Special relativity | Definition & Equation

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class="drawer d-flex flex-column open"> <div class="left-rail-section-content"> <div class="topic-left-rail-header text-truncate bg-gray-50 position-relative text-right d-flex align-items-center"> <div class="tlr-title px-20 py-15 text-left"> <em class="material-icons text-gray-400 d-lg-none" data-icon="toc"></em> <a class="font-serif font-weight-bold text-black link-blue" href="https://www.britannica.com/science/special-relativity">special relativity</a> </div> <button aria-label="Close" class="js-sections-close-button btn-link btn-sm btn d-lg-none position-absolute top-0 p-10 right-0" > <em class="material-icons font-26" data-icon="close"></em> </button> </div> <div class="section-content pl-10 pr-20 pl-sm-50 pr-sm-60 pl-lg-5 pr-lg-10 pt-10 pt-lg-0 bg-gray-50 clear-catfish-ad"> <div class="toc mb-20"> <div class="font-serif font-14 font-weight-bold mx-15 mb-15 mt-20"> Table of Contents </div> <span class="toc-extra-link selected link-gray-900 mt-15"> Introduction </span> <a class="toc-extra-link link-gray-900" href="https://www.britannica.com/science/special-relativity/additional-info">References & Edit History</a> <a class="toc-extra-link link-gray-900" href="/facts/special-relativity">Quick Facts & Related Topics</a> </div> <div class="tlr-media-slider pb-10 mb-30"> <a class="section-header link-gray-900 font-serif font-14 font-weight-bold mb-10 mx-10" href="https://www.britannica.com/science/special-relativity/images-videos">Videos</a> <div class="slider js-slider position-relative d-inline-flex align-items-center mw-100 "> <div class="slider-container js-slider-container overflow-hidden d-flex overflow-hidden text-nowrap ml-15"> <a href="/video/Your-Daily-Equation-04-Relativity-of-Simultaneity/254968" data-href="/media/1/558565/254968" class="media-overlay-link d-inline-block mr-5"> <div class="position-relative --aspect-ratio: 16/9"> <img loading="lazy" 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They write new content and verify and edit content received from contributors.</div> </a> <div data-popper-arrow></div> </div> <span class="btn btn-link editor-link p-0 qa-byline-link gtm-byline font-12 byline-contributor text-decoration-underline"> The Editors of Encyclopaedia Britannica</span></div> <div class="last-updated font-12 font-serif"> <span class="text-gray-700"> Last Updated: <time datetime="2025-01-31T00:00:00CST" >Jan 31, 2025</time> •</span> <a class="byline-edit-history" href="https://www.britannica.com/science/special-relativity/additional-info#history" rel="nofollow">Article History</a> </div></div> </div> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button d-none d-sm-block js-sections-inline-button module-spacing btn d-lg-none"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <div class="d-flex d-sm-none flex-row"> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button js-sections-inline-button module-spacing"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <button class="ai-ask-button btn btn-sm border-2 btn-outline-red-400 border-red-400 module-spacing js-inline-ai-ask-button p-10 ml-5"> Ask the Chatbot </button> </div> <div class="js-qf-module qf-module px-40 px-sm-20 py-15 mx-auto module-spacing font-14 bg-gray-50 rounded"> <div class="facts-list mt-10"> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Key People: </dt> <dd><a href="/biography/Albert-Einstein" topicid="181349">Albert Einstein</a></dd> <dd><a href="/biography/Arthur-Eddington" topicid="178891">Arthur Eddington</a></dd> <dd><a href="/biography/Tomonaga-Shinichiro" topicid="599000">Tomonaga Shin’ichirō</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> </div> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Related Topics: </dt> <dd><a href="/science/relativity" topicid="496904">relativity</a></dd> <dd><a href="/science/quantum-field-theory" topicid="486221">quantum field theory</a></dd> <dd><a href="/science/E-mc2-equation" topicid="1666493">E = mc2</a></dd> <dd><a href="/science/Einsteins-mass-energy-relation" topicid="181422">Einstein’s mass-energy relation</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> </div> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>On the Web: </dt> <dd><a href="https://ocw.mit.edu/courses/8-022-physics-ii-electricity-and-magnetism-fall-2004/f8cd941a21a671e60cc66ba76c395896_relativity.pdf" target="_blank">Massachusetts Institute of Technology - Department of Mathematics - Special Relativity (PDF)</a> (Jan. 31, 2025)</dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> <div class="text-center"> <a class="btn btn-sm btn-link p-0" href="/facts/special-relativity"> See all related content </a> </div> </div> </div> </div><span class="marker before-article"></span><section data-level="1" id="ref1"><span class="marker PREMOD1 mod-inline"></span><p class="topic-paragraph"><strong><span id="ref1070926"></span>special relativity</strong>, part of the wide-ranging physical theory of <a href="https://www.britannica.com/science/relativity" class="md-crosslink " data-show-preview="true">relativity</a> formed by the German-born physicist <a href="https://www.britannica.com/biography/Albert-Einstein" class="md-crosslink " data-show-preview="true">Albert Einstein</a>. It was <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="conceived" href="https://www.britannica.com/dictionary/conceived" data-type="EB">conceived</a> by Einstein in 1905. Along with <a href="https://www.britannica.com/science/quantum-mechanics-physics" class="md-crosslink " data-show-preview="true">quantum mechanics</a>, relativity is central to modern <a href="https://www.britannica.com/science/physics-science" class="md-crosslink " data-show-preview="true">physics</a>.</p><div class="one-good-fact-module"> </div><span class="marker MOD1 mod-inline"></span><span class="marker PREMOD2 mod-inline"></span><div class="assemblies"><div class="w-100"><figure class="md-assembly m-0 mb-md-0 card card-borderless print-false" data-assembly-id="254968" data-asm-type="video"><div class="md-assembly-wrapper card-media" data-type="video" video-id="222283"><a data-id="222283" class="gtm-assembly-link d-flex justify-content-center" style="--aspect-ratio: 16/9" href="/video/Your-Daily-Equation-04-Relativity-of-Simultaneity/-254968"><img src="https://cdn.britannica.com/83/222283-138-93E31BB8/Your-Daily-Equation-04-Relativity-of-Simultaneity.jpg?w=800&h=450&c=crop" alt="relativity of simultaneity" loading="lazy"><script type="application/json"> { "sources": [ { "file" : "//content.jwplatform.com/manifests/Rr3O4tlT.m3u8" } ], "image": "https://cdn.britannica.com/83/222283-138-93E31BB8/Your-Daily-Equation-04-Relativity-of-Simultaneity.jpg" ,"tracks": [ { "file" : "//assets-jpcust.jwpsrv.com/tracks/3Q8IG2jt", "label": "English" } ] ,"adfile": "//content.jwplatform.com/manifests/None.m3u8" } </script><div class="btn btn-xl btn-white btn-circle position-absolute shadow" style="top: 50%; transform: translateY(-50%)"><em class="material-icons" data-icon="play_arrow"></em></div></a></div><figcaption class="card-body"><div class="md-assembly-caption text-muted font-14 font-serif line-clamp"><span><span class="md-assembly-title font-weight-bold mr-5 d-inline font-sans-serif md-video-caption" video-control="222283">relativity of simultaneity</span><span>Brian Greene derives the time discrepancy between two people who are moving relative to one another but who disagree on what happens at the same time. This video is an episode in his <em>Daily Equation</em> series.</span><button class="js-more-btn d-none btn btn-unstyled font-12 bg-white js-content" aria-label="Toggle more/less fact data"><span class="link-blue">(more)</span></button></span></div><a class="font-14 mt-10 d-inline-block" href="/science/special-relativity/images-videos">See all videos for this article</a></figcaption></figure></div></div><p class="topic-paragraph">Special relativity is limited to objects that are moving with respect to inertial frames of reference—i.e., in a state of <a href="https://www.britannica.com/science/linear-motion" class="md-crosslink autoxref " data-show-preview="true">uniform motion</a> with respect to one another such that one cannot, by purely mechanical experiments, distinguish one from the other. Beginning with the behaviour of <a href="https://www.britannica.com/science/light" class="md-crosslink " data-show-preview="true">light</a> (and all other <a href="https://www.britannica.com/science/electromagnetic-radiation" class="md-crosslink " data-show-preview="true">electromagnetic radiation</a>), the theory of special relativity draws conclusions that are contrary to everyday experience but fully confirmed by experiments that examine <a href="https://www.britannica.com/science/subatomic-particle" class="md-crosslink " data-show-preview="true">subatomic particle</a>s at high speeds or measure small changes between clocks traveling at different speeds. Special relativity revealed that the <a href="https://www.britannica.com/science/speed-of-light" class="md-crosslink " data-show-preview="true">speed of light</a> is a limit that can be approached but not reached by any material object. It is the origin of the most famous equation in <a href="https://www.britannica.com/science/science" class="md-crosslink autoxref " data-show-preview="true">science</a>, <a href="https://www.britannica.com/science/E-mc2-equation" class="md-crosslink " data-show-preview="true"><em>E</em> = <em>m</em><em>c</em><sup>2</sup></a>, which expresses the fact that mass and <a href="https://www.britannica.com/science/energy" class="md-crosslink autoxref " data-show-preview="true">energy</a> are the same physical <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="entity" href="https://www.britannica.com/dictionary/entity" data-type="EB">entity</a> and can be changed into each other. (For a more-detailed treatment of special relativity, <em>see</em> <a href="https://www.britannica.com/science/relativity/Special-relativity#ref252878" class="md-crosslink " data-show-preview="true">relativity: Special relativity</a>.)</p><span class="marker MOD2 mod-inline"></span></section> <span class="md-signature font-12"><a href="/editor/The-Editors-of-Encyclopaedia-Britannica/4419">The Editors of Encyclopaedia Britannica</a></span><span class="md-signature font-12">This article was most recently revised and updated by <a href="/editor/Barbara-A-Schreiber/6493">Barbara A. 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Special relativity | Definition & Equation | Britannica