Martins, C. (2025). Motor Skill Development at Preschool Age in Girls and Boys: The Role of Outdoor Free Play. Children, 12(5), Article 594. https://doi.org/10.3390/children12050594 Davenport, C., Kuzik, N., Larouche, R., & Carson, V. (2025). The Associations Between Parental-Reported and Device-Based Measured Outdoor Play and Health Indicators of Physical, Cognitive, and Social–Emotional Development in Preschool-Aged Children. Pediatric Exercise Science, 37(2), 102–111. https://doi.org/10.1123/pes.2023-0119 de Lannoy, L., Barbeau, K., Seguin, N., & Tremblay, M. S. (2023). Scoping review of children’s and youth’s outdoor play publications in Canada. Chronic Diseases in Canada, 43(1), 1–13. https://doi.org/10.24095/hpcdp.43.1.01 Dodd, H. F., Cordwell, K., Hesketh, K., Johnstone, A., de la Torre-Luque, A., & McCrorie, P. (2026). Early outdoor play predicts trajectories of child mental health in a population-based cohort. Journal of Child Psychology and Psychiatry. https://doi.org/10.1111/jcpp.70175 Ferguson, M., Teyhan, A., Lovell, R., Dodd, H., Wheeler, B., & McEachan, R. (2025). The association between park visits, outdoor play and child social-emotional competency in a multi-ethnic, urban cohort. Wellbeing, Space and Society, 9, Article 100293. https://doi.org/10.1016/j.wss.2025.100293 Gross, J. J. (2015). Emotion Regulation: Current Status and Future Prospects. Psychological Inquiry, 26(1), 1–26. https://doi.org/10.1080/1047840X.2014.940781 Lee, E.-Y., de Lannoy, L., Kim, Y.-B., Rathod, A., James, M. E., Lopes, O., Nasrallah, B., Thankarajah, A., Adjei-Boadi, D., de Barros, M. I. A., Duncan, S., Miller, R. M., Mygind, L., Vanderloo, L. M., Wang, P.-Y., & Tremblay, M. S. (2025). 2025 Position statement on active outdoor play. The International Journal of Behavioral Nutrition and Physical Activity, 22(1), Article 117. https://doi.org/10.1186/s12966-025-01813-9 Lee, J. J., Flouri, E., & Jackson, Y. (2025). The Role of Timing and Amount of Outdoor Play in Emotional Dysregulation in Preschool Children. Child: Care, Health & Development, 51(1), Article e70020. https://doi.org/10.1111/cch.70020 Morgenthaler, T., Lynch, H., Loebach, J., Pentland, D., & Schulze, C. (2024). Using the Theory of Affordances to Understand Environment–Play Transactions: Environmental Taxonomy of Outdoor Play Space Features—A Scoping Review. The American Journal of Occupational Therapy, 78(4), Article 7804185120. https://doi.org/10.5014/ajot.2024.050606 Pereira, J. V., Vila-Nova, F., Veiga, G., Lopes, F., & Cordovil, R. (2024). Associations between outdoor play features and children’s behavior and health: A systematic review. Health & Place, 87, Article 103235. https://doi.org/10.1016/j.healthplace.2024.103235 Poulos, A., Hassan, U. A., Wilson, K., Price, P. M., Vanos, J., & Quilla, J. (2026). Differences in Schoolchildren’s Emotional State After Indoor Versus Outdoor Recess in Extreme‐Heat Weather. The Journal of School Health, 96(4), Article e70135. https://doi.org/10.1111/josh.70135 }} ==External links== {{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}} https://www.child-encyclopedia.com/outdoor-play<nowiki/>-Encyclopedia in early childhood development https://www.outdoorplaycanada.ca/wp-content/uploads/2026/03/The-2025-AOP10-Position-Statement.pdf<nowiki/>-Position Statement https://www.who.int/news/item/24-04-2019-to-grow-up-healthy-children-need-to-sit-less-and-play-more<nowiki/>-World Health Organisation [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Children]] [[Category:Motivation and emotion/Book/Nature]] [[Category:Motivation and emotion/Book/Well-being]] gi3l5cp9gmk5f5q6wnhvr7v01d4dz1z 2834549 2834498 2026-09-26T11:58:13Z Mymunu 3106327 /* Emotion regulation */ 2834549 wikitext text/x-wiki {{title|Outdoor play and children's emotional well-being:<br>How does outdoor play influence children's emotional well-being?}} __TOC__ == Overview == {| class="wikitable" [[File:School children happily playing in playground.jpg|thumb|'''Figure 1'''. Children engaged in outdoor play.]] |'''Case study: Part 1''' A child arrives at playground and joins a group of children who are already playing. The children are making their own game and deciding the rules as they play. At first, child enjoys choosing where and what to play and moving between the different activities. During the game, another child changes the rules of the game and argument breaks out. The child becomes frustrated and avoids the activity. After watching for short time, the child returns, suggests for new idea to continue game and re-joins the group. How might experiences like this during outdoor play influence children's emotional well-being? Emotional regulation theory provides one way of understanding on how children may respond to emotional situations during play (see figure 1) (Gross, 2015). |} Outdoor play can involve more than physical movements. It is more than simply being outside and engage in the activities across playgrounds, gardens, streets and natural spaces. Outdoor play involves exploration, social interaction, choice and challenge and engagement with surrounding environment (Dodd et al.,2026; Pereira et al.,2024). These experiences may create emotional situations in which children need to respond to frustration, disagreement, uncertainty or excitement. Gross (2015) [[emotional regulation]] theory provides a [[psychological]] explanation for how children may recognise and respond to these emotional situations. Outdoor play experiences are also shaped by the environment where play takes place. Experiences are shaped by the different opportunities provided by different physical and social environments, which means the same outdoor space may not provide the same experience for every child (Morgenthaler et al.,2024).This chapter examines how [[Emotional regulation|emotional,]] [[Cognitive psychology|cognitive]], social and environmental processes may help explain the relationship between outdoor play and children's emotional well-being. {| class="wikitable" | ;[[File:Bulb Idea Flat Icon GIF Animation.gif|alt=Focus questions|left|100x100px|thumb]] '''Focus questions''' * What are outdoor play and children's emotional well-being? * How does outdoor play influence children's emotional well-being? * How do social and environmental conditions shape children's outdoor play experiences? * How can families, communities and school support outdoor play opportunities that may benefit children's emotional well-being? |} == '''Understanding outdoor play and children's emotional well-being''' == [[File:Water-outdoor-people-girl-play-boy-938233.jpg|thumb|'''Figure 2'''. ''Visualise outdoor play as providing children with opportunities to explore, make choices, interact with others and respond to changing situations through activities such as water play.''|265x265px]] Outdoor play and children's emotional well-being are not measured as single and consistent concepts across recent research. Outdoor play may be examined as voluntary and intrinsically motivated activity, self directed play, parent reported outdoor play, or device-measured outdoor play activity. It should also be distinguished from outdoor moderate to vigorous physical activity because these measures do not represent the same behaviour (Davenport et al., 2025). Children's emotional well-being is also examined through different outcomes, that includes [[emotional regulation]], social-emotional competence, positive and negative affect, and internalising or externalising symptoms. These differences are significant because outdoor play and emotional well-being are not measured as single, consistent constructs across research. === Outdoor play === Outdoor play is voluntary and and intrinsically motivated activity that occurs in outdoor environments like gardens, playgrounds, parks and natural spaces (Dodd et al., 2026). Free play can be also self-directed, which means children to freely interact with the environment and have autonomy to make choices about their activities (Biino et al., 2025). Outdoor play should not be treated as same as outdoor physical activity. Davenport et al., (2025) examined outdoor play separately from outdoor moderate- to- vigorous physical activity (MVPA). This distinction is significant because research on children's outdoor play is not necessarily measuring the same behaviour as research on the intensity of physical activity. === Children's emotional well-being === Children's emotional well-being is not represented by single common outcome across recent outdoor play research. Emotional dysregulation has been examined in relation to the amount and timing of outdoor play (Lee et al., 2025), while social-emotional competence includes difficulties and [[Prosocial behavior/Keywords/Definitions|prosocial behaviour]] (Ferguson et al., 2025). Other studies have examined positive and negative affect following recess (Poulos et al., 2026) and trajectories of internalising and externalising symptoms across childhood (Dodd et al., 2026). These outcomes represent different aspects and timeframes of emotional functioning, so they should not be treated as equivalent when findings are compared. '''Table 1''' ''Emotional outcomes examined in recent research on outdoor play and children's emotional well-being'' {| class="wikitable" |+ !Study !Outcome examined !What the outcome represent |- |Lee et al. (2025) |Emotional dysregulation |Difficulties in emotional regulation; examined in relation to the amount of timing and outdoor play |- |Ferguson et al. (2025) |Social-emotional competence |Social and emotional difficulties and prosocial behaviour |- |Poulos et al. (2026) |Positive and negative affect |Children's affect following recess in different settings |- |Dodd et al. (2026) |Internalising and externalising symptoms |Internalising: emotional symptoms and peer problems Externalising: conduct problems and hyperactivity- inattention |} As shown in Table 1, the studies do not measure the same aspect or time frame of children's emotional functioning. Affect immediately following recess should not be treated as equivalent to emotional dysregulation measured over time or trajectories of internalising and externalising symptoms across childhood. This difference need to be considered when examining whether outdoor play is associated with children's emotional well-being. '''Case study: part 2''' ''What is being measured?'' {| class="wikitable" | valign="top" |[[File:Children marbles.jpg|thumb|177x177px|'''Figure 3'''. ''Children may experience different emotional responses during social outdoor play'']]The child in the case study part 1 becomes frustrated when the rules of the game change. This immediate emotional response is different from a longer-term pattern of emotional dysregulation or internalising symptoms. When research findings are compared, it is important to consider which aspect of emotional well-being is measured. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {A child's positive or negative affect immediately after recess represents the same emotional outcome as longer-term internalising or externalising symptoms. |type="()"} - True + False </quiz> {{Robelbox/close}} |} == '''How does outdoor play influence children's emotional well-being?''' == Outdoor play may be related to children's emotional well-being through emotional, cognitive, and social processes. Possible pathways discussed in the recent research include [[Emotional regulation|emotion regulation]], working memory, social interaction, physical activity, connection with the nature and adventurous play. However, these pathways have not all been directly tested as mechanisms, and many of the outdoor play literatures remain observational (Dodd et al., 2026; de Lannoy et al.,2023). Psychological theory can help to explain how and why outdoor play experiences may influence children's emotional well-being. Although the evidence does not yet show that psychological processes cause the relationship between outdoor play and children's emotional well-being. Emotion involves more than subjective feelings. Scherer (2005) described emotion as coordinated changes across cognitive appraisal, physiological responses, action tendencies, expression and subjective feelings. Therefore, physiological responses are one component of an emotional response rather than a separate explanation for the effects of outdoor play. Scherer (2005) did not examine outdoor play, so this framework does not evidence that outdoor play changes children's physiological responses or emotional well-being. === '''Emotion regulation''' === Emotion regulation provides a psychological framework for understanding how children may manage emotional situations during outdoor play. Gross (2015) described emotional regulation as a process involving identification, selection and implementation. Identification concerns deciding whether to regulate an emotion, selection concerns selecting regulation strategy and implementation concerns applying chosen response into practice. Gross (2015) also described situation selection, situation modification, attentional deployment cognitive change and response modulation. During outdoor play, children may experience frustration, conflict, disagreement, uncertainty or changes to their activity. Gross framework can be applied to these situations to consider how a children recognise an emotional response, choose strategies to manage and act on chosen strategies. However, Gross (2015) did not examine outdoor play, so applying the framework does not show that outdoor play improves children's emotion regulation. {| class="wikitable" | valign="top" |'''Case study: Part 3'''[[File:14Y Ncdc july 5th-802.jpg|thumb|202x202px|'''Figure 4'''. ''Children can respond differently to situations that occur during outdoor play.'']]When the rule of game change, the child becomes frustrated and decided to step away. After a short time the child returns and suggests for different way to continue the game (see Figure 4). Suggesting a change to the game can be considered an example of situation modification. This shows how Gross's emotion regulation framework can be applied to an emotional situation during outdoor play. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {What does Gross (2015) emotion regulation framework show when it is applied to the outdoor-play scenario?. |type="()"} -A. Outdoor play causes better emotion regulation. +B. Situation modification can help explain how the child responds to the situation. -C. Children regulate emotions better outdoors than indoors. -D. Stepping away from play always improves emotional well-being. </quiz> {{Robelbox/close}} |} === '''Working memory and cognitive process''' === Working memory can be one cognitive process involved in the association between outdoor play and emotional dysregulation. Lee et al., (2025) examined 325 preschool children and tested working memory as a statistical mediator. Outdoor play was examined across three periods of the day; wake up to noon, noon to 6 pm, and 6 pm to bedtime. The findings differed according to the timing of outdoor play. More outdoor play between noon and 6 pm was associated with lower emotional dysregulation. In contrast, more outdoor play before noon and 6 pm was associated with higher emotional dysfunction. Afternoon outdoor play was also associated with better working memory, and better working memory was associated with lower emotional dysregulation. When working memory was included in the analysis, the association between afternoon outdoor play and emotional dysregulation was no longer statistically significant. Lee et al., (2025) reported this as full mediation. This suggests working memory may be involved in the association between afternoon play and lower emotional dysregulation. However, the study was observational, so the mediation analysis does not show that outdoor play caused better working memory or lower emotional dysregulation. == '''How does social and environmental conditions influence on children's outdoor play experiences?''' == Outdoor play opportunities depends on the opportunities available in their social and physical environment. Children may have access to same outdoor space but not have same opportunities to take part in play. These difference can be considered through affordance theory, which examines the opportunities for action provided by features of an environment. === Affordance theory and outdoor play environments === Affordance theory provides a way of understanding how features of outdoor environment can provide opportunities for children to interact with different forms of play. Morgenthaler et al. (2024) applied the theory of affordances to examine environment play transactions and development of an environmental taxonomy of outdoor play space features. The review identified 284 different play opportunities afforded by different spaces and objects. This suggests that outdoor environment not only provide a space for play, their physical features can provide different opportunities for how children interact with and use the play space. Research on outdoor play space supports the importance of these environmental features. Pereira et al. (2024) also examined features of outdoor play spaces in systematic review of 51 articles representing 45 primary studies. The review included features such as fixed structures, natural elements, floor markings, loose equipment and available play area. The study found that physical activity was most commonly examined outcome. The study also differed in the environmental features examine, outcomes measures, and study methods, which made difficult to draw a clear conclusions about the effect of individual play space features. Therefore, these findings show that outdoor play differ in the opportunities they provide, but the evidence does not support that one particular features produces better emotional well-being. '''Table 2'''. ''Examples of environmental features and possible affordances'' {| class="wikitable" |+ !Environmental feature !Possible affordance for play |- |Fixed structures (e.g. climbing frame) |Can provide opportunity in different forms of physical activity. For example, climbing, physical play, risk-taking |- |Natural elements (e.g. tree, rocks, sand) |Environmental features can provide opportunities for exploratory play, imaginative play, sensory experiences |- |Floor markings (e.g. painted games) |Can support structured activities like rule based play, social play, active play |- |Loose equipment (e.g. balls, tyre, boxes) |Movable environmental features that can be used during constructive play, imaginative play, creative problem solving play |- |Open play area |Running, group play, or flexible use |} Note. Based on Pereira et al. (2024) and Morgenthaler et al. (2024). Environmental features can afford more than one type of play and the opportunities may vary between children. {| class="wikitable" | valign="top" |'''Case study: Part 4 Same space, different opportunities''' Kim and Leo are both at the same school playground during recess. The playground has climbing feature, sand pit area and open natural space. * Kim quickly joins a group of children in a climbing frame. The climbing frame structure provides him with an opportunity for physical play and social interactions. * Leo uses sand pit area with other child, he plays with loose materials and creates a sand castle and other different structures. The environment gives him an opportunity for imaginative play and social play. Both the examples show how the same outdoor space can afford different forms of play for different children, depending on their interests, skills and social context. {{Robelbox|theme=12|title=Test your learning}} <quiz display=simple> {Which statement best applies affordance theory to the example?. |type="()"} -A. The play ground causes children to be more physically active. +B. The same playground can provide different opportunities for play depending on the child and how they use the environment. -C. Climbing structures always lead to better emotional well-being. -D. Open spaces are only useful for social play. </quiz> {{Robelbox/close}} |} === '''Social relationship and inclusion''' === * Beekhuizen et al. (2025) identified making contact and growing up together as interacting factors in inclusive outdoor play. Some children described familiarity with other children as an easy way to approach, communication and play together. Making contact could also be a barrier when children approaching to another unfamiliar children or joining in play who were already playing. * Children also described the need to adopt games so that children with different abilities could participate. School and communities were identified settings where children with and without disabilities could become familiar with each other (Beekhuizen et al., 2025). * In the recent observational research by Beekhuizen et al. (2026) observed outdoor play among children with and without disability. The researchers found that getting to know each other, making contact and interaction while playing together as process of inclusive outdoor play. These observational findings showed that familiarity and making contact determine social and inclusive play because children chose to play with children they already knew. * Ferguson et al. (2025) also found that the association between outdoor play and social emotional competence was not the same across all ethnic and deprivation groups. In the cross sectional analysis of 2568 children aged 7.1 to 12.6 years from multi ethnic urban cohort, outdoor play was associated with better social-emotional competence. However, associations varies across same ethnic groups and according to weekday or weekend outdoor play. === '''Autonomy, parents and time''' === * Experiencing autonomy was identified as a personal factor in inclusive outdoor play. Children having some independence during outdoor play could promote their sense of independence over what they do and who they play with (Beekhuizen et al., 2025). * Experiencing autonomy also included opportunities to play without direct involvement of parents. Some children with disabilities described wanting to play outside independently, although parental support could make outdoor play possible (Beekhuizen et al., 2025) * Parents were identified as an environmental factors. Beekhuizen et al. (2025) found that parental involvement could support children's participation in outdoor play, specially when child needed help to access or participate in outdoor play. * Time constraints were considered as another environmental factor. Some children with disabilities were described as having limited outdoor play time due to parents work schedule, after-school arrangements or longer travel distance between home and school (Beekhuizen et al., 2025) === '''Outdoor environments and accessibility''' === * The outdoor play environment was identified as an environmental factor that could could support or restrict inclusive outdoor play. Children described both physical and social aspects of outdoor play environments. For example, children discussed the importance of physical and social safety, including traffic near playgrounds and disputes among children. Accessibility was particularly relevant to children with disabilities because opportunities for inclusive outdoor play could be affected by play environments and physical abilities (Beekhuizen et al., 2025). * Pereira et al. (2024) provided evidence about the physical features of outdoor play spaces. Their systematic review included 51 articles representing 45 primary studies aged between 5 to 12 and examined particular environmental features like fixed structures, natural elements, floor marking, loose parts or equipment and available play area. * Pereira et al. (2024) found positive association between outdoor play space features and children's behaviours. However, there was substantial variation between studies so the review could not establish clear conclusions about the effects of particular environmental features. {{ic|Add an APA style table caption}} {| class="wikitable" |+ |Key points * Beekhuizen et al. (2025) identified personal, interacting and environmental factors that could facilitate or restrict inclusive outdoor play. * Social relationships and familiarity affected participation, with children with disabilities reporting more barriers to inclusive outdoor play (Beekhuizen et al., 2025). * Associations between outdoor play and social-emotional competence varied across some population groups and play contexts (Ferguson et al., 2025). |} == '''What does recent research show about outdoor play and children's emotional well-being?''' == * Recent research has examined various aspects of outdoor play and children's emotional well-being and provides mixed evidence. These include emotional dysregulation (Lee et al., 2025), social-emotional competence (Ferguson et al., 2025), positive and negative affect (Poulos et al., 2026), and internalising and externalising symptoms (Dodd et al., 2026). * Ferguson et al. (2025) found that more frequent outdoor play was associated with better social-emotional competence. However, the associations varied across some ethnic groups and according to whether outdoor play occurred on school days or weekends. * Dodd et al. (2026) provides longitudinal evidence from 4,151 children from the Growing Up in Scotland study. Children who played outdoors more frequently between approximately 2 and 4 years of age were more likely to follow a trajectory of low and stable internalising and externalising symptoms through to age 8. * Poulos et al. (2026) examined children's emotional state immediately after recess during hot weather. Among 317 children in years 4 and 5, the positive effect was higher after outdoor recess and gymnasium recess than after classroom recess. There were no significant differences in negative affect between the three recess settings. * Together, these studies show evidence of associations between outdoor play or outdoor recess and several aspects of emotional well-being. However, the studies did not show the common effect because the study differ in children's ages, research designs, measures of outdoor play, and emotional outcomes. === '''Consistency of recent research findings''' === * Recent findings do not show the same effect across all outcomes. Ferguson et al. (2025) found that more frequent outdoor play was associated with lower total difficulties and greater prosocial behaviour. In contrast, Davenport et al. (2024) found that most associations between outdoor play and the physical, cognitive and social-emotional developmental indicators examined were not statistically significant. Therefore, the recent studies have not found significant association across all developmental outcomes. * Findings can also differ according to the emotional outcome being measured. Poulos et al. (2026) found higher positive affect after outdoor and gymnasium recess than after classroom recess, but no significant differences in negative affect between the three recess settings. Lee et al. (2025) found that lower emotional dysregulation associated with greater afternoon outdoor play but higher emotional dysregulation is associated with greater outdoor play earlier and later in the day. * Dodd et al. (2026) provides longer-term evidence. More frequent outdoor play during the preschool years predicted lower odds of belonging to the increasing or decreasing internalising and externalising symptom trajectory groups, relative to the normative low and stable group. This shows an association between early outdoor play and mental-health symptom trajectories across childhood rather than an emotional outcome measured at one point in time. * Associations may also vary across children and outdoor play contexts. Ferguson et al. (2025) reported differences according to ethnicity and whether outdoor play occurred on school days or weekends. * Recent findings suggest that associations between outdoor play and emotional well-being are not the same across all outcomes, children and play contexts. The studies differ in children's age, research designs, measures of outdoor play, and emotional outcomes. Thus, findings should not be treated as evidence of one single effect. === '''Strengths and limitations of current research''' === * Longitudinal research strengthens the evidence concerning temporal relationship. Dodd et al. (2026) analysed 4,151 children from the Growing Up in Scotland study. Outdoor play was measured at approximately 2, 3 and 4 years of age, while internalising and externalising symptoms were measured at approximately 4, 5, 6 and 8 years. This allowed the researchers to examine whether early outdoor play predicted different mental-health symptom trajectories across childhood. * Although, longitudinal evidence does not establish cause and effect. Dodd et al. (2026) identified reliance on parent report measures as a key limitation, while Lee et al. (2025) also discussed about the possibility of reverse causation when interpreting associations between the timing of outdoor play and emotional dysregulation. * Measurement of outdoor play is another important consideration. Davenport et al. (2024) examined both parent reported and device measured outdoor play and also tested whether associations were independent of outdoor moderate to vigorous physical activity. This approach distinguishes outdoor play from outdoor physical activity rather than interchangeable measures. * Limitations are also present across the wider outdoor play literature. De Lannoy et al. (2023) identified 275 Canadian outdoor play publications and found that cross sectional study design was most common. Mental and emotional development had received less research attention in comparison to physical health and development. {| class="wikitable" |+Table 2. Comparison of recent research !Study !Research method !Research strength !Limitation |- | <small>Lee et al. (2025)</small> |Observational; 6 month follow-up |Examined the timing of outdoor play and tested working memory as a statistical mediator of the association with emotional dysregulation. |Observational mediation cannot establish causation; the authors also considered possible reverse causation when interpreting timing-related findings. |- |Ferguson et al. (2025) |Cross sectional; multi ethnic urban cohort (N=2,568) |Large sample allowed associations to be examined across population groups and school-day/weekend outdoor play. |Cross-sectional design cannot establish temporal direction; associations also differed across some groups and play contexts. |- |Davenport et al. (2024) |Observational; preschool sample (N=107) |Used both parent-reported and device-measured outdoor play and distinguished outdoor play from outdoor moderate-to-vigorous physical activity (MVPA) |Small sample , and most tested associations with developmental outcomes were not statistically significant. |- |Dodd et al. (2026) |Longitudinal cohort (N = 4,151) |Outdoor play was measured in the preschool years before later internalising and externalising symptom trajectories. |Outdoor play and symptoms relied on parent reported measures, and the observational design does not establish conclusions. |- |Poulos et al. (2026) |Recess comparison study (N=317) |Compared children's positive and negative affect following outdoor, gymnasium and classroom recess rather than using outdoor recess without a comparison setting. |Examined immediate affect during an extreme-heat context; higher positive affect was also found after gymnasium recess, so the result was not specific to outdoor recess. |} As shown in table 2, the recent evidence has different methodological strengths and limitations. Longitudinal data provide stronger evidence about temporal ordering than cross-sectional studies, while the use of parent-reported and device-measured outdoor play addresses some measurement concerns. However, much of the evidence remains observational, several studies rely on parent-reported measures, and differences in emotional outcomes and play contexts limit the direct comparison between studies.   {| class="wikitable" |Key points * Recent studies report positive, mixed and non-significant findings across different emotional outcomes and measures of outdoor play (Davenport et al., 2024; Ferguson et al., 2025). * Lee et al. (2025) and Dodd et al. (2026) found associations across different emotional outcomes and time frames, from emotional dysregulation to later symptom trajectories. * Differences in study design, measurement, children's age and play context mean the findings should not be interpreted as one consistent effect of outdoor play on emotional well-being. |} == '''How do families, communities and schools support outdoor play opportunities?''' == * Opportunities for outdoor play are influenced by children's social and physical environments. Beekhuizen et al. (2025) identified parents, outdoor play environments, communities and time constraints as environmental factors that could act as facilitators or barriers to inclusive outdoor play. * Support for outdoor play also involves whether children can participate with other children. Beekhuizen et al. (2025) identified experiencing autonomy, growing up together, making contact and adapting ways of playing as factors involved in inclusive outdoor play. * The 2025 Position Statement on Active Outdoor Play recommends increasing opportunities for active outdoor play in settings where people live, learn, work and play. It also emphasises collaboration across sectors, settings and societies to support equitable access to active outdoor play (Lee et al., 2025). === '''Families''' === * Beekhuizen et al. (2025) identified parents as an environmental factor in inclusive outdoor play. Children with disabilities described parents as important in encouraging participation and, for some children, helping to explain their disability to other children. * Experiencing autonomy was identified as an important personal factor. Some children with disabilities wanted their parents to allow them freedom during outdoor play. Some preferred their parents not to accompany them to the playground, while others were comfortable with parents remaining at a reasonable distance (Beekhuizen et al., 2025). * These findings indicate that parental support and children's autonomy can both be relevant to opportunities for outdoor play. For some children with disabilities, support could be necessary for participation while opportunities to play more independently were also valued (Beekhuizen et al., 2025). * Beekhuizen et al. (2025) identified parental support as important for facilitating positive inclusive play experiences. The authors also recommended providing children and parents with knowledge about disabilities and possible adaptations that can support participation * Family level opportunities also need to be interpreted alongside the time constraints. Some children attending special education described long journeys between school and home that reduced the time available for outdoor play (Beekhuizen et al., 2025). This means that opportunities for outdoor play cannot be interpreted only in terms of children's or parents' preferences. === '''Communities''' === * Beekhuizen et al. (2025) identified communities and the outdoor play environment as environmental factors in inclusive outdoor play. Children described physically and socially safe playgrounds as important. While barriers included structure of playgrounds that made participation difficult for some children with disabilities. * The social environment of a community was also important. Children with disabilities described smaller communities, such as villages and schools, the places where other children and parents could become more familiar with disability. This familiarity was associated with greater acceptance and stronger connections with other children (Beekhuizen et al., 2025). * Recent observational research also shows that physical access alone does not explain inclusive outdoor play. Beekhuizen et al. (2026) observed 63 children with and without disabilities during six inclusive outdoor play sessions and assessed both children's playfulness and environmental supportiveness. Children with disabilities showed significantly lower playfulness scores indicating that opportunities for inclusive play were not experienced equally. * The 2025 Position Statement on Active Outdoor Play recommends collaboration across sectors, settings and societies to preserve, promote and value equitable access to active outdoor play. This places responsibility for outdoor play opportunities across communities and wider systems rather than on children and families alone (Lee et al., 2025). === '''Schools''' === * Schools can provide opportunities for children with and without disabilities to become familiar with one another. Beekhuizen et al. (2025) identified growing up together and making contact as interacting factors in inclusive outdoor play. Children described familiarity with other children as making contact easier. * School circumstances can also affect the time and opportunities available for outdoor play. Some children attending special primary education described long travel times between school and home as reducing the time available to play outdoors. Beekhuizen et al. (2025) identified these experiences under time constraints. * Recess provides another school setting in which children's emotional experiences have been examined. Poulos et al. (2026) studied 317 Year 4 and 5 children during extreme heat weather and found significantly higher positive affect after outdoor and gymnasium recess than after classroom recess. There were no significant differences in negative affect between the three recess settings. * Poulos et al. (2026) identified implications for school health, policy and equity, including the need for heat adaptive infrastructure to support access to recess environments during extreme heat. However, the findings do not show that outdoor recess is always better than indoor recess because positive affect was also higher following gymnasium recess. Quiz {{Robelbox|theme=12|title=Quiz}} <quiz display=simple> {Children who have access to the same outdoor playground may still have different opportunities to participate in play. |type="()"} + True - False </quiz> {{Robelbox/close}} {{Robelbox|theme=12|title=Quiz}} <quiz display=simple> {Outdoor play has the same relationship with children's emotional well-being regardless of how door play or emotional well being is measured. |type="()"} - True + False </quiz> {{Robelbox/close}} {| class="wikitable" |1. Children who have access to the same outdoor playground may still have different opportunities to participate in play. True False 2. Outdoor play has the same relationship with children's emotional well-being regardless of how door play or emotional well being is measured. True False |} {| class="wikitable" |Scenario Two primary school aged children A and B enjoy playing outdoors. They both lived near the same playground. Child A was very familiar with the playground and knows several other children who play there and easily join the games. While child B has disability, uses mobility device and does not know other children at playground. Some parts of the playground are difficult to access and joining other children who are already playing can also be challenging. Child B's parents can provide support, although the child also prefers to play more independently. Consider both children can access the same playground, but do they have same level opportunities to take part in outdoor play? |} '''''<u>Note: Answers to the quiz is 1: True and 2 False</u>''''' == '''Conclusion''' == * Outdoor play and children's emotional well-being are measured in different ways across recent research. Outdoor play is not equivalent to outdoor physical activity, while emotional outcomes include emotional dysregulation, social-emotional competence, positive and negative affect, and internalising and externalising symptoms. These differences need to be considered when findings across studies are compared. * Research also provides mixed evidence about how outdoor play may be related to emotional well-being. Gross's (2015) emotion-regulation framework can be applied to emotional situations experienced during play, but it does not show that outdoor play improves emotion regulation. Lee et al. (2025) provides more direct evidence of a possible cognitive process, with working memory statistically mediating the association between afternoon outdoor play and lower emotional dysregulation. However, this observational finding does not establish causation. * Recent findings are not consistent across all outcomes or contexts. Ferguson et al. (2025) reported associations with better social-emotional competence, Dodd et al. (2026) found longitudinal associations with internalising and externalising symptom trajectories, and Poulos et al. (2026) found differences in positive but not negative affect following recess. In contrast, most associations examined by Davenport et al. (2024) were not statistically significant. * Recent findings are not consistent across all outcomes or contexts. Ferguson et al. (2025) reported associations with better social-emotional competence, Dodd et al. (2026) found longitudinal associations with internalising and externalising symptom trajectories, and Poulos et al. (2026) found differences in positive but not negative affect following recess. In contrast, most associations examined by Davenport et al. (2024) were not statistically significant. * Overall, current research supports an association between outdoor play and some aspects of children's emotional well-being but does not establish one consistent effect. Differences in measurement, research design, children and play contexts remain important when interpreting the evidence. ==See also== {{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}} https://www-taylorfrancis-com.ezproxy.canberra.edu.au/books/mono/10.4324/9781003349655/right-child-play-naomi-lott Book Chapter, 2 {{ic|Move to References and cite}} https://en.wikipedia.org/wiki/Emotional_dysregulation<nowiki/>- Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} https://en.wikipedia.org/wiki/Autonomy<nowiki/>- Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} https://en.wikipedia.org/wiki/Longitudinal_study<nowiki/>-Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} [[Cognitive psychology|https://en.wikiversity.org/wiki/Cognitive_psychology]]-Wikipedia article https://en.wikipedia.org/wiki/Affordance<nowiki/>-Wikipedia article {{ic|Use an internal links as shown in Tutorial 2}} ==References== {{Hanging indent|1= Beekhuizen, R. Q., Bolster, E. A. M., Gorter, J. W., Henry, N. L., Visser, K., Wittink, H., Kotte, E. M. W., Sol, M. E., & Bloemen, M. A. T. (2025). Play Together? Unveiling Facilitators and Barriers to Inclusive Outdoor Play for Dutch Children With and Without Disabilities: A Qualitative Study. Child: Care, Health & Development, 51(6), Article e70154. https://doi.org/10.1111/cch.70154 Biino, V., Pesce, C., & Martins, C. (2025). Motor Skill Development at Preschool Age in Girls and Boys: The Role of Outdoor Free Play. Children, 12(5), Article 594. https://doi.org/10.3390/children12050594 Davenport, C., Kuzik, N., Larouche, R., & Carson, V. (2025). The Associations Between Parental-Reported and Device-Based Measured Outdoor Play and Health Indicators of Physical, Cognitive, and Social–Emotional Development in Preschool-Aged Children. Pediatric Exercise Science, 37(2), 102–111. https://doi.org/10.1123/pes.2023-0119 de Lannoy, L., Barbeau, K., Seguin, N., & Tremblay, M. S. (2023). 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E., Lopes, O., Nasrallah, B., Thankarajah, A., Adjei-Boadi, D., de Barros, M. I. A., Duncan, S., Miller, R. M., Mygind, L., Vanderloo, L. M., Wang, P.-Y., & Tremblay, M. S. (2025). 2025 Position statement on active outdoor play. The International Journal of Behavioral Nutrition and Physical Activity, 22(1), Article 117. https://doi.org/10.1186/s12966-025-01813-9 Lee, J. J., Flouri, E., & Jackson, Y. (2025). The Role of Timing and Amount of Outdoor Play in Emotional Dysregulation in Preschool Children. Child: Care, Health & Development, 51(1), Article e70020. https://doi.org/10.1111/cch.70020 Morgenthaler, T., Lynch, H., Loebach, J., Pentland, D., & Schulze, C. (2024). Using the Theory of Affordances to Understand Environment–Play Transactions: Environmental Taxonomy of Outdoor Play Space Features—A Scoping Review. The American Journal of Occupational Therapy, 78(4), Article 7804185120. https://doi.org/10.5014/ajot.2024.050606 Pereira, J. V., Vila-Nova, F., Veiga, G., Lopes, F., & Cordovil, R. (2024). Associations between outdoor play features and children’s behavior and health: A systematic review. Health & Place, 87, Article 103235. https://doi.org/10.1016/j.healthplace.2024.103235 Poulos, A., Hassan, U. A., Wilson, K., Price, P. M., Vanos, J., & Quilla, J. (2026). Differences in Schoolchildren’s Emotional State After Indoor Versus Outdoor Recess in Extreme‐Heat Weather. The Journal of School Health, 96(4), Article e70135. https://doi.org/10.1111/josh.70135 }} ==External links== {{ic|Use bullet points as shown in [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]}} https://www.child-encyclopedia.com/outdoor-play<nowiki/>-Encyclopedia in early childhood development https://www.outdoorplaycanada.ca/wp-content/uploads/2026/03/The-2025-AOP10-Position-Statement.pdf<nowiki/>-Position Statement https://www.who.int/news/item/24-04-2019-to-grow-up-healthy-children-need-to-sit-less-and-play-more<nowiki/>-World Health Organisation [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Children]] [[Category:Motivation and emotion/Book/Nature]] [[Category:Motivation and emotion/Book/Well-being]] 48op8g7mqkd86j7dziueehkejy9fhbu 0 331416 2834499 2830066 2026-09-26T02:15:28Z U3253354 3109187 2834499 wikitext text/x-wiki {{title|Socioemotional selectivity theory and wellbeing in ageing:<br>How do social and emotional experiences affect wellbeing as people age?}} ==Overview== {{RoundBoxTop|theme=3}}Scenario Imagine two adults at different stages of life deciding how to spend their weekend. A younger adult chooses to attend a large social event to meet new people and form new connections, while an older adult chooses to spend time with a smaller group of close family and long-term friends. Although the older adult may have a smaller social network, these relationships may provide greater emotional meaning and satisfaction (see figure 1) {{RoundBoxBottom}}'''Key question:''' Why do social priorities change as people age, and how might these changes influence emotional wellbeing? Socioemotional selectivity theory (SST) provides one explanation for why social and emotional priorities may change across adulthood. SST proposes that people's perceptions of how much time they have remaining influence the goals they prioritise. When future time is perceived as relatively indefinite, long-lasting goals tend to receive greater priority. When future time is perceived as more limited, emotionally meaningful and immediate goals become relatively more important (Carstensen et al., 1999; Carstensen, 2006). These motivational changes may help explain age-related differences in social relationships and emotional experiences. Research has found age-related differences in everyday emotional experience, including greater emotional stability with age (Carstensen et al., 2011). While a meta- analysis found evidence of an age-related positivity effect in attention and memory, although its strength varied across study conditions (Reed et al., 2014). Importantly these findings do not mean that ageing automatically leads to better emotional wellbeing. Instead, social relationships, emotional processes, individual differences, and context all need to be considered when examining wellbeing across adulthood. {{RoundBoxTop}} '''Focus questions''' {{ic|Use a numbered list as shown in Tutorial 2}} # What is socioemotional selectivity theory, and how does perceived future time influence motivation? # How do social relationships and priorities change across adulthood? # How does emotional experience change with age? # How can social and emotional changes influence wellbeing in older adulthood? # What are the limitations of socioemotional selectivity theory in explaining age related differences in wellbeing? {{RoundBoxBottom}} == '''Socioemotional selectivity and future time perspective''' == * Socioemotional Selectivity theory (SST) proposes that understanding of future time influence motivation and the goals people prioritise. When the future is viewed as limited, goals focused on learning and the future tend to receive greater priority (Carstensen et al., 1999). * As future time becomes more limited, priorities tend to shift towards emotionally meaningful and impactful goals (Carstensen et al., 1999). * Although ageing is often linked to having a more limited view of future time, SST suggests that how much time a person believes they have left is more important than their age alone in shaping their social and emotional goals (Carstensen et al., 1999). == '''Changing social relationships across adulthood''' == * Social networks often grow during young adulthood and become smaller in later adulthood, with the greatest reductions occurring in less meaningful social relationships (English & Carstensen, 2014). * Close relationships remain relatively stable despite the overall decrease in social network size, suggesting that people become increasingly selective about the relationships they maintain (English & Carstensen, 2014). * This selective narrowing of social networks may support emotional wellbeing, as older adults reported more positive emotional experiences with people in their social network (English & Carstensen, 2014). == '''Emotional experience and ageing''' == * Emotional wellbeing does not necessarily decline with age. Research has found that overall emotional wellbeing can improve from early adulthood into older age (Carstensen et al., 2011). * Older age has been associated with increased emotional stability, meaning emotional experiences may become more consistent across everyday life (Carstensen et al., 2011). * Older adults may also experience greater emotional complexity, including a better ability to experience positive and negative emotions at the same time (Carstensen et al., 2011). == '''The age-related positivity effect''' == * The age-related positivity effect describes how older adults tend to focus on and remember positive information more than negative information compared with younger adults (Reed et al., 2014). * An analysis of 100 studies found reliable evidence for the positivity effect, with older adults showing a greater preference for positive over negative information compared with younger adults (Reed et al., 2014). * The strength of the positivity effect varies depending on factors such as demands and study characteristics, meaning the effect may not occur equally across all situations (Reed et al., 2014). == '''Socioemotional selectivity, emotional regulation, and wellbeing''' == * SST proposes that when future time is perceived as limited, emotionally meaningful goals become more important, which may contribute to changes in social choices and emotional experiences across adulthood (Carstensen et al., 1999) * Selecting emotionally meaningful relationships and reducing less important social relationships may support more positive emotional experiences in later adulthood (English & Carstensen, 2014). * However, evidence does not always show that older adults are better at regulating their emotions than younger adults. Emotion regulation in later adulthood is complex and may depend on individual and other factors (Isaacowitz, 2022) ==Figures== [[File:Representaciones de los adultos mayores.jpg|thumb|270x270px|Figure 1. Older adults spending time together, illustrating socially meaningful relationships in later adulthood.]] ==Learning features== {{RoundBoxTop|theme=3}} '''Case Study: Changing social priorities''' Maria is 65 and has become more selective about how she spends her social time. Rather than attending a large social gathering, she prefers spending time with a small group of close friends and family. '''Question:''' How could socioemotional selectivity theory help explain Maria's changing social preferences? {{RoundBoxBottom}} ==Conclusion== * Socioemotional selectivity theory suggests that as future time is limited, people tend to prioritise emotionally meaningful goals and relationships, which can shape social and emotional experiences across adulthood (Carstensen et al, 1999) * Social networks may become smaller with age, particularly through cutting less emotionally close relationships while deep relationships tend to remain more stable. This decision may contribute to more positive experiences in later adulthood (English & Carstensen, 2014) * Emotional wellbeing does not necessarily decline with age. Research suggests that older adults may experience greater emotional stability and focus on more positive information, however these experiences can differ between individuals and situations (Carstensen et al., 2011; Reed et al., 2014) * Overall, SST provides an important explanation for how changing social and emotional priorities may contribute to wellbeing in later adulthood, age alone does not determine emotional wellbeing and individual and contextual factors should also be considered (Isaacowitz, 2022) ==See also== ** [https://en.wikipedia.org/wiki/Socioemotional_selectivity_theory? Socioemotional selectivity theory] (Wikipedia) ** [[Emotional self-regulation|Emotion]] (Wikiversity) ==References== {{Hanging indent|1= Carstensen, L. L. (2006). The influence of a sense of time on human development. ''Science, 312''(5782), 1913–1915. https://doi.org/10.1126/science.1127488 Carstensen, L. L., Isaacowitz, D. M., & Charles, S. T. (1999). Taking time seriously: A theory of socioemotional selectivity. ''American Psychologist, 54''(3), 165–181. https://doi.org/10.1037/0003-066X.54.3.165 Carstensen, L. L., Turan, B., Scheibe, S., Ram, N., Ersner-Hershfield, H., Samanez-Larkin, G. R., Brooks, K. P., & Nesselroade, J. R. (2011). Emotional experience improves with age: Evidence based on over 10 years of experience sampling. ''Psychology and Aging, 26''(1), 21–33. https://doi.org/10.1037/a0021285 English, T., & Carstensen, L. L. (2014). Selective narrowing of social networks across adulthood is associated with improved emotional experience in daily life. ''International Journal of Behavioral Development'', ''38''(2), 195–202. https://doi.org/10.1177/0165025413515404 Isaacowitz, D. M. (2022). What do we know about aging and emotion regulation? ''Perspectives on Psychological Science'', ''17''(6), 174569162110598. https://doi.org/10.1177/17456916211059819 Reed, A. E., Chan, L., & Mikels, J. A. (2014). Meta-analysis of the age-related positivity effect: Age differences in preferences for positive over negative information. ''Psychology and Aging, 29''(1), 1–15. https://doi.org/10.1037/a0035194 }} ==External links== * [https://www.apa.org/news/press/releases/2019/11/older-adults-social-networks American Psychological Association - Older adults and social wellbeing] * [https://lifespan.stanford.edu/research?utm_source Stanford Life-span Development Laboratory – Socioemotional selectivity theory] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Ageing]] [[Category:Motivation and emotion/Book/Emotion]] [[Category:Motivation and emotion/Book/Social]] awr1ue8qtxfgovf1o78u6j3o78tazqa 2834502 2834499 2026-09-26T02:43:54Z U3253354 3109187 2834502 wikitext text/x-wiki {{title|Socioemotional selectivity theory and wellbeing in ageing:<br>How do social and emotional experiences affect wellbeing as people age?}} ==Overview== {{RoundBoxTop|theme=3}}Scenario Imagine two adults at different stages of life deciding how to spend their weekend. A younger adult chooses to attend a large social event to meet new people and form new connections, while an older adult chooses to spend time with a smaller group of close family and long-term friends. Although the older adult may have a smaller social network, these relationships may provide greater emotional meaning and satisfaction (see figure 1) {{RoundBoxBottom}}'''Key question:''' Why do social priorities change as people age, and how might these changes influence emotional wellbeing? Socioemotional selectivity theory (SST) provides one explanation for why social and emotional priorities may change across adulthood. SST proposes that people's perceptions of how much time they have remaining influence the goals they prioritise. When future time is perceived as relatively indefinite, long-lasting goals tend to receive greater priority. When future time is perceived as more limited, emotionally meaningful and immediate goals become relatively more important (Carstensen et al., 1999; Carstensen, 2006). These motivational changes may help explain age-related differences in social relationships and emotional experiences. Research has found age-related differences in everyday emotional experience, including greater emotional stability with age (Carstensen et al., 2011). While a meta- analysis found evidence of an age-related positivity effect in attention and memory, although its strength varied across study conditions (Reed et al., 2014). Importantly these findings do not mean that ageing automatically leads to better emotional wellbeing. Instead, social relationships, emotional processes, individual differences, and context all need to be considered when examining wellbeing across adulthood. {{RoundBoxTop}} '''Focus questions''' {{ic|Use a numbered list as shown in Tutorial 2}} # What is socioemotional selectivity theory, and how does perceived future time influence motivation? # How do social relationships and priorities change across adulthood? # How does emotional experience change with age? # How can social and emotional changes influence wellbeing in older adulthood? # What are the limitations of socioemotional selectivity theory in explaining age related differences in wellbeing? {{RoundBoxBottom}} == '''Socioemotional selectivity and future time perspective''' == Socioemotional selectivity theory (SST) proposes that perceptions of future time influence motivation and the goals people prioritise (Carstensen et al., 1999). When the future is perceived as relatively open-ended, people are more likely to prioritise goals such as learning new information, exploring new opportunities, and developing relationships that may provide future benefits. In contrast, when future time is perceived as more limited, emotionally meaningful and present goals become relatively more important (Carstensen et al., 1999; Carstensen, 2006). This shift in priorities may influence the social choices people make. When future time is perceived as limited, people may become more selective about how and with who they spend their time, placing greater priority on established relationships that provide emotional meaning. From an SST perspective, changes in social relationships across adulthood may therefore reflect changing motivational priorities rather than simply a loss of interest in social interaction (Carstensen et al., 1999). Although ageing is often associated with a more limited perception of future time, SST proposes that perceived future time, rather than chronological age alone, plays an important role in shaping social and emotional goals (Carstensen et al., 1999). This distinction is important because it suggests that age-related changes in social priorities may partly reflect changes in how individuals perceive their remaining time. SST therefore provided a theoretical framework for understanding why social priorities may change across adulthood and how these changes could influence emotional experiences and wellbeing. == '''Changing social relationships across adulthood''' == * Social networks often grow during young adulthood and become smaller in later adulthood, with the greatest reductions occurring in less meaningful social relationships (English & Carstensen, 2014). * Close relationships remain relatively stable despite the overall decrease in social network size, suggesting that people become increasingly selective about the relationships they maintain (English & Carstensen, 2014). * This selective narrowing of social networks may support emotional wellbeing, as older adults reported more positive emotional experiences with people in their social network (English & Carstensen, 2014). == '''Emotional experience and ageing''' == * Emotional wellbeing does not necessarily decline with age. Research has found that overall emotional wellbeing can improve from early adulthood into older age (Carstensen et al., 2011). * Older age has been associated with increased emotional stability, meaning emotional experiences may become more consistent across everyday life (Carstensen et al., 2011). * Older adults may also experience greater emotional complexity, including a better ability to experience positive and negative emotions at the same time (Carstensen et al., 2011). == '''The age-related positivity effect''' == * The age-related positivity effect describes how older adults tend to focus on and remember positive information more than negative information compared with younger adults (Reed et al., 2014). * An analysis of 100 studies found reliable evidence for the positivity effect, with older adults showing a greater preference for positive over negative information compared with younger adults (Reed et al., 2014). * The strength of the positivity effect varies depending on factors such as demands and study characteristics, meaning the effect may not occur equally across all situations (Reed et al., 2014). == '''Socioemotional selectivity, emotional regulation, and wellbeing''' == * SST proposes that when future time is perceived as limited, emotionally meaningful goals become more important, which may contribute to changes in social choices and emotional experiences across adulthood (Carstensen et al., 1999) * Selecting emotionally meaningful relationships and reducing less important social relationships may support more positive emotional experiences in later adulthood (English & Carstensen, 2014). * However, evidence does not always show that older adults are better at regulating their emotions than younger adults. Emotion regulation in later adulthood is complex and may depend on individual and other factors (Isaacowitz, 2022) ==Figures== [[File:Representaciones de los adultos mayores.jpg|thumb|270x270px|Figure 1. Older adults spending time together, illustrating socially meaningful relationships in later adulthood.]] ==Learning features== {{RoundBoxTop|theme=3}} '''Case Study: Changing social priorities''' Maria is 65 and has become more selective about how she spends her social time. Rather than attending a large social gathering, she prefers spending time with a small group of close friends and family. '''Question:''' How could socioemotional selectivity theory help explain Maria's changing social preferences? {{RoundBoxBottom}} ==Conclusion== * Socioemotional selectivity theory suggests that as future time is limited, people tend to prioritise emotionally meaningful goals and relationships, which can shape social and emotional experiences across adulthood (Carstensen et al, 1999) * Social networks may become smaller with age, particularly through cutting less emotionally close relationships while deep relationships tend to remain more stable. This decision may contribute to more positive experiences in later adulthood (English & Carstensen, 2014) * Emotional wellbeing does not necessarily decline with age. Research suggests that older adults may experience greater emotional stability and focus on more positive information, however these experiences can differ between individuals and situations (Carstensen et al., 2011; Reed et al., 2014) * Overall, SST provides an important explanation for how changing social and emotional priorities may contribute to wellbeing in later adulthood, age alone does not determine emotional wellbeing and individual and contextual factors should also be considered (Isaacowitz, 2022) ==See also== ** [https://en.wikipedia.org/wiki/Socioemotional_selectivity_theory? Socioemotional selectivity theory] (Wikipedia) ** [[Emotional self-regulation|Emotion]] (Wikiversity) ==References== {{Hanging indent|1= Carstensen, L. L. (2006). The influence of a sense of time on human development. ''Science, 312''(5782), 1913–1915. https://doi.org/10.1126/science.1127488 Carstensen, L. L., Isaacowitz, D. M., & Charles, S. T. (1999). Taking time seriously: A theory of socioemotional selectivity. ''American Psychologist, 54''(3), 165–181. https://doi.org/10.1037/0003-066X.54.3.165 Carstensen, L. L., Turan, B., Scheibe, S., Ram, N., Ersner-Hershfield, H., Samanez-Larkin, G. R., Brooks, K. P., & Nesselroade, J. R. (2011). Emotional experience improves with age: Evidence based on over 10 years of experience sampling. ''Psychology and Aging, 26''(1), 21–33. https://doi.org/10.1037/a0021285 English, T., & Carstensen, L. L. (2014). Selective narrowing of social networks across adulthood is associated with improved emotional experience in daily life. ''International Journal of Behavioral Development'', ''38''(2), 195–202. https://doi.org/10.1177/0165025413515404 Isaacowitz, D. M. (2022). What do we know about aging and emotion regulation? ''Perspectives on Psychological Science'', ''17''(6), 174569162110598. https://doi.org/10.1177/17456916211059819 Reed, A. E., Chan, L., & Mikels, J. A. (2014). Meta-analysis of the age-related positivity effect: Age differences in preferences for positive over negative information. ''Psychology and Aging, 29''(1), 1–15. https://doi.org/10.1037/a0035194 }} ==External links== * [https://www.apa.org/news/press/releases/2019/11/older-adults-social-networks American Psychological Association - Older adults and social wellbeing] * [https://lifespan.stanford.edu/research?utm_source Stanford Life-span Development Laboratory – Socioemotional selectivity theory] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Ageing]] [[Category:Motivation and emotion/Book/Emotion]] [[Category:Motivation and emotion/Book/Social]] md7290fcs3xhiddlcvd9po1b1l0b443 2834512 2834502 2026-09-26T03:52:16Z U3253354 3109187 2834512 wikitext text/x-wiki {{title|Socioemotional selectivity theory and wellbeing in ageing:<br>How do social and emotional experiences affect wellbeing as people age?}} ==Overview== {{RoundBoxTop|theme=3}}Scenario Imagine two adults at different stages of life deciding how to spend their weekend. A younger adult chooses to attend a large social event to meet new people and form new connections, while an older adult chooses to spend time with a smaller group of close family and long-term friends. Although the older adult may have a smaller social network, these relationships may provide greater emotional meaning and satisfaction (see figure 1) {{RoundBoxBottom}}'''Key question:''' Why do social priorities change as people age, and how might these changes influence emotional wellbeing? Socioemotional selectivity theory (SST) provides one explanation for why social and emotional priorities may change across adulthood. SST proposes that people's perceptions of how much time they have remaining influence the goals they prioritise. When future time is perceived as relatively indefinite, long-lasting goals tend to receive greater priority. When future time is perceived as more limited, emotionally meaningful and immediate goals become relatively more important (Carstensen et al., 1999; Carstensen, 2006). These motivational changes may help explain age-related differences in social relationships and emotional experiences. Research has found age-related differences in everyday emotional experience, including greater emotional stability with age (Carstensen et al., 2011). While a meta- analysis found evidence of an age-related positivity effect in attention and memory, although its strength varied across study conditions (Reed et al., 2014). Importantly these findings do not mean that ageing automatically leads to better emotional wellbeing. Instead, social relationships, emotional processes, individual differences, and context all need to be considered when examining wellbeing across adulthood. {{RoundBoxTop}} '''Focus questions''' {{ic|Use a numbered list as shown in Tutorial 2}} # What is socioemotional selectivity theory, and how does perceived future time influence motivation? # How do social relationships and priorities change across adulthood? # How does emotional experience change with age? # How can social and emotional changes influence wellbeing in older adulthood? # What are the limitations of socioemotional selectivity theory in explaining age related differences in wellbeing? {{RoundBoxBottom}} == '''Socioemotional selectivity and future time perspective''' == Socioemotional selectivity theory (SST) proposes that perceptions of future time influence motivation and the goals people prioritise (Carstensen et al., 1999). When the future is perceived as relatively open-ended, people are more likely to prioritise goals such as learning new information, exploring new opportunities, and developing relationships that may provide future benefits. In contrast, when future time is perceived as more limited, emotionally meaningful and present goals become relatively more important (Carstensen et al., 1999; Carstensen, 2006). This shift in priorities may influence the social choices people make. When future time is perceived as limited, people may become more selective about how and with who they spend their time, placing greater priority on established relationships that provide emotional meaning. From an SST perspective, changes in social relationships across adulthood may therefore reflect changing motivational priorities rather than simply a loss of interest in social interaction (Carstensen et al., 1999). Although ageing is often associated with a more limited perception of future time, SST proposes that perceived future time, rather than chronological age alone, plays an important role in shaping social and emotional goals (Carstensen et al., 1999). This distinction is important because it suggests that age-related changes in social priorities may partly reflect changes in how individuals perceive their remaining time. SST therefore provided a theoretical framework for understanding why social priorities may change across adulthood and how these changes could influence emotional experiences and wellbeing. == '''Changing social relationships across adulthood''' == Social networks change across adulthood. English and Carstensen (2014) found that social networks tended to increase during young adulthood before becoming smaller across later adulthood. Importantly, this reduction occurred primarily in more minor social relationships, while emotionally close relationships remained relatively fixed. This suggests that smaller social networks in later adulthood do not necessarily reflect the loss of close relationships. This pattern of selective narrowing is consistent with socioemotional selectivity theory. As future time becomes more limited, emotionally meaningful goals are proposed to become relatively more important, which may influence the relationships people chose to maintain (Carstensen et al., 1999). From this perspective, maintaining close relationships while reducing more minor relationships may reflect increasing selectively in how people use their social time. English and Carstensen (2014) also found that older adults reported more positive and less negative emotional responses to members of their social networks, and that the emotional tone of social networks was associated with everyday emotional experience. These findings suggest that the emotional quality of social relationships may be important when considering wellbeing across adulthood. However, having a smaller social network should not automatically be interpreted as producing greater emotional wellbeing. Instead, the findings are consistent with the idea that the types and emotional quality of relationships people maintain may be important for understanding social and emotional experiences in later adulthood. == '''Emotional experience and ageing''' == * Emotional wellbeing does not necessarily decline with age. Research has found that overall emotional wellbeing can improve from early adulthood into older age (Carstensen et al., 2011). * Older age has been associated with increased emotional stability, meaning emotional experiences may become more consistent across everyday life (Carstensen et al., 2011). * Older adults may also experience greater emotional complexity, including a better ability to experience positive and negative emotions at the same time (Carstensen et al., 2011). == '''The age-related positivity effect''' == * The age-related positivity effect describes how older adults tend to focus on and remember positive information more than negative information compared with younger adults (Reed et al., 2014). * An analysis of 100 studies found reliable evidence for the positivity effect, with older adults showing a greater preference for positive over negative information compared with younger adults (Reed et al., 2014). * The strength of the positivity effect varies depending on factors such as demands and study characteristics, meaning the effect may not occur equally across all situations (Reed et al., 2014). == '''Socioemotional selectivity, emotional regulation, and wellbeing''' == * SST proposes that when future time is perceived as limited, emotionally meaningful goals become more important, which may contribute to changes in social choices and emotional experiences across adulthood (Carstensen et al., 1999) * Selecting emotionally meaningful relationships and reducing less important social relationships may support more positive emotional experiences in later adulthood (English & Carstensen, 2014). * However, evidence does not always show that older adults are better at regulating their emotions than younger adults. Emotion regulation in later adulthood is complex and may depend on individual and other factors (Isaacowitz, 2022) ==Figures== [[File:Representaciones de los adultos mayores.jpg|thumb|270x270px|Figure 1. Older adults spending time together, illustrating socially meaningful relationships in later adulthood.]] ==Learning features== {{RoundBoxTop|theme=3}} '''Case Study: Changing social priorities''' Maria is 65 and has become more selective about how she spends her social time. Rather than attending a large social gathering, she prefers spending time with a small group of close friends and family. '''Question:''' How could socioemotional selectivity theory help explain Maria's changing social preferences? {{RoundBoxBottom}} ==Conclusion== * Socioemotional selectivity theory suggests that as future time is limited, people tend to prioritise emotionally meaningful goals and relationships, which can shape social and emotional experiences across adulthood (Carstensen et al, 1999) * Social networks may become smaller with age, particularly through cutting less emotionally close relationships while deep relationships tend to remain more stable. This decision may contribute to more positive experiences in later adulthood (English & Carstensen, 2014) * Emotional wellbeing does not necessarily decline with age. Research suggests that older adults may experience greater emotional stability and focus on more positive information, however these experiences can differ between individuals and situations (Carstensen et al., 2011; Reed et al., 2014) * Overall, SST provides an important explanation for how changing social and emotional priorities may contribute to wellbeing in later adulthood, age alone does not determine emotional wellbeing and individual and contextual factors should also be considered (Isaacowitz, 2022) ==See also== ** [https://en.wikipedia.org/wiki/Socioemotional_selectivity_theory? Socioemotional selectivity theory] (Wikipedia) ** [[Emotional self-regulation|Emotion]] (Wikiversity) ==References== {{Hanging indent|1= Carstensen, L. L. (2006). The influence of a sense of time on human development. ''Science, 312''(5782), 1913–1915. https://doi.org/10.1126/science.1127488 Carstensen, L. L., Isaacowitz, D. M., & Charles, S. T. (1999). Taking time seriously: A theory of socioemotional selectivity. ''American Psychologist, 54''(3), 165–181. https://doi.org/10.1037/0003-066X.54.3.165 Carstensen, L. L., Turan, B., Scheibe, S., Ram, N., Ersner-Hershfield, H., Samanez-Larkin, G. R., Brooks, K. P., & Nesselroade, J. R. (2011). Emotional experience improves with age: Evidence based on over 10 years of experience sampling. ''Psychology and Aging, 26''(1), 21–33. https://doi.org/10.1037/a0021285 English, T., & Carstensen, L. L. (2014). Selective narrowing of social networks across adulthood is associated with improved emotional experience in daily life. ''International Journal of Behavioral Development'', ''38''(2), 195–202. https://doi.org/10.1177/0165025413515404 Isaacowitz, D. M. (2022). What do we know about aging and emotion regulation? ''Perspectives on Psychological Science'', ''17''(6), 174569162110598. https://doi.org/10.1177/17456916211059819 Reed, A. E., Chan, L., & Mikels, J. A. (2014). Meta-analysis of the age-related positivity effect: Age differences in preferences for positive over negative information. ''Psychology and Aging, 29''(1), 1–15. https://doi.org/10.1037/a0035194 }} ==External links== * [https://www.apa.org/news/press/releases/2019/11/older-adults-social-networks American Psychological Association - Older adults and social wellbeing] * [https://lifespan.stanford.edu/research?utm_source Stanford Life-span Development Laboratory – Socioemotional selectivity theory] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Ageing]] [[Category:Motivation and emotion/Book/Emotion]] [[Category:Motivation and emotion/Book/Social]] 2f1wq2pltwzn7hgjgbvbb6cdumwg1s4 0 331478 2834481 2829604 2026-09-25T15:00:49Z Ayat Al-kabai 3105570 upateing my work 2834481 wikitext text/x-wiki {{title|Epistemic motivation and the need for cognitive closure:<br>How does epistemic motivation and the need for cognitive closure influence our lives?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Necker cube.svg|thumb|200px|'''''Figure 1'''''. The Necker cube can be interpreted in more than one way. It illustrates how ambiguity can permit competing interpretations before cognitive closure is reached.]] ;Scenario Sofia receives two conflicting pieces of advice about an important career decision. She feels uncomfortable with the uncertainty and wants to decide immediately. However, she also wants to examine the evidence, consider different perspectives, and make an informed choice. Sofia’s situation demonstrates two psychological forces: epistemic motivation, which can encourage deeper information processing, and the need for cognitive closure, which can encourage people to reach a definite answer and escape uncertainty. {{RoundBoxBottom}} * Epistemic motivation concerns a person’s willingness to develop a thorough and accurate understanding of a situation through information search and processing (De Dreu et al., 2008). * Need for cognitive closure is the desire to obtain a definite answer rather than remain confused or uncertain (Kruglanski & Webster, 1996). * Both concepts influence how people form judgements, make decisions, communicate with others and respond to uncertainty. * Neither is always beneficial or harmful; the outcome depends on the person, available information and situational demands. * Figure 1 demonstrates how the same ambiguous information may permit more than one interpretation before a person reaches closure. {{RoundBoxTop|theme=3}} '''Focus questions''' * What is epistemic motivation? * What is the need for cognitive closure? * How are epistemic motivation and the need for cognitive closure connected? * How do they influence everyday decisions, learning and relationships? * When is cognitive closure helpful or harmful? {{RoundBoxBottom}} == Epistemic motivation == * [[w:Epistemic motivation|Epistemic motivation]] describes the willingness to invest effort in developing a complete and accurate understanding of the world (De Dreu et al., 2008). * Higher epistemic motivation encourages information search, deliberate reasoning and careful consideration of different perspectives. * Lower epistemic motivation is associated with shallower information processing and greater reliance on existing knowledge, familiar opinions or mental shortcuts. * Epistemic motivation can be influenced by personal characteristics and situational factors, including curiosity, accountability, fatigue, stress and time pressure. * Epistemic motivation should not be understood as intelligence. A capable person may still process information superficially when tired, distracted or under pressure. === Depth of information processing === * Higher epistemic motivation encourages people to attend to, encode, retrieve and integrate relevant information more thoroughly (De Dreu et al., 2008). * Groups with stronger epistemic motivation may exchange more unique information and engage in more information-driven discussion. * Process accountability can increase epistemic motivation because people expect to explain how they reached a decision (De Dreu et al., 2006). * Deeper processing can improve decision quality, especially when a problem is complicated and important information is distributed among several people. === Influencing factors === * Time pressure and environmental noise can decrease the opportunity or motivation to consider multiple explanations (Kruglanski & Webster, 1996). * Fear of making an invalid judgement may increase information search and delay closure. * Fatigue can make sustained reasoning more difficult and increase the appeal of a quick, simple answer. * Personal relevance may increase information processing, although people may also process information selectively when an issue threatens an important belief or identity. == Need for cognitive closure == * Need for cognitive closure refers to the motivation to reach a definite conclusion and avoid uncertainty or ambiguity (Kruglanski & Webster, 1996). * It can operate as a relatively stable individual difference and as a temporary state produced by circumstances such as fatigue, time pressure and stress. * Webster and Kruglanski (1994) identified several associated preferences, including predictability, order, decisiveness and reduced comfort with ambiguity. * The effects of need for closure are commonly explained through the urgency and permanence tendencies. === Urgency tendency === * The urgency tendency involves wanting to reach closure as quickly as possible (Kruglanski & Webster, 1996). * It may cause people to “seize” on information encountered early in the decision-making process. * Urgency can be helpful when immediate action is genuinely necessary, such as during an emergency. * However, it can also produce premature conclusions when the available information is incomplete, inaccurate or misleading. === Permanence tendency === * The permanence tendency involves wanting to preserve an existing conclusion for as long as possible (Kruglanski & Webster, 1996). * It may cause people to “freeze” on their initial judgement and resist information that challenges it. * Permanence can create consistency, confidence and coordination after a decision has been made. * Excessive permanence may contribute to inflexible thinking, stereotyping and resistance to corrective evidence. === Individual differences === * The Need for Closure Scale was developed to measure individual differences related to predictability, order, decisiveness, ambiguity and closed-mindedness (Webster & Kruglanski, 1994). * A shorter revised measure has also demonstrated that urgency and permanence are important dimensions of the construct (Roets & Van Hiel, 2011). * A high score does not mean that someone is unintelligent or incapable of careful reasoning. * Need for closure can change across situations; therefore, a person may tolerate uncertainty in one context but urgently seek certainty in another. == Relationship between epistemic motivation and cognitive closure == * Need for cognitive closure is a form of epistemic motivation because it concerns how people acquire and maintain knowledge (Kruglanski & Webster, 1996). * Epistemic motivation is the broader concept, whereas need for closure specifically concerns motivation to end uncertainty by reaching a conclusion. * Strong motivation to understand a problem may promote extensive information search, while strong motivation for immediate closure may shorten that search. * High-quality judgement therefore depends on balancing sufficient investigation with the practical need to reach a decision. '''Table 1.''' ''Comparison of epistemic motivation and need for cognitive closure'' {| class="wikitable" ! Concept ! Main goal ! Possible benefit ! Possible limitation |- | Epistemic motivation | Develop an accurate and comprehensive understanding | Deeper information processing and consideration of alternatives | Decision-making may require more time and effort |- | Urgency tendency | Reach closure quickly | Supports timely action | May produce premature conclusions |- | Permanence tendency | Maintain an established conclusion | Supports consistency and commitment | May create resistance to corrective evidence |} * Table 1 shows that these motivational processes involve different goals and trade-offs. * Epistemic motivation can improve decision quality by promoting systematic information processing, particularly in group settings (De Dreu et al., 2008). * However, continuously seeking more information can also delay decisions when the available information is already sufficient. * Cognitive closure can support action and coordination, but early closure may prevent consideration of important alternatives. {{RoundBoxTop|theme=3}} '''Case study''' Jordan sees a social-media post claiming that a familiar food causes a serious illness. Feeling anxious, Jordan immediately accepts the claim and shares it. Later, a friend encourages Jordan to locate the original research, examine reliable sources and consider alternative explanations. Jordan’s initial response may demonstrate the urgency tendency because uncertainty is ended by accepting the first available explanation. Greater epistemic motivation could encourage Jordan to examine the quality of the evidence before forming and sharing a conclusion. {{RoundBoxBottom}} <quiz display=simple> {Which response best demonstrates the urgency tendency? |type="()"} - Continuing to compare evidence without ever reaching a decision + Accepting the first plausible explanation to eliminate uncertainty - Changing an opinion after receiving reliable contradictory evidence - Asking several experts to explain their different perspectives || The urgency tendency involves attempting to reach cognitive closure as quickly as possible. } {Which response best demonstrates higher epistemic motivation? |type="()"} - Ignoring information that challenges an existing belief - Selecting the simplest answer without examining its source + Comparing evidence and considering alternative explanations - Repeating an opinion because it is familiar || Higher epistemic motivation generally involves more thorough information search and processing. } {The permanence tendency is most closely associated with: |type="()"} - Curiosity about new information + Maintaining an existing judgement - Avoiding all decisions - Forgetting a previous conclusion || The permanence tendency involves preserving closure after a judgement has been formed. } </quiz> == Influence on everyday life == * Epistemic motivation and need for closure influence behaviour across educational, interpersonal, organisational and social settings. * Their effects depend on the complexity of the problem, the quality of available information and whether rapid action is required. * Understanding these motivations may help people recognise when they are investigating a question carefully and when they are closing it prematurely. === Learning and education === * Higher epistemic motivation may promote curiosity, critical thinking and deeper engagement with learning materials. * Students who evaluate evidence and compare alternative explanations are more likely to develop an integrated understanding than students who rely only on memorisation. * A strong need for closure may make unclear instructions, conflicting theories and open-ended assignments uncomfortable. * Clear structure can support learning, but excessive reliance on one definite answer may be problematic when a subject requires critical evaluation. === Decision-making === * Epistemic motivation can improve decision quality by encouraging people to search for and integrate relevant information (De Dreu et al., 2006). * Under genuine time pressure, rapid closure may be adaptive because delaying action could have serious consequences. * When time is available, seizing on the first acceptable explanation may cause important evidence or alternative options to be overlooked. * Effective decision-making involves identifying how much information is required and establishing an appropriate point at which to decide. === Relationships and group behaviour === * First impressions can provide cognitive closure, but they may become inaccurate when people freeze on an early judgement. * Need for closure can influence intergroup language and strengthen biased descriptions of in-group and out-group behaviour (Webster et al., 1997). * Groups with higher epistemic motivation may exchange information more thoroughly and reach better-informed decisions (De Dreu et al., 2008). * Encouraging respectful disagreement can prevent premature consensus and allow group members to identify overlooked evidence. === Information and misinformation === * Online environments can expose people to large amounts of contradictory information, increasing confusion and the desire for simple answers. * A strong need for closure may increase reliance on information that quickly resolves uncertainty, even when its reliability has not been established. * Freezing on an initial interpretation can make later corrective evidence more difficult to accept. * Research suggests that need for closure can influence memory processes and vulnerability to misleading post-event information (Pica et al., 2014). == Balancing understanding and closure == * Neither endless information search nor immediate closure is appropriate in every situation. * The most effective approach depends on the consequences of error, the urgency of action and the availability of reliable evidence. * People can improve decisions by recognising their reactions to uncertainty and deliberately choosing whether additional investigation is necessary. === Potential benefits === * Epistemic motivation can support critical thinking, learning and informed decision-making. * Urgent closure can allow people to act efficiently during emergencies or under strict deadlines. * Permanent closure can create stability, commitment and coordination after an adequately informed decision. * Shared closure can also help groups organise action around an agreed understanding. === Potential limitations === * Excessive information search may create indecision or unnecessary delay. * Urgency can cause people to seize on incomplete or unreliable information. * Permanence can create inflexible beliefs and resistance to corrective evidence. * Need for closure may contribute to stereotyping when simplified group judgements replace individualised information (Kruglanski & Webster, 1996; Webster et al., 1997). === Practical strategies === * Pause before important decisions and identify whether time pressure is genuine or self-imposed. * Separate established facts, interpretations and assumptions. * Consider at least one alternative explanation before reaching a conclusion. * Seek information from reliable sources and perspectives that challenge the initial judgement. * Establish a reasonable decision deadline so that information search does not continue indefinitely. * Reconsider an existing conclusion when credible new evidence becomes available. {{RoundBoxTop|theme=3}} '''Reflection exercise''' Think about an important decision you made recently. # What information did you examine? # Did you feel pressure to reach an answer quickly? # Did you consider an alternative explanation? # What evidence might have changed your decision? # Did your response reflect epistemic motivation, urgency, permanence or a combination of these processes? {{RoundBoxBottom}} == Conclusion == * Epistemic motivation influences the depth and thoroughness with which people search for, process and integrate information. * Need for cognitive closure motivates people to reach and preserve definite conclusions, particularly when uncertainty is uncomfortable. * The urgency tendency can lead people to seize on early information, while the permanence tendency can lead them to freeze on an established judgement. * These processes affect learning, decision-making, relationships, group behaviour and responses to online information. * Cognitive closure is not inherently harmful because it can support timely action, consistency and coordination. * The central challenge is to balance the desire for accurate understanding with the practical need to reach a conclusion. {{RoundBoxTop|theme=3}} '''Take-home message''' Good judgement requires knowing when to continue searching and when to decide. People can make better decisions by tolerating uncertainty long enough to examine reliable evidence while still establishing a reasonable point for reaching closure. {{RoundBoxBottom}} == See also == * [[Motivation and emotion/Book/2023/Actively open-minded thinking|Actively open-minded thinking]] (Book chapter, 2023) * [[w:Epistemic motivation|Epistemic motivation]] (Wikipedia) == References == {{Hanging indent|1= De Dreu, C. K. W., Beersma, B., Stroebe, K., & Euwema, M. C. (2006). Motivated information processing, strategic choice, and the quality of negotiated agreement. ''Journal of Personality and Social Psychology'', ''90''(6), 927–943. <nowiki>https://doi.org/10.1037/0022-3514.90.6.927</nowiki> De Dreu, C. K. W., Nijstad, B. A., & van Knippenberg, D. (2008). Motivated information processing in group judgment and decision making. ''Personality and Social Psychology Review'', ''12''(1), 22–49. <nowiki>https://doi.org/10.1177/1088868307304092</nowiki> Kruglanski, A. W., & Webster, D. M. (1996). Motivated closing of the mind: “Seizing” and “freezing.” ''Psychological Review'', ''103''(2), 263–283. <nowiki>https://doi.org/10.1037/0033-295X.103.2.263</nowiki> Pica, G., Pierro, A., & Kruglanski, A. W. (2014). The role of need for cognitive closure in retrieval-induced forgetting and misinformation effects in eyewitness memory. ''Social Cognition'', ''32''(4), 337–359. <nowiki>https://doi.org/10.1521/soco.2014.32.4.337</nowiki> Roets, A., & Van Hiel, A. (2011). Item selection and validation of a brief, 15-item version of the Need for Closure Scale. ''Personality and Individual Differences'', ''50''(1), 90–94. <nowiki>https://doi.org/10.1016/j.paid.2010.09.004</nowiki> Webster, D. M., & Kruglanski, A. W. (1994). Individual differences in need for cognitive closure. ''Journal of Personality and Social Psychology'', ''67''(6), 1049–1062. <nowiki>https://doi.org/10.1037/0022-3514.67.6.1049</nowiki> Webster, D. M., Kruglanski, A. W., & Pattison, D. A. (1997). Motivated language use in intergroup contexts: Need-for-closure effects on the linguistic intergroup bias. ''Journal of Personality and Social Psychology'', ''72''(5), 1122–1131. <nowiki>https://doi.org/10.1037/0022-3514.72.5.1122</nowiki> }} == External links == * [https://dictionary.apa.org/need-for-closure Need for closure] (APA Dictionary of Psychology) * [https://sjdm.org/dmidi/Need_for_%28Cognitive%29_Closure_Scale.html Need for (Cognitive) Closure Scale] (Decision Making Individual Differences Inventory) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Decision-making]] [[Category:Motivation and emotion/Book/Epistemic motivation]] {{title|Epistemic motivation and the need for cognitive closure:<br>How does epistemic motivation and the need for cognitive closure influence our lives?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Necker cube.svg|thumb|200px|'''''Figure 1'''''. The Necker cube can be interpreted in more than one way. It illustrates how ambiguity can permit competing interpretations before cognitive closure is reached.]] ;Scenario Sofia receives two conflicting pieces of advice about an important career decision. She feels uncomfortable with the uncertainty and wants to decide immediately. However, she also wants to examine the evidence, consider different perspectives, and make an informed choice. Sofia’s situation demonstrates two psychological forces: epistemic motivation, which can encourage deeper information processing, and the need for cognitive closure, which can encourage people to reach a definite answer and escape uncertainty. {{RoundBoxBottom}} * Epistemic motivation concerns a person’s willingness to develop a thorough and accurate understanding of a situation through information search and processing (De Dreu et al., 2008). * Need for cognitive closure is the desire to obtain a definite answer rather than remain confused or uncertain (Kruglanski & Webster, 1996). * Both concepts influence how people form judgements, make decisions, communicate with others and respond to uncertainty. * Neither is always beneficial or harmful; the outcome depends on the person, available information and situational demands. * Figure 1 demonstrates how the same ambiguous information may permit more than one interpretation before a person reaches closure. In everyday life, uncertainty is not simply a lack of knowledge; it can also be emotionally uncomfortable. People therefore differ in both how much effort they invest in understanding a problem and how quickly they want uncertainty to end. These motives shape which information is noticed, how alternatives are compared, and whether an initial judgement is revised. The practical problem is that a fast answer can feel reassuring even when it is poorly supported, whereas prolonged information searching can delay necessary action. This chapter examines how people can balance accuracy with the need to decide. {{RoundBoxTop|theme=3}} '''Focus questions''' * What is epistemic motivation? * What is the need for cognitive closure? * How are epistemic motivation and the need for cognitive closure connected? * How do they influence everyday decisions, learning and relationships? * When is cognitive closure helpful or harmful? {{RoundBoxBottom}} == Epistemic motivation == * [[w:Epistemic motivation|Epistemic motivation]] describes the willingness to invest effort in developing a complete and accurate understanding of the world (De Dreu et al., 2008). * Higher epistemic motivation encourages information search, deliberate reasoning and careful consideration of different perspectives. * Lower epistemic motivation is associated with shallower information processing and greater reliance on existing knowledge, familiar opinions or mental shortcuts. * Epistemic motivation can be influenced by personal characteristics and situational factors, including curiosity, accountability, fatigue, stress and time pressure. * Epistemic motivation should not be understood as intelligence. A capable person may still process information superficially when tired, distracted or under pressure. Epistemic motivation is best understood through motivated information processing. According to this perspective, judgement depends on both capacity and motivation: a person must be able to process information and also be willing to invest the necessary effort (De Dreu et al., 2008). This distinction explains why the same person may reason carefully about an important health decision but accept the first plausible answer to a minor question. It also separates epistemic motivation from [[w:Need for cognition|need for cognition]], a tendency to enjoy effortful thought, although the constructs overlap (Cacioppo & Petty, 1982). The quality of processing therefore depends on the person, the task and the surrounding conditions rather than on a fixed label such as “deep thinker”. === Depth of information processing === * Higher epistemic motivation encourages people to attend to, encode, retrieve and integrate relevant information more thoroughly (De Dreu et al., 2008). * Groups with stronger epistemic motivation may exchange more unique information and engage in more information-driven discussion. * Process accountability can increase epistemic motivation because people expect to explain how they reached a decision (De Dreu et al., 2006). * Deeper processing can improve decision quality, especially when a problem is complicated and important information is distributed among several people. === Influencing factors === * Time pressure and environmental noise can decrease the opportunity or motivation to consider multiple explanations (Kruglanski & Webster, 1996). * Fear of making an invalid judgement may increase information search and delay closure. * Fatigue can make sustained reasoning more difficult and increase the appeal of a quick, simple answer. * Personal relevance may increase information processing, although people may also process information selectively when an issue threatens an important belief or identity. Research also shows that accountability matters, but its timing is important. When people expect to explain the process by which they reached a judgement, they are more likely to examine information carefully and integrate competing evidence (De Dreu et al., 2006). By contrast, accountability for defending a preferred outcome can encourage selective reasoning. Thus, asking “How did you reach this conclusion?” may promote epistemic motivation more effectively than asking someone merely to justify a conclusion they have already announced. == Need for cognitive closure == * Need for cognitive closure refers to the motivation to reach a definite conclusion and avoid uncertainty or ambiguity (Kruglanski & Webster, 1996). * It can operate as a relatively stable individual difference and as a temporary state produced by circumstances such as fatigue, time pressure and stress. * Webster and Kruglanski (1994) identified several associated preferences, including predictability, order, decisiveness and reduced comfort with ambiguity. * The effects of need for closure are commonly explained through the urgency and permanence tendencies. The need for closure is grounded in lay epistemic theory, which treats knowledge formation as a motivated process rather than a purely rational one (Kruglanski & Webster, 1996). Closure can be valued because it reduces uncertainty, enables action and creates a stable understanding of events. It can also be avoided when a person fears that any available conclusion will be invalid. Consequently, the theory predicts not a universal preference for quick answers, but an interaction between the desirability of closure, the information available and the costs of making an error. === Urgency tendency === * The urgency tendency involves wanting to reach closure as quickly as possible (Kruglanski & Webster, 1996). * It may cause people to “seize” on information encountered early in the decision-making process. * Urgency can be helpful when immediate action is genuinely necessary, such as during an emergency. * However, it can also produce premature conclusions when the available information is incomplete, inaccurate or misleading. === Permanence tendency === * The permanence tendency involves wanting to preserve an existing conclusion for as long as possible (Kruglanski & Webster, 1996). * It may cause people to “freeze” on their initial judgement and resist information that challenges it. * Permanence can create consistency, confidence and coordination after a decision has been made. * Excessive permanence may contribute to inflexible thinking, stereotyping and resistance to corrective evidence. === Individual differences === * The Need for Closure Scale was developed to measure individual differences related to predictability, order, decisiveness, ambiguity and closed-mindedness (Webster & Kruglanski, 1994). * A shorter revised measure has also demonstrated that urgency and permanence are important dimensions of the construct (Roets & Van Hiel, 2011). * A high score does not mean that someone is unintelligent or incapable of careful reasoning. * Need for closure can change across situations; therefore, a person may tolerate uncertainty in one context but urgently seek certainty in another. Measurement requires some caution. The original Need for Closure Scale assesses preferences for order, predictability and decisiveness, as well as discomfort with ambiguity and closed-mindedness (Webster & Kruglanski, 1994). Later psychometric work suggested that decisiveness does not always function in the same way as the other facets, and that ability to decide should not be confused with motivation to obtain closure (Roets & Van Hiel, 2007). The brief scale improves efficiency, but self-report scores still describe tendencies rather than directly observing how a person processes evidence in a specific situation (Roets & Van Hiel, 2011). == Relationship between epistemic motivation and cognitive closure == * Need for cognitive closure is a form of epistemic motivation because it concerns how people acquire and maintain knowledge (Kruglanski & Webster, 1996). * Epistemic motivation is the broader concept, whereas need for closure specifically concerns motivation to end uncertainty by reaching a conclusion. * Strong motivation to understand a problem may promote extensive information search, while strong motivation for immediate closure may shorten that search. * High-quality judgement therefore depends on balancing sufficient investigation with the practical need to reach a decision. '''Table 1.''' ''Comparison of epistemic motivation and need for cognitive closure'' {| class="wikitable" ! Concept ! Main goal ! Possible benefit ! Possible limitation |- | Epistemic motivation | Develop an accurate and comprehensive understanding | Deeper information processing and consideration of alternatives | Decision-making may require more time and effort |- | Urgency tendency | Reach closure quickly | Supports timely action | May produce premature conclusions |- | Permanence tendency | Maintain an established conclusion | Supports consistency and commitment | May create resistance to corrective evidence |} * Table 1 shows that these motivational processes involve different goals and trade-offs. * Epistemic motivation can improve decision quality by promoting systematic information processing, particularly in group settings (De Dreu et al., 2008). * However, continuously seeking more information can also delay decisions when the available information is already sufficient. * Cognitive closure can support action and coordination, but early closure may prevent consideration of important alternatives. The relationship is therefore not a simple opposition between “good” epistemic motivation and “bad” closure. Need for closure is itself an epistemic motive, but it directs processing toward a definite and stable answer. High epistemic motivation can improve judgement when the evidence is reliable and the task rewards accuracy; it can also be used to defend an identity-consistent conclusion. Likewise, closure can be adaptive when delay is costly. The decisive issue is whether the timing and content of closure match the demands of the situation. {{RoundBoxTop|theme=3}} '''Case study''' Jordan sees a social-media post claiming that a familiar food causes a serious illness. Feeling anxious, Jordan immediately accepts the claim and shares it. Later, a friend encourages Jordan to locate the original research, examine reliable sources and consider alternative explanations. Jordan’s initial response may demonstrate the urgency tendency because uncertainty is ended by accepting the first available explanation. Greater epistemic motivation could encourage Jordan to examine the quality of the evidence before forming and sharing a conclusion. {{RoundBoxBottom}} <quiz display=simple> {Which response best demonstrates the urgency tendency? |type="()"} - Continuing to compare evidence without ever reaching a decision + Accepting the first plausible explanation to eliminate uncertainty - Changing an opinion after receiving reliable contradictory evidence - Asking several experts to explain their different perspectives || The urgency tendency involves attempting to reach cognitive closure as quickly as possible. } {Which response best demonstrates higher epistemic motivation? |type="()"} - Ignoring information that challenges an existing belief - Selecting the simplest answer without examining its source + Comparing evidence and considering alternative explanations - Repeating an opinion because it is familiar || Higher epistemic motivation generally involves more thorough information search and processing. } {The permanence tendency is most closely associated with: |type="()"} - Curiosity about new information + Maintaining an existing judgement - Avoiding all decisions - Forgetting a previous conclusion || The permanence tendency involves preserving closure after a judgement has been formed. } </quiz> == Influence on everyday life == * Epistemic motivation and need for closure influence behaviour across educational, interpersonal, organisational and social settings. * Their effects depend on the complexity of the problem, the quality of available information and whether rapid action is required. * Understanding these motivations may help people recognise when they are investigating a question carefully and when they are closing it prematurely. Evidence across settings supports these applications, but much of it is correlational, laboratory-based or based on university samples. Such research can identify mechanisms under controlled conditions, yet it may not fully capture high-stakes decisions made over longer periods or across cultures. Findings should therefore be applied as probabilistic tendencies rather than rules about individuals. === Learning and education === * Higher epistemic motivation may promote curiosity, critical thinking and deeper engagement with learning materials. * Students who evaluate evidence and compare alternative explanations are more likely to develop an integrated understanding than students who rely only on memorisation. * A strong need for closure may make unclear instructions, conflicting theories and open-ended assignments uncomfortable. * Clear structure can support learning, but excessive reliance on one definite answer may be problematic when a subject requires critical evaluation. Educators can respond by combining structure with productive uncertainty. Clear assessment criteria reduce unnecessary confusion, while activities that require comparison of explanations keep multiple possibilities open long enough for critical thought. Process-focused prompts—such as asking students to identify disconfirming evidence—may be more useful than simply telling them to “think harder”. However, excessive ambiguity can overload learners, so scaffolding should be gradually reduced as knowledge and confidence develop. === Decision-making === * Epistemic motivation can improve decision quality by encouraging people to search for and integrate relevant information (De Dreu et al., 2006). * Under genuine time pressure, rapid closure may be adaptive because delaying action could have serious consequences. * When time is available, seizing on the first acceptable explanation may cause important evidence or alternative options to be overlooked. * Effective decision-making involves identifying how much information is required and establishing an appropriate point at which to decide. A useful decision rule is to match the search effort to the consequences of error. Reversible, low-cost choices may justify quick closure, whereas irreversible or safety-critical choices require stronger evidence and independent checking. This rule does not guarantee accuracy, but it makes the stopping point explicit. It also prevents anxiety alone from determining when information search ends. === Relationships and group behaviour === * First impressions can provide cognitive closure, but they may become inaccurate when people freeze on an early judgement. * Need for closure can influence intergroup language and strengthen biased descriptions of in-group and out-group behaviour (Webster et al., 1997). * Groups with higher epistemic motivation may exchange information more thoroughly and reach better-informed decisions (De Dreu et al., 2008). * Encouraging respectful disagreement can prevent premature consensus and allow group members to identify overlooked evidence. Group outcomes also depend on whether members possess different information. Motivated information processing theory predicts that epistemic motivation is especially valuable when unique knowledge must be exchanged and integrated (De Dreu et al., 2008). Yet discussion alone is insufficient: status differences, conformity and a shared preference for certainty can suppress dissent. Leaders can counter this by requesting reasons before preferences, assigning a devil’s advocate, and delaying an initial vote until evidence has been discussed. === Information and misinformation === * Online environments can expose people to large amounts of contradictory information, increasing confusion and the desire for simple answers. * A strong need for closure may increase reliance on information that quickly resolves uncertainty, even when its reliability has not been established. * Freezing on an initial interpretation can make later corrective evidence more difficult to accept. * Research suggests that need for closure can influence memory processes and vulnerability to misleading post-event information (Pica et al., 2014). Pica et al. (2014) found that need for closure influenced retrieval-induced forgetting and misinformation effects in eyewitness memory. This application is important because confidence and accuracy are not identical: closure may make a coherent account feel certain even after misleading details have been incorporated. Nevertheless, the study does not show that everyone high in need for closure will accept misinformation. Source credibility, prior knowledge and opportunities to verify a claim remain important moderators. Online, a practical response is to pause before sharing, trace a claim to its original source and look for credible evidence that could disconfirm it. == Balancing understanding and closure == * Neither endless information search nor immediate closure is appropriate in every situation. * The most effective approach depends on the consequences of error, the urgency of action and the availability of reliable evidence. * People can improve decisions by recognising their reactions to uncertainty and deliberately choosing whether additional investigation is necessary. === Potential benefits === * Epistemic motivation can support critical thinking, learning and informed decision-making. * Urgent closure can allow people to act efficiently during emergencies or under strict deadlines. * Permanent closure can create stability, commitment and coordination after an adequately informed decision. * Shared closure can also help groups organise action around an agreed understanding. === Potential limitations === * Excessive information search may create indecision or unnecessary delay. * Urgency can cause people to seize on incomplete or unreliable information. * Permanence can create inflexible beliefs and resistance to corrective evidence. * Need for closure may contribute to stereotyping when simplified group judgements replace individualised information (Kruglanski & Webster, 1996; Webster et al., 1997). These limitations show why context matters. A preference for closure may strengthen whichever interpretation is most accessible, not necessarily a negative one. For example, Kossowska et al. (2015) found that need for closure could be associated with more positive attitudes toward a negatively stereotyped outgroup when the ability to achieve closure was low. This qualification challenges the idea that need for closure automatically produces prejudice and illustrates why researchers must distinguish motivational direction from the specific belief that becomes fixed. === Practical strategies === * Pause before important decisions and identify whether time pressure is genuine or self-imposed. * Separate established facts, interpretations and assumptions. * Consider at least one alternative explanation before reaching a conclusion. * Seek information from reliable sources and perspectives that challenge the initial judgement. * Establish a reasonable decision deadline so that information search does not continue indefinitely. * Reconsider an existing conclusion when credible new evidence becomes available. These strategies work best as “decision hygiene” rather than as personality correction. Before deciding, a person can state what evidence would change the conclusion, compare at least two plausible explanations, and obtain one independent source. During group decisions, members can record their initial views privately before discussion and evaluate the reasoning process rather than rewarding confidence alone. After deciding, a scheduled review point allows permanence to support action without making the conclusion immune to correction. {{RoundBoxTop|theme=3}} '''Reflection exercise''' Think about an important decision you made recently. # What information did you examine? # Did you feel pressure to reach an answer quickly? # Did you consider an alternative explanation? # What evidence might have changed your decision? # Did your response reflect epistemic motivation, urgency, permanence or a combination of these processes? {{RoundBoxBottom}} == Conclusion == * Epistemic motivation influences the depth and thoroughness with which people search for, process and integrate information. * Need for cognitive closure motivates people to reach and preserve definite conclusions, particularly when uncertainty is uncomfortable. * The urgency tendency can lead people to seize on early information, while the permanence tendency can lead them to freeze on an established judgement. * These processes affect learning, decision-making, relationships, group behaviour and responses to online information. * Cognitive closure is not inherently harmful because it can support timely action, consistency and coordination. * The central challenge is to balance the desire for accurate understanding with the practical need to reach a conclusion. {{RoundBoxTop|theme=3}} '''Take-home message''' Good judgement requires knowing when to continue searching and when to decide. People can make better decisions by tolerating uncertainty long enough to examine reliable evidence while still establishing a reasonable point for reaching closure. {{RoundBoxBottom}} == Acknowledgements == Generative AI : was helping with coding == See also == * [[Motivation and emotion/Book/2023/Actively open-minded thinking|Actively open-minded thinking]] (Book chapter, 2023) * [[w:Epistemic motivation|Epistemic motivation]] (Wikipedia) == References == {{Hanging indent|1= De Dreu, C. K. W., Beersma, B., Stroebe, K., & Euwema, M. C. (2006). Motivated information processing, strategic choice, and the quality of negotiated agreement. ''Journal of Personality and Social Psychology'', ''90''(6), 927–943. <nowiki>https://doi.org/10.1037/0022-3514.90.6.927</nowiki> De Dreu, C. K. W., Nijstad, B. A., & van Knippenberg, D. (2008). Motivated information processing in group judgment and decision making. ''Personality and Social Psychology Review'', ''12''(1), 22–49. <nowiki>https://doi.org/10.1177/1088868307304092</nowiki> Cacioppo, J. T., & Petty, R. E. (1982). The need for cognition. ''Journal of Personality and Social Psychology'', ''42''(1), 116–131. <nowiki>https://doi.org/10.1037/0022-3514.42.1.116</nowiki> Kossowska, M., Dragon, P., & Bukowski, M. (2015). When need for closure leads to positive attitudes towards a negatively stereotyped outgroup. ''Motivation and Emotion'', ''39'', 88–98. <nowiki>https://doi.org/10.1007/s11031-014-9414-5</nowiki> Kruglanski, A. W., & Webster, D. M. (1996). Motivated closing of the mind: “Seizing” and “freezing.” ''Psychological Review'', ''103''(2), 263–283. <nowiki>https://doi.org/10.1037/0033-295X.103.2.263</nowiki> Pica, G., Pierro, A., & Kruglanski, A. W. (2014). The role of need for cognitive closure in retrieval-induced forgetting and misinformation effects in eyewitness memory. ''Social Cognition'', ''32''(4), 337–359. <nowiki>https://doi.org/10.1521/soco.2014.32.4.337</nowiki> Roets, A., & Van Hiel, A. (2011). Item selection and validation of a brief, 15-item version of the Need for Closure Scale. ''Personality and Individual Differences'', ''50''(1), 90–94. <nowiki>https://doi.org/10.1016/j.paid.2010.09.004</nowiki> Roets, A., & Van Hiel, A. (2007). Separating ability from need: Clarifying the dimensional structure of the need for closure scale. ''Personality and Social Psychology Bulletin'', ''33''(2), 266–280. <nowiki>https://doi.org/10.1177/0146167206294744</nowiki> Webster, D. M., & Kruglanski, A. W. (1994). Individual differences in need for cognitive closure. ''Journal of Personality and Social Psychology'', ''67''(6), 1049–1062. <nowiki>https://doi.org/10.1037/0022-3514.67.6.1049</nowiki> Webster, D. M., Kruglanski, A. W., & Pattison, D. A. (1997). Motivated language use in intergroup contexts: Need-for-closure effects on the linguistic intergroup bias. ''Journal of Personality and Social Psychology'', ''72''(5), 1122–1131. <nowiki>https://doi.org/10.1037/0022-3514.72.5.1122</nowiki> }} == External links == * [https://dictionary.apa.org/need-for-closure Need for closure] (APA Dictionary of Psychology) * [https://sjdm.org/dmidi/Need_for_%28Cognitive%29_Closure_Scale.html Need for (Cognitive) Closure Scale] (Decision Making Individual Differences Inventory) * [https://www.apa.org/topics/critical-thinking Critical thinking] (American Psychological Association) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Decision-making]] [[Category:Motivation and emotion/Book/Epistemic motivation]] l36ghebbgu4hvhsm2khn2xntwi7ggde 2834482 2834481 2026-09-25T15:03:35Z Ayat Al-kabai 3105570 2834482 wikitext text/x-wiki {{title|Epistemic motivation and the need for cognitive closure:<br>How does epistemic motivation and the need for cognitive closure influence our lives?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Necker cube.svg|thumb|200px|'''''Figure 1'''''. The Necker cube can be interpreted in more than one way. It illustrates how ambiguity can permit competing interpretations before cognitive closure is reached.]] ;Scenario Sofia receives two conflicting pieces of advice about an important career decision. She feels uncomfortable with the uncertainty and wants to decide immediately. However, she also wants to examine the evidence, consider different perspectives, and make an informed choice. Sofia’s situation demonstrates two psychological forces: epistemic motivation, which can encourage deeper information processing, and the need for cognitive closure, which can encourage people to reach a definite answer and escape uncertainty. {{RoundBoxBottom}} * Epistemic motivation concerns a person’s willingness to develop a thorough and accurate understanding of a situation through information search and processing (De Dreu et al., 2008). * Need for cognitive closure is the desire to obtain a definite answer rather than remain confused or uncertain (Kruglanski & Webster, 1996). * Both concepts influence how people form judgements, make decisions, communicate with others and respond to uncertainty. * Neither is always beneficial or harmful; the outcome depends on the person, available information and situational demands. * Figure 1 demonstrates how the same ambiguous information may permit more than one interpretation before a person reaches closure. In everyday life, uncertainty is not simply a lack of knowledge; it can also be emotionally uncomfortable. People therefore differ in both how much effort they invest in understanding a problem and how quickly they want uncertainty to end. These motives shape which information is noticed, how alternatives are compared, and whether an initial judgement is revised. The practical problem is that a fast answer can feel reassuring even when it is poorly supported, whereas prolonged information searching can delay necessary action. This chapter examines how people can balance accuracy with the need to decide. {{RoundBoxTop|theme=3}} '''Focus questions''' * What is epistemic motivation? * What is the need for cognitive closure? * How are epistemic motivation and the need for cognitive closure connected? * How do they influence everyday decisions, learning and relationships? * When is cognitive closure helpful or harmful? {{RoundBoxBottom}} == Epistemic motivation == * [[w:Epistemic motivation|Epistemic motivation]] describes the willingness to invest effort in developing a complete and accurate understanding of the world (De Dreu et al., 2008). * Higher epistemic motivation encourages information search, deliberate reasoning and careful consideration of different perspectives. * Lower epistemic motivation is associated with shallower information processing and greater reliance on existing knowledge, familiar opinions or mental shortcuts. * Epistemic motivation can be influenced by personal characteristics and situational factors, including curiosity, accountability, fatigue, stress and time pressure. * Epistemic motivation should not be understood as intelligence. A capable person may still process information superficially when tired, distracted or under pressure. Epistemic motivation is best understood through motivated information processing. According to this perspective, judgement depends on both capacity and motivation: a person must be able to process information and also be willing to invest the necessary effort (De Dreu et al., 2008). This distinction explains why the same person may reason carefully about an important health decision but accept the first plausible answer to a minor question. It also separates epistemic motivation from [[w:Need for cognition|need for cognition]], a tendency to enjoy effortful thought, although the constructs overlap (Cacioppo & Petty, 1982). The quality of processing therefore depends on the person, the task and the surrounding conditions rather than on a fixed label such as “deep thinker”. === Depth of information processing === * Higher epistemic motivation encourages people to attend to, encode, retrieve and integrate relevant information more thoroughly (De Dreu et al., 2008). * Groups with stronger epistemic motivation may exchange more unique information and engage in more information-driven discussion. * Process accountability can increase epistemic motivation because people expect to explain how they reached a decision (De Dreu et al., 2006). * Deeper processing can improve decision quality, especially when a problem is complicated and important information is distributed among several people. === Influencing factors === * Time pressure and environmental noise can decrease the opportunity or motivation to consider multiple explanations (Kruglanski & Webster, 1996). * Fear of making an invalid judgement may increase information search and delay closure. * Fatigue can make sustained reasoning more difficult and increase the appeal of a quick, simple answer. * Personal relevance may increase information processing, although people may also process information selectively when an issue threatens an important belief or identity. Research also shows that accountability matters, but its timing is important. When people expect to explain the process by which they reached a judgement, they are more likely to examine information carefully and integrate competing evidence (De Dreu et al., 2006). By contrast, accountability for defending a preferred outcome can encourage selective reasoning. Thus, asking “How did you reach this conclusion?” may promote epistemic motivation more effectively than asking someone merely to justify a conclusion they have already announced. == Need for cognitive closure == * Need for cognitive closure refers to the motivation to reach a definite conclusion and avoid uncertainty or ambiguity (Kruglanski & Webster, 1996). * It can operate as a relatively stable individual difference and as a temporary state produced by circumstances such as fatigue, time pressure and stress. * Webster and Kruglanski (1994) identified several associated preferences, including predictability, order, decisiveness and reduced comfort with ambiguity. * The effects of need for closure are commonly explained through the urgency and permanence tendencies. The need for closure is grounded in lay epistemic theory, which treats knowledge formation as a motivated process rather than a purely rational one (Kruglanski & Webster, 1996). Closure can be valued because it reduces uncertainty, enables action and creates a stable understanding of events. It can also be avoided when a person fears that any available conclusion will be invalid. Consequently, the theory predicts not a universal preference for quick answers, but an interaction between the desirability of closure, the information available and the costs of making an error. === Urgency tendency === * The urgency tendency involves wanting to reach closure as quickly as possible (Kruglanski & Webster, 1996). * It may cause people to “seize” on information encountered early in the decision-making process. * Urgency can be helpful when immediate action is genuinely necessary, such as during an emergency. * However, it can also produce premature conclusions when the available information is incomplete, inaccurate or misleading. === Permanence tendency === * The permanence tendency involves wanting to preserve an existing conclusion for as long as possible (Kruglanski & Webster, 1996). * It may cause people to “freeze” on their initial judgement and resist information that challenges it. * Permanence can create consistency, confidence and coordination after a decision has been made. * Excessive permanence may contribute to inflexible thinking, stereotyping and resistance to corrective evidence. === Individual differences === * The Need for Closure Scale was developed to measure individual differences related to predictability, order, decisiveness, ambiguity and closed-mindedness (Webster & Kruglanski, 1994). * A shorter revised measure has also demonstrated that urgency and permanence are important dimensions of the construct (Roets & Van Hiel, 2011). * A high score does not mean that someone is unintelligent or incapable of careful reasoning. * Need for closure can change across situations; therefore, a person may tolerate uncertainty in one context but urgently seek certainty in another. Measurement requires some caution. The original Need for Closure Scale assesses preferences for order, predictability and decisiveness, as well as discomfort with ambiguity and closed-mindedness (Webster & Kruglanski, 1994). Later psychometric work suggested that decisiveness does not always function in the same way as the other facets, and that ability to decide should not be confused with motivation to obtain closure (Roets & Van Hiel, 2007). The brief scale improves efficiency, but self-report scores still describe tendencies rather than directly observing how a person processes evidence in a specific situation (Roets & Van Hiel, 2011). == Relationship between epistemic motivation and cognitive closure == * Need for cognitive closure is a form of epistemic motivation because it concerns how people acquire and maintain knowledge (Kruglanski & Webster, 1996). * Epistemic motivation is the broader concept, whereas need for closure specifically concerns motivation to end uncertainty by reaching a conclusion. * Strong motivation to understand a problem may promote extensive information search, while strong motivation for immediate closure may shorten that search. * High-quality judgement therefore depends on balancing sufficient investigation with the practical need to reach a decision. '''Table 1.''' ''Comparison of epistemic motivation and need for cognitive closure'' {| class="wikitable" ! Concept ! Main goal ! Possible benefit ! Possible limitation |- | Epistemic motivation | Develop an accurate and comprehensive understanding | Deeper information processing and consideration of alternatives | Decision-making may require more time and effort |- | Urgency tendency | Reach closure quickly | Supports timely action | May produce premature conclusions |- | Permanence tendency | Maintain an established conclusion | Supports consistency and commitment | May create resistance to corrective evidence |} * Table 1 shows that these motivational processes involve different goals and trade-offs. * Epistemic motivation can improve decision quality by promoting systematic information processing, particularly in group settings (De Dreu et al., 2008). * However, continuously seeking more information can also delay decisions when the available information is already sufficient. * Cognitive closure can support action and coordination, but early closure may prevent consideration of important alternatives. The relationship is therefore not a simple opposition between “good” epistemic motivation and “bad” closure. Need for closure is itself an epistemic motive, but it directs processing toward a definite and stable answer. High epistemic motivation can improve judgement when the evidence is reliable and the task rewards accuracy; it can also be used to defend an identity-consistent conclusion. Likewise, closure can be adaptive when delay is costly. The decisive issue is whether the timing and content of closure match the demands of the situation. {{RoundBoxTop|theme=3}} '''Case study''' Jordan sees a social-media post claiming that a familiar food causes a serious illness. Feeling anxious, Jordan immediately accepts the claim and shares it. Later, a friend encourages Jordan to locate the original research, examine reliable sources and consider alternative explanations. Jordan’s initial response may demonstrate the urgency tendency because uncertainty is ended by accepting the first available explanation. Greater epistemic motivation could encourage Jordan to examine the quality of the evidence before forming and sharing a conclusion. {{RoundBoxBottom}} <quiz display=simple> {Which response best demonstrates the urgency tendency? |type="()"} - Continuing to compare evidence without ever reaching a decision + Accepting the first plausible explanation to eliminate uncertainty - Changing an opinion after receiving reliable contradictory evidence - Asking several experts to explain their different perspectives || The urgency tendency involves attempting to reach cognitive closure as quickly as possible. } {Which response best demonstrates higher epistemic motivation? |type="()"} - Ignoring information that challenges an existing belief - Selecting the simplest answer without examining its source + Comparing evidence and considering alternative explanations - Repeating an opinion because it is familiar || Higher epistemic motivation generally involves more thorough information search and processing. } {The permanence tendency is most closely associated with: |type="()"} - Curiosity about new information + Maintaining an existing judgement - Avoiding all decisions - Forgetting a previous conclusion || The permanence tendency involves preserving closure after a judgement has been formed. } </quiz> == Influence on everyday life == * Epistemic motivation and need for closure influence behaviour across educational, interpersonal, organisational and social settings. * Their effects depend on the complexity of the problem, the quality of available information and whether rapid action is required. * Understanding these motivations may help people recognise when they are investigating a question carefully and when they are closing it prematurely. Evidence across settings supports these applications, but much of it is correlational, laboratory-based or based on university samples. Such research can identify mechanisms under controlled conditions, yet it may not fully capture high-stakes decisions made over longer periods or across cultures. Findings should therefore be applied as probabilistic tendencies rather than rules about individuals. === Learning and education === * Higher epistemic motivation may promote curiosity, critical thinking and deeper engagement with learning materials. * Students who evaluate evidence and compare alternative explanations are more likely to develop an integrated understanding than students who rely only on memorisation. * A strong need for closure may make unclear instructions, conflicting theories and open-ended assignments uncomfortable. * Clear structure can support learning, but excessive reliance on one definite answer may be problematic when a subject requires critical evaluation. Educators can respond by combining structure with productive uncertainty. Clear assessment criteria reduce unnecessary confusion, while activities that require comparison of explanations keep multiple possibilities open long enough for critical thought. Process-focused prompts—such as asking students to identify disconfirming evidence—may be more useful than simply telling them to “think harder”. However, excessive ambiguity can overload learners, so scaffolding should be gradually reduced as knowledge and confidence develop. === Decision-making === * Epistemic motivation can improve decision quality by encouraging people to search for and integrate relevant information (De Dreu et al., 2006). * Under genuine time pressure, rapid closure may be adaptive because delaying action could have serious consequences. * When time is available, seizing on the first acceptable explanation may cause important evidence or alternative options to be overlooked. * Effective decision-making involves identifying how much information is required and establishing an appropriate point at which to decide. A useful decision rule is to match the search effort to the consequences of error. Reversible, low-cost choices may justify quick closure, whereas irreversible or safety-critical choices require stronger evidence and independent checking. This rule does not guarantee accuracy, but it makes the stopping point explicit. It also prevents anxiety alone from determining when information search ends. === Relationships and group behaviour === * First impressions can provide cognitive closure, but they may become inaccurate when people freeze on an early judgement. * Need for closure can influence intergroup language and strengthen biased descriptions of in-group and out-group behaviour (Webster et al., 1997). * Groups with higher epistemic motivation may exchange information more thoroughly and reach better-informed decisions (De Dreu et al., 2008). * Encouraging respectful disagreement can prevent premature consensus and allow group members to identify overlooked evidence. Group outcomes also depend on whether members possess different information. Motivated information processing theory predicts that epistemic motivation is especially valuable when unique knowledge must be exchanged and integrated (De Dreu et al., 2008). Yet discussion alone is insufficient: status differences, conformity and a shared preference for certainty can suppress dissent. Leaders can counter this by requesting reasons before preferences, assigning a devil’s advocate, and delaying an initial vote until evidence has been discussed. === Information and misinformation === * Online environments can expose people to large amounts of contradictory information, increasing confusion and the desire for simple answers. * A strong need for closure may increase reliance on information that quickly resolves uncertainty, even when its reliability has not been established. * Freezing on an initial interpretation can make later corrective evidence more difficult to accept. * Research suggests that need for closure can influence memory processes and vulnerability to misleading post-event information (Pica et al., 2014). Pica et al. (2014) found that need for closure influenced retrieval-induced forgetting and misinformation effects in eyewitness memory. This application is important because confidence and accuracy are not identical: closure may make a coherent account feel certain even after misleading details have been incorporated. Nevertheless, the study does not show that everyone high in need for closure will accept misinformation. Source credibility, prior knowledge and opportunities to verify a claim remain important moderators. Online, a practical response is to pause before sharing, trace a claim to its original source and look for credible evidence that could disconfirm it. == Balancing understanding and closure == * Neither endless information search nor immediate closure is appropriate in every situation. * The most effective approach depends on the consequences of error, the urgency of action and the availability of reliable evidence. * People can improve decisions by recognising their reactions to uncertainty and deliberately choosing whether additional investigation is necessary. === Potential benefits === * Epistemic motivation can support critical thinking, learning and informed decision-making. * Urgent closure can allow people to act efficiently during emergencies or under strict deadlines. * Permanent closure can create stability, commitment and coordination after an adequately informed decision. * Shared closure can also help groups organise action around an agreed understanding. === Potential limitations === * Excessive information search may create indecision or unnecessary delay. * Urgency can cause people to seize on incomplete or unreliable information. * Permanence can create inflexible beliefs and resistance to corrective evidence. * Need for closure may contribute to stereotyping when simplified group judgements replace individualised information (Kruglanski & Webster, 1996; Webster et al., 1997). These limitations show why context matters. A preference for closure may strengthen whichever interpretation is most accessible, not necessarily a negative one. For example, Kossowska et al. (2015) found that need for closure could be associated with more positive attitudes toward a negatively stereotyped outgroup when the ability to achieve closure was low. This qualification challenges the idea that need for closure automatically produces prejudice and illustrates why researchers must distinguish motivational direction from the specific belief that becomes fixed. === Practical strategies === * Pause before important decisions and identify whether time pressure is genuine or self-imposed. * Separate established facts, interpretations and assumptions. * Consider at least one alternative explanation before reaching a conclusion. * Seek information from reliable sources and perspectives that challenge the initial judgement. * Establish a reasonable decision deadline so that information search does not continue indefinitely. * Reconsider an existing conclusion when credible new evidence becomes available. These strategies work best as “decision hygiene” rather than as personality correction. Before deciding, a person can state what evidence would change the conclusion, compare at least two plausible explanations, and obtain one independent source. During group decisions, members can record their initial views privately before discussion and evaluate the reasoning process rather than rewarding confidence alone. After deciding, a scheduled review point allows permanence to support action without making the conclusion immune to correction. {{RoundBoxTop|theme=3}} '''Reflection exercise''' Think about an important decision you made recently. # What information did you examine? # Did you feel pressure to reach an answer quickly? # Did you consider an alternative explanation? # What evidence might have changed your decision? # Did your response reflect epistemic motivation, urgency, permanence or a combination of these processes? {{RoundBoxBottom}} == Conclusion == * Epistemic motivation influences the depth and thoroughness with which people search for, process and integrate information. * Need for cognitive closure motivates people to reach and preserve definite conclusions, particularly when uncertainty is uncomfortable. * The urgency tendency can lead people to seize on early information, while the permanence tendency can lead them to freeze on an established judgement. * These processes affect learning, decision-making, relationships, group behaviour and responses to online information. * Cognitive closure is not inherently harmful because it can support timely action, consistency and coordination. * The central challenge is to balance the desire for accurate understanding with the practical need to reach a conclusion. {{RoundBoxTop|theme=3}} '''Take-home message''' Good judgement requires knowing when to continue searching and when to decide. People can make better decisions by tolerating uncertainty long enough to examine reliable evidence while still establishing a reasonable point for reaching closure. {{RoundBoxBottom}} == Acknowledgements == Generative AI : was helping with coding == See also == * [[Motivation and emotion/Book/2023/Actively open-minded thinking|Actively open-minded thinking]] (Book chapter, 2023) * [[w:Epistemic motivation|Epistemic motivation]] (Wikipedia) == References == {{Hanging indent|1= De Dreu, C. K. W., Beersma, B., Stroebe, K., & Euwema, M. C. (2006). Motivated information processing, strategic choice, and the quality of negotiated agreement. ''Journal of Personality and Social Psychology'', ''90''(6), 927–943. <nowiki>https://doi.org/10.1037/0022-3514.90.6.927</nowiki> De Dreu, C. K. W., Nijstad, B. A., & van Knippenberg, D. (2008). Motivated information processing in group judgment and decision making. ''Personality and Social Psychology Review'', ''12''(1), 22–49. <nowiki>https://doi.org/10.1177/1088868307304092</nowiki> Cacioppo, J. T., & Petty, R. E. (1982). The need for cognition. ''Journal of Personality and Social Psychology'', ''42''(1), 116–131. <nowiki>https://doi.org/10.1037/0022-3514.42.1.116</nowiki> Kossowska, M., Dragon, P., & Bukowski, M. (2015). When need for closure leads to positive attitudes towards a negatively stereotyped outgroup. ''Motivation and Emotion'', ''39'', 88–98. <nowiki>https://doi.org/10.1007/s11031-014-9414-5</nowiki> Kruglanski, A. W., & Webster, D. M. (1996). Motivated closing of the mind: “Seizing” and “freezing.” ''Psychological Review'', ''103''(2), 263–283. <nowiki>https://doi.org/10.1037/0033-295X.103.2.263</nowiki> Pica, G., Pierro, A., & Kruglanski, A. W. (2014). The role of need for cognitive closure in retrieval-induced forgetting and misinformation effects in eyewitness memory. ''Social Cognition'', ''32''(4), 337–359. <nowiki>https://doi.org/10.1521/soco.2014.32.4.337</nowiki> Roets, A., & Van Hiel, A. (2011). Item selection and validation of a brief, 15-item version of the Need for Closure Scale. ''Personality and Individual Differences'', ''50''(1), 90–94. <nowiki>https://doi.org/10.1016/j.paid.2010.09.004</nowiki> Roets, A., & Van Hiel, A. (2007). Separating ability from need: Clarifying the dimensional structure of the need for closure scale. ''Personality and Social Psychology Bulletin'', ''33''(2), 266–280. <nowiki>https://doi.org/10.1177/0146167206294744</nowiki> Webster, D. M., & Kruglanski, A. W. (1994). Individual differences in need for cognitive closure. ''Journal of Personality and Social Psychology'', ''67''(6), 1049–1062. <nowiki>https://doi.org/10.1037/0022-3514.67.6.1049</nowiki> Webster, D. M., Kruglanski, A. W., & Pattison, D. A. (1997). Motivated language use in intergroup contexts: Need-for-closure effects on the linguistic intergroup bias. ''Journal of Personality and Social Psychology'', ''72''(5), 1122–1131. <nowiki>https://doi.org/10.1037/0022-3514.72.5.1122</nowiki> }} == External links == * [https://dictionary.apa.org/need-for-closure Need for closure] (APA Dictionary of Psychology) * [https://sjdm.org/dmidi/Need_for_%28Cognitive%29_Closure_Scale.html Need for (Cognitive) Closure Scale] (Decision Making Individual Differences Inventory) * [https://www.apa.org/topics/critical-thinking Critical thinking] (American Psychological Association) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Decision-making]] [[Category:Motivation and emotion/Book/Epistemic motivation]] bbz995xyiqdbhqp0ebbuzlrhib3j9t2 2834483 2834482 2026-09-25T15:23:36Z Ayat Al-kabai 3105570 2834483 wikitext text/x-wiki {{title|Epistemic motivation and the need for cognitive closure:<br>How does epistemic motivation and the need for cognitive closure influence our lives?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Necker cube.svg|thumb|200px|'''''Figure 1'''''. The Necker cube can be interpreted in more than one way. It illustrates how ambiguity can permit competing interpretations before cognitive closure is reached.]] ;Scenario Sofia receives two conflicting pieces of advice about an important career decision. She feels uncomfortable with the uncertainty and wants to decide immediately. However, she also wants to examine the evidence, consider different perspectives, and make an informed choice. Sofia’s situation demonstrates two psychological forces: epistemic motivation, which can encourage deeper information processing, and the need for cognitive closure, which can encourage people to reach a definite answer and escape uncertainty. {{RoundBoxBottom}} * Epistemic motivation concerns a person’s willingness to develop a thorough and accurate understanding of a situation through information search and processing (De Dreu et al., 2008). * Need for cognitive closure is the desire to obtain a definite answer rather than remain confused or uncertain (Kruglanski & Webster, 1996). * Both concepts influence how people form judgements, make decisions, communicate with others and respond to uncertainty. * Neither is always beneficial or harmful; the outcome depends on the person, available information and situational demands. * Figure 1 demonstrates how the same ambiguous information may permit more than one interpretation before a person reaches closure. Uncertainty can be emotionally uncomfortable. People differ in how much effort they invest in understanding a problem and how quickly they want uncertainty to end. These motives shape which information is noticed, whether alternatives are compared and whether an initial judgement is revised. A fast answer may feel reassuring despite weak evidence, while prolonged searching may delay action. This chapter examines how to balance accuracy with the need to decide. {{RoundBoxTop|theme=3}} '''Focus questions''' * What is epistemic motivation? * What is the need for cognitive closure? * How are epistemic motivation and the need for cognitive closure connected? * How do they influence everyday decisions, learning and relationships? * When is cognitive closure helpful or harmful? {{RoundBoxBottom}} == Epistemic motivation == * [[w:Epistemic motivation|Epistemic motivation]] describes the willingness to invest effort in developing a complete and accurate understanding of the world (De Dreu et al., 2008). * Higher epistemic motivation encourages information search, deliberate reasoning and careful consideration of different perspectives. * Lower epistemic motivation is associated with shallower information processing and greater reliance on existing knowledge, familiar opinions or mental shortcuts. * Epistemic motivation can be influenced by personal characteristics and situational factors, including curiosity, accountability, fatigue, stress and time pressure. * Epistemic motivation should not be understood as intelligence. A capable person may still process information superficially when tired, distracted or under pressure. [[File:Duck-Rabbit illusion.jpg|thumb|220px|'''''Figure 2'''''. The duck–rabbit illusion shows how identical information can support competing interpretations.]] Epistemic motivation is best understood through motivated information processing. According to this perspective, judgement depends on both capacity and motivation: a person must be able to process information and also be willing to invest the necessary effort (De Dreu et al., 2008). This distinction explains why the same person may reason carefully about an important health decision but accept the first plausible answer to a minor question. It also separates epistemic motivation from [[w:Need for cognition|need for cognition]], a tendency to enjoy effortful thought, although the constructs overlap (Cacioppo & Petty, 1982). The quality of processing therefore depends on the person, the task and the surrounding conditions rather than on a fixed label such as “deep thinker”. Figure 2 illustrates why delaying closure can be useful when evidence permits more than one interpretation. === Depth of information processing === * Higher epistemic motivation encourages people to attend to, encode, retrieve and integrate relevant information more thoroughly (De Dreu et al., 2008). * Groups with stronger epistemic motivation may exchange more unique information and engage in more information-driven discussion. * Process accountability can increase epistemic motivation because people expect to explain how they reached a decision (De Dreu et al., 2006). * Deeper processing can improve decision quality, especially when a problem is complicated and important information is distributed among several people. === Influencing factors === * Time pressure and environmental noise can decrease the opportunity or motivation to consider multiple explanations (Kruglanski & Webster, 1996). * Fear of making an invalid judgement may increase information search and delay closure. * Fatigue can make sustained reasoning more difficult and increase the appeal of a quick, simple answer. * Personal relevance may increase information processing, although people may also process information selectively when an issue threatens an important belief or identity. Research also shows that accountability matters, but its timing is important. When people expect to explain the process by which they reached a judgement, they are more likely to examine information carefully and integrate competing evidence (De Dreu et al., 2006). By contrast, accountability for defending a preferred outcome can encourage selective reasoning. Thus, asking “How did you reach this conclusion?” may promote epistemic motivation more effectively than asking someone merely to justify a conclusion they have already announced. == Need for cognitive closure == * Need for cognitive closure refers to the motivation to reach a definite conclusion and avoid uncertainty or ambiguity (Kruglanski & Webster, 1996). * It can operate as a relatively stable individual difference and as a temporary state produced by circumstances such as fatigue, time pressure and stress. * Webster and Kruglanski (1994) identified several associated preferences, including predictability, order, decisiveness and reduced comfort with ambiguity. * The effects of need for closure are commonly explained through the urgency and permanence tendencies. The need for closure is grounded in lay epistemic theory, which treats knowledge formation as a motivated process rather than a purely rational one (Kruglanski & Webster, 1996). Closure can be valued because it reduces uncertainty, enables action and creates a stable understanding of events. It can also be avoided when a person fears that any available conclusion will be invalid. Consequently, the theory predicts not a universal preference for quick answers, but an interaction between the desirability of closure, the information available and the costs of making an error. === Urgency tendency === * The urgency tendency involves wanting to reach closure as quickly as possible (Kruglanski & Webster, 1996). * It may cause people to “seize” on information encountered early in the decision-making process. * Urgency can be helpful when immediate action is genuinely necessary, such as during an emergency. * However, it can also produce premature conclusions when the available information is incomplete, inaccurate or misleading. Experimental evidence supports this account. Kruglanski et al. (1993) found that conditions increasing the desire for closure made participants more resistant to persuasion after they had formed an opinion, but more receptive to early information when no prior position existed. This pattern demonstrates both tendencies: urgency increases reliance on an initial message, while permanence protects an existing judgement. Because persuasion experiments simplify real-world belief change, the findings identify a mechanism rather than determining how every individual will respond. === Permanence tendency === * The permanence tendency involves wanting to preserve an existing conclusion for as long as possible (Kruglanski & Webster, 1996). * It may cause people to “freeze” on their initial judgement and resist information that challenges it. * Permanence can create consistency, confidence and coordination after a decision has been made. * Excessive permanence may contribute to inflexible thinking, stereotyping and resistance to corrective evidence. === Individual differences === * The Need for Closure Scale was developed to measure individual differences related to predictability, order, decisiveness, ambiguity and closed-mindedness (Webster & Kruglanski, 1994). * A shorter revised measure has also demonstrated that urgency and permanence are important dimensions of the construct (Roets & Van Hiel, 2011). * A high score does not mean that someone is unintelligent or incapable of careful reasoning. * Need for closure can change across situations; therefore, a person may tolerate uncertainty in one context but urgently seek certainty in another. Measurement requires caution. The Need for Closure Scale assesses order, predictability, decisiveness, discomfort with ambiguity and closed-mindedness (Webster & Kruglanski, 1994). However, decisiveness may function differently from other facets, and ability to decide is not the same as motivation for closure (Roets & Van Hiel, 2007). Self-reports describe tendencies rather than directly observing information processing in a specific situation (Roets & Van Hiel, 2011). == Relationship between epistemic motivation and cognitive closure == * Need for cognitive closure is a form of epistemic motivation because it concerns how people acquire and maintain knowledge (Kruglanski & Webster, 1996). * Epistemic motivation is the broader concept, whereas need for closure specifically concerns motivation to end uncertainty by reaching a conclusion. * Strong motivation to understand a problem may promote extensive information search, while strong motivation for immediate closure may shorten that search. * High-quality judgement therefore depends on balancing sufficient investigation with the practical need to reach a decision. '''Table 1.''' ''Comparison of epistemic motivation and need for cognitive closure'' {| class="wikitable" ! Concept ! Main goal ! Possible benefit ! Possible limitation |- | Epistemic motivation | Develop an accurate and comprehensive understanding | Deeper information processing and consideration of alternatives | Decision-making may require more time and effort |- | Urgency tendency | Reach closure quickly | Supports timely action | May produce premature conclusions |- | Permanence tendency | Maintain an established conclusion | Supports consistency and commitment | May create resistance to corrective evidence |} * Table 1 shows that these motivational processes involve different goals and trade-offs. * Epistemic motivation can improve decision quality by promoting systematic information processing, particularly in group settings (De Dreu et al., 2008). * However, continuously seeking more information can also delay decisions when the available information is already sufficient. * Cognitive closure can support action and coordination, but early closure may prevent consideration of important alternatives. The relationship is therefore not a simple opposition between “good” epistemic motivation and “bad” closure. Need for closure is itself an epistemic motive, but it directs processing toward a definite and stable answer. High epistemic motivation can improve judgement when the evidence is reliable and the task rewards accuracy; it can also be used to defend an identity-consistent conclusion. Likewise, closure can be adaptive when delay is costly. The decisive issue is whether the timing and content of closure match the demands of the situation. {{RoundBoxTop|theme=2}} '''Key points''' * Epistemic motivation concerns how thoroughly information is processed. * Urgency encourages rapid “seizing” on an answer. * Permanence encourages “freezing” on an established answer. * Accuracy depends on matching processing to the decision. {{RoundBoxBottom}} {{RoundBoxTop|theme=3}} '''Case study''' Jordan sees a social-media post claiming that a familiar food causes a serious illness. Feeling anxious, Jordan immediately accepts the claim and shares it. Later, a friend encourages Jordan to locate the original research, examine reliable sources and consider alternative explanations. Jordan’s initial response may demonstrate the urgency tendency because uncertainty is ended by accepting the first available explanation. Greater epistemic motivation could encourage Jordan to examine the quality of the evidence before forming and sharing a conclusion. {{RoundBoxBottom}} <quiz display=simple> {Which response best demonstrates the urgency tendency? |type="()"} - Continuing to compare evidence without ever reaching a decision + Accepting the first plausible explanation to eliminate uncertainty - Changing an opinion after receiving reliable contradictory evidence - Asking several experts to explain their different perspectives || The urgency tendency involves attempting to reach cognitive closure as quickly as possible. } {Which response best demonstrates higher epistemic motivation? |type="()"} - Ignoring information that challenges an existing belief - Selecting the simplest answer without examining its source + Comparing evidence and considering alternative explanations - Repeating an opinion because it is familiar || Higher epistemic motivation generally involves more thorough information search and processing. } {The permanence tendency is most closely associated with: |type="()"} - Curiosity about new information + Maintaining an existing judgement - Avoiding all decisions - Forgetting a previous conclusion || The permanence tendency involves preserving closure after a judgement has been formed. } </quiz> == Influence on everyday life == * Epistemic motivation and need for closure influence behaviour across educational, interpersonal, organisational and social settings. * Their effects depend on the complexity of the problem, the quality of available information and whether rapid action is required. * Understanding these motivations may help people recognise when they are investigating a question carefully and when they are closing it prematurely. Evidence across settings supports these applications, but much of it is correlational, laboratory-based or based on university samples. Such research can identify mechanisms under controlled conditions, yet it may not fully capture high-stakes decisions made over longer periods or across cultures. Findings should therefore be applied as probabilistic tendencies rather than rules about individuals. === Learning and education === * Higher epistemic motivation may promote curiosity, critical thinking and deeper engagement with learning materials. * Students who evaluate evidence and compare alternative explanations are more likely to develop an integrated understanding than students who rely only on memorisation. * A strong need for closure may make unclear instructions, conflicting theories and open-ended assignments uncomfortable. * Clear structure can support learning, but excessive reliance on one definite answer may be problematic when a subject requires critical evaluation. Educators can combine structure with productive uncertainty. Clear criteria reduce unnecessary confusion, while comparing explanations keeps alternatives open for critical thought. Prompts asking students to identify disconfirming evidence may be more useful than simply telling them to “think harder”. Because excessive ambiguity can overload learners, support should be reduced gradually as knowledge develops. === Decision-making === * Epistemic motivation can improve decision quality by encouraging people to search for and integrate relevant information (De Dreu et al., 2006). * Under genuine time pressure, rapid closure may be adaptive because delaying action could have serious consequences. * When time is available, seizing on the first acceptable explanation may cause important evidence or alternative options to be overlooked. * Effective decision-making involves identifying how much information is required and establishing an appropriate point at which to decide. A useful decision rule is to match the search effort to the consequences of error. Reversible, low-cost choices may justify quick closure, whereas irreversible or safety-critical choices require stronger evidence and independent checking. This rule does not guarantee accuracy, but it makes the stopping point explicit. It also prevents anxiety alone from determining when information search ends. === Relationships and group behaviour === * First impressions can provide cognitive closure, but they may become inaccurate when people freeze on an early judgement. * Need for closure can influence intergroup language and strengthen biased descriptions of in-group and out-group behaviour (Webster et al., 1997). * Groups with higher epistemic motivation may exchange information more thoroughly and reach better-informed decisions (De Dreu et al., 2008). * Encouraging respectful disagreement can prevent premature consensus and allow group members to identify overlooked evidence. [[File:Emile Friant La Discussion politique.jpg|thumb|240px|'''''Figure 3'''''. Discussion can expose competing interpretations when members exchange and evaluate information rather than rush toward agreement.]] Group outcomes also depend on whether members possess different information. Scholten et al. (2007) found that process accountability increased systematic information processing and decision quality, particularly when group members began with different preferences. Bechtoldt et al. (2010) similarly showed that epistemic motivation supported group creativity when members pursued collective rather than purely personal goals. However, status differences, conformity and a shared preference for certainty can still suppress dissent. Figure 3 illustrates the social exchange through which alternatives can be tested. Leaders can request reasons before preferences, assign a devil’s advocate and delay an initial vote until evidence has been discussed. === Information and misinformation === * Online environments can expose people to large amounts of contradictory information, increasing confusion and the desire for simple answers. * A strong need for closure may increase reliance on information that quickly resolves uncertainty, even when its reliability has not been established. * Freezing on an initial interpretation can make later corrective evidence more difficult to accept. * Research suggests that need for closure can influence memory processes and vulnerability to misleading post-event information (Pica et al., 2014). Pica et al. (2014) found that need for closure influenced retrieval-induced forgetting and misinformation effects in eyewitness memory. Confidence and accuracy are not identical: closure may make a coherent account feel certain after misleading details are incorporated. This does not mean everyone high in need for closure accepts misinformation; source credibility, prior knowledge and verification opportunities still matter. Online, readers can pause before sharing, trace the original source and seek disconfirming evidence. == Balancing understanding and closure == * Neither endless information search nor immediate closure is appropriate in every situation. * The most effective approach depends on the consequences of error, the urgency of action and the availability of reliable evidence. * People can improve decisions by recognising their reactions to uncertainty and deliberately choosing whether additional investigation is necessary. === Potential benefits === * Epistemic motivation can support critical thinking, learning and informed decision-making. * Urgent closure can allow people to act efficiently during emergencies or under strict deadlines. * Permanent closure can create stability, commitment and coordination after an adequately informed decision. * Shared closure can also help groups organise action around an agreed understanding. === Potential limitations === * Excessive information search may create indecision or unnecessary delay. * Urgency can cause people to seize on incomplete or unreliable information. * Permanence can create inflexible beliefs and resistance to corrective evidence. * Need for closure may contribute to stereotyping when simplified group judgements replace individualised information (Kruglanski & Webster, 1996; Webster et al., 1997). These limitations show why context matters. A preference for closure may strengthen whichever interpretation is most accessible, not necessarily a negative one. For example, Kossowska et al. (2015) found that need for closure could be associated with more positive attitudes toward a negatively stereotyped outgroup when the ability to achieve closure was low. This qualification challenges the idea that need for closure automatically produces prejudice and illustrates why researchers must distinguish motivational direction from the specific belief that becomes fixed. === Practical strategies === * Pause before important decisions and identify whether time pressure is genuine or self-imposed. * Separate established facts, interpretations and assumptions. * Consider at least one alternative explanation before reaching a conclusion. * Seek information from reliable sources and perspectives that challenge the initial judgement. * Establish a reasonable decision deadline so that information search does not continue indefinitely. * Reconsider an existing conclusion when credible new evidence becomes available. [[File:Consensus Flowchart.svg|thumb|240px|'''''Figure 4'''''. A decision process can include opportunities to question, revise and consolidate a conclusion.]] '''Table 2.''' ''Matching information search to the decision'' {| class="wikitable" ! Decision condition ! Recommended response |- | Urgent and reversible | Decide using the best available evidence |- | Important and irreversible | Seek independent evidence and test alternatives |- | Credible new evidence appears | Reopen and revise the conclusion |} These strategies work best as “decision hygiene” rather than as personality correction. Before deciding, a person can state what evidence would change the conclusion, compare at least two plausible explanations, and obtain one independent source. During group decisions, members can record their initial views privately before discussion and evaluate the reasoning process rather than rewarding confidence alone. After deciding, a scheduled review point allows permanence to support action without making the conclusion immune to correction. Table 2 and Figure 4 show how closure can be treated as reviewable rather than irreversible. {{RoundBoxTop|theme=3}} '''Reflection exercise''' Think about an important decision you made recently. # What information did you examine? # Did you feel pressure to reach an answer quickly? # Did you consider an alternative explanation? # What evidence might have changed your decision? # Did your response reflect epistemic motivation, urgency, permanence or a combination of these processes? {{RoundBoxBottom}} == Conclusion == * Epistemic motivation influences the depth and thoroughness with which people search for, process and integrate information. * Need for cognitive closure motivates people to reach and preserve definite conclusions, particularly when uncertainty is uncomfortable. * The urgency tendency can lead people to seize on early information, while the permanence tendency can lead them to freeze on an established judgement. * These processes affect learning, decision-making, relationships, group behaviour and responses to online information. * Cognitive closure is not inherently harmful because it can support timely action, consistency and coordination. * The central challenge is to balance the desire for accurate understanding with the practical need to reach a conclusion. {{RoundBoxTop|theme=3}} '''Take-home message''' Good judgement requires knowing when to continue searching and when to decide. People can make better decisions by tolerating uncertainty long enough to examine reliable evidence while still establishing a reasonable point for reaching closure. {{RoundBoxBottom}} == Acknowledgements == Generative AI (OpenAI ChatGPT) was used to support drafting, research organisation and copyediting. The author reviewed and takes responsibility for the final chapter. == See also == * [[Motivation and emotion/Book/2023/Actively open-minded thinking|Actively open-minded thinking]] (Book chapter, 2023) * [[w:Epistemic motivation|Epistemic motivation]] (Wikipedia) == References == {{Hanging indent|1= Bechtoldt, M. N., De Dreu, C. K. W., Nijstad, B. A., & Choi, H.-S. (2010). Motivated information processing, social tuning, and group creativity. ''Journal of Personality and Social Psychology'', ''99''(4), 622–637. <nowiki>https://doi.org/10.1037/a0019386</nowiki> Cacioppo, J. T., & Petty, R. E. (1982). The need for cognition. ''Journal of Personality and Social Psychology'', ''42''(1), 116–131. <nowiki>https://doi.org/10.1037/0022-3514.42.1.116</nowiki> De Dreu, C. K. W., Beersma, B., Stroebe, K., & Euwema, M. C. (2006). Motivated information processing, strategic choice, and the quality of negotiated agreement. ''Journal of Personality and Social Psychology'', ''90''(6), 927–943. <nowiki>https://doi.org/10.1037/0022-3514.90.6.927</nowiki> De Dreu, C. K. W., Nijstad, B. A., & van Knippenberg, D. (2008). Motivated information processing in group judgment and decision making. ''Personality and Social Psychology Review'', ''12''(1), 22–49. <nowiki>https://doi.org/10.1177/1088868307304092</nowiki> Kossowska, M., Dragon, P., & Bukowski, M. (2015). When need for closure leads to positive attitudes towards a negatively stereotyped outgroup. ''Motivation and Emotion'', ''39'', 88–98. <nowiki>https://doi.org/10.1007/s11031-014-9414-5</nowiki> Kruglanski, A. W., & Webster, D. M. (1996). Motivated closing of the mind: “Seizing” and “freezing.” ''Psychological Review'', ''103''(2), 263–283. <nowiki>https://doi.org/10.1037/0033-295X.103.2.263</nowiki> Kruglanski, A. W., Webster, D. M., & Klem, A. (1993). Motivated resistance and openness to persuasion in the presence or absence of prior information. ''Journal of Personality and Social Psychology'', ''65''(5), 861–876. <nowiki>https://doi.org/10.1037/0022-3514.65.5.861</nowiki> Pica, G., Pierro, A., & Kruglanski, A. W. (2014). The role of need for cognitive closure in retrieval-induced forgetting and misinformation effects in eyewitness memory. ''Social Cognition'', ''32''(4), 337–359. <nowiki>https://doi.org/10.1521/soco.2014.32.4.337</nowiki> Roets, A., & Van Hiel, A. (2007). Separating ability from need: Clarifying the dimensional structure of the need for closure scale. ''Personality and Social Psychology Bulletin'', ''33''(2), 266–280. <nowiki>https://doi.org/10.1177/0146167206294744</nowiki> Roets, A., & Van Hiel, A. (2011). Item selection and validation of a brief, 15-item version of the Need for Closure Scale. ''Personality and Individual Differences'', ''50''(1), 90–94. <nowiki>https://doi.org/10.1016/j.paid.2010.09.004</nowiki> Scholten, L., van Knippenberg, D., Nijstad, B. A., & De Dreu, C. K. W. (2007). Motivated information processing and group decision-making: Effects of process accountability on information processing and decision quality. ''Journal of Experimental Social Psychology'', ''43''(4), 539–552. <nowiki>https://doi.org/10.1016/j.jesp.2006.05.010</nowiki> Webster, D. M., & Kruglanski, A. W. (1994). Individual differences in need for cognitive closure. ''Journal of Personality and Social Psychology'', ''67''(6), 1049–1062. <nowiki>https://doi.org/10.1037/0022-3514.67.6.1049</nowiki> Webster, D. M., Kruglanski, A. W., & Pattison, D. A. (1997). Motivated language use in intergroup contexts: Need-for-closure effects on the linguistic intergroup bias. ''Journal of Personality and Social Psychology'', ''72''(5), 1122–1131. <nowiki>https://doi.org/10.1037/0022-3514.72.5.1122</nowiki> }} == External links == * [https://dictionary.apa.org/need-for-closure Need for closure] (APA Dictionary of Psychology) * [https://sjdm.org/dmidi/Need_for_%28Cognitive%29_Closure_Scale.html Need for (Cognitive) Closure Scale] (Decision Making Individual Differences Inventory) * [https://www.apa.org/topics/critical-thinking Critical thinking] (American Psychological Association) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Decision-making]] [[Category:Motivation and emotion/Book/Epistemic motivation]] qnrywcjz2l1pvs43jscenuh3x53qi6e 2834484 2834483 2026-09-25T15:25:46Z Ayat Al-kabai 3105570 /* Acknowledgements */ 2834484 wikitext text/x-wiki {{title|Epistemic motivation and the need for cognitive closure:<br>How does epistemic motivation and the need for cognitive closure influence our lives?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Necker cube.svg|thumb|200px|'''''Figure 1'''''. The Necker cube can be interpreted in more than one way. It illustrates how ambiguity can permit competing interpretations before cognitive closure is reached.]] ;Scenario Sofia receives two conflicting pieces of advice about an important career decision. She feels uncomfortable with the uncertainty and wants to decide immediately. However, she also wants to examine the evidence, consider different perspectives, and make an informed choice. Sofia’s situation demonstrates two psychological forces: epistemic motivation, which can encourage deeper information processing, and the need for cognitive closure, which can encourage people to reach a definite answer and escape uncertainty. {{RoundBoxBottom}} * Epistemic motivation concerns a person’s willingness to develop a thorough and accurate understanding of a situation through information search and processing (De Dreu et al., 2008). * Need for cognitive closure is the desire to obtain a definite answer rather than remain confused or uncertain (Kruglanski & Webster, 1996). * Both concepts influence how people form judgements, make decisions, communicate with others and respond to uncertainty. * Neither is always beneficial or harmful; the outcome depends on the person, available information and situational demands. * Figure 1 demonstrates how the same ambiguous information may permit more than one interpretation before a person reaches closure. Uncertainty can be emotionally uncomfortable. People differ in how much effort they invest in understanding a problem and how quickly they want uncertainty to end. These motives shape which information is noticed, whether alternatives are compared and whether an initial judgement is revised. A fast answer may feel reassuring despite weak evidence, while prolonged searching may delay action. This chapter examines how to balance accuracy with the need to decide. {{RoundBoxTop|theme=3}} '''Focus questions''' * What is epistemic motivation? * What is the need for cognitive closure? * How are epistemic motivation and the need for cognitive closure connected? * How do they influence everyday decisions, learning and relationships? * When is cognitive closure helpful or harmful? {{RoundBoxBottom}} == Epistemic motivation == * [[w:Epistemic motivation|Epistemic motivation]] describes the willingness to invest effort in developing a complete and accurate understanding of the world (De Dreu et al., 2008). * Higher epistemic motivation encourages information search, deliberate reasoning and careful consideration of different perspectives. * Lower epistemic motivation is associated with shallower information processing and greater reliance on existing knowledge, familiar opinions or mental shortcuts. * Epistemic motivation can be influenced by personal characteristics and situational factors, including curiosity, accountability, fatigue, stress and time pressure. * Epistemic motivation should not be understood as intelligence. A capable person may still process information superficially when tired, distracted or under pressure. [[File:Duck-Rabbit illusion.jpg|thumb|220px|'''''Figure 2'''''. The duck–rabbit illusion shows how identical information can support competing interpretations.]] Epistemic motivation is best understood through motivated information processing. According to this perspective, judgement depends on both capacity and motivation: a person must be able to process information and also be willing to invest the necessary effort (De Dreu et al., 2008). This distinction explains why the same person may reason carefully about an important health decision but accept the first plausible answer to a minor question. It also separates epistemic motivation from [[w:Need for cognition|need for cognition]], a tendency to enjoy effortful thought, although the constructs overlap (Cacioppo & Petty, 1982). The quality of processing therefore depends on the person, the task and the surrounding conditions rather than on a fixed label such as “deep thinker”. Figure 2 illustrates why delaying closure can be useful when evidence permits more than one interpretation. === Depth of information processing === * Higher epistemic motivation encourages people to attend to, encode, retrieve and integrate relevant information more thoroughly (De Dreu et al., 2008). * Groups with stronger epistemic motivation may exchange more unique information and engage in more information-driven discussion. * Process accountability can increase epistemic motivation because people expect to explain how they reached a decision (De Dreu et al., 2006). * Deeper processing can improve decision quality, especially when a problem is complicated and important information is distributed among several people. === Influencing factors === * Time pressure and environmental noise can decrease the opportunity or motivation to consider multiple explanations (Kruglanski & Webster, 1996). * Fear of making an invalid judgement may increase information search and delay closure. * Fatigue can make sustained reasoning more difficult and increase the appeal of a quick, simple answer. * Personal relevance may increase information processing, although people may also process information selectively when an issue threatens an important belief or identity. Research also shows that accountability matters, but its timing is important. When people expect to explain the process by which they reached a judgement, they are more likely to examine information carefully and integrate competing evidence (De Dreu et al., 2006). By contrast, accountability for defending a preferred outcome can encourage selective reasoning. Thus, asking “How did you reach this conclusion?” may promote epistemic motivation more effectively than asking someone merely to justify a conclusion they have already announced. == Need for cognitive closure == * Need for cognitive closure refers to the motivation to reach a definite conclusion and avoid uncertainty or ambiguity (Kruglanski & Webster, 1996). * It can operate as a relatively stable individual difference and as a temporary state produced by circumstances such as fatigue, time pressure and stress. * Webster and Kruglanski (1994) identified several associated preferences, including predictability, order, decisiveness and reduced comfort with ambiguity. * The effects of need for closure are commonly explained through the urgency and permanence tendencies. The need for closure is grounded in lay epistemic theory, which treats knowledge formation as a motivated process rather than a purely rational one (Kruglanski & Webster, 1996). Closure can be valued because it reduces uncertainty, enables action and creates a stable understanding of events. It can also be avoided when a person fears that any available conclusion will be invalid. Consequently, the theory predicts not a universal preference for quick answers, but an interaction between the desirability of closure, the information available and the costs of making an error. === Urgency tendency === * The urgency tendency involves wanting to reach closure as quickly as possible (Kruglanski & Webster, 1996). * It may cause people to “seize” on information encountered early in the decision-making process. * Urgency can be helpful when immediate action is genuinely necessary, such as during an emergency. * However, it can also produce premature conclusions when the available information is incomplete, inaccurate or misleading. Experimental evidence supports this account. Kruglanski et al. (1993) found that conditions increasing the desire for closure made participants more resistant to persuasion after they had formed an opinion, but more receptive to early information when no prior position existed. This pattern demonstrates both tendencies: urgency increases reliance on an initial message, while permanence protects an existing judgement. Because persuasion experiments simplify real-world belief change, the findings identify a mechanism rather than determining how every individual will respond. === Permanence tendency === * The permanence tendency involves wanting to preserve an existing conclusion for as long as possible (Kruglanski & Webster, 1996). * It may cause people to “freeze” on their initial judgement and resist information that challenges it. * Permanence can create consistency, confidence and coordination after a decision has been made. * Excessive permanence may contribute to inflexible thinking, stereotyping and resistance to corrective evidence. === Individual differences === * The Need for Closure Scale was developed to measure individual differences related to predictability, order, decisiveness, ambiguity and closed-mindedness (Webster & Kruglanski, 1994). * A shorter revised measure has also demonstrated that urgency and permanence are important dimensions of the construct (Roets & Van Hiel, 2011). * A high score does not mean that someone is unintelligent or incapable of careful reasoning. * Need for closure can change across situations; therefore, a person may tolerate uncertainty in one context but urgently seek certainty in another. Measurement requires caution. The Need for Closure Scale assesses order, predictability, decisiveness, discomfort with ambiguity and closed-mindedness (Webster & Kruglanski, 1994). However, decisiveness may function differently from other facets, and ability to decide is not the same as motivation for closure (Roets & Van Hiel, 2007). Self-reports describe tendencies rather than directly observing information processing in a specific situation (Roets & Van Hiel, 2011). == Relationship between epistemic motivation and cognitive closure == * Need for cognitive closure is a form of epistemic motivation because it concerns how people acquire and maintain knowledge (Kruglanski & Webster, 1996). * Epistemic motivation is the broader concept, whereas need for closure specifically concerns motivation to end uncertainty by reaching a conclusion. * Strong motivation to understand a problem may promote extensive information search, while strong motivation for immediate closure may shorten that search. * High-quality judgement therefore depends on balancing sufficient investigation with the practical need to reach a decision. '''Table 1.''' ''Comparison of epistemic motivation and need for cognitive closure'' {| class="wikitable" ! Concept ! Main goal ! Possible benefit ! Possible limitation |- | Epistemic motivation | Develop an accurate and comprehensive understanding | Deeper information processing and consideration of alternatives | Decision-making may require more time and effort |- | Urgency tendency | Reach closure quickly | Supports timely action | May produce premature conclusions |- | Permanence tendency | Maintain an established conclusion | Supports consistency and commitment | May create resistance to corrective evidence |} * Table 1 shows that these motivational processes involve different goals and trade-offs. * Epistemic motivation can improve decision quality by promoting systematic information processing, particularly in group settings (De Dreu et al., 2008). * However, continuously seeking more information can also delay decisions when the available information is already sufficient. * Cognitive closure can support action and coordination, but early closure may prevent consideration of important alternatives. The relationship is therefore not a simple opposition between “good” epistemic motivation and “bad” closure. Need for closure is itself an epistemic motive, but it directs processing toward a definite and stable answer. High epistemic motivation can improve judgement when the evidence is reliable and the task rewards accuracy; it can also be used to defend an identity-consistent conclusion. Likewise, closure can be adaptive when delay is costly. The decisive issue is whether the timing and content of closure match the demands of the situation. {{RoundBoxTop|theme=2}} '''Key points''' * Epistemic motivation concerns how thoroughly information is processed. * Urgency encourages rapid “seizing” on an answer. * Permanence encourages “freezing” on an established answer. * Accuracy depends on matching processing to the decision. {{RoundBoxBottom}} {{RoundBoxTop|theme=3}} '''Case study''' Jordan sees a social-media post claiming that a familiar food causes a serious illness. Feeling anxious, Jordan immediately accepts the claim and shares it. Later, a friend encourages Jordan to locate the original research, examine reliable sources and consider alternative explanations. Jordan’s initial response may demonstrate the urgency tendency because uncertainty is ended by accepting the first available explanation. Greater epistemic motivation could encourage Jordan to examine the quality of the evidence before forming and sharing a conclusion. {{RoundBoxBottom}} <quiz display=simple> {Which response best demonstrates the urgency tendency? |type="()"} - Continuing to compare evidence without ever reaching a decision + Accepting the first plausible explanation to eliminate uncertainty - Changing an opinion after receiving reliable contradictory evidence - Asking several experts to explain their different perspectives || The urgency tendency involves attempting to reach cognitive closure as quickly as possible. } {Which response best demonstrates higher epistemic motivation? |type="()"} - Ignoring information that challenges an existing belief - Selecting the simplest answer without examining its source + Comparing evidence and considering alternative explanations - Repeating an opinion because it is familiar || Higher epistemic motivation generally involves more thorough information search and processing. } {The permanence tendency is most closely associated with: |type="()"} - Curiosity about new information + Maintaining an existing judgement - Avoiding all decisions - Forgetting a previous conclusion || The permanence tendency involves preserving closure after a judgement has been formed. } </quiz> == Influence on everyday life == * Epistemic motivation and need for closure influence behaviour across educational, interpersonal, organisational and social settings. * Their effects depend on the complexity of the problem, the quality of available information and whether rapid action is required. * Understanding these motivations may help people recognise when they are investigating a question carefully and when they are closing it prematurely. Evidence across settings supports these applications, but much of it is correlational, laboratory-based or based on university samples. Such research can identify mechanisms under controlled conditions, yet it may not fully capture high-stakes decisions made over longer periods or across cultures. Findings should therefore be applied as probabilistic tendencies rather than rules about individuals. === Learning and education === * Higher epistemic motivation may promote curiosity, critical thinking and deeper engagement with learning materials. * Students who evaluate evidence and compare alternative explanations are more likely to develop an integrated understanding than students who rely only on memorisation. * A strong need for closure may make unclear instructions, conflicting theories and open-ended assignments uncomfortable. * Clear structure can support learning, but excessive reliance on one definite answer may be problematic when a subject requires critical evaluation. Educators can combine structure with productive uncertainty. Clear criteria reduce unnecessary confusion, while comparing explanations keeps alternatives open for critical thought. Prompts asking students to identify disconfirming evidence may be more useful than simply telling them to “think harder”. Because excessive ambiguity can overload learners, support should be reduced gradually as knowledge develops. === Decision-making === * Epistemic motivation can improve decision quality by encouraging people to search for and integrate relevant information (De Dreu et al., 2006). * Under genuine time pressure, rapid closure may be adaptive because delaying action could have serious consequences. * When time is available, seizing on the first acceptable explanation may cause important evidence or alternative options to be overlooked. * Effective decision-making involves identifying how much information is required and establishing an appropriate point at which to decide. A useful decision rule is to match the search effort to the consequences of error. Reversible, low-cost choices may justify quick closure, whereas irreversible or safety-critical choices require stronger evidence and independent checking. This rule does not guarantee accuracy, but it makes the stopping point explicit. It also prevents anxiety alone from determining when information search ends. === Relationships and group behaviour === * First impressions can provide cognitive closure, but they may become inaccurate when people freeze on an early judgement. * Need for closure can influence intergroup language and strengthen biased descriptions of in-group and out-group behaviour (Webster et al., 1997). * Groups with higher epistemic motivation may exchange information more thoroughly and reach better-informed decisions (De Dreu et al., 2008). * Encouraging respectful disagreement can prevent premature consensus and allow group members to identify overlooked evidence. [[File:Emile Friant La Discussion politique.jpg|thumb|240px|'''''Figure 3'''''. Discussion can expose competing interpretations when members exchange and evaluate information rather than rush toward agreement.]] Group outcomes also depend on whether members possess different information. Scholten et al. (2007) found that process accountability increased systematic information processing and decision quality, particularly when group members began with different preferences. Bechtoldt et al. (2010) similarly showed that epistemic motivation supported group creativity when members pursued collective rather than purely personal goals. However, status differences, conformity and a shared preference for certainty can still suppress dissent. Figure 3 illustrates the social exchange through which alternatives can be tested. Leaders can request reasons before preferences, assign a devil’s advocate and delay an initial vote until evidence has been discussed. === Information and misinformation === * Online environments can expose people to large amounts of contradictory information, increasing confusion and the desire for simple answers. * A strong need for closure may increase reliance on information that quickly resolves uncertainty, even when its reliability has not been established. * Freezing on an initial interpretation can make later corrective evidence more difficult to accept. * Research suggests that need for closure can influence memory processes and vulnerability to misleading post-event information (Pica et al., 2014). Pica et al. (2014) found that need for closure influenced retrieval-induced forgetting and misinformation effects in eyewitness memory. Confidence and accuracy are not identical: closure may make a coherent account feel certain after misleading details are incorporated. This does not mean everyone high in need for closure accepts misinformation; source credibility, prior knowledge and verification opportunities still matter. Online, readers can pause before sharing, trace the original source and seek disconfirming evidence. == Balancing understanding and closure == * Neither endless information search nor immediate closure is appropriate in every situation. * The most effective approach depends on the consequences of error, the urgency of action and the availability of reliable evidence. * People can improve decisions by recognising their reactions to uncertainty and deliberately choosing whether additional investigation is necessary. === Potential benefits === * Epistemic motivation can support critical thinking, learning and informed decision-making. * Urgent closure can allow people to act efficiently during emergencies or under strict deadlines. * Permanent closure can create stability, commitment and coordination after an adequately informed decision. * Shared closure can also help groups organise action around an agreed understanding. === Potential limitations === * Excessive information search may create indecision or unnecessary delay. * Urgency can cause people to seize on incomplete or unreliable information. * Permanence can create inflexible beliefs and resistance to corrective evidence. * Need for closure may contribute to stereotyping when simplified group judgements replace individualised information (Kruglanski & Webster, 1996; Webster et al., 1997). These limitations show why context matters. A preference for closure may strengthen whichever interpretation is most accessible, not necessarily a negative one. For example, Kossowska et al. (2015) found that need for closure could be associated with more positive attitudes toward a negatively stereotyped outgroup when the ability to achieve closure was low. This qualification challenges the idea that need for closure automatically produces prejudice and illustrates why researchers must distinguish motivational direction from the specific belief that becomes fixed. === Practical strategies === * Pause before important decisions and identify whether time pressure is genuine or self-imposed. * Separate established facts, interpretations and assumptions. * Consider at least one alternative explanation before reaching a conclusion. * Seek information from reliable sources and perspectives that challenge the initial judgement. * Establish a reasonable decision deadline so that information search does not continue indefinitely. * Reconsider an existing conclusion when credible new evidence becomes available. [[File:Consensus Flowchart.svg|thumb|240px|'''''Figure 4'''''. A decision process can include opportunities to question, revise and consolidate a conclusion.]] '''Table 2.''' ''Matching information search to the decision'' {| class="wikitable" ! Decision condition ! Recommended response |- | Urgent and reversible | Decide using the best available evidence |- | Important and irreversible | Seek independent evidence and test alternatives |- | Credible new evidence appears | Reopen and revise the conclusion |} These strategies work best as “decision hygiene” rather than as personality correction. Before deciding, a person can state what evidence would change the conclusion, compare at least two plausible explanations, and obtain one independent source. During group decisions, members can record their initial views privately before discussion and evaluate the reasoning process rather than rewarding confidence alone. After deciding, a scheduled review point allows permanence to support action without making the conclusion immune to correction. Table 2 and Figure 4 show how closure can be treated as reviewable rather than irreversible. {{RoundBoxTop|theme=3}} '''Reflection exercise''' Think about an important decision you made recently. # What information did you examine? # Did you feel pressure to reach an answer quickly? # Did you consider an alternative explanation? # What evidence might have changed your decision? # Did your response reflect epistemic motivation, urgency, permanence or a combination of these processes? {{RoundBoxBottom}} == Conclusion == * Epistemic motivation influences the depth and thoroughness with which people search for, process and integrate information. * Need for cognitive closure motivates people to reach and preserve definite conclusions, particularly when uncertainty is uncomfortable. * The urgency tendency can lead people to seize on early information, while the permanence tendency can lead them to freeze on an established judgement. * These processes affect learning, decision-making, relationships, group behaviour and responses to online information. * Cognitive closure is not inherently harmful because it can support timely action, consistency and coordination. * The central challenge is to balance the desire for accurate understanding with the practical need to reach a conclusion. {{RoundBoxTop|theme=3}} '''Take-home message''' Good judgement requires knowing when to continue searching and when to decide. People can make better decisions by tolerating uncertainty long enough to examine reliable evidence while still establishing a reasonable point for reaching closure. {{RoundBoxBottom}} == Acknowledgements == (Generative AI) was used to support with coding and organising it == See also == * [[Motivation and emotion/Book/2023/Actively open-minded thinking|Actively open-minded thinking]] (Book chapter, 2023) * [[w:Epistemic motivation|Epistemic motivation]] (Wikipedia) == References == {{Hanging indent|1= Bechtoldt, M. N., De Dreu, C. K. W., Nijstad, B. A., & Choi, H.-S. (2010). Motivated information processing, social tuning, and group creativity. ''Journal of Personality and Social Psychology'', ''99''(4), 622–637. <nowiki>https://doi.org/10.1037/a0019386</nowiki> Cacioppo, J. T., & Petty, R. E. (1982). The need for cognition. ''Journal of Personality and Social Psychology'', ''42''(1), 116–131. <nowiki>https://doi.org/10.1037/0022-3514.42.1.116</nowiki> De Dreu, C. K. W., Beersma, B., Stroebe, K., & Euwema, M. C. (2006). Motivated information processing, strategic choice, and the quality of negotiated agreement. ''Journal of Personality and Social Psychology'', ''90''(6), 927–943. <nowiki>https://doi.org/10.1037/0022-3514.90.6.927</nowiki> De Dreu, C. K. W., Nijstad, B. A., & van Knippenberg, D. (2008). Motivated information processing in group judgment and decision making. ''Personality and Social Psychology Review'', ''12''(1), 22–49. <nowiki>https://doi.org/10.1177/1088868307304092</nowiki> Kossowska, M., Dragon, P., & Bukowski, M. (2015). When need for closure leads to positive attitudes towards a negatively stereotyped outgroup. ''Motivation and Emotion'', ''39'', 88–98. <nowiki>https://doi.org/10.1007/s11031-014-9414-5</nowiki> Kruglanski, A. W., & Webster, D. M. (1996). Motivated closing of the mind: “Seizing” and “freezing.” ''Psychological Review'', ''103''(2), 263–283. <nowiki>https://doi.org/10.1037/0033-295X.103.2.263</nowiki> Kruglanski, A. W., Webster, D. M., & Klem, A. (1993). Motivated resistance and openness to persuasion in the presence or absence of prior information. ''Journal of Personality and Social Psychology'', ''65''(5), 861–876. <nowiki>https://doi.org/10.1037/0022-3514.65.5.861</nowiki> Pica, G., Pierro, A., & Kruglanski, A. W. (2014). The role of need for cognitive closure in retrieval-induced forgetting and misinformation effects in eyewitness memory. ''Social Cognition'', ''32''(4), 337–359. <nowiki>https://doi.org/10.1521/soco.2014.32.4.337</nowiki> Roets, A., & Van Hiel, A. (2007). Separating ability from need: Clarifying the dimensional structure of the need for closure scale. ''Personality and Social Psychology Bulletin'', ''33''(2), 266–280. <nowiki>https://doi.org/10.1177/0146167206294744</nowiki> Roets, A., & Van Hiel, A. (2011). Item selection and validation of a brief, 15-item version of the Need for Closure Scale. ''Personality and Individual Differences'', ''50''(1), 90–94. <nowiki>https://doi.org/10.1016/j.paid.2010.09.004</nowiki> Scholten, L., van Knippenberg, D., Nijstad, B. A., & De Dreu, C. K. W. (2007). Motivated information processing and group decision-making: Effects of process accountability on information processing and decision quality. ''Journal of Experimental Social Psychology'', ''43''(4), 539–552. <nowiki>https://doi.org/10.1016/j.jesp.2006.05.010</nowiki> Webster, D. M., & Kruglanski, A. W. (1994). Individual differences in need for cognitive closure. ''Journal of Personality and Social Psychology'', ''67''(6), 1049–1062. <nowiki>https://doi.org/10.1037/0022-3514.67.6.1049</nowiki> Webster, D. M., Kruglanski, A. W., & Pattison, D. A. (1997). Motivated language use in intergroup contexts: Need-for-closure effects on the linguistic intergroup bias. ''Journal of Personality and Social Psychology'', ''72''(5), 1122–1131. <nowiki>https://doi.org/10.1037/0022-3514.72.5.1122</nowiki> }} == External links == * [https://dictionary.apa.org/need-for-closure Need for closure] (APA Dictionary of Psychology) * [https://sjdm.org/dmidi/Need_for_%28Cognitive%29_Closure_Scale.html Need for (Cognitive) Closure Scale] (Decision Making Individual Differences Inventory) * [https://www.apa.org/topics/critical-thinking Critical thinking] (American Psychological Association) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Decision-making]] [[Category:Motivation and emotion/Book/Epistemic motivation]] giizosaq9zbyfq2j9wwk5z9ptzcg8hh 0 331908 2834487 2832881 2026-09-25T19:40:36Z The Citer 3110681 2834487 wikitext text/x-wiki [[Image:GINKGOBAUM-2.jpg|thumb|300px|right|This is a ''ginkgo''.]] Ginkgos are a class/phylum/divison of gymnosperms defined by Sergei V. Meyen in 1984 to encompass Ginkgoales (which contains the living Ginkgo) alongside a number of extinct seed plant groups, which he considered to be closely related based on similarities of morphology of pollen, seeds, cuticles, short shoots and leaves. ==Information== Name Meaning: Ginkgo-like plant English Common Name: Ginkgo, maidenhair tree Major distinguishing characteristics: Seeds not protected by fruit Approximate number of species described: 1 living, about 50 extinct ==Evolutionary history== Ginkgophyta and [[/Cycadophyta/]] have a very ancient divergence dating to the Mississippian.<ref>{{Cite journal|last1=Stull|first1=Gregory W.|last2=Qu|first2=Xiao-Jian|last3=Parins-Fukuchi|first3=Caroline|last4=Yang|first4=Ying-Ying|last5=Yang|first5=Jun-Bo|last6=Yang|first6=Zhi-Yun|last7=Hu|first7=Yi|last8=Ma|first8=Hong|last9=Soltis|first9=Pamela S.|last10=Soltis|first10=Douglas E.|last11=Li|first11=De-Zhu|date=19 July 2021|title=Gene duplications and phylogenomic conflict underlie major pulses of phenotypic evolution in gymnosperms|url=https://www.nature.com/articles/s41477-021-00964-4|journal=Nature Plants|language=en|volume=7|issue=8|pages=1015–1025|doi=10.1038/s41477-021-00964-4|pmid=34282286 |bibcode=2021NatPl...7.1015S |s2cid=236141481 |issn=2055-0278|url-access=subscription}}</ref> The earliest representative of the group in the fossil record is probably ''Trichopitys'' from the Asselian (299-293 million years ago) of France. Alongside other, related forms such as ''Yimaia'' and ''Karkenia'', which have differently arranged reproductive structures and seeds associated with ''Ginkgo''-like leaves, the earliest representatives of ''Ginkgo'', represented by reproductive organs similar to the living species, first appear in the Middle Jurassic, <ref>{{Cite journal|last=Zhou|first=Zhi-Yan|date=March 2009|title=An overview of fossil Ginkgoales|url=https://linkinghub.elsevier.com/retrieve/pii/S1871174X0900002X|journal=Palaeoworld|language=en|volume=18|issue=1|pages=1–22|doi=10.1016/j.palwor.2009.01.001|url-access=subscription}}</ref><ref name=":0">{{Cite book|title=Paleobotany, Second Edition: The Biology and Evolution of Fossil Plants|last1=Taylor|first1=Thomas N.|last2=Taylor|first2=Edith L.|last3=Krings|first3=Michael|date=29 December 2008|publisher=Academic Press|isbn=9780123739728|edition=2nd|language=en}}</ref> The diversity of Ginkgoales declined during the Late Cretaceous and Cenozoic, coincident with the rise of [[Plant Divisions (Phyla)/Magnoliophyta|Magnoliophytes]], with all Ginkgophytes aside from ''Ginkgo'' being extinct by the end of the Cretaceous.<ref name=":1">{{Cite journal|url=http://accessscience.com/content/289700|title=Ginkgoales|last=Beck|first=Charles|date=2014|website=Access Science|doi=10.1036/1097-8542.289700 |access-date=13 April 2017|url-access=subscription}}</ref><ref name=":0" /> The only remaining Ginkgophyte was ''Ginkgo adiantoides'' – a polymorphic species.<ref name=":2">{{Cite web|url=http://www.ucmp.berkeley.edu/seedplants/ginkgoales/ginkgo.html|title=Introduction to the Ginkgoales|author=Jalalpour, Julie|author2=Malkin, Matt|author3=Poon, Peter|author4=Rehrmann, Liz|author5=Yu, Jerry|date=1997|website=www.ucmp.berkeley.edu|access-date=20 April 2017}}</ref> Modern ''Ginkgo'' trees are native to China.<ref name=":1" /> ==References== [[Wikipedia:Ginkgoopsida]] [[Category:Plants]] [[Category:Taxonomy]] [[Category:Botany]] [[Category:Biology]] 1yrwvygxiqiq9bho2gf6p6pak5uw95w 0 332222 2834488 2834424 2026-09-25T19:44:37Z The Citer 3110681 Better? 2834488 wikitext text/x-wiki [[File:Diversity of plants (Streptophyta) version 2.png|thumb|500x500px]] Streptophyta (/strɛpˈtɒfɪtə, ˈstrɛptoʊfaɪtə/), informally the streptophytes (/ˈstrɛptəfaɪts/, from the Greek strepto 'twisted', for the morphology of the sperm of some members), is a clade of plants. The composition of the clade varies considerably between authors, but the definition employed here includes land plants and all green algae except the Chlorophyta and the more basal Prasinodermophyta.<ref name=Jeffrey1967>{{cite journal | author = Jeffrey C | year = 1967 | title = The origin and differentiation of the Archegoniate land plants: A second contribution | journal = Kew Bull. | volume = 21 | issue = 2| pages = 335–349 | doi=10.2307/4108533| jstor = 4108533 | bibcode = 1967KewBu..21..335J }}</ref><ref>{{Cite journal|last1=Sánchez-Baracaldo|first1=Patricia|last2=Raven|first2=John A.|last3=Pisani|first3=Davide|last4=Knoll|first4=Andrew H.|date=2017-09-12|title=Early photosynthetic eukaryotes inhabited low-salinity habitats|journal=Proceedings of the National Academy of Sciences|volume=114|issue=37|pages=E7737–E7745|doi=10.1073/pnas.1620089114|url=https://research-information.bristol.ac.uk/ws/files/132985852/pnas.1620089114.sapp.pdf|pmid=28808007|pmc=5603991|bibcode=2017PNAS..114E7737S |doi-access=free}}</ref> ==Information== Name Meaning: Twisted plant English Common Name: Streptophytes Major distinguishing characteristics: Approximate number of species described: >350,000 ==Classification== The composition of Streptophyta and similar groups (Streptophytina, [[Plant_Divisions_(Phyla)/Charophyta|Charophyta]]) varies in each classification.<ref>{{Cite web |title=Die Schwestergruppe der Landpflanzen |trans-title=The sister group of land plants |url=https://www.protisten.de/german/docs/Phylogeny_in_Streptophyta.pdf |access-date=7 November 2023 |website=www.protisten.de |language=de}}</ref>{{citation needed|reason=cited source is in German. An English-language source is required|date=September 2026}} Some authors include only the Charales and Embryophyta (e.g., Streptophyta,<ref name=Jeffrey1967/><ref name=Adletal2012>{{cite journal |author=Adl, S.M.; Simpson, A.G.B.; Lane, C.E.; Lukeš, J.; Bass, D.; Bowser, S.S.; Brown, M.W.; Burki, F.; Dunthorn, M mentioned as source without citation.; Hampl, V.; Heiss, A.; Hoppenrath, M.; Lara, E.; le Gall, L.; Lynn, D.H.; McManus, H.; Mitchell, E.A.D.; Mozley-Stanridge, S.E.; Parfrey, L.W.; Pawlowski, J.; Rueckert, S.; Shadwick, L.; Schoch, C.L.; Smirnov, A.; Spiegel, F.W. |date=2012 |title=The revised classification of Eukaryotes |journal=Journal of Eukaryotic Microbiology |volume=59 |issue=5 |pages=429–514 |doi=10.1111/j.1550-7408.2012.00644.x| pmc=3483872|pmid=23020233 }}</ref> Streptophytina<ref name="Lewis&McCourt-2004"/>); others include more groups (e.g., Charophyta,<ref name="Lewis&McCourt-2004"/><!-- Karol et al. 2009--><ref name=Adletal2012/> Streptophyta,<ref name=Bremer1985>{{cite journal |author=Bremer, K. |date=1985 |title=Summary of green plant phylogeny and classification |journal=Cladistics |volume=1 |issue=4 |pages=369–385 |doi=10.1111/j.1096-0031.1985.tb00434.x |pmid=34965683 }}</ref><!-- de Reviers 2002; --><ref name=Leliaert-2012>{{cite journal |last1=Leliaert |first1=Frederik |last2=Smith |first2=David R. |last3=Moreau |first3=Hervé |last4=Herron |first4=Matthew D. |last5=Verbruggen |first5=Heroen |last6=Delwiche |first6=Charles F. |last7=De Clerck |first7=Olivier |title=Phylogeny and Molecular Evolution of the Green Algae |date=2012 |journal=Critical Reviews in Plant Sciences |volume=31 |issue=1 |pages=1–46 |bibcode=2012CRvPS..31....1L |doi=10.1080/07352689.2011.615705 |url=http://www.vliz.be/imisdocs/publications/248853.pdf }}</ref> Streptobionta<ref>{{cite book|last1=Kenrick|first1=Paul|last2=Crane|first2=Peter|title=The Origin and Early Diversification of Land Plants: A Cladistic Study|date=1997|publisher=[[Smithsonian Institution Press]]|location=Washington, D.C. |isbn=9781560987291}}</ref>); some authors use this broader definition, but exclude the Embryophyta (e.g., Charophyta,<ref name="Cavalier-Smith1993">{{cite book|author=Cavalier-Smith, T. |date=1993| chapter=The origin, losses and gains of chloroplasts. |title=Origins of plastids |pages=291–348 |publisher=Springer US}}</ref><ref name=Leliaert-2012/> Charophyceae{{citation needed|reason=Mattox & Stewart, 1984 mentioned as source without citation|date=April 2024}}, Streptophycophytes{{citation needed|reason=de Reviers, 2002 meantion as source without citation|date=April 2024}}). The clade Streptophyta includes both unicellular and multicellular organisms. Streptophyta contains the freshwater charophyte green algae and all land plants that reproduce sexually by conjugation. ''Mesostigma viride'', a unicellular green flagellate alga may be a basal Streptophyte.<ref name=Liang2020>{{cite journal |last1=Liang |first1=Z |last2=Geng |first2=Y |last3=Ji |first3=C |last4=Du |first4=H |last5=Wong |first5=CE |last6=Zhang |first6=Q |last7=Yu |first7=H |date=2020 |title=''Mesostigma viride'' genome and transcriptome provide insights into the origin and evolution of Streptophyta |journal=Advanced Science |volume=7 |issue=1 |doi=10.1002/advs.2019018501901850 |doi-broken-date=11 August 2026 |doi-access=free }}</ref><ref name=Nedelcu2006>{{cite journal |last1=Nedelcu |first1=AM |last2=Borza |first2=T |last3=Lee |first3=RW |date=2006 |title=A land plant–specific multigene family in the unicellular ''Mesostigma'' argues for its close relationship to Streptophyta |journal=Molecular Biology and Evolution |volume=23 |issue=5 |pages=1011–1015 |doi=10.1093/molbev/msj108 |pmid=16476689 }}</ref> ==Phylogeny== Below is a reconstruction of '''Streptophyta''' relationships, based on genomic data.<ref>{{Cite journal|author1=Linzhou Li|author2=Sibo Wang|author3=Hongli Wang|author4=Sunil Kumar Sahu|author5=Birger Marin|author6=Haoyuan Li|author7=Yan Xu|author8=Hongping Liang|author9=Zhen Li|author10=Shifeng Chen|author11=Tanja Reder|date=22 June 2020|title=The genome of Prasinoderma coloniale unveils the existence of a third phylum within green plants|journal=Nature Ecology & Evolution|volume=4|issue=9|pages=1220–1231|doi=10.1038/s41559-020-1221-7|pmc=7455551|pmid=32572216|doi-access=free|author22=Yves Van de Peer|author23=Michael Melkonian|author24=Huan Liu|author21=Xin Liu|author20=Xun Xu|author19=Gane Ka-Shu Wong|author17=Huanming Yang|author16=Hongli Du|author15=Barbara Melkonian|author14=Morten Petersen|author13=Sebastian Wittek|author12=Zehra Çebi|author18=Jian Wang|bibcode=2020NatEE...4.1220L }}</ref><ref>{{Cite journal|last1=Puttick|first1=Mark N.|last2=Morris|first2=Jennifer L.|last3=Williams|first3=Tom A.|last4=Cox|first4=Cymon J.|last5=Edwards|first5=Dianne|last6=Kenrick|first6=Paul|last7=Pressel|first7=Silvia|last8=Wellman|first8=Charles H.|last9=Schneider|first9=Harald|date=2018|title=The Interrelationships of Land Plants and the Nature of the Ancestral Embryophyte|journal=Current Biology|volume=28|issue=5|pages=733–745.e2|doi=10.1016/j.cub.2018.01.063|pmid=29456145|doi-access=free|bibcode=2018CBio...28E.733P |hdl=1983/ad32d4da-6cb3-4ed6-add2-2415f81b46da|hdl-access=free}}</ref><ref>{{Cite journal|last1=Sánchez-Baracaldo|first1=Patricia|last2=Raven|first2=John A.|last3=Pisani|first3=Davide|last4=Knoll|first4=Andrew H.|date=2017-09-12|title=Early photosynthetic eukaryotes inhabited low-salinity habitats|journal=Proceedings of the National Academy of Sciences|volume=114|issue=37|pages=E7737–E7745|doi=10.1073/pnas.1620089114|url=https://research-information.bristol.ac.uk/ws/files/132985852/pnas.1620089114.sapp.pdf|pmid=28808007|pmc=5603991|bibcode=2017PNAS..114E7737S |doi-access=free}}</ref> (Warning, this phylogenetic picture needs to be improved (See talk).) {{clade |1=Mesostigmatophyceae [[File:Mesostigma viride 534857918.jpg|60px]]` |2={{clade |1=Chlorokybophyceae [[File:Chlorokybus atmophyticus.jpg|60px]] |2={{clade |1=''Streptofilum'' [[File:Streptofilum capillatum.pdf|60px]] |2={{clade |1=Klebsormidiophyceae [[File:Klebsormidium bilatum Belgium (14759117646).jpg|60px]] |label2=Phragmoplastophyta |2={{clade |1=Charophyceae (Stoneworts & musk grasses) [[File:CharaFragilis.jpg|60px]] |2={{clade |1=Zygnematophyceae (desmids, water silk etc.) [[File:The freshwater alga Spirogyra.jpg|60px]] |2={{clade |1=Coleochaetophyceae [[File:Spirogyra-bgiu.jpg|60px]] |2=Embryophytes [[File:GINKGOBAUM-2.jpg|60px]] }} }} }} }} }} }}}} ==Diversity== There are many species of Streptophytes. These are just the phyla: ===Anthocerotophytes=== [[File:Dendroceros.jpg|thumb|200x200px]] Main article: [[Plant Divisions (Phyla)/Anthocerotophyta]]<br> Name Meaning: Anthoceros-like plant English Common Name: Hornworts Major distinguishing characteristics: Horn-shaped sporophytes, no vascular system Approximate number of species described: 100-300 Classes: Anthocerotopsida, Leiosporocerotopsida ===Bryophytes=== [[File:Tionesta-ac-moss2.jpg|thumb|200x200px]] Main article: [[Plant Divisions (Phyla)/Bryophyta]]<br> Name Meaning: Bryum-like plant, moss plant English Common Name: Moss Major distinguishing characteristics: Persistent branched sporophytes, no vascular system Approximate number of species described: 12,000 Classes: Andreaeobryopsida, Andreaeopsida, Bryopsida, Oedipodiopsida, Sphagnopsida, Takakiopsida, Tetraphidopsida ==References== hm0cf3bxn8tl5lvtp0dm3onuct8qidm 2834489 2834488 2026-09-25T19:45:44Z The Citer 3110681 /* Phylogeny */ 2834489 wikitext text/x-wiki [[File:Diversity of plants (Streptophyta) version 2.png|thumb|500x500px]] Streptophyta (/strɛpˈtɒfɪtə, ˈstrɛptoʊfaɪtə/), informally the streptophytes (/ˈstrɛptəfaɪts/, from the Greek strepto 'twisted', for the morphology of the sperm of some members), is a clade of plants. The composition of the clade varies considerably between authors, but the definition employed here includes land plants and all green algae except the Chlorophyta and the more basal Prasinodermophyta.<ref name=Jeffrey1967>{{cite journal | author = Jeffrey C | year = 1967 | title = The origin and differentiation of the Archegoniate land plants: A second contribution | journal = Kew Bull. | volume = 21 | issue = 2| pages = 335–349 | doi=10.2307/4108533| jstor = 4108533 | bibcode = 1967KewBu..21..335J }}</ref><ref>{{Cite journal|last1=Sánchez-Baracaldo|first1=Patricia|last2=Raven|first2=John A.|last3=Pisani|first3=Davide|last4=Knoll|first4=Andrew H.|date=2017-09-12|title=Early photosynthetic eukaryotes inhabited low-salinity habitats|journal=Proceedings of the National Academy of Sciences|volume=114|issue=37|pages=E7737–E7745|doi=10.1073/pnas.1620089114|url=https://research-information.bristol.ac.uk/ws/files/132985852/pnas.1620089114.sapp.pdf|pmid=28808007|pmc=5603991|bibcode=2017PNAS..114E7737S |doi-access=free}}</ref> ==Information== Name Meaning: Twisted plant English Common Name: Streptophytes Major distinguishing characteristics: Approximate number of species described: >350,000 ==Classification== The composition of Streptophyta and similar groups (Streptophytina, [[Plant_Divisions_(Phyla)/Charophyta|Charophyta]]) varies in each classification.<ref>{{Cite web |title=Die Schwestergruppe der Landpflanzen |trans-title=The sister group of land plants |url=https://www.protisten.de/german/docs/Phylogeny_in_Streptophyta.pdf |access-date=7 November 2023 |website=www.protisten.de |language=de}}</ref>{{citation needed|reason=cited source is in German. An English-language source is required|date=September 2026}} Some authors include only the Charales and Embryophyta (e.g., Streptophyta,<ref name=Jeffrey1967/><ref name=Adletal2012>{{cite journal |author=Adl, S.M.; Simpson, A.G.B.; Lane, C.E.; Lukeš, J.; Bass, D.; Bowser, S.S.; Brown, M.W.; Burki, F.; Dunthorn, M mentioned as source without citation.; Hampl, V.; Heiss, A.; Hoppenrath, M.; Lara, E.; le Gall, L.; Lynn, D.H.; McManus, H.; Mitchell, E.A.D.; Mozley-Stanridge, S.E.; Parfrey, L.W.; Pawlowski, J.; Rueckert, S.; Shadwick, L.; Schoch, C.L.; Smirnov, A.; Spiegel, F.W. |date=2012 |title=The revised classification of Eukaryotes |journal=Journal of Eukaryotic Microbiology |volume=59 |issue=5 |pages=429–514 |doi=10.1111/j.1550-7408.2012.00644.x| pmc=3483872|pmid=23020233 }}</ref> Streptophytina<ref name="Lewis&McCourt-2004"/>); others include more groups (e.g., Charophyta,<ref name="Lewis&McCourt-2004"/><!-- Karol et al. 2009--><ref name=Adletal2012/> Streptophyta,<ref name=Bremer1985>{{cite journal |author=Bremer, K. |date=1985 |title=Summary of green plant phylogeny and classification |journal=Cladistics |volume=1 |issue=4 |pages=369–385 |doi=10.1111/j.1096-0031.1985.tb00434.x |pmid=34965683 }}</ref><!-- de Reviers 2002; --><ref name=Leliaert-2012>{{cite journal |last1=Leliaert |first1=Frederik |last2=Smith |first2=David R. |last3=Moreau |first3=Hervé |last4=Herron |first4=Matthew D. |last5=Verbruggen |first5=Heroen |last6=Delwiche |first6=Charles F. |last7=De Clerck |first7=Olivier |title=Phylogeny and Molecular Evolution of the Green Algae |date=2012 |journal=Critical Reviews in Plant Sciences |volume=31 |issue=1 |pages=1–46 |bibcode=2012CRvPS..31....1L |doi=10.1080/07352689.2011.615705 |url=http://www.vliz.be/imisdocs/publications/248853.pdf }}</ref> Streptobionta<ref>{{cite book|last1=Kenrick|first1=Paul|last2=Crane|first2=Peter|title=The Origin and Early Diversification of Land Plants: A Cladistic Study|date=1997|publisher=[[Smithsonian Institution Press]]|location=Washington, D.C. |isbn=9781560987291}}</ref>); some authors use this broader definition, but exclude the Embryophyta (e.g., Charophyta,<ref name="Cavalier-Smith1993">{{cite book|author=Cavalier-Smith, T. |date=1993| chapter=The origin, losses and gains of chloroplasts. |title=Origins of plastids |pages=291–348 |publisher=Springer US}}</ref><ref name=Leliaert-2012/> Charophyceae{{citation needed|reason=Mattox & Stewart, 1984 mentioned as source without citation|date=April 2024}}, Streptophycophytes{{citation needed|reason=de Reviers, 2002 meantion as source without citation|date=April 2024}}). The clade Streptophyta includes both unicellular and multicellular organisms. Streptophyta contains the freshwater charophyte green algae and all land plants that reproduce sexually by conjugation. ''Mesostigma viride'', a unicellular green flagellate alga may be a basal Streptophyte.<ref name=Liang2020>{{cite journal |last1=Liang |first1=Z |last2=Geng |first2=Y |last3=Ji |first3=C |last4=Du |first4=H |last5=Wong |first5=CE |last6=Zhang |first6=Q |last7=Yu |first7=H |date=2020 |title=''Mesostigma viride'' genome and transcriptome provide insights into the origin and evolution of Streptophyta |journal=Advanced Science |volume=7 |issue=1 |doi=10.1002/advs.2019018501901850 |doi-broken-date=11 August 2026 |doi-access=free }}</ref><ref name=Nedelcu2006>{{cite journal |last1=Nedelcu |first1=AM |last2=Borza |first2=T |last3=Lee |first3=RW |date=2006 |title=A land plant–specific multigene family in the unicellular ''Mesostigma'' argues for its close relationship to Streptophyta |journal=Molecular Biology and Evolution |volume=23 |issue=5 |pages=1011–1015 |doi=10.1093/molbev/msj108 |pmid=16476689 }}</ref> ==Phylogeny== Below is a reconstruction of '''Streptophyta''' relationships, based on genomic data.<ref>{{Cite journal|author1=Linzhou Li|author2=Sibo Wang|author3=Hongli Wang|author4=Sunil Kumar Sahu|author5=Birger Marin|author6=Haoyuan Li|author7=Yan Xu|author8=Hongping Liang|author9=Zhen Li|author10=Shifeng Chen|author11=Tanja Reder|date=22 June 2020|title=The genome of Prasinoderma coloniale unveils the existence of a third phylum within green plants|journal=Nature Ecology & Evolution|volume=4|issue=9|pages=1220–1231|doi=10.1038/s41559-020-1221-7|pmc=7455551|pmid=32572216|doi-access=free|author22=Yves Van de Peer|author23=Michael Melkonian|author24=Huan Liu|author21=Xin Liu|author20=Xun Xu|author19=Gane Ka-Shu Wong|author17=Huanming Yang|author16=Hongli Du|author15=Barbara Melkonian|author14=Morten Petersen|author13=Sebastian Wittek|author12=Zehra Çebi|author18=Jian Wang|bibcode=2020NatEE...4.1220L }}</ref><ref>{{Cite journal|last1=Puttick|first1=Mark N.|last2=Morris|first2=Jennifer L.|last3=Williams|first3=Tom A.|last4=Cox|first4=Cymon J.|last5=Edwards|first5=Dianne|last6=Kenrick|first6=Paul|last7=Pressel|first7=Silvia|last8=Wellman|first8=Charles H.|last9=Schneider|first9=Harald|date=2018|title=The Interrelationships of Land Plants and the Nature of the Ancestral Embryophyte|journal=Current Biology|volume=28|issue=5|pages=733–745.e2|doi=10.1016/j.cub.2018.01.063|pmid=29456145|doi-access=free|bibcode=2018CBio...28E.733P |hdl=1983/ad32d4da-6cb3-4ed6-add2-2415f81b46da|hdl-access=free}}</ref><ref>{{Cite journal|last1=Sánchez-Baracaldo|first1=Patricia|last2=Raven|first2=John A.|last3=Pisani|first3=Davide|last4=Knoll|first4=Andrew H.|date=2017-09-12|title=Early photosynthetic eukaryotes inhabited low-salinity habitats|journal=Proceedings of the National Academy of Sciences|volume=114|issue=37|pages=E7737–E7745|doi=10.1073/pnas.1620089114|url=https://research-information.bristol.ac.uk/ws/files/132985852/pnas.1620089114.sapp.pdf|pmid=28808007|pmc=5603991|bibcode=2017PNAS..114E7737S |doi-access=free}}</ref> (Warning, this phylogenetic picture needs to be improved (See [[Talk:Streptophytes|talk]]).) {{clade |1=Mesostigmatophyceae [[File:Mesostigma viride 534857918.jpg|60px]]` |2={{clade |1=Chlorokybophyceae [[File:Chlorokybus atmophyticus.jpg|60px]] |2={{clade |1=''Streptofilum'' [[File:Streptofilum capillatum.pdf|60px]] |2={{clade |1=Klebsormidiophyceae [[File:Klebsormidium bilatum Belgium (14759117646).jpg|60px]] |label2=Phragmoplastophyta |2={{clade |1=Charophyceae (Stoneworts & musk grasses) [[File:CharaFragilis.jpg|60px]] |2={{clade |1=Zygnematophyceae (desmids, water silk etc.) [[File:The freshwater alga Spirogyra.jpg|60px]] |2={{clade |1=Coleochaetophyceae [[File:Spirogyra-bgiu.jpg|60px]] |2=Embryophytes [[File:GINKGOBAUM-2.jpg|60px]] }} }} }} }} }} }}}} ==Diversity== There are many species of Streptophytes. These are just the phyla: ===Anthocerotophytes=== [[File:Dendroceros.jpg|thumb|200x200px]] Main article: [[Plant Divisions (Phyla)/Anthocerotophyta]]<br> Name Meaning: Anthoceros-like plant English Common Name: Hornworts Major distinguishing characteristics: Horn-shaped sporophytes, no vascular system Approximate number of species described: 100-300 Classes: Anthocerotopsida, Leiosporocerotopsida ===Bryophytes=== [[File:Tionesta-ac-moss2.jpg|thumb|200x200px]] Main article: [[Plant Divisions (Phyla)/Bryophyta]]<br> Name Meaning: Bryum-like plant, moss plant English Common Name: Moss Major distinguishing characteristics: Persistent branched sporophytes, no vascular system Approximate number of species described: 12,000 Classes: Andreaeobryopsida, Andreaeopsida, Bryopsida, Oedipodiopsida, Sphagnopsida, Takakiopsida, Tetraphidopsida ==References== q6asrs51s04dwb9lby354b6qr647omb 2 332225 2834475 2834470 2026-09-25T12:07:53Z 202 Xup iartkab lakarg 3111500 /* The Lost Zodiac */ 2834475 wikitext text/x-wiki {{Infobox | title = The Lost Zodiac | image = | caption = | label1 = Author | data1 = Tahmid Arian Borno | label2 = Year | data2 = 2026 | label3 = Status | data3 = Proposed hypothesis; under development | label4 = Subject | data4 = Astrology / stellar symbolism }} == The Lost Zodiac == '''The Lost Zodiac''' is a proposed hypothesis developed by [[Tahmid Arian Borno]] in 2026. It is an experimental astrological framework based on selected stars and constellational figures, their associated date ranges, and a proposed method for converting conventional natal-chart positions into Lost Zodiac positions. <div style="clear: both; width: auto; margin: 1em 0;"> <!-- Research Project Box --> <div style="border-left: 10px solid #0066cc; background-color: #f0f8ff; padding: 0.5em 1em; margin-bottom: 0.5em; box-sizing: border-box; width: 100%;"> '''This is a research project at Wikiversity.''' </div> <!-- Hypothesis Warning Box --> <div style="border-left: 10px solid #f28500; background-color: #fef6e7; padding: 0.5em 1em; box-sizing: border-box; width: 100%;"> '''This article describes a personal hypothesis that is currently under development. It is not presented as an established astronomical or astrological system. The astronomical information underlying individual stars and constellations is supported by external sources; the organization of the periods and the natal-chart conversion methodology are proposed by the author.''' </div> </div> == Background == The Lost Zodiac proposes a set of zodiacal periods associated with stars and constellational figures. The system contains 31 periods, built from 22 distinct constellational figures, several of which recur across non-adjacent periods, distributed throughout the year. The repetition of certain constellational figures is intentional. In InteractiveStars.com's Lost Zodiac, the periods track the Sun's proximity to individual prominent stars rather than dividing the sky into continuous, side-by-side sectors like the traditional zodiac. Consequently, the same constellation may appear in multiple non-adjacent periods when different stars associated with it are involved. The system was created by astrologer Catherine Tennant and features 22 "lost" star signs based on major constellations located north and south of the main zodiac belt. Source: InteractiveStars.com, "The Lost Zodiac" (accessed September 23, 2026). Link to be added once this account is autoconfirmed. Period boundaries, associated constellational figures, and star assignments are sourced from InteractiveStars.com. The explanation of the recurring constellational figures is also based on the design of that source system. The proposed organization of the periods within this article and the natal-chart conversion methodology below are original to the author. Per-sign source links for each row of the table below will be added once this account reaches autoconfirmed status. == The Lost Zodiac Signs == {| class="wikitable sortable" ! Sign ! Period ! Associated star(s) ! Source |- | The Lyre of Orpheus | December 29 – January 13 | Vega | InteractiveStars.com |- | The Eagle | January 14 – January 28 | Altair | InteractiveStars.com |- | The Dolphin | January 29 – February 8 | Rotanev and Sualocin | InteractiveStars.com |- | The Swan | February 9 – February 28/29 | Sadir | InteractiveStars.com |- | The River of Night | March 1 – March 12 | Achernar | InteractiveStars.com |- | Pegasus | March 13 – April 1 | Markab, Scheat and Algenib | InteractiveStars.com |- | Andromeda | April 2 – April 9 | Alpheratz | InteractiveStars.com |- | The River of Night | April 10 – April 18 | Acamar | InteractiveStars.com |- | Andromeda | April 19 – May 8 | Mirach and Alamach | InteractiveStars.com |- | The River of Night | May 9 – May 15 | Rana and Zanrak | InteractiveStars.com |- | Perseus | May 16 – May 31 | Algol and Mirfak | InteractiveStars.com |- | Orion | June 1 – June 7 | Rigel | InteractiveStars.com |- | The Charioteer | June 8 – June 16 | Capella | InteractiveStars.com |- | Orion | June 17 – June 27 | Betelgeuse | InteractiveStars.com |- | The Dogs | June 28 – July 7 | Sirius | InteractiveStars.com |- | The Ship of the Argonauts | July 8 – July 17 | Canopus | InteractiveStars.com |- | The Dogs | July 18 – July 25 | Procyon | InteractiveStars.com |- | The Dragon | July 26 – August 7 | Gianfar | InteractiveStars.com |- | The Great Bear | August 8 – August 15 | Dubhe and Merak | InteractiveStars.com |- | The Sea Serpent | August 16 – August 23 | Alphard | InteractiveStars.com |- | The Great Bear | August 24 – September 10 | Phekda, Megrez, Alioth and Mizar | InteractiveStars.com |- | The Cup | September 11 – September 21 | Alkes | InteractiveStars.com |- | The Ship of the Argonauts | September 22 – September 28 | Markeb | InteractiveStars.com |- | The Raven | September 29 – October 11 | Minkar and Algorab | InteractiveStars.com |- | The Bear Keeper | October 12 – October 26 | Arcturus and Izar | InteractiveStars.com |- | The Crown of the North Wind | October 27 – November 10 | Alphecca | InteractiveStars.com |- | The Serpent | November 11 – November 19 | Unuk Elhaia | InteractiveStars.com |- | The Wise Centaur | November 20 – December 5 | Toliman (Alpha Centauri) | InteractiveStars.com |- | Ophiuchus | December 6 – December 16 | Han, Sabik and Ras Alhague | InteractiveStars.com |- | The Dragon | December 17 – December 23 | Grumium and Etanin | InteractiveStars.com |- | The Serpent | December 24 – December 28 | Alya | InteractiveStars.com |} == Natal-chart conversion methodology == The Lost Zodiac proposes a proportional conversion between a conventional zodiacal position and the corresponding Lost Zodiac period. A placement is first treated as a position within its conventional zodiac sign. That position is converted into a corresponding calendar date and time. The resulting date and time are then located within the relevant Lost Zodiac period. Each listed period includes the full span of every calendar date in its range. The starting date begins at 12:00 a.m., and the ending date concludes at 11:59 p.m. For example, a period ending on February 28 includes the entire day of February 28. In leap years, the Swan period ends at 11:59 p.m. on February 29. For a Lost Zodiac period, the beginning of the period is treated as 0°00′ and the end of the period as 29°59′. The beginning boundary is midnight at the start of the first listed date, while the ending boundary is 11:59 p.m. on the last listed date. The proposed formula is: <math> L = \frac{t-t_0}{t_1-t_0}\times29^\circ 59' </math> where: * <math>L</math> = resulting Lost Zodiac degree * <math>t</math> = the corresponding date and time of the natal placement * <math>t_0</math> = beginning of the Lost Zodiac period * <math>t_1</math> = end boundary of the Lost Zodiac period === Example === A tropical Sun position of Pisces 1°29′ corresponds to February 20, 2009 at approximately 6:25 AM in the example used by the author. The Swan period runs from February 9 through the last day of February, ending on February 28 in a common year or February 29 in a leap year. The position of February 20 at 6:25 AM is approximately 56.34% through the Swan period. Therefore: <math> 29^\circ 59'\times0.5634\approx16^\circ 53' </math> The resulting proposed Lost Zodiac position is therefore: '''Swan 16°53′''' == Reference natal chart == The following conventional natal-chart placements are used as the reference positions for the Lost Zodiac conversion. {| class="wikitable" ! Natal point ! Conventional natal position ! House |- | Sun | Pisces 1°29′ | 1st House |- | Ascendant | Aquarius 29°24′ | — |- | Moon | Capricorn 5°24′ | 11th House |- | Mercury | Aquarius 6°07′ | 12th House |- | Venus | Aries 11°30′ | 2nd House |- | Mars | Aquarius 11°55′ | 12th House |- | Jupiter | Aquarius 10°38′ | 12th House |- | Saturn | Virgo 19°41′ Rx | 7th House |- | Uranus | Pisces 21°25′ | 1st House |- | Neptune | Aquarius 24°13′ | 12th House |- | Pluto | Capricorn 2°47′ | 10th House |- | North Node | Aquarius 8°18′ Rx | 12th House |- | Lilith | Capricorn 5°16′ | 11th House |- | Chiron | Aquarius 21°52′ | 12th House |- | Fortune | Aries 25°29′ | 2nd House |- | Vertex | Virgo 17°15′ | 7th House |- | MC | Sagittarius 8°28′ | — |} == Example: author's Lost Zodiac natal chart == Using the conversion methodology described above, the author's proposed Lost Zodiac natal placements are: {| class="wikitable" ! Natal point ! Lost Zodiac placement |- | Sun | Swan 16°53′ |- | Ascendant | Swan 14°06′ |- | Moon | Serpent 20°23′ |- | Mercury | Eagle 24°13′ |- | Venus | Pegasus 29°14′ |- | Mars | Dolphin 7°57′ |- | Jupiter | Dolphin 4°27′ |- | Saturn | Cup 1°52′ |- | Uranus | River of Night 28°32′ |- | Neptune | Swan 6°19′ |- | Pluto | Serpent 4°42′ |- | North Node | Eagle 28°35′ |- | Lilith | Serpent 19°35′ |- | Chiron | Swan 2°48′ |- | Fortune | River of Night 18°16′ |- | Vertex | Great Bear 27°04′ |- | MC | Wise Centaur 19°37′ |} d0rkqk2rn5cnukfljrswlxq77j5ml91 2 332227 2834479 2026-09-25T13:50:48Z Chronicrookie 3111598 Created page with "{{Search}}<br> <br> '''{{UserStatistics}}<br> ===== ~~~~ ''ROOKIE'' =====" 2834479 wikitext text/x-wiki {{Search}}<br> <br> '''{{UserStatistics}}<br> ===== [[User:Chronicrookie|Chronicrookie]] ([[User talk:Chronicrookie|discuss]] • [[Special:Contributions/Chronicrookie|contribs]]) 13:50, 25 September 2026 (UTC) ''ROOKIE'' ===== n2r6kymb1bn1367udmbp9id4hkld50d 3 332228 2834480 2026-09-25T13:52:43Z Chronicrookie 3111598 Created page with "{{Date}} ~~~~" 2834480 wikitext text/x-wiki {{Date}} [[User:Chronicrookie|Chronicrookie]] ([[User talk:Chronicrookie|discuss]] • [[Special:Contributions/Chronicrookie|contribs]]) 13:52, 25 September 2026 (UTC) 5re0gbvdtc8inggmunlrfi0gyqkk0hb 0 332230 2834490 2026-09-25T20:01:11Z The Citer 3110681 I'll add classes later. 2834490 wikitext text/x-wiki [[File:Haeckel Siphoneae.jpg|thumb|300x300px|right|Diversity of chorophytes.]] '''Chlorophyta'''{{Sfn|Margulis|Chapman|2009|p=200}} or '''chlorophytes''' is a major division of green algae,\ and is sister taxon to the other major division [[Plant_Divisions_(Phyla)/Charophyta|Charophyta]], a paraphyletic group of predominantly freshwater green algae, which form the monophyletic clade: [[Streptophytes|Streptophyta]] after including all Embryophytes as well as the proposed basal clade Prasinodermophyta. Chlorophytes are eukaryotic organisms composed of cells with a variety of coverings or walls, and usually a single green chloroplast in each cell.{{Sfn|Adl|Bass|Lane|Lukeš|2019|p=36}} Most groups are unicellular. ==Information== Name Meaning: Yellow-green plant English Common Name: Chlorophytes Major distinguishing characteristics: mainly autotrophs with exceptions and have the same chlorophyll a and b pigments as "higher" plant divisions Approximate number of species described: 8,000 ==Evolutionary History== ''Proterocladus antiquus'' is believed to be one of the oldest examples of a multicellular chlorophyte, being 1000my old. It is currently classified as a member of order Cladophorales, class Ulvophyceae.{{Sfn|Tang|Pang|Yuan|Xiao|2020}} In 2023, a study calculated the molecular age of green algae as calibrated by this fossil. The study estimated the origin of Chlorophyta within the [[Wikipedia:Mesoproterozoic|Mesoproterozoic]] era, at around 2.04–1.23 billion years ago.{{Sfn|Yang|Ma|Wang|Tian|2023}} ==References== l76veeum11y36calxk696o2n09wog8i 3 332231 2834500 2026-09-26T02:28:00Z MathXplore 2888076 vandalism1 ([[m:User:ZbVl/VD|Vandoom]]) 2834500 wikitext text/x-wiki == 2026-09-26 == [[File:Information.svg|25px|alt=Information icon]] Hello, I’m letting you know that one or more of your recent contributions have been reverted because they did not appear constructive. If you would like to experiment, please use the [[Wikiversity:Sandbox|sandbox]] or ask for assistance at the [[Wikiversity:Colloquium|Colloquium]]. Thank you.<!-- Glow-vandalism1 @ 1790389676446.5s --><nowiki></nowiki> [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:28, 26 September 2026 (UTC) php2yt2yr57p4jx57nwi6qb48h31pr5 6 332232 2834528 2026-09-26T08:05:44Z Young1lim 21186 {{Information |Description=Block CLA 2B Single Level (20260924 - 20260923) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2834528 wikitext text/x-wiki == Summary == {{Information |Description=Block CLA 2B Single Level (20260924 - 20260923) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 7deem4qv68s73tiokzdrrps8k4uc0s3 6 332233 2834530 2026-09-26T08:06:33Z Young1lim 21186 {{Information |Description=Block CLA 2B Single Level (20260925 - 20260924) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2834530 wikitext text/x-wiki == Summary == {{Information |Description=Block CLA 2B Single Level (20260925 - 20260924) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} t8tqxd25sm8zod4b30q0fiml8loiity 6 332234 2834532 2026-09-26T08:07:32Z Young1lim 21186 {{Information |Description=Block CLA 2B Single Level (20260926 - 20260925) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2834532 wikitext text/x-wiki == Summary == {{Information |Description=Block CLA 2B Single Level (20260926 - 20260925) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} ikj1yq1cp6hndk923cwnb76aa2ilepm 6 332235 2834533 2026-09-26T08:08:13Z Young1lim 21186 {{Information |Description=Block CLA 2B Single Level (20260924 - 20260923) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2834533 wikitext text/x-wiki == Summary == {{Information |Description=Block CLA 2B Single Level (20260924 - 20260923) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 7deem4qv68s73tiokzdrrps8k4uc0s3 6 332236 2834535 2026-09-26T08:09:12Z Young1lim 21186 {{Information |Description=Block CLA 2B Single Level (20260925 - 20260924) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2834535 wikitext text/x-wiki == Summary == {{Information |Description=Block CLA 2B Single Level (20260925 - 20260924) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} t8tqxd25sm8zod4b30q0fiml8loiity 6 332237 2834538 2026-09-26T08:10:11Z Young1lim 21186 {{Information |Description=Block CLA 2B Single Level (20260926 - 20260925) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2834538 wikitext text/x-wiki == Summary == {{Information |Description=Block CLA 2B Single Level (20260926 - 20260925) |Source={{own|Young1lim}} |Date=2026-09-26 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} ikj1yq1cp6hndk923cwnb76aa2ilepm 3 332238 2834547 2026-09-26T10:28:53Z MathXplore 2888076 delete1 ([[m:User:ZbVl/VD|Vandoom]]) 2834547 wikitext text/x-wiki == 2026-09-26 == <div class="mw-content-ltr" dir="ltr" style="text-align: left" lang="en">[[File:Information.svg|25px|alt=Information icon]] Hello. Apologies for writing this in English, but I wanted to let you know that one or more of [[Special:Contributions/&#126;2026-51826-91|your recent contributions]] have been undone because you removed content without adequately explaining why. In the future, it would be helpful to others if you described your changes to <span style="white-space:nowrap">Wikiversity</span> with an accurate [[:m:en:Help:Edit summary|edit summary]]. If this was a mistake, don't worry; the removed content has been restored. If you would like to experiment, please use the sandbox. Thanks. </div><!-- Glow-delete1 @ 1790418527911.2s --><nowiki></nowiki> [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 10:28, 26 September 2026 (UTC) 6c5io94rz4isxi9nampa85s1o4i03ck