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transformation</span> </div> </a> <ul id="toc-Lorentz_transformation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Accelerated_observers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Accelerated_observers"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Accelerated observers</span> </div> </a> <ul id="toc-Accelerated_observers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" 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mw-list-item"><a href="https://cs.wikipedia.org/wiki/Relativnost_sou%C4%8Dasnosti" title="Relativnost současnosti – Czech" lang="cs" hreflang="cs" data-title="Relativnost současnosti" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Relativit%C3%A4t_der_Gleichzeitigkeit" title="Relativität der Gleichzeitigkeit – German" lang="de" hreflang="de" data-title="Relativität der Gleichzeitigkeit" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Relatividad_de_la_simultaneidad" title="Relatividad de la simultaneidad – Spanish" lang="es" hreflang="es" data-title="Relatividad de la simultaneidad" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D8%B3%D8%A8%DB%8C%D8%AA_%D9%87%D9%85%D8%B2%D9%85%D8%A7%D9%86%DB%8C" title="نسبیت همزمانی – Persian" lang="fa" hreflang="fa" data-title="نسبیت همزمانی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8F%99%EC%8B%9C%EC%84%B1%EC%9D%98_%EC%83%81%EB%8C%80%EC%84%B1" title="동시성의 상대성 – Korean" lang="ko" hreflang="ko" data-title="동시성의 상대성" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%AB%D5%A1%D5%AA%D5%A1%D5%B4%D5%A1%D5%B6%D5%A1%D5%AF%D5%B8%D6%82%D5%A9%D5%B5%D5%A1%D5%B6_%D5%B0%D5%A1%D6%80%D5%A1%D5%A2%D5%A5%D6%80%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Միաժամանակության հարաբերականություն – Armenian" lang="hy" hreflang="hy" data-title="Միաժամանակության հարաբերականություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Relativitas_simultanitas" title="Relativitas simultanitas – Indonesian" lang="id" hreflang="id" data-title="Relativitas simultanitas" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%99%D7%97%D7%A1%D7%99%D7%95%D7%AA_%D7%94%D7%A1%D7%99%D7%9E%D7%95%D7%9C%D7%98%D7%A0%D7%99%D7%95%D7%AA" title="יחסיות הסימולטניות – Hebrew" lang="he" hreflang="he" data-title="יחסיות הסימולטניות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Az_egyidej%C5%B1s%C3%A9g_relativit%C3%A1sa" title="Az egyidejűség relativitása – Hungarian" lang="hu" hreflang="hu" data-title="Az egyidejűség relativitása" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BB%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82_%D0%BD%D0%B0_%D0%B5%D0%B4%D0%BD%D0%BE%D0%B2%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BE%D1%81%D1%82%D0%B0" title="Релативност на едновременоста – Macedonian" lang="mk" hreflang="mk" data-title="Релативност на едновременоста" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/R%C3%B3wnoczesno%C5%9B%C4%87" title="Równoczesność – Polish" lang="pl" hreflang="pl" data-title="Równoczesność" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Relatividade_da_simultaneidade" title="Relatividade da simultaneidade – Portuguese" lang="pt" hreflang="pt" data-title="Relatividade da simultaneidade" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Relativitatea_simultaneit%C4%83%C8%9Bii" title="Relativitatea simultaneității – Romanian" lang="ro" hreflang="ro" data-title="Relativitatea simultaneității" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D0%BE%D0%B4%D0%BD%D0%BE%D0%B2%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Относительность одновременности – Russian" lang="ru" hreflang="ru" data-title="Относительность одновременности" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Relat%C3%ADvnos%C5%A5_s%C3%BA%C4%8Dasnosti" title="Relatívnosť súčasnosti – Slovak" lang="sk" hreflang="sk" data-title="Relatívnosť súčasnosti" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Relativnost_istovremenosti" title="Relativnost istovremenosti – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Relativnost istovremenosti" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a 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id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Concept that simultaneity depends on choice of reference frame</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Lead_too_short plainlinks metadata ambox ambox-content ambox-lead_too_short" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article's <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Length" title="Wikipedia:Manual of Style/Lead section">lead section</a> <b>may be too short to adequately <a href="/wiki/Wikipedia:Summary_style" title="Wikipedia:Summary style">summarize</a> the key points</b>.<span class="hide-when-compact"> Please consider expanding the lead to <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Provide_an_accessible_overview" title="Wikipedia:Manual of Style/Lead section">provide an accessible overview</a> of all important aspects of the article.</span> <span class="date-container"><i>(<span class="date">October 2022</span>)</i></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:RoundTripToVega.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/RoundTripToVega.gif/300px-RoundTripToVega.gif" decoding="async" width="300" height="116" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/c/cc/RoundTripToVega.gif 1.5x" data-file-width="425" data-file-height="165" /></a><figcaption>On spaceships, map-clocks may look unsynchronized.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Relativity_of_Simultaneity.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Relativity_of_Simultaneity.svg/220px-Relativity_of_Simultaneity.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Relativity_of_Simultaneity.svg/330px-Relativity_of_Simultaneity.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Relativity_of_Simultaneity.svg/440px-Relativity_of_Simultaneity.svg.png 2x" data-file-width="563" data-file-height="563" /></a><figcaption>Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Relativity_of_Simultaneity_Animation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Relativity_of_Simultaneity_Animation.gif/220px-Relativity_of_Simultaneity_Animation.gif" decoding="async" width="220" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Relativity_of_Simultaneity_Animation.gif/330px-Relativity_of_Simultaneity_Animation.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/7/78/Relativity_of_Simultaneity_Animation.gif 2x" data-file-width="400" data-file-height="430" /></a><figcaption>Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.</figcaption></figure> <p>In <a href="/wiki/Physics" title="Physics">physics</a>, the <b>relativity of simultaneity</b> is the concept that <i>distant <a href="https://en.wiktionary.org/wiki/simultaneity" class="extiw" title="wikt:simultaneity">simultaneity</a></i> – whether two spatially separated events occur at the same <a href="/wiki/Time_in_physics" title="Time in physics">time</a> – is not <a href="/wiki/Absolute_time_and_space" class="mw-redirect" title="Absolute time and space">absolute</a>, but depends on the <a href="/wiki/Observer%27s_reference_frame" class="mw-redirect" title="Observer's reference frame">observer's reference frame</a>. This possibility was raised by mathematician <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> in 1900, and thereafter became a central idea in the <a href="/wiki/Special_relativity" title="Special relativity">special theory of relativity</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=1" title="Edit section: Description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to the special theory of relativity introduced by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, it is impossible to say in an <i>absolute</i> sense that two distinct <a href="/wiki/Event_(relativity)" title="Event (relativity)">events</a> occur at the same time if those events are separated in space. If one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events (the only exception being when motion is exactly perpendicular to the line connecting the locations of both events). </p><p>For example, a car crash in London and another in New York that appear to happen at the same time to an observer on Earth will appear to have occurred at slightly different times to an observer on an airplane flying between London and New York. Furthermore, if the two events cannot be causally connected, depending on the state of motion, the crash in London may appear to occur first in a given frame, and the New York crash may appear to occur first in another. However, if the events can be causally connected, precedence order is preserved in all frames of reference.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/History_of_special_relativity" title="History of special relativity">History of special relativity</a>, <a href="/wiki/History_of_Lorentz_transformations" title="History of Lorentz transformations">History of Lorentz transformations</a>, and <a href="/wiki/Lorentz_ether_theory" title="Lorentz ether theory">Lorentz ether theory</a></div> <p>In 1892 and 1895, <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a> used a mathematical method called "local time" <i>t' = t – v x/c</i><sup>2</sup> for explaining the negative <a href="/wiki/Luminiferous_aether" title="Luminiferous aether">aether</a> drift experiments.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> However, Lorentz gave no physical explanation of this effect. This was done by <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> who already emphasized in 1898 the conventional nature of simultaneity and who argued that it is convenient to postulate the constancy of the speed of light in all directions. However, this paper did not contain any discussion of Lorentz's theory or the possible difference in defining simultaneity for observers in different states of motion.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> This was done in 1900, when Poincaré derived local time by assuming that the speed of light is invariant within the aether. Due to the "principle of relative motion", moving observers within the aether also assume that they are at rest and that the speed of light is constant in all directions (only to first order in <i>v/c</i>). Therefore, if they synchronize their clocks by using light signals, they will only consider the transit time for the signals, but not their motion in respect to the aether. So the moving clocks are not synchronous and do not indicate the "true" time. Poincaré calculated that this synchronization error corresponds to Lorentz's local time.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> In 1904, Poincaré emphasized the connection between the principle of relativity, "local time", and light speed invariance; however, the reasoning in that paper was presented in a qualitative and conjectural manner.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> used a similar method in 1905 to derive the time transformation for all orders in <i>v/c</i>, i.e., the complete Lorentz transformation. Poincaré obtained the full transformation earlier in 1905 but in the papers of that year he did not mention his synchronization procedure. This derivation was completely based on light speed invariance and the relativity principle, so Einstein noted that for the electrodynamics of moving bodies the aether is superfluous. Thus, the separation into "true" and "local" times of Lorentz and Poincaré vanishes – all times are equally valid and therefore the relativity of length and time is a natural consequence.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>In 1908, <a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Hermann Minkowski</a> introduced the concept of a <a href="/wiki/World_line" title="World line">world line</a> of a particle<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> in his model of the cosmos called <a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a>. In Minkowski's view, the naïve notion of <a href="/wiki/Velocity" title="Velocity">velocity</a> is replaced with <a href="/wiki/Rapidity" title="Rapidity">rapidity</a>, and the ordinary sense of simultaneity becomes dependent on <a href="/wiki/Hyperbolic_orthogonality" title="Hyperbolic orthogonality">hyperbolic orthogonality</a> of spatial directions to the worldline associated to the rapidity. Then every <a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">inertial frame of reference</a> has a rapidity and a <a href="/wiki/World_line#Simultaneous_hyperplane" title="World line">simultaneous hyperplane</a>. </p><p>In 1990, <a href="/wiki/Robert_Goldblatt" title="Robert Goldblatt">Robert Goldblatt</a> wrote <i>Orthogonality and Spacetime Geometry</i>, directly addressing the structure Minkowski had put in place for simultaneity.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In 2006, <a href="/wiki/Max_Jammer" title="Max Jammer">Max Jammer</a>, through <a href="/wiki/Project_MUSE" class="mw-redirect" title="Project MUSE">Project MUSE</a>, published <i>Concepts of Simultaneity: from antiquity to Einstein and beyond</i>. The book culminates in chapter 6, "The transition to the relativistic conception of simultaneity". Jammer indicates that <a href="/wiki/Ernst_Mach" title="Ernst Mach">Ernst Mach</a> demythologized the absolute time of Newtonian physics. </p><p>Naturally the mathematical notions preceded physical interpretation. For instance, <a href="/wiki/Conjugate_diameters" title="Conjugate diameters">conjugate diameters</a> of <a href="/wiki/Conjugate_hyperbola" title="Conjugate hyperbola">conjugate hyperbolas</a> are related as space and time. The <a href="/wiki/Principle_of_relativity" title="Principle of relativity">principle of relativity</a> can be expressed as the arbitrariness of which pair are taken to represent space and time in a plane.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Thought_experiments">Thought experiments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=3" title="Edit section: Thought experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Einstein%27s_thought_experiments" title="Einstein's thought experiments">Einstein's thought experiments</a></div> <div class="mw-heading mw-heading3"><h3 id="Einstein's_train"><span id="Einstein.27s_train"></span>Einstein's train</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=4" title="Edit section: Einstein's train"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Einstein_train_relativity_of_simultaneity.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Einstein_train_relativity_of_simultaneity.png/250px-Einstein_train_relativity_of_simultaneity.png" decoding="async" width="250" height="385" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Einstein_train_relativity_of_simultaneity.png/375px-Einstein_train_relativity_of_simultaneity.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Einstein_train_relativity_of_simultaneity.png/500px-Einstein_train_relativity_of_simultaneity.png 2x" data-file-width="2278" data-file-height="3509" /></a><figcaption>Einstein imagined a stationary observer who witnessed two lightning bolts simultaneously striking both ends of a moving train. He concluded that an observer standing on the train would measure the bolts to strike at different times.</figcaption></figure> <p>Einstein's version of the experiment<sup id="cite_ref-Einsteins_train_15-0" class="reference"><a href="#cite_note-Einsteins_train-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> presumed that one observer was sitting midway inside a speeding traincar and another was standing on a platform as the train moved past. As measured by the standing observer, the train is struck by two bolts of lightning simultaneously, but at different positions along the axis of train movement (back and front of the train car). In the inertial frame of the standing observer, there are three events which are spatially dislocated, but simultaneous: standing observer facing the moving observer (i.e., the center of the train), lightning striking the front of the train car, and lightning striking the back of the car. </p><p>Since the events are placed along the axis of train movement, their time coordinates become projected to different time coordinates in the moving train's inertial frame. Events which occurred at space coordinates in the direction of train movement happen <i>earlier</i> than events at coordinates opposite to the direction of train movement. In the moving train's inertial frame, this means that lightning will strike the front of the train car <i>before</i> the two observers align (face each other). </p> <div class="mw-heading mw-heading3"><h3 id="The_train-and-platform">The train-and-platform</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=5" title="Edit section: The train-and-platform"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Traincar_Relativity1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Traincar_Relativity1.svg/220px-Traincar_Relativity1.svg.png" decoding="async" width="220" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Traincar_Relativity1.svg/330px-Traincar_Relativity1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Traincar_Relativity1.svg/440px-Traincar_Relativity1.svg.png 2x" data-file-width="735" data-file-height="558" /></a><figcaption>The train-and-platform experiment from the reference frame of an observer on board the train</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Traincar_Relativity2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Traincar_Relativity2.svg/220px-Traincar_Relativity2.svg.png" decoding="async" width="220" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Traincar_Relativity2.svg/330px-Traincar_Relativity2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Traincar_Relativity2.svg/440px-Traincar_Relativity2.svg.png 2x" data-file-width="862" data-file-height="558" /></a><figcaption>Reference frame of an observer standing on the platform (length contraction not depicted)</figcaption></figure> <p>A popular picture for understanding this idea is provided by a thought experiment similar to those suggested by <a href="/wiki/Daniel_Frost_Comstock" title="Daniel Frost Comstock">Daniel Frost Comstock</a> in 1910<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and Einstein in 1917.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Einsteins_train_15-1" class="reference"><a href="#cite_note-Einsteins_train-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> It also consists of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past. </p><p>A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on board the train, the front and back of the traincar are at fixed distances from the light source and as such, according to this observer, the light will reach the front and back of the traincar at the same time. </p><p>For the observer standing on the platform, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the flash was given off, and the front of the traincar is moving away from it. As the speed of light is, according to the second <a href="/wiki/Postulates_of_special_relativity#Postulates_of_special_relativity" title="Postulates of special relativity">postulate of special relativity</a>, same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:TrainAndPlatformDiagram1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/TrainAndPlatformDiagram1.svg/250px-TrainAndPlatformDiagram1.svg.png" decoding="async" width="250" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/TrainAndPlatformDiagram1.svg/375px-TrainAndPlatformDiagram1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/TrainAndPlatformDiagram1.svg/500px-TrainAndPlatformDiagram1.svg.png 2x" data-file-width="598" data-file-height="401" /></a><figcaption>The spacetime diagram in the frame of the observer on the train</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:TrainAndPlatformDiagram2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/TrainAndPlatformDiagram2.svg/250px-TrainAndPlatformDiagram2.svg.png" decoding="async" width="250" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/TrainAndPlatformDiagram2.svg/375px-TrainAndPlatformDiagram2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/TrainAndPlatformDiagram2.svg/500px-TrainAndPlatformDiagram2.svg.png 2x" data-file-width="609" data-file-height="402" /></a><figcaption>The same diagram in the frame of an observer who sees the train moving to the right</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Spacetime_diagrams">Spacetime diagrams</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=6" title="Edit section: Spacetime diagrams"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It may be helpful to visualize this situation using <a href="/wiki/Spacetime_diagram" title="Spacetime diagram">spacetime diagrams</a>. For a given observer, the <i>t</i>-axis is defined to be a point traced out in time by the origin of the spatial coordinate <i>x</i>, and is drawn vertically. The <i>x</i>-axis is defined as the set of all points in space at the time <i>t</i> = 0, and is drawn horizontally. The statement that the speed of light is the same for all observers is represented by drawing a light ray as a 45° line, regardless of the speed of the source relative to the speed of the observer. </p><p>In the first diagram, the two ends of the train are drawn as grey lines. Because the ends of the train are stationary with respect to the observer on the train, these lines are just vertical lines, showing their motion through time but not space. The flash of light is shown as the 45° red lines. The points at which the two light flashes hit the ends of the train are at the same level in the diagram. This means that the events are simultaneous. </p><p>In the second diagram, the two ends of the train moving to the right, are shown by parallel lines. The flash of light is given off at a point exactly halfway between the two ends of the train, and again form two 45° lines, expressing the constancy of the speed of light. In this picture, however, the points at which the light flashes hit the ends of the train are <i>not</i> at the same level; they are <i>not</i> simultaneous. </p> <div class="mw-heading mw-heading2"><h2 id="Lorentz_transformation">Lorentz transformation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=7" title="Edit section: Lorentz transformation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></div> <p>The relativity of simultaneity can be demonstrated using the Lorentz transformation, which relates the coordinates used by one observer to coordinates used by another in uniform relative motion with respect to the first. </p><p>Assume that the first observer uses coordinates labeled <i>t</i>, <i>x</i>, <i>y</i>, and <i>z</i>, while the second observer uses coordinates labeled <i>t′</i>, <i>x′</i>, <i>y′</i>, and <i>z′</i>. Now suppose that the first observer sees the second observer moving in the <i>x</i>-direction at a velocity <i>v</i>. And suppose that the observers' coordinate axes are parallel and that they have the same origin. Then the Lorentz transformation expresses how the coordinates are related: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t'={\frac {t-{v\,x/c^{2}}}{\sqrt {1-v^{2}/c^{2}}}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>t</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mspace width="thinmathspace" /> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t'={\frac {t-{v\,x/c^{2}}}{\sqrt {1-v^{2}/c^{2}}}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/798061909b6ceb7f04b6d98e813bcb65380f5c6f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.225ex; height:7.176ex;" alt="{\displaystyle t'={\frac {t-{v\,x/c^{2}}}{\sqrt {1-v^{2}/c^{2}}}}\,,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x'={\frac {x-v\,t}{\sqrt {1-v^{2}/c^{2}}}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mi>v</mi> <mspace width="thinmathspace" /> <mi>t</mi> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x'={\frac {x-v\,t}{\sqrt {1-v^{2}/c^{2}}}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61e1640a844869189560d28f0ef887c03d014d0d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.715ex; height:6.509ex;" alt="{\displaystyle x'={\frac {x-v\,t}{\sqrt {1-v^{2}/c^{2}}}}\,,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y'=y\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>y</mi> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y'=y\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1aacab207d1fe8c407abd11907187abc61a8eeae" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.133ex; height:2.843ex;" alt="{\displaystyle y'=y\,,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z'=z\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>z</mi> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z'=z\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/311ca6193d0a8eaf4218bf4d96d2c80ac9f4a068" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.996ex; height:2.843ex;" alt="{\displaystyle z'=z\,,}"></span> where <i>c</i> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>. If two events happen at the same time in the frame of the first observer, they will have identical values of the <i>t</i>-coordinate. However, if they have different values of the <i>x</i>-coordinate (different positions in the <i>x</i>-direction), they will have different values of the <i>t'</i> coordinate, so they will happen at different times in that frame. The term that accounts for the failure of absolute simultaneity is the <i>vx</i>/<i>c</i><sup>2</sup>. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Simultaneity_Lines.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Simultaneity_Lines.svg/250px-Simultaneity_Lines.svg.png" decoding="async" width="250" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Simultaneity_Lines.svg/375px-Simultaneity_Lines.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Simultaneity_Lines.svg/500px-Simultaneity_Lines.svg.png 2x" data-file-width="602" data-file-height="406" /></a><figcaption>A spacetime diagram showing the set of points regarded as simultaneous by a stationary observer (horizontal dotted line) and the set of points regarded as simultaneous by an observer moving at v = 0.25c (dashed line)</figcaption></figure> <p>The equation <i>t′</i> = constant defines a "line of simultaneity" in the (<i>x′</i>, <i>t′</i>) coordinate system for the second (moving) observer, just as the equation <i>t</i> = constant defines the "line of simultaneity" for the first (stationary) observer in the (<i>x</i>, <i>t</i>) coordinate system. From the above equations for the Lorentz transform it can be seen that <i>t'</i> is constant if and only if <i>t</i> − <i>vx</i>/<i>c</i><sup>2</sup> = constant. Thus the set of points that make <i>t</i> constant are different from the set of points that makes <i>t' </i>constant. That is, the set of events which are regarded as simultaneous depends on the frame of reference used to make the comparison. </p><p>Graphically, this can be represented on a spacetime diagram by the fact that a plot of the set of points regarded as simultaneous generates a line which depends on the observer. In the spacetime diagram, the dashed line represents a set of points considered to be simultaneous with the origin by an observer moving with a velocity <i>v</i> of one-quarter of the speed of light. The dotted horizontal line represents the set of points regarded as simultaneous with the origin by a stationary observer. This diagram is drawn using the (<i>x</i>, <i>t</i>) coordinates of the stationary observer, and is scaled so that the speed of light is one, i.e., so that a ray of light would be represented by a line with a 45° angle from the <i>x</i> axis. From our previous analysis, given that <i>v</i> = 0.25 and <i>c</i> = 1, the equation of the dashed line of simultaneity is <i>t</i> − 0.25<i>x</i> = 0 and with <i>v</i> = 0, the equation of the dotted line of simultaneity is <i>t</i> = 0. </p><p>In general the second observer traces out a <a href="/wiki/Worldline" class="mw-redirect" title="Worldline">worldline</a> in the spacetime of the first observer described by <i>t</i> = <i>x</i>/<i>v</i>, and the set of simultaneous events for the second observer (at the origin) is described by the line <i>t</i> = <i>vx</i>. Note the <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">multiplicative inverse</a> relation of the <a href="/wiki/Slope" title="Slope">slopes</a> of the worldline and simultaneous events, in accord with the principle of <a href="/wiki/Hyperbolic_orthogonality" title="Hyperbolic orthogonality">hyperbolic orthogonality</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Accelerated_observers">Accelerated observers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=8" title="Edit section: Accelerated observers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:TwentyFiveZones.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/TwentyFiveZones.png/250px-TwentyFiveZones.png" decoding="async" width="250" height="257" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/85/TwentyFiveZones.png 1.5x" data-file-width="372" data-file-height="382" /></a><figcaption>Roundtrip radar-time isocontours</figcaption></figure> <p>The Lorentz-transform calculation above uses a definition of extended-simultaneity (i.e. of when and where events occur <i>at which you were not present</i>) that might be referred to as the co-moving or "tangent free-float-frame" definition. This definition is naturally extrapolated to events in gravitationally-curved spacetimes, and to accelerated observers, through use of a radar-time/distance definition that (unlike the tangent free-float-frame definition for accelerated frames) assigns a unique time and position to any event.<sup id="cite_ref-Dolby2001_18-0" class="reference"><a href="#cite_note-Dolby2001-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>The radar-time definition of extended-simultaneity further facilitates visualization of the way that acceleration curves spacetime for travelers in the absence of any gravitating objects. This is illustrated in the figure at right, which shows radar time/position isocontours for events in flat spacetime as experienced by a traveler (red trajectory) taking a constant <a href="/wiki/Proper_acceleration" title="Proper acceleration">proper-acceleration</a> roundtrip. One caveat of this approach is that the time and place of remote events are not fully defined until light from such an event is able to reach our traveler. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Andromeda_paradox" class="mw-redirect" title="Andromeda paradox">Andromeda paradox</a></li> <li><a href="/wiki/Causal_structure" title="Causal structure">Causal structure</a></li> <li><a href="/wiki/Einstein%27s_thought_experiments" title="Einstein's thought experiments">Einstein's thought experiments</a></li> <li><a href="/wiki/Ehrenfest%27s_paradox" class="mw-redirect" title="Ehrenfest's paradox">Ehrenfest's paradox</a></li> <li><a href="/wiki/Einstein_synchronisation" title="Einstein synchronisation">Einstein synchronisation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativity_of_simultaneity&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns 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a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMamone-Capria,_Marco2012" class="citation cs2">Mamone-Capria, Marco (2012), <a rel="nofollow" class="external text" href="https://link.springer.com/article/10.1007/s10701-012-9674-4">"Simultaneity as an invariant equivalence relation"</a>, <i><a href="/wiki/Foundations_of_Physics" title="Foundations of Physics">Foundations of Physics</a></i>, <b>42</b> (11): <span class="nowrap">1365–</span>1383, <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1202.6578">1202.6578</a></span>, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012FoPh...42.1365M">2012FoPh...42.1365M</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10701-012-9674-4">10.1007/s10701-012-9674-4</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:254513121">254513121</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Foundations+of+Physics&rft.atitle=Simultaneity+as+an+invariant+equivalence+relation&rft.volume=42&rft.issue=11&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1365-%3C%2Fspan%3E1383&rft.date=2012&rft_id=info%3Aarxiv%2F1202.6578&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A254513121%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs10701-012-9674-4&rft_id=info%3Abibcode%2F2012FoPh...42.1365M&rft.au=Mamone-Capria%2C+Marco&rft_id=https%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs10701-012-9674-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLorentz,_Hendrik_Antoon1895" class="citation cs2">Lorentz, Hendrik Antoon (1895), <span class="cs1-ws-icon" title="s:de:Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern"><a class="external text" href="https://en.wikisource.org/wiki/de:Versuch_einer_Theorie_der_electrischen_und_optischen_Erscheinungen_in_bewegten_K%C3%B6rpern"><i>Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern</i> </a></span>, Leiden: E.J. Brill</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Versuch+einer+Theorie+der+electrischen+und+optischen+Erscheinungen+in+bewegten+K%C3%B6rpern&rft.place=Leiden&rft.pub=E.J.+Brill&rft.date=1895&rft.au=Lorentz%2C+Hendrik+Antoon&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_Henri1898–1913" class="citation cs2">Poincaré, Henri (1898–1913), <span class="cs1-ws-icon" title="s:The Measure of Time"><a class="external text" href="https://en.wikisource.org/wiki/The_Measure_of_Time">"The Measure of Time" </a></span>, <i>The foundations of science</i>, New York: Science Press, pp. <span class="nowrap">222–</span>234</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Measure+of+Time&rft.btitle=The+foundations+of+science&rft.place=New+York&rft.pages=%3Cspan+class%3D%22nowrap%22%3E222-%3C%2Fspan%3E234&rft.pub=Science+Press&rft.date=1898%2F1913&rft.au=Poincar%C3%A9%2C+Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGalison,_Peter2003" class="citation cs2">Galison, Peter (2003), <i>Einstein's Clocks, Poincaré's Maps: Empires of Time</i>, New York: W.W. Norton, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-393-32604-7" title="Special:BookSources/0-393-32604-7"><bdi>0-393-32604-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Einstein%27s+Clocks%2C+Poincar%C3%A9%27s+Maps%3A+Empires+of+Time&rft.place=New+York&rft.pub=W.W.+Norton&rft.date=2003&rft.isbn=0-393-32604-7&rft.au=Galison%2C+Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_Henri1900" class="citation cs2">Poincaré, Henri (1900), <span class="cs1-ws-icon" title="s:fr:La théorie de Lorentz et le principe de réaction"><a class="external text" href="https://en.wikisource.org/wiki/fr:La_th%C3%A9orie_de_Lorentz_et_le_principe_de_r%C3%A9action">"La théorie de Lorentz et le principe de réaction" </a></span>, <i>Archives Néerlandaises des Sciences Exactes et Naturelles</i>, <b>5</b>: <span class="nowrap">252–</span>278</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archives+N%C3%A9erlandaises+des+Sciences+Exactes+et+Naturelles&rft.atitle=La+th%C3%A9orie+de+Lorentz+et+le+principe+de+r%C3%A9action&rft.volume=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E252-%3C%2Fspan%3E278&rft.date=1900&rft.au=Poincar%C3%A9%2C+Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span>. See also the <a rel="nofollow" class="external text" href="http://www.physicsinsights.org/poincare-1900.pdf">English translation</a>.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDarrigol,_Olivier2005" class="citation cs2">Darrigol, Olivier (2005), <a rel="nofollow" class="external text" href="http://www.bourbaphy.fr/darrigol2.pdf">"The Genesis of the theory of relativity"</a> <span class="cs1-format">(PDF)</span>, <i>Séminaire Poincaré</i>, <b>1</b>: <span class="nowrap">1–</span>22, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006eins.book....1D">2006eins.book....1D</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-7643-7436-5_1">10.1007/3-7643-7436-5_1</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-7643-7435-8" title="Special:BookSources/978-3-7643-7435-8"><bdi>978-3-7643-7435-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=S%C3%A9minaire+Poincar%C3%A9&rft.atitle=The+Genesis+of+the+theory+of+relativity&rft.volume=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E22&rft.date=2005&rft_id=info%3Adoi%2F10.1007%2F3-7643-7436-5_1&rft_id=info%3Abibcode%2F2006eins.book....1D&rft.isbn=978-3-7643-7435-8&rft.au=Darrigol%2C+Olivier&rft_id=http%3A%2F%2Fwww.bourbaphy.fr%2Fdarrigol2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_Henri1904–1906" class="citation cs2">Poincaré, Henri (1904–1906), <span class="cs1-ws-icon" title="s:The Principles of Mathematical Physics"><a class="external text" href="https://en.wikisource.org/wiki/The_Principles_of_Mathematical_Physics">"The Principles of Mathematical Physics" </a></span>, <i>Congress of arts and science, universal exposition, St. Louis, 1904</i>, vol. 1, Boston and New York: Houghton, Mifflin and Company, pp. <span class="nowrap">604–</span>622</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Principles+of+Mathematical+Physics&rft.btitle=Congress+of+arts+and+science%2C+universal+exposition%2C+St.+Louis%2C+1904&rft.place=Boston+and+New+York&rft.pages=%3Cspan+class%3D%22nowrap%22%3E604-%3C%2Fspan%3E622&rft.pub=Houghton%2C+Mifflin+and+Company&rft.date=1904%2F1906&rft.au=Poincar%C3%A9%2C+Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHolton,_Gerald1988" class="citation cs2">Holton, Gerald (1988), <i><a href="/wiki/Thematic_Origins_of_Scientific_Thought:_Kepler_to_Einstein" class="mw-redirect" title="Thematic Origins of Scientific Thought: Kepler to Einstein">Thematic Origins of Scientific Thought: Kepler to Einstein</a></i>, Harvard University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-674-87747-0" title="Special:BookSources/0-674-87747-0"><bdi>0-674-87747-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thematic+Origins+of+Scientific+Thought%3A+Kepler+to+Einstein&rft.pub=Harvard+University+Press&rft.date=1988&rft.isbn=0-674-87747-0&rft.au=Holton%2C+Gerald&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein,_Albert1905" class="citation cs2">Einstein, Albert (1905), <a rel="nofollow" class="external text" href="http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_891-921.pdf">"Zur Elektrodynamik bewegter Körper"</a> <span class="cs1-format">(PDF)</span>, <i>Annalen der Physik</i>, <b>322</b> (10): <span class="nowrap">891–</span>921, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1905AnP...322..891E">1905AnP...322..891E</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19053221004">10.1002/andp.19053221004</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Zur+Elektrodynamik+bewegter+K%C3%B6rper&rft.volume=322&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E891-%3C%2Fspan%3E921&rft.date=1905&rft_id=info%3Adoi%2F10.1002%2Fandp.19053221004&rft_id=info%3Abibcode%2F1905AnP...322..891E&rft.au=Einstein%2C+Albert&rft_id=http%3A%2F%2Fwww.physik.uni-augsburg.de%2Fannalen%2Fhistory%2Feinstein-papers%2F1905_17_891-921.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span>. See also: <a rel="nofollow" class="external text" href="http://www.fourmilab.ch/etexts/einstein/specrel/">English translation</a>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMiller,_Arthur_I.1981" class="citation cs2">Miller, Arthur I. (1981), <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/alberteinsteinss0000mill"><i>Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911)</i></a></span>, Reading: Addison–Wesley, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-04679-2" title="Special:BookSources/0-201-04679-2"><bdi>0-201-04679-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Albert+Einstein%27s+special+theory+of+relativity.+Emergence+%281905%29+and+early+interpretation+%281905%E2%80%931911%29&rft.place=Reading&rft.pub=Addison%E2%80%93Wesley&rft.date=1981&rft.isbn=0-201-04679-2&rft.au=Miller%2C+Arthur+I.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Falberteinsteinss0000mill&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPais,_Abraham1982" class="citation cs2">Pais, Abraham (1982), <i><a href="/wiki/Subtle_is_the_Lord:_The_Science_and_the_Life_of_Albert_Einstein" class="mw-redirect" title="Subtle is the Lord: The Science and the Life of Albert Einstein">Subtle is the Lord: The Science and the Life of Albert Einstein</a></i>, New York: Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-520438-7" title="Special:BookSources/0-19-520438-7"><bdi>0-19-520438-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Subtle+is+the+Lord%3A+The+Science+and+the+Life+of+Albert+Einstein&rft.place=New+York&rft.pub=Oxford+University+Press&rft.date=1982&rft.isbn=0-19-520438-7&rft.au=Pais%2C+Abraham&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinkowski,_Hermann1909" class="citation cs2">Minkowski, Hermann (1909), <span class="cs1-ws-icon" title="s:de:Raum und Zeit (Minkowski)"><a class="external text" href="https://en.wikisource.org/wiki/de:Raum_und_Zeit_(Minkowski)">"Raum und Zeit" </a></span>, <i>Physikalische Zeitschrift</i>, <b>10</b>: <span class="nowrap">75–</span>88</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physikalische+Zeitschrift&rft.atitle=Raum+und+Zeit&rft.volume=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E75-%3C%2Fspan%3E88&rft.date=1909&rft.au=Minkowski%2C+Hermann&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span> <ul><li>Various English translations on Wikisource: <a href="https://en.wikisource.org/wiki/Space_and_Time" class="extiw" title="s:Space and Time">Space and Time</a></li></ul> </span></li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">A.D. Taimanov (1989) "Review of <i>Orthogonality and Spacetime Geometry</i>", <a href="/wiki/Bulletin_of_the_American_Mathematical_Society" title="Bulletin of the American Mathematical Society">Bulletin of the American Mathematical Society</a> 21(1)</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhittaker,_E.T.1910" class="citation book cs1"><a href="/wiki/E._T._Whittaker" title="E. T. Whittaker">Whittaker, E.T.</a> (1910). <i><a href="/wiki/A_History_of_the_Theories_of_Aether_and_Electricity" title="A History of the Theories of Aether and Electricity">A History of the Theories of Aether and Electricity</a></i> (1 ed.). Dublin: Longman, Green and Co. p. <a rel="nofollow" class="external text" href="https://archive.org/details/historyoftheorie00whitrich/page/441">441</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+the+Theories+of+Aether+and+Electricity&rft.place=Dublin&rft.pages=441&rft.edition=1&rft.pub=Longman%2C+Green+and+Co.&rft.date=1910&rft.au=Whittaker%2C+E.T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-Einsteins_train-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-Einsteins_train_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Einsteins_train_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein2017" class="citation cs2">Einstein, Albert (2017), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DrA8DwAAQBAJ"><i>Relativity - The Special and General Theory</i></a>, Samaira Book Publishers, pp. <span class="nowrap">30–</span>33, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-81-935401-7-6" title="Special:BookSources/978-81-935401-7-6"><bdi>978-81-935401-7-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativity+-+The+Special+and+General+Theory&rft.pages=%3Cspan+class%3D%22nowrap%22%3E30-%3C%2Fspan%3E33&rft.pub=Samaira+Book+Publishers&rft.date=2017&rft.isbn=978-81-935401-7-6&rft.aulast=Einstein&rft.aufirst=Albert&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DDrA8DwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged October 2023">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DrA8DwAAQBAJ&pg=PT46">Chapter IX</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201012114104/https://books.google.com/books?id=DrA8DwAAQBAJ&pg=PT46">Archived</a> 2020-10-12 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">The thought experiment by Comstock described two platforms in relative motion. See: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFComstock,_D.F.1910" class="citation cs2">Comstock, D.F. (1910), <span class="cs1-ws-icon" title="s:The Principle of Relativity (Comstock)"><a class="external text" href="https://en.wikisource.org/wiki/The_Principle_of_Relativity_(Comstock)">"The principle of relativity" </a></span>, <i>Science</i>, <b>31</b> (803): <span class="nowrap">767–</span>772, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1910Sci....31..767C">1910Sci....31..767C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.31.803.767">10.1126/science.31.803.767</a>, <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17758464">17758464</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:33246058">33246058</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=The+principle+of+relativity&rft.volume=31&rft.issue=803&rft.pages=%3Cspan+class%3D%22nowrap%22%3E767-%3C%2Fspan%3E772&rft.date=1910&rft_id=info%3Adoi%2F10.1126%2Fscience.31.803.767&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A33246058%23id-name%3DS2CID&rft_id=info%3Apmid%2F17758464&rft_id=info%3Abibcode%2F1910Sci....31..767C&rft.au=Comstock%2C+D.F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span>.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Einstein's thought experiment used two light rays starting at both ends of the platform. See: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein_A.1917" class="citation cs2">Einstein A. (1917), <span class="cs1-ws-icon" title="s:Relativity: The Special and General Theory"><a class="external text" href="https://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory"><i>Relativity: The Special and General Theory</i> </a></span>, Springer</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativity%3A+The+Special+and+General+Theory&rft.pub=Springer&rft.date=1917&rft.au=Einstein+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> <li id="cite_note-Dolby2001-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dolby2001_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDolbyGull2001" class="citation journal cs1">Dolby, Carl E.; Gull, Stephen F. (December 2001). "On radar time and the twin "paradox"<span class="cs1-kern-right"></span>". <i>American Journal of Physics</i>. <b>69</b> (12): <span class="nowrap">1257–</span>1261. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0104077">gr-qc/0104077</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001AmJPh..69.1257D">2001AmJPh..69.1257D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1407254">10.1119/1.1407254</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119067219">119067219</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=On+radar+time+and+the+twin+%22paradox%22&rft.volume=69&rft.issue=12&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1257-%3C%2Fspan%3E1261&rft.date=2001-12&rft_id=info%3Aarxiv%2Fgr-qc%2F0104077&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119067219%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1119%2F1.1407254&rft_id=info%3Abibcode%2F2001AmJPh..69.1257D&rft.aulast=Dolby&rft.aufirst=Carl+E.&rft.au=Gull%2C+Stephen+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelativity+of+simultaneity" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a 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href="/wiki/Special_relativity" title="Special relativity">Special<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Principle_of_relativity" title="Principle of relativity">Principle of relativity</a> (<a href="/wiki/Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li> <li><a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a>)</li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/Doubly_special_relativity" title="Doubly special relativity">Doubly special relativity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Frame_of_reference" title="Frame of reference">Frame of reference</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a></li> <li><a href="/wiki/Hyperbolic_orthogonality" title="Hyperbolic orthogonality">Hyperbolic orthogonality</a></li> <li><a href="/wiki/Rapidity" title="Rapidity">Rapidity</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></li> <li><a href="/wiki/Proper_length" title="Proper length">Proper length</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Proper_acceleration" title="Proper acceleration">Proper acceleration</a></li> <li><a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li> <li><a href="/wiki/List_of_textbooks_on_relativity" title="List of textbooks on relativity">Textbooks</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence (E=mc<sup>2</sup>)</a></li> <li><a href="/wiki/Length_contraction" title="Length contraction">Length contraction</a></li> <li><a class="mw-selflink selflink">Relativity of simultaneity</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li> <li><a href="/wiki/Thomas_precession" title="Thomas precession">Thomas precession</a></li> <li><a href="/wiki/Ladder_paradox" title="Ladder paradox">Ladder paradox</a></li> <li><a href="/wiki/Twin_paradox" title="Twin paradox">Twin paradox</a></li> <li><a href="/wiki/Terrell_rotation" title="Terrell rotation">Terrell rotation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Light_cone" title="Light cone">Light cone</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Minkowski diagram</a></li> <li><a href="/wiki/Biquaternion" title="Biquaternion">Biquaternions</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/General_relativity" title="General relativity">General<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li> <li><a href="/wiki/Riemannian_geometry" title="Riemannian geometry">Riemannian geometry</a></li> <li><a href="/wiki/Penrose_diagram" title="Penrose diagram">Penrose diagram</a></li> <li><a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li> <li><a href="/wiki/Mach%27s_principle" title="Mach's principle">Mach's principle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM formalism</a></li> <li><a href="/wiki/BSSN_formalism" title="BSSN formalism">BSSN formalism</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian formalism</a></li> <li><a href="/wiki/Raychaudhuri_equation" title="Raychaudhuri equation">Raychaudhuri equation</a></li> <li><a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein equation</a></li> <li><a href="/wiki/Ernst_equation" title="Ernst equation">Ernst equation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_hole" title="Black hole">Black hole</a></li> <li><a href="/wiki/Event_horizon" title="Event horizon">Event horizon</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Singularity</a></li> <li><a href="/wiki/Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Two-body problem</a></li></ul> <ul><li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a>: <a href="/wiki/Gravitational-wave_astronomy" title="Gravitational-wave astronomy">astronomy</a></li> <li><a href="/wiki/Gravitational-wave_observatory" title="Gravitational-wave observatory">detectors</a> (<a href="/wiki/LIGO" title="LIGO">LIGO</a> and <a href="/wiki/LIGO_Scientific_Collaboration" title="LIGO Scientific Collaboration">collaboration</a></li> <li><a href="/wiki/Virgo_interferometer" title="Virgo interferometer">Virgo</a></li> <li><a href="/wiki/LISA_Pathfinder" title="LISA Pathfinder">LISA Pathfinder</a></li> <li><a href="/wiki/GEO600" title="GEO600">GEO</a>)</li> <li><a href="/wiki/Hulse%E2%80%93Taylor_binary" class="mw-redirect" title="Hulse–Taylor binary">Hulse–Taylor binary</a></li></ul> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Other tests</a>: <a href="/wiki/Apsidal_precession" title="Apsidal precession">precession</a> of Mercury</li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">lensing</a> (together with <a href="/wiki/Einstein_cross" class="mw-redirect" title="Einstein cross">Einstein cross</a> and <a href="/wiki/Einstein_rings" class="mw-redirect" title="Einstein rings">Einstein rings</a>)</li> <li><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">redshift</a></li> <li><a href="/wiki/Shapiro_time_delay" title="Shapiro time delay">Shapiro delay</a></li> <li><a href="/wiki/Frame-dragging" title="Frame-dragging">frame-dragging</a> / <a href="/wiki/Geodetic_effect" title="Geodetic effect">geodetic effect</a> (<a href="/wiki/Lense%E2%80%93Thirring_precession" title="Lense–Thirring precession">Lense–Thirring precession</a>)</li> <li><a href="/wiki/Pulsar_timing_array" title="Pulsar timing array">pulsar timing arrays</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Advanced<br />theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brans%E2%80%93Dicke_theory" title="Brans–Dicke theory">Brans–Dicke theory</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Cosmological: <a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Friedmann–Lemaître–Robertson–Walker</a> (<a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a>)</li> <li><a href="/wiki/Lema%C3%AEtre%E2%80%93Tolman_metric" title="Lemaître–Tolman metric">Lemaître–Tolman</a></li> <li><a href="/wiki/Kasner_metric" title="Kasner metric">Kasner</a></li> <li><a href="/wiki/BKL_singularity" title="BKL singularity">BKL singularity</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel</a></li> <li><a href="/wiki/Milne_model" title="Milne model">Milne</a></li></ul> <ul><li>Spherical: <a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="/wiki/Interior_Schwarzschild_metric" title="Interior Schwarzschild metric">interior</a></li> <li><a href="/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation" title="Tolman–Oppenheimer–Volkoff equation">Tolman–Oppenheimer–Volkoff equation</a>)</li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li></ul> <ul><li>Axisymmetric: <a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a> (<a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a>)</li> <li><a href="/wiki/Weyl%E2%88%92Lewis%E2%88%92Papapetrou_coordinates" class="mw-redirect" title="Weyl−Lewis−Papapetrou coordinates">Weyl−Lewis−Papapetrou</a></li> <li><a href="/wiki/Taub%E2%80%93NUT_space" title="Taub–NUT space">Taub–NUT</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a href="/wiki/Relativistic_disk" title="Relativistic disk">discs</a></li></ul> <ul><li>Others: <a href="/wiki/Pp-wave_spacetime" title="Pp-wave spacetime">pp-wave</a></li> <li><a href="/wiki/Ozsv%C3%A1th%E2%80%93Sch%C3%BCcking_metric" title="Ozsváth–Schücking metric">Ozsváth–Schücking</a></li> <li><a href="/wiki/Alcubierre_drive" title="Alcubierre drive">Alcubierre</a></li></ul> <ul><li>In computational physics: <a href="/wiki/Numerical_relativity" title="Numerical relativity">Numerical relativity</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Scientists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Karl_Schwarzschild" title="Karl Schwarzschild">Schwarzschild</a></li> <li><a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Eddington</a></li> <li><a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li> <li><a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li> <li><a href="/wiki/Yvonne_Choquet-Bruhat" title="Yvonne Choquet-Bruhat">Choquet-Bruhat</a></li> <li><a href="/wiki/Roy_Kerr" title="Roy Kerr">Kerr</a></li> <li><a href="/wiki/Yakov_Zeldovich" title="Yakov Zeldovich">Zel'dovich</a></li> <li><a href="/wiki/Igor_Dmitriyevich_Novikov" title="Igor Dmitriyevich Novikov">Novikov</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Robert_Geroch" title="Robert Geroch">Geroch</a></li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking</a></li> <li><a href="/wiki/Joseph_Hooton_Taylor_Jr." title="Joseph Hooton Taylor Jr.">Taylor</a></li> <li><a href="/wiki/Russell_Alan_Hulse" title="Russell Alan Hulse">Hulse</a></li> <li><a href="/wiki/Hermann_Bondi" title="Hermann Bondi">Bondi</a></li> <li><a href="/wiki/Charles_W._Misner" title="Charles W. Misner">Misner</a></li> <li><a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a></li> <li><a href="/wiki/Kip_Thorne" title="Kip Thorne">Thorne</a></li> <li><a href="/wiki/Rainer_Weiss" title="Rainer Weiss">Weiss</a></li> <li><a href="/wiki/List_of_contributors_to_general_relativity" title="List of contributors to general relativity"><i>others</i></a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Theory_of_relativity" title="Category:Theory of relativity">Category</a></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Relativity_of_simultaneity&oldid=1270655932">https://en.wikipedia.org/w/index.php?title=Relativity_of_simultaneity&oldid=1270655932</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Special_relativity" title="Category:Special relativity">Special relativity</a></li><li><a href="/wiki/Category:History_of_physics" title="Category:History of physics">History of physics</a></li><li><a href="/wiki/Category:Thought_experiments_in_physics" title="Category:Thought experiments in physics">Thought experiments in physics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:All_articles_with_dead_external_links" title="Category:All articles with dead external links">All articles with dead external links</a></li><li><a href="/wiki/Category:Articles_with_dead_external_links_from_October_2023" title="Category:Articles with dead external links from October 2023">Articles with dead external links from October 2023</a></li><li><a href="/wiki/Category:Articles_with_permanently_dead_external_links" title="Category:Articles with permanently dead external links">Articles with permanently dead external links</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Wikipedia_introduction_cleanup_from_October_2022" title="Category:Wikipedia introduction cleanup from October 2022">Wikipedia introduction cleanup from October 2022</a></li><li><a href="/wiki/Category:All_pages_needing_cleanup" title="Category:All pages needing cleanup">All pages needing cleanup</a></li><li><a href="/wiki/Category:Articles_covered_by_WikiProject_Wikify_from_October_2022" title="Category:Articles covered by WikiProject Wikify from October 2022">Articles covered by WikiProject Wikify from October 2022</a></li><li><a href="/wiki/Category:All_articles_covered_by_WikiProject_Wikify" title="Category:All articles covered by WikiProject Wikify">All articles covered by WikiProject Wikify</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 20 January 2025, at 16:00<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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