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<span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Definitions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definitions"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Definitions</span> </div> </a> <button aria-controls="toc-Definitions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Definitions subsection</span> </button> <ul id="toc-Definitions-sublist" class="vector-toc-list"> <li id="toc-Weak_equivalence_principle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Weak_equivalence_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Weak equivalence principle</span> </div> </a> <ul id="toc-Weak_equivalence_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Einstein_equivalence_principle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Einstein_equivalence_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Einstein equivalence principle</span> </div> </a> <ul id="toc-Einstein_equivalence_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strong_equivalence_principle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Strong_equivalence_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Strong equivalence principle</span> </div> </a> <ul id="toc-Strong_equivalence_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Active,_passive,_and_inertial_masses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Active,_passive,_and_inertial_masses"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Active, passive, and inertial masses</span> </div> </a> <ul id="toc-Active,_passive,_and_inertial_masses-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Experimental_tests" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Experimental_tests"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Experimental tests</span> </div> </a> <button aria-controls="toc-Experimental_tests-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Experimental tests subsection</span> </button> <ul id="toc-Experimental_tests-sublist" class="vector-toc-list"> <li id="toc-Tests_of_the_weak_equivalence_principle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tests_of_the_weak_equivalence_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Tests of the weak equivalence principle</span> </div> </a> <ul id="toc-Tests_of_the_weak_equivalence_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tests_of_the_Einstein_equivalence_principle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tests_of_the_Einstein_equivalence_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Tests of the Einstein equivalence principle</span> </div> </a> <ul id="toc-Tests_of_the_Einstein_equivalence_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tests_of_the_strong_equivalence_principle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tests_of_the_strong_equivalence_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Tests of the strong equivalence principle</span> </div> </a> <ul id="toc-Tests_of_the_strong_equivalence_principle-sublist" class="vector-toc-list"> </ul> </li> </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">5</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">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-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" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Equivalence principle: Difference between revisions</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 43 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-43" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">43 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%A8%D8%AF%D8%A3_%D8%A7%D9%84%D8%AA%D9%83%D8%A7%D9%81%D8%A4" title="مبدأ التكافؤ – Arabic" lang="ar" hreflang="ar" data-title="مبدأ التكافؤ" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D1%8B%D0%BD%D1%86%D1%8B%D0%BF_%D1%8D%D0%BA%D0%B2%D1%96%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%B0%D1%81%D1%86%D1%96_%D1%81%D1%96%D0%BB_%D0%B3%D1%80%D0%B0%D0%B2%D1%96%D1%82%D0%B0%D1%86%D1%8B%D1%96_%D1%96_%D1%96%D0%BD%D0%B5%D1%80%D1%86%D1%8B%D1%96" title="Прынцып эквівалентнасці сіл гравітацыі і інерцыі – Belarusian" lang="be" hreflang="be" data-title="Прынцып эквівалентнасці сіл гравітацыі і інерцыі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF_%D0%BD%D0%B0_%D0%B5%D0%BA%D0%B2%D0%B8%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BD%D0%BE%D1%81%D1%82" title="Принцип на еквивалентност – Bulgarian" lang="bg" hreflang="bg" data-title="Принцип на еквивалентност" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Principi_d%27equival%C3%A8ncia" title="Principi d'equivalència – Catalan" lang="ca" hreflang="ca" data-title="Principi d'equivalència" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%AD%D0%BA%D0%B2%D0%B8%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D0%BB%C4%83%D1%85_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF%C4%95_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Эквивалентлăх принципĕ (физика) – Chuvash" lang="cv" hreflang="cv" data-title="Эквивалентлăх принципĕ (физика)" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Princip_ekvivalence" title="Princip ekvivalence – Czech" lang="cs" hreflang="cs" data-title="Princip ekvivalence" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/%C3%86kvivalensprincip" title="Ækvivalensprincip – Danish" lang="da" hreflang="da" data-title="Ækvivalensprincip" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/%C3%84quivalenzprinzip_(Physik)" title="Äquivalenzprinzip (Physik) – German" lang="de" hreflang="de" data-title="Äquivalenzprinzip (Physik)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CF%87%CE%AE_%CF%84%CE%B7%CF%82_%CE%B9%CF%83%CE%BF%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%AF%CE%B1%CF%82" title="Αρχή της ισοδυναμίας – Greek" lang="el" hreflang="el" data-title="Αρχή της ισοδυναμίας" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Principio_de_equivalencia" title="Principio de equivalencia – Spanish" lang="es" hreflang="es" data-title="Principio de equivalencia" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Baliokidetasun_printzipio" title="Baliokidetasun printzipio – Basque" lang="eu" hreflang="eu" data-title="Baliokidetasun printzipio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B5%D9%84_%D9%87%D9%85%E2%80%8C%D8%A7%D8%B1%D8%B2%DB%8C" title="اصل هم‌ارزی – Persian" lang="fa" hreflang="fa" data-title="اصل هم‌ارزی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Principe_d%27%C3%A9quivalence" title="Principe d'équivalence – French" lang="fr" hreflang="fr" data-title="Principe d'équivalence" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Prionsabal_na_coibh%C3%A9ise" title="Prionsabal na coibhéise – Irish" lang="ga" hreflang="ga" data-title="Prionsabal na coibhéise" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Principio_de_equivalencia" title="Principio de equivalencia – Galician" lang="gl" hreflang="gl" data-title="Principio de equivalencia" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%93%B1%EA%B0%80%EC%9B%90%EB%A6%AC" title="등가원리 – Korean" lang="ko" hreflang="ko" data-title="등가원리" 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%80%D5%A1%D5%B4%D5%A1%D6%80%D5%AA%D5%A5%D6%84%D5%B8%D6%82%D5%A9%D5%B5%D5%A1%D5%B6_%D5%BD%D5%AF%D5%A6%D5%A2%D5%B8%D6%82%D5%B6%D6%84" title="Համարժեքության սկզբունք – Armenian" lang="hy" hreflang="hy" data-title="Համարժեքության սկզբունք" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/%E1%BB%A4kp%E1%BB%A5r%E1%BB%A5_nhata" title="Ụkpụrụ nhata – Igbo" lang="ig" hreflang="ig" data-title="Ụkpụrụ nhata" data-language-autonym="Igbo" data-language-local-name="Igbo" class="interlanguage-link-target"><span>Igbo</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Prinsip_ekuivalensi" title="Prinsip ekuivalensi – Indonesian" lang="id" hreflang="id" data-title="Prinsip ekuivalensi" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Principio_di_equivalenza" title="Principio di equivalenza – Italian" lang="it" hreflang="it" data-title="Principio di equivalenza" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%A7%D7%A8%D7%95%D7%9F_%D7%94%D7%A9%D7%A7%D7%99%D7%9C%D7%95%D7%AA" title="עקרון השקילות – Hebrew" lang="he" hreflang="he" data-title="עקרון השקילות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BA%D0%B2%D0%B8%D0%B2%D0%B0%D0%BB%D0%B5%D0%BD%D1%82%D1%82%D1%96%D0%BB%D1%96%D0%BA_%D0%BF%D1%80%D0%B8%D0%BD%D1%86%D0%B8%D0%BF%D1%96" title="Эквиваленттілік принципі – Kazakh" lang="kk" hreflang="kk" data-title="Эквиваленттілік принципі" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ekvivalenciaelv" title="Ekvivalenciaelv – Hungarian" lang="hu" hreflang="hu" data-title="Ekvivalenciaelv" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Equivalentieprincipe" title="Equivalentieprincipe – Dutch" lang="nl" hreflang="nl" data-title="Equivalentieprincipe" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%AD%89%E4%BE%A1%E5%8E%9F%E7%90%86" title="等価原理 – Japanese" lang="ja" hreflang="ja" data-title="等価原理" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Ekvivalensprinsippet" title="Ekvivalensprinsippet – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Ekvivalensprinsippet" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Ekvivalensprinsippet" title="Ekvivalensprinsippet – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Ekvivalensprinsippet" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%87%E0%A8%95%E0%A9%81%E0%A8%88%E0%A8%B5%E0%A9%87%E0%A8%B2%E0%A9%88%E0%A8%82%E0%A8%B8_%E0%A8%AA%E0%A9%8D%E0%A8%B0%E0%A8%BF%E0%A9%B0%E0%A8%B8%E0%A9%80%E0%A8%AA%E0%A8%B2" title="ਇਕੁਈਵੇਲੈਂਸ ਪ੍ਰਿੰਸੀਪਲ – Punjabi" lang="pa" hreflang="pa" data-title="ਇਕੁਈਵੇਲੈਂਸ ਪ੍ਰਿੰਸੀਪਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zasada_r%C3%B3wnowa%C5%BCno%C5%9Bci" title="Zasada równoważności – Polish" lang="pl" hreflang="pl" data-title="Zasada równoważności" data-language-autonym="Polski" data-language-local-name="Polish" 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colspan="2" class="diff-ntitle diff-side-added"><div id="mw-diff-ntitle1"><strong><a href="/w/index.php?title=Equivalence_principle&oldid=1258816116" title="Equivalence principle">Revision as of 19:58, 21 November 2024</a> <span class="mw-diff-edit"><a href="/w/index.php?title=Equivalence_principle&action=edit&oldid=1258816116" title="Equivalence principle">edit</a></span><span class="mw-diff-timestamp" data-timestamp="2024-11-21T19:58:53Z"></span> <span class="mw-diff-undo"><a href="/w/index.php?title=Equivalence_principle&action=edit&undoafter=1257611278&undo=1258816116" title=""Undo" reverts this edit and opens the edit form in preview mode. 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He compared the periods of pendulums composed of different materials and found them to be identical. From this, he inferred that gravitational and inertial mass are the same thing. The form of this assertion, where the equivalence principle is taken to follow from empirical consistency, later became known as "weak equivalence".<ref name=Everitt/></div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>Newton, just 50 years after Galileo, investigated whether gravitational and inertial mass might be different concepts. He compared the periods of pendulums composed of different materials and found them to be identical. From this, he inferred that gravitational and inertial mass are the same thing. The form of this assertion, where the equivalence principle is taken to follow from empirical consistency, later became known as "weak equivalence".<ref name=Everitt/></div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>A version of the equivalence principle consistent with <del class="diffchange diffchange-inline">[[</del>special relativity<del class="diffchange diffchange-inline">]]</del> was introduced by [[Albert Einstein]] in 1907, when he observed that identical physical laws are observed in two systems, one subject to a constant gravitational field causing acceleration and the other subject to constant acceleration like a rocket far from any gravitational field.<ref name="WhittakerII"/>{{rp|152}} Since the physical laws are the same, Einstein assumed the gravitational field and the acceleration were "physically equivalent". Einstein stated this hypothesis by saying he would:</div></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div>A version of the equivalence principle consistent with special relativity was introduced by [[Albert Einstein]] in 1907, when he observed that identical physical laws are observed in two systems, one subject to a constant gravitational field causing acceleration and the other subject to constant acceleration like a rocket far from any gravitational field.<ref name="WhittakerII"/>{{rp|152}} Since the physical laws are the same, Einstein assumed the gravitational field and the acceleration were "physically equivalent". Einstein stated this hypothesis by saying he would:</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>{{blockquote|...assume the complete physical equivalence of a gravitational field and a corresponding [[accelerated reference frame|acceleration of the reference system]].|Einstein, 1907<ref>Einstein, Albert. "On the relativity principle and the conclusions drawn from it." Jahrb Radioaktivitat Elektronik 4 (1907): 411–462.</ref>}}</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>{{blockquote|...assume the complete physical equivalence of a gravitational field and a corresponding [[accelerated reference frame|acceleration of the reference system]].|Einstein, 1907<ref>Einstein, Albert. "On the relativity principle and the conclusions drawn from it." Jahrb Radioaktivitat Elektronik 4 (1907): 411–462.</ref>}}</div></td> </tr> </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>Revision as of 19:58, 21 November 2024</h2> <div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Hypothesis that inertial and gravitational masses are equivalent</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">This article is about the principle in gravitation. For the principle in electromagnetism, see <a href="/wiki/Surface_equivalence_principle" title="Surface equivalence principle">surface equivalence principle</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Elevator_gravity.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Elevator_gravity.svg/330px-Elevator_gravity.svg.png" decoding="async" width="330" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Elevator_gravity.svg/495px-Elevator_gravity.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Elevator_gravity.svg/660px-Elevator_gravity.svg.png 2x" data-file-width="600" data-file-height="400" /></a><figcaption>A falling object behaves exactly the same on a planet or in an equivalent accelerating frame of reference.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output 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href="/wiki/File:Spacetime_lattice_analogy.svg" class="mw-file-description" title="Spacetime curvature schematic"><img alt="Spacetime curvature schematic" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/220px-Spacetime_lattice_analogy.svg.png" decoding="async" width="220" height="82" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/330px-Spacetime_lattice_analogy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/440px-Spacetime_lattice_analogy.svg.png 2x" data-file-width="1260" data-file-height="469" /></a></span><div class="sidebar-caption" style="padding:0.5em 0.2em 0.6em;border-bottom:1px solid #aaa; display:block;margin-bottom:0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Λ</mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>κ</mi> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/124ab80fcb17e2733cc17ff6f93da5e52f355c77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.468ex; height:2.843ex;" alt="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}"></span></div></td></tr><tr><td class="sidebar-content" style="padding-bottom:0.75em;"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><div class="hlist"><ul><li><a href="/wiki/History_of_general_relativity" title="History of general relativity">History</a></li><li><a href="/wiki/Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">Timeline</a></li><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Tests</a></li></ul></div></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Fundamental concepts</div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a class="mw-selflink selflink">Equivalence principle</a></li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Pseudo-Riemannian_manifold" title="Pseudo-Riemannian manifold">Pseudo-Riemannian manifold</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Phenomena</div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Kepler problem</a></li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">Gravitational lensing</a></li> <li><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></li> <li><a href="/wiki/Gravitational_time_dilation" title="Gravitational time dilation">Gravitational time dilation</a></li> <li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a></li> <li><a href="/wiki/Frame-dragging" title="Frame-dragging">Frame-dragging</a></li> <li><a href="/wiki/Geodetic_effect" title="Geodetic effect">Geodetic effect</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/Black_hole" title="Black hole">Black hole</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ececff; font-style:italic;font-weight:normal;"> <a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Spacetime_diagram" title="Spacetime diagram">Spacetime diagrams</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li> <li><a href="/wiki/Wormhole" title="Wormhole">Einstein–Rosen bridge</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist"><ul><li>Equations</li><li>Formalisms</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;padding-bottom:0;margin-bottom:0;"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Equations</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann</a></li> <li><a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li> <li><a href="/wiki/Mathisson%E2%80%93Papapetrou%E2%80%93Dixon_equations" title="Mathisson–Papapetrou–Dixon equations">Mathisson–Papapetrou–Dixon</a></li> <li><a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Formalisms</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM</a></li> <li><a href="/wiki/BSSN_formalism" title="BSSN formalism">BSSN</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Advanced theory</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><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/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li> <li><a href="/wiki/Einstein%E2%80%93Rosen_metric" title="Einstein–Rosen metric">Einstein–Rosen waves</a></li> <li><a href="/wiki/Wormhole" title="Wormhole">Wormhole</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel</a></li> <li><a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman%E2%80%93de%E2%80%93Sitter_metric" title="Kerr–Newman–de–Sitter metric">Kerr–Newman–de Sitter</a></li> <li><a href="/wiki/Kasner_metric" title="Kasner metric">Kasner</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/Taub%E2%80%93NUT_space" title="Taub–NUT space">Taub–NUT</a></li> <li><a href="/wiki/Milne_model" title="Milne model">Milne</a></li> <li><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Robertson–Walker</a></li> <li><a href="/wiki/Oppenheimer%E2%80%93Snyder_model" title="Oppenheimer–Snyder model">Oppenheimer–Snyder</a></li> <li><a href="/wiki/Pp-wave_spacetime" title="Pp-wave spacetime">pp-wave</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a href="/wiki/Weyl%E2%80%93Lewis%E2%80%93Papapetrou_coordinates" title="Weyl–Lewis–Papapetrou coordinates">Weyl−Lewis−Papapetrou</a></li> <li><a href="/wiki/Hartle%E2%80%93Thorne_metric" title="Hartle–Thorne metric">Hartle–Thorne</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Scientists</div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</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/Hans_Reissner" title="Hans Reissner">Reissner</a></li> <li><a href="/wiki/Gunnar_Nordstr%C3%B6m" title="Gunnar Nordström">Nordström</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/Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li> <li><a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/J._Robert_Oppenheimer" title="J. Robert Oppenheimer">Oppenheimer</a></li> <li><a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Gödel</a></li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li> <li><a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li> <li><a href="/wiki/James_M._Bardeen" title="James M. Bardeen">Bardeen</a></li> <li><a href="/wiki/Arthur_Geoffrey_Walker" title="Arthur Geoffrey Walker">Walker</a></li> <li><a href="/wiki/Roy_Kerr" title="Roy Kerr">Kerr</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</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/Amal_Kumar_Raychaudhuri" title="Amal Kumar Raychaudhuri">Raychaudhuri</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/Willem_Jacob_van_Stockum" title="Willem Jacob van Stockum">van Stockum</a></li> <li><a href="/wiki/Abraham_H._Taub" title="Abraham H. Taub">Taub</a></li> <li><a href="/wiki/Ezra_T._Newman" title="Ezra T. Newman">Newman</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/List_of_contributors_to_general_relativity" title="List of contributors to general relativity"><i>others</i></a></li></ul></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><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:General_relativity" title="Category:General relativity">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:General_relativity_sidebar" title="Template:General relativity sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:General_relativity_sidebar" title="Template talk:General relativity sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:General_relativity_sidebar" title="Special:EditPage/Template:General relativity sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>equivalence principle</b> is the hypothesis that the observed equivalence of <a href="/wiki/Gravitational_mass" class="mw-redirect" title="Gravitational mass">gravitational</a> and <a href="/wiki/Mass#Inertial_mass" title="Mass">inertial mass</a> is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times. The extended form by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> requires <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> to also hold in free fall and requires the weak equivalence to be valid everywhere. This form was a critical input for the development of the theory of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>. The strong form requires Einstein's form to work for stellar objects. Highly precise experimental tests of the principle limit possible deviations from equivalence to be very small. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Concept">Concept</h2></div> <p>In classical mechanics, <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's equation of motion in a gravitational field</a>, written out in full, is: </p> <dl><dd><a href="/wiki/Inertial_mass" class="mw-redirect" title="Inertial mass">inertial mass</a> × <a href="/wiki/Acceleration" title="Acceleration">acceleration</a> = <a href="/wiki/Gravitational_mass" class="mw-redirect" title="Gravitational mass">gravitational mass</a> × intensity of the <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a></dd></dl> <p>Very careful experiments have shown that the inertial mass on the left side and gravitational mass on the right side are numerically equal and independent of the material composing the masses. The equivalence principle is the hypothesis that this numerical equality of inertial and gravitational mass is a consequence of their fundamental identity.<sup id="cite_ref-EinsteinMeaning_1-0" class="reference"><a href="#cite_note-EinsteinMeaning-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 32">: 32 </span></sup> </p><p>The equivalence principle can be considered an extension of the principle of relativity, the principle that the laws of physics are <a href="/wiki/Invariant_(physics)" title="Invariant (physics)">invariant</a> under uniform motion. An observer in a windowless room cannot distinguish between being on the surface of the Earth and being in a spaceship in deep space accelerating at 1<i>g</i> and the laws of physics are unable to distinguish these cases.<sup id="cite_ref-EinsteinMeaning_1-1" class="reference"><a href="#cite_note-EinsteinMeaning-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 33">: 33 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2></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/History_of_gravitational_theory" title="History of gravitational theory">History of gravitational theory</a></div> <p>By <a href="/wiki/Experiment" title="Experiment">experimenting</a> with the <a href="/wiki/Acceleration" title="Acceleration">acceleration</a> of different materials, <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a> determined that <a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">gravitation</a> is independent of the amount of <a href="/wiki/Mass" title="Mass">mass</a> being accelerated.<sup id="cite_ref-Everitt_2-0" class="reference"><a href="#cite_note-Everitt-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Newton, just 50 years after Galileo, investigated whether gravitational and inertial mass might be different concepts. He compared the periods of pendulums composed of different materials and found them to be identical. From this, he inferred that gravitational and inertial mass are the same thing. The form of this assertion, where the equivalence principle is taken to follow from empirical consistency, later became known as "weak equivalence".<sup id="cite_ref-Everitt_2-1" class="reference"><a href="#cite_note-Everitt-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>A version of the equivalence principle consistent with special relativity was introduced by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> in 1907, when he observed that identical physical laws are observed in two systems, one subject to a constant gravitational field causing acceleration and the other subject to constant acceleration like a rocket far from any gravitational field.<sup id="cite_ref-WhittakerII_3-0" class="reference"><a href="#cite_note-WhittakerII-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 152">: 152 </span></sup> Since the physical laws are the same, Einstein assumed the gravitational field and the acceleration were "physically equivalent". Einstein stated this hypothesis by saying he would: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>...assume the complete physical equivalence of a gravitational field and a corresponding <a href="/wiki/Accelerated_reference_frame" class="mw-redirect" title="Accelerated reference frame">acceleration of the reference system</a>.</p><div class="templatequotecite">— <cite>Einstein, 1907<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></cite></div></blockquote> <p>In 1911 Einstein demonstrated the power of the equivalence principle by using it to predict that clocks run at different rates in a <a href="/wiki/Gravitational_potential" title="Gravitational potential">gravitational potential</a>, and light rays <a href="/wiki/Bending_of_starlight" class="mw-redirect" title="Bending of starlight">bend</a> in a gravitational field.<sup id="cite_ref-WhittakerII_3-1" class="reference"><a href="#cite_note-WhittakerII-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 153">: 153 </span></sup> He connected the equivalence principle to his earlier principle of special relativity: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p> This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course.</p><div class="templatequotecite">— <cite>Einstein, 1911<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></cite></div></blockquote> <p>Soon after completing work on his theory of gravity (known as <a href="/wiki/General_relativity" title="General relativity">general relativity</a>)<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><sup class="reference nowrap"><span title="Page / location: 111">: 111 </span></sup> and then also in later years, Einstein recalled the importance of the equivalence principle to his work: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p> The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly a thought struck me: If a man falls freely, he would not feel his weight. I was taken aback. This simple thought experiment made a deep impression on me. This led me to the theory of gravity.</p><div class="templatequotecite">— <cite>Einstein, 1922<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></cite></div></blockquote> <p>Einstein's development of general relativity necessitated some means of empirically discriminating the theory from other theories of gravity compatible with <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>. Accordingly, <a href="/wiki/Robert_H._Dicke" title="Robert H. Dicke">Robert Dicke</a> developed a test program incorporating two new principles—the <a href="#Einstein_equivalence_principle">§ Einstein equivalence principle</a>, and the <a href="#Strong_equivalence_principle">§ Strong equivalence principle</a>—each of which assumes the weak equivalence principle as a starting point. </p> <div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Apollo_15_feather_and_hammer_drop.ogv/220px--Apollo_15_feather_and_hammer_drop.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="161" data-durationhint="48" data-mwtitle="Apollo_15_feather_and_hammer_drop.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Apollo_15_feather_and_hammer_drop.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="654" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/e/e8/Apollo_15_feather_and_hammer_drop.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="654" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="196" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="328" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="490" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/Apollo_15_feather_and_hammer_drop.ogv/Apollo_15_feather_and_hammer_drop.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="490" data-height="360" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=en&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="en" label="English ‪(en)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=fr&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="fr" label="français ‪(fr)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=pt-br&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="pt-BR" label="português do Brasil ‪(pt-br)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=pt&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="pt" label="português ‪(pt)‬" data-dir="ltr" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3AApollo_15_feather_and_hammer_drop.ogv&lang=tok&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="tok" label="toki pona ‪(tok)‬" data-dir="ltr" /></video></span><figcaption>During the <a href="/wiki/Apollo_15" title="Apollo 15">Apollo 15</a> mission in 1971, astronaut <a href="/wiki/David_Scott" title="David Scott">David Scott</a> showed that Galileo was right: acceleration is the same for all bodies subject to gravity on the Moon, even for a hammer and a feather.</figcaption></figure><p>Three main forms of the equivalence principle are in current use: weak (Galilean), Einsteinian, and strong.<sup id="cite_ref-CliftonFerreiraPadilla_8-0" class="reference"><a href="#cite_note-CliftonFerreiraPadilla-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 6">: 6 </span></sup> Some proposals also suggest finer divisions or minor alterations.<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> </p><div class="mw-heading mw-heading3"><h3 id="Weak_equivalence_principle"><span class="anchor" id="Weak"></span> Weak equivalence principle</h3></div> <p>The weak equivalence principle, also known as the universality of free fall or the Galilean equivalence principle can be stated in many ways. The strong equivalence principle, a generalization of the weak equivalence principle, includes astronomic bodies with gravitational self-binding energy.<sup id="cite_ref-WagnerSchalmminger_11-0" class="reference"><a href="#cite_note-WagnerSchalmminger-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Instead, the weak equivalence principle assumes falling bodies are self-bound by non-gravitational forces only (e.g. a stone). Either way: </p> <ul><li>"All uncharged, freely falling test particles follow the same trajectories, once an initial position and velocity have been prescribed".<sup id="cite_ref-CliftonFerreiraPadilla_8-1" class="reference"><a href="#cite_note-CliftonFerreiraPadilla-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 6">: 6 </span></sup></li> <li>"... in a uniform gravitational field all objects, regardless of their composition, fall with precisely the same acceleration." "The weak equivalence principle implicitly assumes that the falling objects are bound by non-gravitational forces."<sup id="cite_ref-WagnerSchalmminger_11-1" class="reference"><a href="#cite_note-WagnerSchalmminger-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li> <li>"... in a gravitational field the acceleration of a test particle is independent of its properties, including its rest mass."<sup id="cite_ref-Wesson_12-0" class="reference"><a href="#cite_note-Wesson-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li> <li>Mass (measured with a balance) and weight (measured with a scale) are locally in identical ratio for all bodies (the opening page to Newton's <i><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Philosophiæ Naturalis Principia Mathematica</a></i>, 1687).</li></ul> <p>Uniformity of the gravitational field eliminates measurable tidal forces originating from a radial divergent gravitational field (e.g., the Earth) upon finite sized physical bodies. </p> <div class="mw-heading mw-heading3"><h3 id="Einstein_equivalence_principle">Einstein equivalence principle</h3></div> <p>What is now called the "Einstein equivalence principle" states that the weak equivalence principle holds, and that: </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent" style="padding-left: 1.5em;"><i>the outcome of any local, non-gravitational test experiment is independent of the experimental apparatus' velocity relative to the gravitational field and is independent of where and when in the gravitational field the experiment is performed.</i><sup id="cite_ref-Lāmmerzahl_13-0" class="reference"><a href="#cite_note-Lāmmerzahl-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></div> <p>Here <i>local</i> means that experimental setup must be small compared to variations in the gravitational field, called <a href="/wiki/Tidal_forces" class="mw-redirect" title="Tidal forces">tidal forces</a>. The <i>test</i> experiment must be small enough so that its gravitational potential does not alter the result. </p><p>The two additional constraints added to the weak principle to get the Einstein form − (1) the independence of the outcome on relative velocity (local <a href="/wiki/Lorentz_invariance" class="mw-redirect" title="Lorentz invariance">Lorentz invariance</a>) and (2) independence of "where" known as (local positional invariance) − have far reaching consequences. With these constraints alone Einstein was able to predict the <a href="/wiki/Gravitational_redshift" title="Gravitational redshift">gravitational redshift</a>.<sup id="cite_ref-Lāmmerzahl_13-1" class="reference"><a href="#cite_note-Lāmmerzahl-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Theories of gravity that obey the Einstein equivalence principle must be "metric theories", meaning that trajectories of freely falling bodies are <a href="/wiki/Geodesics" class="mw-redirect" title="Geodesics">geodesics</a> of symmetric metric.<sup id="cite_ref-Will2014_14-0" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 9">: 9 </span></sup> </p><p>Around 1960 <a href="/wiki/Leonard_I._Schiff" title="Leonard I. Schiff">Leonard I. Schiff</a> conjectured that any complete and consistent theory of gravity that embodies the weak equivalence principle implies the Einstein equivalence principle; the conjecture can't be proven but has several plausibility arguments in its favor.<sup id="cite_ref-Will2014_14-1" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 20">: 20 </span></sup> Nonetheless, the two principles are tested with very different kinds of experiments. </p><p>The Einstein equivalence principle has been criticized as imprecise, because there is no universally accepted way to distinguish gravitational from non-gravitational experiments (see for instance Hadley<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> and Durand<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>). </p> <div class="mw-heading mw-heading3"><h3 id="Strong_equivalence_principle">Strong equivalence principle</h3></div> <p>The strong equivalence principle applies the same constraints as the Einstein equivalence principle, but allows the freely falling bodies to be massive gravitating objects as well as test particles.<sup id="cite_ref-CliftonFerreiraPadilla_8-2" class="reference"><a href="#cite_note-CliftonFerreiraPadilla-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Thus this is a version of the equivalence principle that applies to objects that exert a gravitational force on themselves, such as stars, planets, black holes or <a href="/wiki/Cavendish_experiment" title="Cavendish experiment">Cavendish experiments</a>. It requires that the <a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a> be the same everywhere in the universe<sup id="cite_ref-Will2014_14-2" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 49">: 49 </span></sup> and is incompatible with a <a href="/wiki/Fifth_force" title="Fifth force">fifth force</a>. It is much more restrictive than the Einstein equivalence principle. </p><p>Like the Einstein equivalence principle, the strong equivalence principle requires gravity is geometrical by nature, but in addition it forbids any extra fields, so the <a href="/wiki/Metric_tensor_(general_relativity)" title="Metric tensor (general relativity)">metric</a> alone determines all of the effects of gravity. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe. Einstein's theory of general relativity (including the <a href="/wiki/Cosmological_constant" title="Cosmological constant">cosmological constant</a>) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as <a href="/wiki/Brans%E2%80%93Dicke_theory" title="Brans–Dicke theory">Brans–Dicke theory</a> and the <a href="/wiki/Einstein-aether_theory" title="Einstein-aether theory">Einstein-aether theory</a> add additional fields.<sup id="cite_ref-CliftonFerreiraPadilla_8-3" class="reference"><a href="#cite_note-CliftonFerreiraPadilla-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Active,_passive,_and_inertial_masses"><span id="Active.2C_passive.2C_and_inertial_masses"></span>Active, passive, and inertial masses</h3></div> <p>Some of the tests of the equivalence principle use names for the different ways mass appears in physical formulae. In nonrelativistic physics three kinds of mass can be distinguished:<sup id="cite_ref-Will2014_14-3" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Inertial mass intrinsic to an object, the sum of all of its mass–energy.</li> <li>Passive mass, the response to gravity, the object's weight.</li> <li>Active mass, the mass that determines the objects gravitational effect.</li></ol> <p>By definition of active and passive gravitational mass, the force on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/577d686fc81d1d1eb3ae54e78aeee8957baf6718" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.308ex; height:2.509ex;" alt="{\displaystyle M_{1}}"></span> due to the gravitational field of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/909a62f3ff41169372143733d3767afe0ad3b14d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.308ex; height:2.509ex;" alt="{\displaystyle M_{0}}"></span> is: <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 F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc68065d51f35f67d7df83343229bdbcc70bc6c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.169ex; height:6.176ex;" alt="{\displaystyle F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}}"></span> Likewise the force on a second object of arbitrary mass<sub>2</sub> due to the gravitational field of mass<sub>0</sub> is: <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 F_{2}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{2}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21ba88cc1a1bd6fd9132f01f695b9d899a029039" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.169ex; height:6.176ex;" alt="{\displaystyle F_{2}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}}}}"></span> </p><p>By definition of inertial mass:<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 F=m^{\mathrm {inert} }a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msup> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=m^{\mathrm {inert} }a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5025489641564b0420831d57a6de9d7d066e69c9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.727ex; height:2.676ex;" alt="{\displaystyle F=m^{\mathrm {inert} }a}"></span>if <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31aafa60e48d39ccce922404c0b80340b2cc777a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.095ex; height:2.009ex;" alt="{\displaystyle m_{1}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ecebe334d5cadc3ffcf245eb02919034d7a2ec8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.095ex; height:2.009ex;" alt="{\displaystyle m_{2}}"></span> are the same distance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a6ff51ee949104fe6fae553cfbdfba29d5fac1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.095ex; height:2.009ex;" alt="{\displaystyle m_{0}}"></span> then, by the weak equivalence principle, they fall at the same rate (i.e. their accelerations are the same). <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 a_{1}={\frac {F_{1}}{m_{1}^{\mathrm {inert} }}}=a_{2}={\frac {F_{2}}{m_{2}^{\mathrm {inert} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1}={\frac {F_{1}}{m_{1}^{\mathrm {inert} }}}=a_{2}={\frac {F_{2}}{m_{2}^{\mathrm {inert} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4af53957ab6acc7441670d46060e690e00c507dc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:26.852ex; height:6.343ex;" alt="{\displaystyle a_{1}={\frac {F_{1}}{m_{1}^{\mathrm {inert} }}}=a_{2}={\frac {F_{2}}{m_{2}^{\mathrm {inert} }}}}"></span> </p><p>Hence: <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 {\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}m_{1}^{\mathrm {inert} }}}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}m_{2}^{\mathrm {inert} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}m_{1}^{\mathrm {inert} }}}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}m_{2}^{\mathrm {inert} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d395f6838324025110d02b0e6e76c555901ef642" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:26.142ex; height:7.009ex;" alt="{\displaystyle {\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}m_{1}^{\mathrm {inert} }}}={\frac {M_{0}^{\mathrm {act} }M_{2}^{\mathrm {pass} }}{r^{2}m_{2}^{\mathrm {inert} }}}}"></span> </p><p>Therefore: <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 {\frac {M_{1}^{\mathrm {pass} }}{m_{1}^{\mathrm {inert} }}}={\frac {M_{2}^{\mathrm {pass} }}{m_{2}^{\mathrm {inert} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {M_{1}^{\mathrm {pass} }}{m_{1}^{\mathrm {inert} }}}={\frac {M_{2}^{\mathrm {pass} }}{m_{2}^{\mathrm {inert} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e5368ea894e6155bbe98e2066312ba799d2afde" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:16.296ex; height:7.009ex;" alt="{\displaystyle {\frac {M_{1}^{\mathrm {pass} }}{m_{1}^{\mathrm {inert} }}}={\frac {M_{2}^{\mathrm {pass} }}{m_{2}^{\mathrm {inert} }}}}"></span> </p><p>In other words, passive gravitational mass must be proportional to inertial mass for objects, independent of their material composition if the weak equivalence principle is obeyed. </p><p>The dimensionless <i><a href="/wiki/E%C3%B6tv%C3%B6s_experiment" title="Eötvös experiment">Eötvös</a>-parameter</i> or <i>Eötvös ratio</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta (A,B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta (A,B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eefc683070e3cc4ff9e4efea90586fbcafb82e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.52ex; height:2.843ex;" alt="{\displaystyle \eta (A,B)}"></span> is the difference of the ratios of gravitational and inertial masses divided by their average for the two sets of test masses "A" and "B". <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 \eta (A,B)=2{\frac {\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}-\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}{\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}+\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </mrow> <mi>a</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> <mi>n</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </mrow> <mi>a</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> <mi>n</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </mrow> <mi>a</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> <mi>n</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </mrow> <mi>a</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> <mi>n</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta (A,B)=2{\frac {\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}-\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}{\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}+\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d47500feacb93aa5652d0b0b72e67c5cd559cc8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:35.242ex; height:10.176ex;" alt="{\displaystyle \eta (A,B)=2{\frac {\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}-\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}{\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{A}+\left({\frac {m_{{\textrm {p}}ass}}{m_{{\textrm {i}}nert}}}\right)_{B}}}.}"></span> Values of this parameter are used to compare tests of the equivalence principle.<sup id="cite_ref-Will2014_14-4" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 10">: 10 </span></sup> </p><p>A similar parameter can be used to compare passive and active mass. By <a href="/wiki/Newton%27s_third_law_of_motion" class="mw-redirect" title="Newton's third law of motion">Newton's third law of motion</a>: <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 F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc68065d51f35f67d7df83343229bdbcc70bc6c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.169ex; height:6.176ex;" alt="{\displaystyle F_{1}={\frac {M_{0}^{\mathrm {act} }M_{1}^{\mathrm {pass} }}{r^{2}}}}"></span> must be equal and opposite to <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 F_{0}={\frac {M_{1}^{\mathrm {act} }M_{0}^{\mathrm {pass} }}{r^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}={\frac {M_{1}^{\mathrm {act} }M_{0}^{\mathrm {pass} }}{r^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7feabbe860095f777fcc04c8cf9c0c01509c136f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.169ex; height:6.176ex;" alt="{\displaystyle F_{0}={\frac {M_{1}^{\mathrm {act} }M_{0}^{\mathrm {pass} }}{r^{2}}}}"></span> </p><p>It follows that: <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 {\frac {M_{0}^{\mathrm {act} }}{M_{0}^{\mathrm {pass} }}}={\frac {M_{1}^{\mathrm {act} }}{M_{1}^{\mathrm {pass} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {M_{0}^{\mathrm {act} }}{M_{0}^{\mathrm {pass} }}}={\frac {M_{1}^{\mathrm {act} }}{M_{1}^{\mathrm {pass} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/910d8dd5c6a35912c8d5a849ab7298cf0b3be9e4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:16.296ex; height:6.843ex;" alt="{\displaystyle {\frac {M_{0}^{\mathrm {act} }}{M_{0}^{\mathrm {pass} }}}={\frac {M_{1}^{\mathrm {act} }}{M_{1}^{\mathrm {pass} }}}}"></span> </p><p>In words, passive gravitational mass must be proportional to active gravitational mass for all objects. The difference, <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 S_{0,1}={\frac {M_{0}^{\mathrm {act} }}{M_{0}^{\mathrm {pass} }}}-{\frac {M_{1}^{\mathrm {act} }}{M_{1}^{\mathrm {pass} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msubsup> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0,1}={\frac {M_{0}^{\mathrm {act} }}{M_{0}^{\mathrm {pass} }}}-{\frac {M_{1}^{\mathrm {act} }}{M_{1}^{\mathrm {pass} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/115bd39af2998e9e905d4580dea621cdb6f4c319" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:22.895ex; height:6.843ex;" alt="{\displaystyle S_{0,1}={\frac {M_{0}^{\mathrm {act} }}{M_{0}^{\mathrm {pass} }}}-{\frac {M_{1}^{\mathrm {act} }}{M_{1}^{\mathrm {pass} }}}}"></span> is used to quantify differences between passive and active mass.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Experimental_tests">Experimental tests</h2></div> <div class="mw-heading mw-heading3"><h3 id="Tests_of_the_weak_equivalence_principle">Tests of the weak equivalence principle</h3></div> <p>Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. An obvious test is dropping different objects and verifying that they land at the same time. Historically this was the first approach—though probably not by <a href="/wiki/Galileo%27s_Leaning_Tower_of_Pisa_experiment" title="Galileo's Leaning Tower of Pisa experiment">Galileo's Leaning Tower of Pisa experiment</a><sup id="cite_ref-Drake_18-0" class="reference"><a href="#cite_note-Drake-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 19–21">: 19–21 </span></sup> but instead earlier by Simon Stevin,<sup id="cite_ref-Devreese_19-0" class="reference"><a href="#cite_note-Devreese-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> who dropped lead balls of different masses off the <a href="/wiki/Nieuwe_Kerk_(Delft)" title="Nieuwe Kerk (Delft)">Delft churchtower</a> and listened for the sound of them hitting a wooden plank. </p><p><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> measured the <a href="/wiki/Frequency" title="Frequency">period</a> of pendulums made with different materials as an alternative test giving the first precision measurements.<sup id="cite_ref-Everitt_2-2" class="reference"><a href="#cite_note-Everitt-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Lor%C3%A1nd_E%C3%B6tv%C3%B6s" title="Loránd Eötvös">Loránd Eötvös</a>'s approach in 1908 used a very sensitive <a href="/wiki/Torsion_balance" class="mw-redirect" title="Torsion balance">torsion balance</a> to give precision approaching 1 in a billion. Modern experiments have improved this by another factor of a million. </p><p>A popular exposition of this measurement was done on the Moon by <a href="/wiki/David_Scott" title="David Scott">David Scott</a> in 1971. He dropped a falcon feather and a hammer at the same time, showing on video<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> that they landed at the same time. </p> <table class="wikitable"> <caption>Chronology of weak equivalence principles tests<sup id="cite_ref-CiufoliniWheeler_21-0" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th>Year </th> <th>Investigator </th> <th>Sensitivity </th> <th>Method </th></tr> <tr> <td>500? </td> <td><a href="/wiki/John_Philoponus" title="John Philoponus">John Philoponus</a><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </td> <td>"small" </td> <td>Drop tower </td></tr> <tr> <td>1585 </td> <td><a href="/wiki/Simon_Stevin" title="Simon Stevin">Simon Stevin</a><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Devreese_19-1" class="reference"><a href="#cite_note-Devreese-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td><span class="nowrap"><span data-sort-value="6998500000000000000♠"></span>5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−2</sup></span> </td> <td>Drop tower </td></tr> <tr> <td>1590? </td> <td><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-1" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6997200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−3</sup></span> </td> <td>Pendulum, drop tower </td></tr> <tr> <td>1686 </td> <td><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-2" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6997100000000000000♠"></span>10<sup>−3</sup></span> </td> <td>Pendulum </td></tr> <tr> <td>1832 </td> <td><a href="/wiki/Friedrich_Wilhelm_Bessel" title="Friedrich Wilhelm Bessel">Friedrich Wilhelm Bessel</a><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-3" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6995200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−5</sup></span> </td> <td>Pendulum </td></tr> <tr> <td>1908 (1922) </td> <td><a href="/wiki/Lor%C3%A1nd_E%C3%B6tv%C3%B6s" title="Loránd Eötvös">Loránd Eötvös</a><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-4" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 92">: 92 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6991200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−9</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>1910 </td> <td>Southerns<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-5" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6994499999999999999♠"></span>5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−6</sup></span> </td> <td>Pendulum </td></tr> <tr> <td>1918 </td> <td>Zeeman<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-6" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6992300000000000000♠"></span>3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−8</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>1923 </td> <td>Potter<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-7" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6994300000000000000♠"></span>3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−6</sup></span> </td> <td>Pendulum </td></tr> <tr> <td>1935 </td> <td>Renner<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-8" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 92">: 92 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6991200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−9</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>1964 </td> <td>Roll, Krotkov, <a href="/wiki/Robert_H._Dicke" title="Robert H. Dicke">Dicke</a><sup id="cite_ref-RollKrotkovDicke_32-0" class="reference"><a href="#cite_note-RollKrotkovDicke-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </td> <td><span class="nowrap"><span data-sort-value="6989300000000000000♠"></span>3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−11</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>1972 </td> <td><a href="/wiki/Vladimir_Braginsky" title="Vladimir Braginsky">Braginsky</a>, Panov<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-9" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 92">: 92 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6988100000000000000♠"></span>10<sup>−12</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>1976 </td> <td>Shapiro, et al.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-10" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 92">: 92 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6988100000000000000♠"></span>10<sup>−12</sup></span> </td> <td>Lunar laser ranging </td></tr> <tr> <td>1979 </td> <td>Keiser, Faller<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-11" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 93">: 93 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6989400000000000000♠"></span>4<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−11</sup></span> </td> <td>Fluid support </td></tr> <tr> <td>1987 </td> <td>Niebauer, et al.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-12" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 95">: 95 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6990100000000000000♠"></span>10<sup>−10</sup></span> </td> <td>Drop tower </td></tr> <tr> <td>1989 </td> <td>Stubbs, et al.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-13" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 93">: 93 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6989100000000000000♠"></span>10<sup>−11</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>1990 </td> <td>Adelberger, Eric G.; et al.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CiufoliniWheeler_21-14" class="reference"><a href="#cite_note-CiufoliniWheeler-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 95">: 95 </span></sup> </td> <td><span class="nowrap"><span data-sort-value="6988100000000000000♠"></span>10<sup>−12</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>1999 </td> <td>Baessler, et al.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </td> <td><span class="nowrap"><span data-sort-value="6986500000000000000♠"></span>5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−14</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>2008 </td> <td>Schlamminger, et al.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </td> <td><span class="nowrap"><span data-sort-value="6987100000000000000♠"></span>10<sup>−13</sup></span> </td> <td>Torsion balance </td></tr> <tr> <td>2017 </td> <td><a href="/wiki/MICROSCOPE" title="MICROSCOPE">MICROSCOPE</a><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </td> <td>10<sup>−15</sup> </td> <td>Earth orbit </td></tr></tbody></table> <p>Experiments are still being performed at the <a href="/wiki/University_of_Washington" title="University of Washington">University of Washington</a> which have placed limits on the differential acceleration of objects towards the Earth, the Sun and towards <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a> in the <a href="/wiki/Galactic_Center" title="Galactic Center">Galactic Center</a>.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Future satellite experiments<sup id="cite_ref-Dittus_45-0" class="reference"><a href="#cite_note-Dittus-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> – <a href="/wiki/STEP_(satellite)" title="STEP (satellite)">Satellite Test of the Equivalence Principle</a><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> and Galileo Galilei – will test the weak equivalence principle in space, to much higher accuracy.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>With the first successful production of antimatter, in particular anti-hydrogen, a new approach to test the weak equivalence principle has been proposed. Experiments to compare the gravitational behavior of matter and antimatter are currently being developed.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p><p>Proposals that may lead to a <a href="/wiki/Quantum_gravity" title="Quantum gravity">quantum theory of gravity</a> such as <a href="/wiki/String_theory" title="String theory">string theory</a> and <a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">loop quantum gravity</a> predict violations of the weak equivalence principle because they contain many light <a href="/wiki/Scalar_field" title="Scalar field">scalar fields</a> with long <a href="/wiki/Compton_wavelength" title="Compton wavelength">Compton wavelengths</a>, which should generate <a href="/wiki/Fifth_force" title="Fifth force">fifth forces</a> and variation of the fundamental constants. Heuristic arguments suggest that the magnitude of these equivalence principle violations could be in the 10<sup>−13</sup> to 10<sup>−18</sup> range.<sup id="cite_ref-Overduin2009_49-0" class="reference"><a href="#cite_note-Overduin2009-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p><p>Currently envisioned tests of the weak equivalence principle are approaching a degree of sensitivity such that <i>non-discovery</i> of a violation would be just as profound a result as discovery of a violation. Non-discovery of equivalence principle violation in this range would suggest that gravity is so fundamentally different from other forces as to require a major reevaluation of current attempts to unify gravity with the other forces of nature. A positive detection, on the other hand, would provide a major guidepost towards unification.<sup id="cite_ref-Overduin2009_49-1" class="reference"><a href="#cite_note-Overduin2009-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Tests_of_the_Einstein_equivalence_principle">Tests of the Einstein equivalence principle</h3></div> <p>In addition to the tests of the weak equivalence principle, the Einstein equivalence principle requires testing the local Lorentz invariance and local positional invariance conditions. </p><p>Testing local Lorentz invariance amounts to testing special relativity, a theory with vast number of existing tests.<sup id="cite_ref-Will2014_14-5" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 12">: 12 </span></sup> Nevertheless, attempts to look for quantum gravity require even more precise tests. The modern tests include looking for directional variations in the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> (called "clock anisotropy tests") and new forms of the <a href="/wiki/Michelson-Morley_experiment" class="mw-redirect" title="Michelson-Morley experiment">Michelson-Morley experiment</a>. The anisotropy measures less than one part in 10<sup>−20</sup>.<sup id="cite_ref-Will2014_14-6" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 14">: 14 </span></sup> </p><p>Testing local positional invariance divides in to tests in space and in time.<sup id="cite_ref-Will2014_14-7" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 17">: 17 </span></sup> Space-based tests use measurements of the <a href="/wiki/Gravitational_redshift" title="Gravitational redshift">gravitational redshift</a>, the classic is the <a href="/wiki/Pound%E2%80%93Rebka_experiment" title="Pound–Rebka experiment">Pound–Rebka experiment</a> in the 1960s. The most precise measurement was done in 1976 by flying a hydrogen maser and comparing it to one on the ground. The <a href="/wiki/Global_positioning_system" class="mw-redirect" title="Global positioning system">Global positioning system</a> requires compensation for this redshift to give accurate position values. </p><p>Time-based tests search for variation of <a href="/wiki/Dimensionless" class="mw-redirect" title="Dimensionless">dimensionless</a> <a href="/wiki/Fundamental_physical_constants" class="mw-redirect" title="Fundamental physical constants">constants and mass ratios</a>.<sup id="cite_ref-Uzan_50-0" class="reference"><a href="#cite_note-Uzan-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> For example, Webb et al.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> reported detection of variation (at the 10<sup>−5</sup> level) of the fine-structure constant from measurements of distant <a href="/wiki/Quasar" title="Quasar">quasars</a>. Other researchers dispute these findings.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p><p>The present best limits on the variation of the fundamental constants have mainly been set by studying the naturally occurring <a href="/wiki/Oklo" title="Oklo">Oklo</a> <a href="/wiki/Natural_nuclear_fission_reactor" title="Natural nuclear fission reactor">natural nuclear fission reactor</a>, where nuclear reactions similar to ones we observe today have been shown to have occurred underground approximately two billion years ago. These reactions are extremely sensitive to the values of the fundamental constants. </p> <table class="wikitable"> <caption>Tests of changes in fundamental constants<sup id="cite_ref-Will2014_14-8" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 19">: 19 </span></sup> </caption> <tbody><tr> <th>Constant </th> <th>Year </th> <th>Method </th> <th>Limit on fractional change per year </th></tr> <tr> <td><a href="/wiki/Weak_interaction" title="Weak interaction">weak interaction</a> constant </td> <td>1976 </td> <td>Oklo </td> <td>10<sup>−11</sup> </td></tr> <tr> <td><a href="/wiki/Fine-structure_constant" title="Fine-structure constant">fine-structure constant</a> </td> <td>1976 </td> <td>Oklo </td> <td>10<sup>−16</sup> </td></tr> <tr> <td><a href="/wiki/Electron" title="Electron">electron</a>–<a href="/wiki/Proton" title="Proton">proton</a> mass ratio </td> <td>2002 </td> <td>quasars </td> <td>10<sup>−15</sup> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Tests_of_the_strong_equivalence_principle">Tests of the strong equivalence principle</h3></div> <p>The strong equivalence principle can be tested by 1) finding orbital variations in massive bodies (Sun-Earth-Moon), 2) variations in the gravitational constant (<i>G</i>) depending on nearby sources of gravity or on motion, or 3) searching for a variation of Newton's gravitational constant over the life of the universe<sup id="cite_ref-Will2014_14-9" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 47">: 47 </span></sup> </p><p>Orbital variations due to gravitational self-energy should cause a "polarization" of solar system orbits called the <a href="/wiki/Nordtvedt_effect" title="Nordtvedt effect">Nordtvedt effect</a>. This effect has been sensitively tested by the <a href="/wiki/Lunar_Laser_Ranging_Experiment" class="mw-redirect" title="Lunar Laser Ranging Experiment">Lunar Laser Ranging Experiment</a>.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Up to the limit of one part in 10<sup>13</sup> there is no Nordtvedt effect. </p><p>A tight bound on the effect of nearby gravitational fields on the strong equivalence principle comes from modeling the orbits of binary stars and comparing the results to <a href="/wiki/Pulsar" title="Pulsar">pulsar</a> timing data.<sup id="cite_ref-Will2014_14-10" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 49">: 49 </span></sup> In 2014, astronomers discovered a stellar triple system containing a millisecond pulsar <a href="/wiki/PSR_J0337%2B1715" title="PSR J0337+1715">PSR J0337+1715</a> and two <a href="/wiki/White_dwarf" title="White dwarf">white dwarfs</a> orbiting it. The system provided them a chance to test the strong equivalence principle in a strong gravitational field with high accuracy.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p><p>Most alternative theories of gravity predict a change in the gravity constant over time. Studies of <a href="/wiki/Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Big Bang nucleosynthesis</a>, analysis of pulsars, and the lunar laser ranging data have shown that <i>G</i> cannot have varied by more than 10% since the creation of the universe. The best data comes from studies of the <a href="/wiki/Ephemeris" title="Ephemeris">ephemeris</a> of Mars, based on three successive NASA missions, <a href="/wiki/Mars_Global_Surveyor" title="Mars Global Surveyor">Mars Global Surveyor</a>, <a href="/wiki/Mars_Odyssey" class="mw-redirect" title="Mars Odyssey">Mars Odyssey</a>, and <a href="/wiki/Mars_Reconnaissance_Orbiter" title="Mars Reconnaissance Orbiter">Mars Reconnaissance Orbiter</a>.<sup id="cite_ref-Will2014_14-11" class="reference"><a href="#cite_note-Will2014-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 50">: 50 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/E%C3%B6tv%C3%B6s_experiment" title="Eötvös experiment">Eötvös experiment</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/Gauge_gravitation_theory" title="Gauge gravitation theory">Gauge gravitation theory</a></li> <li><a href="/wiki/General_covariance" title="General covariance">General covariance</a></li> <li><a href="/wiki/Mach%27s_principle" title="Mach's principle">Mach's principle</a></li> <li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Tests of general relativity</a></li> <li><a href="/wiki/Unsolved_problems_in_astronomy" class="mw-redirect" title="Unsolved problems in astronomy">Unsolved problems in astronomy</a></li> <li><a href="/wiki/Unsolved_problems_in_physics" class="mw-redirect" title="Unsolved problems in physics">Unsolved problems in physics</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></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 li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-EinsteinMeaning-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-EinsteinMeaning_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-EinsteinMeaning_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free 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="CITEREFEinstein2003" class="citation book cs1">Einstein, Albert (2003). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/meaningrelativit00aein"><i>The Meaning of Relativity</i></a></span>. Routledge. p. <a rel="nofollow" class="external text" href="https://archive.org/details/meaningrelativit00aein/page/n67">59</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781134449798" title="Special:BookSources/9781134449798"><bdi>9781134449798</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Meaning+of+Relativity&rft.pages=59&rft.pub=Routledge&rft.date=2003&rft.isbn=9781134449798&rft.aulast=Einstein&rft.aufirst=Albert&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmeaningrelativit00aein&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Everitt-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Everitt_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Everitt_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Everitt_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEverittDamourNordtvedtReinhard2003" class="citation journal cs1">Everitt, C.W.F.; Damour, T.; Nordtvedt, K.; Reinhard, R. (October 2003). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0273117703903358">"Historical perspective on testing the Equivalence Principle"</a>. <i>Advances in Space Research</i>. <b>32</b> (7): 1297–1300. <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/2003AdSpR..32.1297E">2003AdSpR..32.1297E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0273-1177%2803%2990335-8">10.1016/S0273-1177(03)90335-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Advances+in+Space+Research&rft.atitle=Historical+perspective+on+testing+the+Equivalence+Principle&rft.volume=32&rft.issue=7&rft.pages=1297-1300&rft.date=2003-10&rft_id=info%3Adoi%2F10.1016%2FS0273-1177%2803%2990335-8&rft_id=info%3Abibcode%2F2003AdSpR..32.1297E&rft.aulast=Everitt&rft.aufirst=C.W.F.&rft.au=Damour%2C+T.&rft.au=Nordtvedt%2C+K.&rft.au=Reinhard%2C+R.&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0273117703903358&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-WhittakerII-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-WhittakerII_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-WhittakerII_3-1"><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="CITEREFWhittaker1989" class="citation book cs1">Whittaker, Sir Edmund (1 January 1989). <i>A History of the Theories of Aether and Electricity</i>. Vol. 2. Courier Dover Publications. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-26126-3" title="Special:BookSources/0-486-26126-3"><bdi>0-486-26126-3</bdi></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.pub=Courier+Dover+Publications&rft.date=1989-01-01&rft.isbn=0-486-26126-3&rft.aulast=Whittaker&rft.aufirst=Sir+Edmund&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" 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">Einstein, Albert. "On the relativity principle and the conclusions drawn from it." Jahrb Radioaktivitat Elektronik 4 (1907): 411–462.</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">Einstein, Albert. "On the Influence of Gravitation on the Propagation of Light." Annalen der Physik 35.898–908 (1911): 906.</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">Lorentz, Hendrik Antoon, et al. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=oy_Z3o7p6zwC">The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity</a>. United Kingdom, Dover Publications, 1923.</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">Einstein, Albert, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151222085312/http://inpac.ucsd.edu/students/courses/winter2012/physics2d/einsteinonrelativity.pdf"><i>How I Constructed the Theory of Relativity</i></a>, translated by Masahiro Morikawa from the text recorded in Japanese by Jun Ishiwara, Association of Asia Pacific Physical Societies (AAPPS) Bulletin, Vol. 15, No. 2, pp. 17–19, April 2005. Einstein recalls events of 1907 in a talk in Japan on 14 December 1922.</span> </li> <li id="cite_note-CliftonFerreiraPadilla-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-CliftonFerreiraPadilla_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-CliftonFerreiraPadilla_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-CliftonFerreiraPadilla_8-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-CliftonFerreiraPadilla_8-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCliftonFerreiraPadillaSkordis2012" class="citation journal cs1">Clifton, Timothy; Ferreira, Pedro G.; Padilla, Antonio; Skordis, Constantinos (March 2012). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0370157312000105">"Modified gravity and cosmology"</a>. <i>Physics Reports</i>. <b>513</b> (1–3): 1–189. <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/1106.2476">1106.2476</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/2012PhR...513....1C">2012PhR...513....1C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physrep.2012.01.001">10.1016/j.physrep.2012.01.001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Reports&rft.atitle=Modified+gravity+and+cosmology&rft.volume=513&rft.issue=1%E2%80%933&rft.pages=1-189&rft.date=2012-03&rft_id=info%3Aarxiv%2F1106.2476&rft_id=info%3Adoi%2F10.1016%2Fj.physrep.2012.01.001&rft_id=info%3Abibcode%2F2012PhR...513....1C&rft.aulast=Clifton&rft.aufirst=Timothy&rft.au=Ferreira%2C+Pedro+G.&rft.au=Padilla%2C+Antonio&rft.au=Skordis%2C+Constantinos&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0370157312000105&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" 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="CITEREFDi_CasolaLiberatiSonego2015" class="citation journal cs1">Di Casola, Eolo; Liberati, Stefano; Sonego, Sebastiano (1 January 2015). <a rel="nofollow" class="external text" href="https://pubs.aip.org/ajp/article/83/1/39/1042100/Nonequivalence-of-equivalence-principles">"Nonequivalence of equivalence principles"</a>. <i>American Journal of Physics</i>. <b>83</b> (1): 39–46. <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/1310.7426">1310.7426</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/2015AmJPh..83...39D">2015AmJPh..83...39D</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%2F1.4895342">10.1119/1.4895342</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9505">0002-9505</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:119110646">119110646</a>. <q>We have seen that the various formulations of the equivalence principle form hierarchy (or rather, a nested sequence of statements narrowing down the type of gravitational theory),</q></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=Nonequivalence+of+equivalence+principles&rft.volume=83&rft.issue=1&rft.pages=39-46&rft.date=2015-01-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119110646%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2015AmJPh..83...39D&rft_id=info%3Aarxiv%2F1310.7426&rft.issn=0002-9505&rft_id=info%3Adoi%2F10.1119%2F1.4895342&rft.aulast=Di+Casola&rft.aufirst=Eolo&rft.au=Liberati%2C+Stefano&rft.au=Sonego%2C+Sebastiano&rft_id=https%3A%2F%2Fpubs.aip.org%2Fajp%2Farticle%2F83%2F1%2F39%2F1042100%2FNonequivalence-of-equivalence-principles&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></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="CITEREFGhinsBudden2001" class="citation journal cs1">Ghins, Michel; Budden, Tim (March 2001). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S1355219800000381">"The Principle of Equivalence"</a>. <i>Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics</i>. <b>32</b> (1): 33–51. <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/2001SHPMP..32...33G">2001SHPMP..32...33G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS1355-2198%2800%2900038-1">10.1016/S1355-2198(00)00038-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Science+Part+B%3A+Studies+in+History+and+Philosophy+of+Modern+Physics&rft.atitle=The+Principle+of+Equivalence&rft.volume=32&rft.issue=1&rft.pages=33-51&rft.date=2001-03&rft_id=info%3Adoi%2F10.1016%2FS1355-2198%2800%2900038-1&rft_id=info%3Abibcode%2F2001SHPMP..32...33G&rft.aulast=Ghins&rft.aufirst=Michel&rft.au=Budden%2C+Tim&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS1355219800000381&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-WagnerSchalmminger-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-WagnerSchalmminger_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-WagnerSchalmminger_11-1"><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="CITEREFWagnerSchlammingerGundlachAdelberger2012" class="citation journal cs1">Wagner, Todd A.; Schlamminger, Stephan; Gundlach, Jens H.; Adelberger, Eric G. (2012). "Torsion-balance tests of the weak equivalence principle". <i>Classical and Quantum Gravity</i>. <b>29</b> (18): 184002. <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/1207.2442">1207.2442</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/2012CQGra..29r4002W">2012CQGra..29r4002W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0264-9381%2F29%2F18%2F184002">10.1088/0264-9381/29/18/184002</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:59141292">59141292</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Classical+and+Quantum+Gravity&rft.atitle=Torsion-balance+tests+of+the+weak+equivalence+principle&rft.volume=29&rft.issue=18&rft.pages=184002&rft.date=2012&rft_id=info%3Aarxiv%2F1207.2442&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A59141292%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0264-9381%2F29%2F18%2F184002&rft_id=info%3Abibcode%2F2012CQGra..29r4002W&rft.aulast=Wagner&rft.aufirst=Todd+A.&rft.au=Schlamminger%2C+Stephan&rft.au=Gundlach%2C+Jens+H.&rft.au=Adelberger%2C+Eric+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Wesson-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wesson_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWesson2006" class="citation book cs1">Wesson, Paul S. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=dSv8ksxHR0oC&q=intitle:Five+intitle:Dimensional+intitle:Physics"><i>Five-dimensional Physics</i></a>. World Scientific. p. 82. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-256-661-4" title="Special:BookSources/978-981-256-661-4"><bdi>978-981-256-661-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Five-dimensional+Physics&rft.pages=82&rft.pub=World+Scientific&rft.date=2006&rft.isbn=978-981-256-661-4&rft.aulast=Wesson&rft.aufirst=Paul+S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DdSv8ksxHR0oC%26q%3Dintitle%3AFive%2Bintitle%3ADimensional%2Bintitle%3APhysics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Lāmmerzahl-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Lāmmerzahl_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Lāmmerzahl_13-1"><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="CITEREFHaugenLämmerzahl2001" class="citation book cs1">Haugen, Mark P.; Lämmerzahl, Claus (2001). "Principles of Equivalence: Their Role in Gravitation Physics and Experiments That Test Them.". <i>Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space. Lecture Notes in Physics</i>. Vol. 562. pp. 195–212. <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/0103067">gr-qc/0103067</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/2001LNP...562..195H">2001LNP...562..195H</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%2F3-540-40988-2_10">10.1007/3-540-40988-2_10</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-41236-6" title="Special:BookSources/978-3-540-41236-6"><bdi>978-3-540-41236-6</bdi></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:15430387">15430387</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Principles+of+Equivalence%3A+Their+Role+in+Gravitation+Physics+and+Experiments+That+Test+Them.&rft.btitle=Gyros%2C+Clocks%2C+Interferometers...%3A+Testing+Relativistic+Gravity+in+Space.+Lecture+Notes+in+Physics&rft.pages=195-212&rft.date=2001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15430387%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2001LNP...562..195H&rft_id=info%3Aarxiv%2Fgr-qc%2F0103067&rft_id=info%3Adoi%2F10.1007%2F3-540-40988-2_10&rft.isbn=978-3-540-41236-6&rft.aulast=Haugen&rft.aufirst=Mark+P.&rft.au=L%C3%A4mmerzahl%2C+Claus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-Will2014-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Will2014_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Will2014_14-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Will2014_14-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Will2014_14-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Will2014_14-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Will2014_14-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Will2014_14-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-Will2014_14-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-Will2014_14-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-Will2014_14-9"><sup><i><b>j</b></i></sup></a> <a href="#cite_ref-Will2014_14-10"><sup><i><b>k</b></i></sup></a> <a href="#cite_ref-Will2014_14-11"><sup><i><b>l</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWill2014" class="citation journal cs1">Will, Clifford M. (December 2014). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255900">"The Confrontation between General Relativity and Experiment"</a>. <i>Living Reviews in Relativity</i>. <b>17</b> (1): 4. <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/1403.7377">1403.7377</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/2014LRR....17....4W">2014LRR....17....4W</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/10.12942%2Flrr-2014-4">10.12942/lrr-2014-4</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2367-3613">2367-3613</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255900">5255900</a></span>. <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/28179848">28179848</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Living+Reviews+in+Relativity&rft.atitle=The+Confrontation+between+General+Relativity+and+Experiment&rft.volume=17&rft.issue=1&rft.pages=4&rft.date=2014-12&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5255900%23id-name%3DPMC&rft_id=info%3Abibcode%2F2014LRR....17....4W&rft_id=info%3Aarxiv%2F1403.7377&rft.issn=2367-3613&rft_id=info%3Adoi%2F10.12942%2Flrr-2014-4&rft_id=info%3Apmid%2F28179848&rft.aulast=Will&rft.aufirst=Clifford+M.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5255900&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHadley1997" class="citation journal cs1">Hadley, Mark J. (1997). "The Logic of Quantum Mechanics Derived from Classical General Relativity". <i>Foundations of Physics Letters</i>. <b>10</b> (1): 43–60. <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/quant-ph/9706018">quant-ph/9706018</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/1997FoPhL..10...43H">1997FoPhL..10...43H</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.6335">10.1.1.252.6335</a></span>. <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%2FBF02764119">10.1007/BF02764119</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:15007947">15007947</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+Letters&rft.atitle=The+Logic+of+Quantum+Mechanics+Derived+from+Classical+General+Relativity&rft.volume=10&rft.issue=1&rft.pages=43-60&rft.date=1997&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15007947%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1997FoPhL..10...43H&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.252.6335%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1007%2FBF02764119&rft_id=info%3Aarxiv%2Fquant-ph%2F9706018&rft.aulast=Hadley&rft.aufirst=Mark+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDurand2002" class="citation journal cs1">Durand, Stéphane (2002). <a rel="nofollow" class="external text" href="http://stacks.iop.org/ob/4/S351">"An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel"</a>. <i>Journal of Optics B: Quantum and Semiclassical Optics</i>. <b>4</b> (4): S351–S357. <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/2002JOptB...4S.351D">2002JOptB...4S.351D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1464-4266%2F4%2F4%2F319">10.1088/1464-4266/4/4/319</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Optics+B%3A+Quantum+and+Semiclassical+Optics&rft.atitle=An+amusing+analogy%3A+modelling+quantum-type+behaviours+with+wormhole-based+time+travel&rft.volume=4&rft.issue=4&rft.pages=S351-S357&rft.date=2002&rft_id=info%3Adoi%2F10.1088%2F1464-4266%2F4%2F4%2F319&rft_id=info%3Abibcode%2F2002JOptB...4S.351D&rft.aulast=Durand&rft.aufirst=St%C3%A9phane&rft_id=http%3A%2F%2Fstacks.iop.org%2Fob%2F4%2FS351&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSinghMüllerBiskupekHackmann2023" class="citation journal cs1">Singh, Vishwa Vijay; Müller, Jürgen; Biskupek, Liliane; Hackmann, Eva; Lämmerzahl, Claus (13 July 2023). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRevLett.131.021401">"Equivalence of Active and Passive Gravitational Mass Tested with Lunar Laser Ranging"</a>. <i>Physical Review Letters</i>. <b>131</b> (2): 021401. <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/2212.09407">2212.09407</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/2023PhRvL.131b1401S">2023PhRvL.131b1401S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.131.021401">10.1103/PhysRevLett.131.021401</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9007">0031-9007</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/37505941">37505941</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Equivalence+of+Active+and+Passive+Gravitational+Mass+Tested+with+Lunar+Laser+Ranging&rft.volume=131&rft.issue=2&rft.pages=021401&rft.date=2023-07-13&rft_id=info%3Abibcode%2F2023PhRvL.131b1401S&rft_id=info%3Aarxiv%2F2212.09407&rft_id=info%3Apmid%2F37505941&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.131.021401&rft.issn=0031-9007&rft.aulast=Singh&rft.aufirst=Vishwa+Vijay&rft.au=M%C3%BCller%2C+J%C3%BCrgen&rft.au=Biskupek%2C+Liliane&rft.au=Hackmann%2C+Eva&rft.au=L%C3%A4mmerzahl%2C+Claus&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FPhysRevLett.131.021401&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Drake-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Drake_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDrake2003" class="citation book cs1">Drake, Stillman (2003). <i>Galileo at Work: His Scientific Biography</i> (Facsim. ed.). Mineola (N.Y.): Dover publ. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780486495422" title="Special:BookSources/9780486495422"><bdi>9780486495422</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Galileo+at+Work%3A+His+Scientific+Biography&rft.place=Mineola+%28N.Y.%29&rft.edition=Facsim.&rft.pub=Dover+publ.&rft.date=2003&rft.isbn=9780486495422&rft.aulast=Drake&rft.aufirst=Stillman&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Devreese-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-Devreese_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Devreese_19-1"><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="CITEREFDevreeseVanden_Berghe2008" class="citation book cs1"><a href="/wiki/Jozef_T._Devreese" title="Jozef T. Devreese">Devreese, Jozef T.</a>; Vanden Berghe, Guido (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?isbn=1845643917"><i><span></span>'Magic Is No Magic': The Wonderful World of Simon Stevin</i></a>. WIT Press. p. 154. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781845643911" title="Special:BookSources/9781845643911"><bdi>9781845643911</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%27Magic+Is+No+Magic%27%3A+The+Wonderful+World+of+Simon+Stevin&rft.pages=154&rft.pub=WIT+Press&rft.date=2008&rft.isbn=9781845643911&rft.aulast=Devreese&rft.aufirst=Jozef+T.&rft.au=Vanden+Berghe%2C+Guido&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fisbn%3D1845643917&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=MJyUDpm9Kvk">"Weak Equivalence Principle test on the moon"</a>. <i><a href="/wiki/YouTube" title="YouTube">YouTube</a></i>. 18 May 2007. <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211221/MJyUDpm9Kvk">Archived</a> from the original on 21 December 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=YouTube&rft.atitle=Weak+Equivalence+Principle+test+on+the+moon&rft.date=2007-05-18&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DMJyUDpm9Kvk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-CiufoliniWheeler-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-CiufoliniWheeler_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-9"><sup><i><b>j</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-10"><sup><i><b>k</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-11"><sup><i><b>l</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-12"><sup><i><b>m</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-13"><sup><i><b>n</b></i></sup></a> <a href="#cite_ref-CiufoliniWheeler_21-14"><sup><i><b>o</b></i></sup></a></span> <span class="reference-text">Ciufolini, Ignazio; Wheeler, John A.; <i>Gravitation and Inertia</i>, Princeton, New Jersey: Princeton University Press, 1995, pp. 117–119</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text">Philoponus, John; "Corollaries on Place and Void", translated by David Furley, Ithaca, New York: Cornell University Press, 1987</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">Stevin, Simon; <i>De Beghinselen der Weeghconst ["Principles of the Art of Weighing"]</i>, Leyden, 1586; Dijksterhuis, Eduard J.; "The Principal Works of Simon Stevin", Amsterdam, 1955</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">Galilei, Galileo; "Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze", Leida: Appresso gli Elsevirii, 1638; "Discourses and Mathematical Demonstrations Concerning Two New Sciences", Leiden: Elsevier Press, 1638</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">Newton, Isaac; "Philosophiae Naturalis Principia Mathematica" [Mathematical Principles of Natural Philosophy and his System of the World], translated by Andrew Motte, revised by Florian Cajori, Berkeley, California: University of California Press, 1934; Newton, Isaac; "The Principia: Mathematical Principles of Natural Philosophy", translated by I. Bernard Cohen and Anne Whitman, with the assistance of Julia Budenz, Berkeley, California: University of California Press, 1999</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">Bessel, Friedrich W.; "Versuche Uber die Kraft, mit welcher die Erde Körper von verschiedner Beschaffenhelt anzieht", <i>Annalen der Physik und Chemie</i>, Berlin: J. Ch. Poggendorff, 25 401–408 (1832)</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">R. v. Eötvös 1890 <a rel="nofollow" class="external text" href="https://archive.org/details/mathematischeund818891890magy"><i>Mathematische und Naturwissenschaftliche Berichte aus Ungarn</i></a>, 8, 65; <i>Annalen der Physik</i> (Leipzig) 68 11 (1922); <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmithHoyleGundlachAdelberger1999" class="citation journal cs1">Smith, G. L.; Hoyle, C. D.; Gundlach, J. H.; Adelberger, E. G.; Heckel, B. R.; Swanson, H. E. (1999). "Short-range tests of the equivalence principle". <i>Physical Review D</i>. <b>61</b> (2): 022001. <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/2405.10982">2405.10982</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/1999PhRvD..61b2001S">1999PhRvD..61b2001S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.61.022001">10.1103/PhysRevD.61.022001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Short-range+tests+of+the+equivalence+principle&rft.volume=61&rft.issue=2&rft.pages=022001&rft.date=1999&rft_id=info%3Aarxiv%2F2405.10982&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.61.022001&rft_id=info%3Abibcode%2F1999PhRvD..61b2001S&rft.aulast=Smith&rft.aufirst=G.+L.&rft.au=Hoyle%2C+C.+D.&rft.au=Gundlach%2C+J.+H.&rft.au=Adelberger%2C+E.+G.&rft.au=Heckel%2C+B.+R.&rft.au=Swanson%2C+H.+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoutherns1910" class="citation journal cs1">Southerns, Leonard (1910). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1910.0078">"A Determination of the Ratio of Mass to Weight for a Radioactive Substance"</a>. <i>Proceedings of the Royal Society of London</i>. <b>84</b> (571): 325–344. <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/1910RSPSA..84..325S">1910RSPSA..84..325S</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/10.1098%2Frspa.1910.0078">10.1098/rspa.1910.0078</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+of+London&rft.atitle=A+Determination+of+the+Ratio+of+Mass+to+Weight+for+a+Radioactive+Substance&rft.volume=84&rft.issue=571&rft.pages=325-344&rft.date=1910&rft_id=info%3Adoi%2F10.1098%2Frspa.1910.0078&rft_id=info%3Abibcode%2F1910RSPSA..84..325S&rft.aulast=Southerns&rft.aufirst=Leonard&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frspa.1910.0078&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Zeeman, Pieter (1918) "Some experiments on gravitation: The ratio of mass to weight for crystals and radioactive substances", <i>Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen</i>, Amsterdam 20(4) 542–553</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPotter1923" class="citation journal cs1">Potter, Harold H. (1923). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1923.0130">"Some Experiments on the Proportionality of Mass and Weight"</a>. <i>Proceedings of the Royal Society of London</i>. <b>104</b> (728): 588–610. <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/1923RSPSA.104..588P">1923RSPSA.104..588P</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/10.1098%2Frspa.1923.0130">10.1098/rspa.1923.0130</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+of+London&rft.atitle=Some+Experiments+on+the+Proportionality+of+Mass+and+Weight&rft.volume=104&rft.issue=728&rft.pages=588-610&rft.date=1923&rft_id=info%3Adoi%2F10.1098%2Frspa.1923.0130&rft_id=info%3Abibcode%2F1923RSPSA.104..588P&rft.aulast=Potter&rft.aufirst=Harold+H.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frspa.1923.0130&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRenner1935" class="citation journal cs1">Renner, János (1935). "Kísérleti vizsgálatok a tömegvonzás és tehetetlenség arányosságáról". <i>Mathematikai és Természettudományi Értesítő</i>. <b>53</b>: 569.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematikai+%C3%A9s+Term%C3%A9szettudom%C3%A1nyi+%C3%89rtes%C3%ADt%C5%91&rft.atitle=K%C3%ADs%C3%A9rleti+vizsg%C3%A1latok+a+t%C3%B6megvonz%C3%A1s+%C3%A9s+tehetetlens%C3%A9g+ar%C3%A1nyoss%C3%A1g%C3%A1r%C3%B3l&rft.volume=53&rft.pages=569&rft.date=1935&rft.aulast=Renner&rft.aufirst=J%C3%A1nos&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-RollKrotkovDicke-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-RollKrotkovDicke_32-0">^</a></b></span> <span class="reference-text">Roll, Peter G.; Krotkov, Robert; Dicke, Robert H.; <i>The equivalence of inertial and passive gravitational mass</i>, Annals of Physics, Volume 26, Issue 3, 20 February 1964, pp. 442–517</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBraginskiPanov1971" class="citation journal cs1">Braginski, Vladimir Borisovich; Panov, Vladimir Ivanovich (1971). "Журнал Экспериментальной и Теоретической Физики". <i>(Zhurnal Éksperimental'noĭ I Teoreticheskoĭ Fiziki, Journal of Experimental and Theoretical Physics)</i>. <b>61</b>: 873.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=%28Zhurnal+%C3%89ksperimental%27no%C4%AD+I+Teoretichesko%C4%AD+Fiziki%2C+Journal+of+Experimental+and+Theoretical+Physics%29&rft.atitle=%D0%96%D1%83%D1%80%D0%BD%D0%B0%D0%BB+%D0%AD%D0%BA%D1%81%D0%BF%D0%B5%D1%80%D0%B8%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9+%D0%B8+%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9+%D0%A4%D0%B8%D0%B7%D0%B8%D0%BA%D0%B8&rft.volume=61&rft.pages=873&rft.date=1971&rft.aulast=Braginski&rft.aufirst=Vladimir+Borisovich&rft.au=Panov%2C+Vladimir+Ivanovich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShapiroCounselmanCharlesKing1976" class="citation journal cs1">Shapiro, Irwin I.; Counselman, III; Charles, C.; King, Robert W. (1976). <a rel="nofollow" class="external text" href="https://archive.today/20140122182435/http://prl.aps.org/pdf/PRL/v36/i11/p555_1">"Verification of the principle of equivalence for massive bodies"</a>. <i>Physical Review Letters</i>. <b>36</b> (11): 555–558. <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/1976PhRvL..36..555S">1976PhRvL..36..555S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevlett.36.555">10.1103/physrevlett.36.555</a>. Archived from <a rel="nofollow" class="external text" href="http://prl.aps.org/pdf/PRL/v36/i11/p555_1">the original</a> on 22 January 2014.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Verification+of+the+principle+of+equivalence+for+massive+bodies&rft.volume=36&rft.issue=11&rft.pages=555-558&rft.date=1976&rft_id=info%3Adoi%2F10.1103%2Fphysrevlett.36.555&rft_id=info%3Abibcode%2F1976PhRvL..36..555S&rft.aulast=Shapiro&rft.aufirst=Irwin+I.&rft.au=Counselman%2C+III&rft.au=Charles%2C+C.&rft.au=King%2C+Robert+W.&rft_id=http%3A%2F%2Fprl.aps.org%2Fpdf%2FPRL%2Fv36%2Fi11%2Fp555_1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKeiserFaller1979" class="citation journal cs1">Keiser, George M.; Faller, James E. (1979). "New approach to the Eötvös experiment". <i>Bulletin of the American Physical Society</i>. <b>24</b>: 579.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Physical+Society&rft.atitle=New+approach+to+the+E%C3%B6tv%C3%B6s+experiment&rft.volume=24&rft.pages=579&rft.date=1979&rft.aulast=Keiser&rft.aufirst=George+M.&rft.au=Faller%2C+James+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNiebauerMcHughFaller1987" class="citation journal cs1">Niebauer, Timothy M.; McHugh, Martin P.; Faller, James E. (1987). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1233860">"Galilean test for the fifth force"</a>. <i>Physical Review Letters</i> (Submitted manuscript). <b>59</b> (6): 609–612. <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/1987PhRvL..59..609N">1987PhRvL..59..609N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevlett.59.609">10.1103/physrevlett.59.609</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/10035824">10035824</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Galilean+test+for+the+fifth+force&rft.volume=59&rft.issue=6&rft.pages=609-612&rft.date=1987&rft_id=info%3Apmid%2F10035824&rft_id=info%3Adoi%2F10.1103%2Fphysrevlett.59.609&rft_id=info%3Abibcode%2F1987PhRvL..59..609N&rft.aulast=Niebauer&rft.aufirst=Timothy+M.&rft.au=McHugh%2C+Martin+P.&rft.au=Faller%2C+James+E.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1233860&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStubbsAdelbergerHeckelRogers1989" class="citation journal cs1">Stubbs, Christopher W.; Adelberger, Eric G.; Heckel, Blayne R.; Rogers, Warren F.; Swanson, H. Erik; Watanabe, R.; Gundlach, Jens H.; Raab, Frederick J. (1989). "Limits on Composition-Dependent Interactions Using a Laboratory Source: Is There a "Fifth Force" Coupled to Isospin?". <i>Physical Review Letters</i>. <b>62</b> (6): 609–612. <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/1989PhRvL..62..609S">1989PhRvL..62..609S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevlett.62.609">10.1103/physrevlett.62.609</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/10040283">10040283</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Limits+on+Composition-Dependent+Interactions+Using+a+Laboratory+Source%3A+Is+There+a+%22Fifth+Force%22+Coupled+to+Isospin%3F&rft.volume=62&rft.issue=6&rft.pages=609-612&rft.date=1989&rft_id=info%3Apmid%2F10040283&rft_id=info%3Adoi%2F10.1103%2Fphysrevlett.62.609&rft_id=info%3Abibcode%2F1989PhRvL..62..609S&rft.aulast=Stubbs&rft.aufirst=Christopher+W.&rft.au=Adelberger%2C+Eric+G.&rft.au=Heckel%2C+Blayne+R.&rft.au=Rogers%2C+Warren+F.&rft.au=Swanson%2C+H.+Erik&rft.au=Watanabe%2C+R.&rft.au=Gundlach%2C+Jens+H.&rft.au=Raab%2C+Frederick+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdelbergerStubbsHeckelSu1990" class="citation journal cs1">Adelberger, Eric G.; Stubbs, Christopher W.; Heckel, Blayne R.; Su, Y.; Swanson, H. Erik; Smith, G. L.; Gundlach, Jens H.; Rogers, Warren F. (1990). "Testing the equivalence principle in the field of the Earth: Particle physics at masses below 1 μeV?". <i>Physical Review D</i>. <b>42</b> (10): 3267–3292. <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/1990PhRvD..42.3267A">1990PhRvD..42.3267A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevd.42.3267">10.1103/physrevd.42.3267</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/10012726">10012726</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Testing+the+equivalence+principle+in+the+field+of+the+Earth%3A+Particle+physics+at+masses+below+1+%CE%BCeV%3F&rft.volume=42&rft.issue=10&rft.pages=3267-3292&rft.date=1990&rft_id=info%3Apmid%2F10012726&rft_id=info%3Adoi%2F10.1103%2Fphysrevd.42.3267&rft_id=info%3Abibcode%2F1990PhRvD..42.3267A&rft.aulast=Adelberger&rft.aufirst=Eric+G.&rft.au=Stubbs%2C+Christopher+W.&rft.au=Heckel%2C+Blayne+R.&rft.au=Su%2C+Y.&rft.au=Swanson%2C+H.+Erik&rft.au=Smith%2C+G.+L.&rft.au=Gundlach%2C+Jens+H.&rft.au=Rogers%2C+Warren+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaeßler2001" class="citation journal cs1">Baeßler, Stefan; et al. (2001). "Remarks by Heinrich Hertz (1857–94) on the equivalence principle". <i>Classical and Quantum Gravity</i>. <b>18</b> (13): 2393. <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/2001CQGra..18.2393B">2001CQGra..18.2393B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0264-9381%2F18%2F13%2F301">10.1088/0264-9381/18/13/301</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:250758089">250758089</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Classical+and+Quantum+Gravity&rft.atitle=Remarks+by+Heinrich+Hertz+%281857%E2%80%9394%29+on+the+equivalence+principle&rft.volume=18&rft.issue=13&rft.pages=2393&rft.date=2001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250758089%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0264-9381%2F18%2F13%2F301&rft_id=info%3Abibcode%2F2001CQGra..18.2393B&rft.aulast=Bae%C3%9Fler&rft.aufirst=Stefan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaeßlerHeckelAdelbergerGundlach1999" class="citation journal cs1">Baeßler, Stefan; Heckel, Blayne R.; Adelberger, Eric G.; Gundlach, Jens H.; Schmidt, Ulrich; Swanson, H. Erik (1999). "Improved Test of the Equivalence Principle for Gravitational Self-Energy". <i>Physical Review Letters</i>. <b>83</b> (18): 3585. <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/1999PhRvL..83.3585B">1999PhRvL..83.3585B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevlett.83.3585">10.1103/physrevlett.83.3585</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Improved+Test+of+the+Equivalence+Principle+for+Gravitational+Self-Energy&rft.volume=83&rft.issue=18&rft.pages=3585&rft.date=1999&rft_id=info%3Adoi%2F10.1103%2Fphysrevlett.83.3585&rft_id=info%3Abibcode%2F1999PhRvL..83.3585B&rft.aulast=Bae%C3%9Fler&rft.aufirst=Stefan&rft.au=Heckel%2C+Blayne+R.&rft.au=Adelberger%2C+Eric+G.&rft.au=Gundlach%2C+Jens+H.&rft.au=Schmidt%2C+Ulrich&rft.au=Swanson%2C+H.+Erik&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchlammingerChoiWagnerGundlach2008" class="citation journal cs1">Schlamminger, Stephan; Choi, Ki-Young; Wagner, Todd A.; Gundlach, Jens H.; Adelberger, Eric G. (2008). "Test of the Equivalence Principle Using a Rotating Torsion Balance". <i>Physical Review Letters</i>. <b>100</b> (4): 041101. <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/0712.0607">0712.0607</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/2008PhRvL.100d1101S">2008PhRvL.100d1101S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.100.041101">10.1103/PhysRevLett.100.041101</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/18352252">18352252</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:18653407">18653407</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Test+of+the+Equivalence+Principle+Using+a+Rotating+Torsion+Balance&rft.volume=100&rft.issue=4&rft.pages=041101&rft.date=2008&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18653407%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2008PhRvL.100d1101S&rft_id=info%3Aarxiv%2F0712.0607&rft_id=info%3Apmid%2F18352252&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.100.041101&rft.aulast=Schlamminger&rft.aufirst=Stephan&rft.au=Choi%2C+Ki-Young&rft.au=Wagner%2C+Todd+A.&rft.au=Gundlach%2C+Jens+H.&rft.au=Adelberger%2C+Eric+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTouboulMétrisRodriguesAndré2017" class="citation journal cs1">Touboul, Pierre; Métris, Gilles; Rodrigues, Manuel; André, Yves; Baghi, Quentin; Bergé, Joël; Boulanger, Damien; Bremer, Stefanie; Carle, Patrice; Chhun, Ratana; Christophe, Bruno; Cipolla, Valerio; Damour, Thibault; Danto, Pascale; Dittus, Hansjoerg; Fayet, Pierre; Foulon, Bernard; Gageant, Claude; Guidotti, Pierre-Yves; Hagedorn, Daniel; Hardy, Emilie; Huynh, Phuong-Anh; Inchauspe, Henri; Kayser, Patrick; Lala, Stéphanie; Lämmerzahl, Claus; Lebat, Vincent; Leseur, Pierre; Liorzou, Françoise; et al. (2017). "MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle". <i>Physical Review Letters</i>. <b>119</b> (23): 231101. <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/1712.01176">1712.01176</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/2017PhRvL.119w1101T">2017PhRvL.119w1101T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.119.231101">10.1103/PhysRevLett.119.231101</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/29286705">29286705</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:6211162">6211162</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=MICROSCOPE+Mission%3A+First+Results+of+a+Space+Test+of+the+Equivalence+Principle&rft.volume=119&rft.issue=23&rft.pages=231101&rft.date=2017&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A6211162%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2017PhRvL.119w1101T&rft_id=info%3Aarxiv%2F1712.01176&rft_id=info%3Apmid%2F29286705&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.119.231101&rft.aulast=Touboul&rft.aufirst=Pierre&rft.au=M%C3%A9tris%2C+Gilles&rft.au=Rodrigues%2C+Manuel&rft.au=Andr%C3%A9%2C+Yves&rft.au=Baghi%2C+Quentin&rft.au=Berg%C3%A9%2C+Jo%C3%ABl&rft.au=Boulanger%2C+Damien&rft.au=Bremer%2C+Stefanie&rft.au=Carle%2C+Patrice&rft.au=Chhun%2C+Ratana&rft.au=Christophe%2C+Bruno&rft.au=Cipolla%2C+Valerio&rft.au=Damour%2C+Thibault&rft.au=Danto%2C+Pascale&rft.au=Dittus%2C+Hansjoerg&rft.au=Fayet%2C+Pierre&rft.au=Foulon%2C+Bernard&rft.au=Gageant%2C+Claude&rft.au=Guidotti%2C+Pierre-Yves&rft.au=Hagedorn%2C+Daniel&rft.au=Hardy%2C+Emilie&rft.au=Huynh%2C+Phuong-Anh&rft.au=Inchauspe%2C+Henri&rft.au=Kayser%2C+Patrick&rft.au=Lala%2C+St%C3%A9phanie&rft.au=L%C3%A4mmerzahl%2C+Claus&rft.au=Lebat%2C+Vincent&rft.au=Leseur%2C+Pierre&rft.au=Liorzou%2C+Fran%C3%A7oise&rft.au=List%2C+Meike&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTouboul,_P.,_Métris,_G.,_Rodrigues,_M.,_Bergé,_J.,_Robert,_A.,_Baghi,_Q.,_André,_Y.,_Bedouet,_J.,_Boulanger,_D.,_Bremer,_S._and_Carle,_P.2022" class="citation journal cs1">Touboul, P., Métris, G., Rodrigues, M., Bergé, J., Robert, A., Baghi, Q., André, Y., Bedouet, J., Boulanger, D., Bremer, S. and Carle, P. (2022). <a rel="nofollow" class="external text" href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.121102">"MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle"</a>. <i>Physical Review Letters</i>. <b>129</b> (12): 121102. <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/2209.15487">2209.15487</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/2022PhRvL.129l1102T">2022PhRvL.129l1102T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.129.121102">10.1103/PhysRevLett.129.121102</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/36179190">36179190</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:252468544">252468544</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=MICROSCOPE+Mission%3A+Final+Results+of+the+Test+of+the+Equivalence+Principle.&rft.volume=129&rft.issue=12&rft.pages=121102&rft.date=2022&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A252468544%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2022PhRvL.129l1102T&rft_id=info%3Aarxiv%2F2209.15487&rft_id=info%3Apmid%2F36179190&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.129.121102&rft.au=Touboul%2C+P.%2C+M%C3%A9tris%2C+G.%2C+Rodrigues%2C+M.%2C+Berg%C3%A9%2C+J.%2C+Robert%2C+A.%2C+Baghi%2C+Q.%2C+Andr%C3%A9%2C+Y.%2C+Bedouet%2C+J.%2C+Boulanger%2C+D.%2C+Bremer%2C+S.+and+Carle%2C+P.&rft_id=https%3A%2F%2Fjournals.aps.org%2Fprl%2Fabstract%2F10.1103%2FPhysRevLett.129.121102&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.npl.washington.edu/eotwash/">"The Eöt-Wash Group | Laboratory Tests of Gravitational and sub-Gravitational Physics"</a>. <i>www.npl.washington.edu</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.npl.washington.edu&rft.atitle=The+E%C3%B6t-Wash+Group+%26%23124%3B+Laboratory+Tests+of+Gravitational+and+sub-Gravitational+Physics&rft_id=http%3A%2F%2Fwww.npl.washington.edu%2Feotwash%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Dittus-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dittus_45-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDittusLāmmerzahl2005" class="citation conference cs1">Dittus, Hansjörg; Lāmmerzahl, Claus (2005). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081217040845/http://www.zarm.uni-bremen.de/2forschung/gravi/publications/papers/2005DittusLaemmerzahl.pdf"><i>Experimental Tests of the Equivalence Principle and Newton's Law in Space</i></a> <span class="cs1-format">(PDF)</span>. Gravitation and Cosmology: 2nd Mexican Meeting on Mathematical and Experimental Physics, AIP Conference Proceedings. Vol. 758. p. 95. <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/2005AIPC..758...95D">2005AIPC..758...95D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1900510">10.1063/1.1900510</a>. Archived from <a rel="nofollow" class="external text" href="http://www.zarm.uni-bremen.de/2forschung/gravi/publications/papers/2005DittusLaemmerzahl.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 17 December 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Experimental+Tests+of+the+Equivalence+Principle+and+Newton%27s+Law+in+Space&rft.pages=95&rft.date=2005&rft_id=info%3Adoi%2F10.1063%2F1.1900510&rft_id=info%3Abibcode%2F2005AIPC..758...95D&rft.aulast=Dittus&rft.aufirst=Hansj%C3%B6rg&rft.au=L%C4%81mmerzahl%2C+Claus&rft_id=http%3A%2F%2Fwww.zarm.uni-bremen.de%2F2forschung%2Fgravi%2Fpublications%2Fpapers%2F2005DittusLaemmerzahl.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://einstein.stanford.edu/STEP/">"S T e P"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=S+T+e+P&rft_id=http%3A%2F%2Feinstein.stanford.edu%2FSTEP%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://eotvos.dm.unipi.it/nobili/">"<span class="cs1-kern-left"></span>"GALILEO GALILEI" GG Small Mission Project"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%22GALILEO+GALILEI%22+GG+Small+Mission+Project&rft_id=http%3A%2F%2Feotvos.dm.unipi.it%2Fnobili%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKimuraAghionAmslerAriga2015" class="citation journal cs1">Kimura, M.; Aghion, S.; Amsler, C.; Ariga, A.; Ariga, T.; Belov, A.; Bonomi, G.; Bräunig, P.; Bremer, J.; Brusa, R. S.; Cabaret, L.; Caccia, M.; Caravita, R.; Castelli, F.; Cerchiari, G.; Chlouba, K.; Cialdi, S.; Comparat, D.; Consolati, G.; Demetrio, A.; Derking, H.; Di Noto, L.; Doser, M.; Dudarev, A.; Ereditato, A.; Ferragut, R.; Fontana, A.; Gerber, S.; Giammarchi, M.; et al. (2015). <a rel="nofollow" class="external text" href="http://stacks.iop.org/1742-6596/631/i=1/a=012047">"Testing the Weak Equivalence Principle with an antimatter beam at CERN"</a>. <i>Journal of Physics: Conference Series</i>. <b>631</b> (1): 012047. <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/2015JPhCS.631a2047K">2015JPhCS.631a2047K</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/10.1088%2F1742-6596%2F631%2F1%2F012047">10.1088/1742-6596/631/1/012047</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2434%2F457743">2434/457743</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physics%3A+Conference+Series&rft.atitle=Testing+the+Weak+Equivalence+Principle+with+an+antimatter+beam+at+CERN&rft.volume=631&rft.issue=1&rft.pages=012047&rft.date=2015&rft_id=info%3Ahdl%2F2434%2F457743&rft_id=info%3Adoi%2F10.1088%2F1742-6596%2F631%2F1%2F012047&rft_id=info%3Abibcode%2F2015JPhCS.631a2047K&rft.aulast=Kimura&rft.aufirst=M.&rft.au=Aghion%2C+S.&rft.au=Amsler%2C+C.&rft.au=Ariga%2C+A.&rft.au=Ariga%2C+T.&rft.au=Belov%2C+A.&rft.au=Bonomi%2C+G.&rft.au=Br%C3%A4unig%2C+P.&rft.au=Bremer%2C+J.&rft.au=Brusa%2C+R.+S.&rft.au=Cabaret%2C+L.&rft.au=Caccia%2C+M.&rft.au=Caravita%2C+R.&rft.au=Castelli%2C+F.&rft.au=Cerchiari%2C+G.&rft.au=Chlouba%2C+K.&rft.au=Cialdi%2C+S.&rft.au=Comparat%2C+D.&rft.au=Consolati%2C+G.&rft.au=Demetrio%2C+A.&rft.au=Derking%2C+H.&rft.au=Di+Noto%2C+L.&rft.au=Doser%2C+M.&rft.au=Dudarev%2C+A.&rft.au=Ereditato%2C+A.&rft.au=Ferragut%2C+R.&rft.au=Fontana%2C+A.&rft.au=Gerber%2C+S.&rft.au=Giammarchi%2C+M.&rft.au=Gligorova%2C+A.&rft_id=http%3A%2F%2Fstacks.iop.org%2F1742-6596%2F631%2Fi%3D1%2Fa%3D012047&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Overduin2009-49"><span class="mw-cite-backlink">^ <a href="#cite_ref-Overduin2009_49-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Overduin2009_49-1"><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="CITEREFOverduinEverittMesterWorden2009" class="citation journal cs1">Overduin, James; Everitt, Francis; Mester, John; Worden, Paul (2009). "The Science Case for STEP". <i>Advances in Space Research</i>. <b>43</b> (10): 1532–1537. <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/0902.2247">0902.2247</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/2009AdSpR..43.1532O">2009AdSpR..43.1532O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.asr.2009.02.012">10.1016/j.asr.2009.02.012</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:8019480">8019480</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Advances+in+Space+Research&rft.atitle=The+Science+Case+for+STEP&rft.volume=43&rft.issue=10&rft.pages=1532-1537&rft.date=2009&rft_id=info%3Aarxiv%2F0902.2247&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A8019480%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.asr.2009.02.012&rft_id=info%3Abibcode%2F2009AdSpR..43.1532O&rft.aulast=Overduin&rft.aufirst=James&rft.au=Everitt%2C+Francis&rft.au=Mester%2C+John&rft.au=Worden%2C+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-Uzan-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-Uzan_50-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUzan2003" class="citation journal cs1">Uzan, Jean-Philippe (7 April 2003). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/RevModPhys.75.403">"The fundamental constants and their variation: observational and theoretical status"</a>. <i>Reviews of Modern Physics</i>. <b>75</b> (2): 403–455. <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/hep-ph/0205340">hep-ph/0205340</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/2003RvMP...75..403U">2003RvMP...75..403U</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.75.403">10.1103/RevModPhys.75.403</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0034-6861">0034-6861</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:118684485">118684485</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.atitle=The+fundamental+constants+and+their+variation%3A+observational+and+theoretical+status&rft.volume=75&rft.issue=2&rft.pages=403-455&rft.date=2003-04-07&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118684485%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2003RvMP...75..403U&rft_id=info%3Aarxiv%2Fhep-ph%2F0205340&rft.issn=0034-6861&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.75.403&rft.aulast=Uzan&rft.aufirst=Jean-Philippe&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FRevModPhys.75.403&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWebbMurphyFlambaumDzuba2001" class="citation journal cs1">Webb, John K.; Murphy, Michael T.; Flambaum, Victor V.; Dzuba, Vladimir A.; Barrow, John D.; Churchill, Chris W.; Prochaska, Jason X.; Wolfe, Arthur M. (2001). "Further Evidence for Cosmological Evolution of the Fine Structure Constant". <i>Physical Review Letters</i>. <b>87</b> (9): 091301. <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/astro-ph/0012539">astro-ph/0012539</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/2001PhRvL..87i1301W">2001PhRvL..87i1301W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.87.091301">10.1103/PhysRevLett.87.091301</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/11531558">11531558</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:40461557">40461557</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Further+Evidence+for+Cosmological+Evolution+of+the+Fine+Structure+Constant&rft.volume=87&rft.issue=9&rft.pages=091301&rft.date=2001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A40461557%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2001PhRvL..87i1301W&rft_id=info%3Aarxiv%2Fastro-ph%2F0012539&rft_id=info%3Apmid%2F11531558&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.87.091301&rft.aulast=Webb&rft.aufirst=John+K.&rft.au=Murphy%2C+Michael+T.&rft.au=Flambaum%2C+Victor+V.&rft.au=Dzuba%2C+Vladimir+A.&rft.au=Barrow%2C+John+D.&rft.au=Churchill%2C+Chris+W.&rft.au=Prochaska%2C+Jason+X.&rft.au=Wolfe%2C+Arthur+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRochaTrottaMartinsMelchiorri2003" class="citation journal cs1">Rocha, G; Trotta, R; Martins, C.J.A.P; Melchiorri, A; Avelino, P.P; Viana, P.T.P (November 2003). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S1387647303001532">"New constraints on varying α"</a>. <i>New Astronomy Reviews</i>. <b>47</b> (8–10): 863–869. <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/astro-ph/0309205">astro-ph/0309205</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/2003NewAR..47..863R">2003NewAR..47..863R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.newar.2003.07.018">10.1016/j.newar.2003.07.018</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:9280269">9280269</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+Astronomy+Reviews&rft.atitle=New+constraints+on+varying+%CE%B1&rft.volume=47&rft.issue=8%E2%80%9310&rft.pages=863-869&rft.date=2003-11&rft_id=info%3Aarxiv%2Fastro-ph%2F0309205&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9280269%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.newar.2003.07.018&rft_id=info%3Abibcode%2F2003NewAR..47..863R&rft.aulast=Rocha&rft.aufirst=G&rft.au=Trotta%2C+R&rft.au=Martins%2C+C.J.A.P&rft.au=Melchiorri%2C+A&rft.au=Avelino%2C+P.P&rft.au=Viana%2C+P.T.P&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS1387647303001532&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20161128185551/http://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html">"Fundamental Physics of Space – Technical Details"</a>. Archived from <a rel="nofollow" class="external text" href="https://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html">the original</a> on 28 November 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">7 May</span> 2005</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Fundamental+Physics+of+Space+%E2%80%93+Technical+Details&rft_id=http%3A%2F%2Ffunphysics.jpl.nasa.gov%2Ftechnical%2Fgrp%2Flunar-laser.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFViswanathanFiengaMinazzoliBernus2018" class="citation journal cs1">Viswanathan, V; Fienga, A; Minazzoli, O; Bernus, L; Laskar, J; Gastineau, M (May 2018). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2Fsty096">"The new lunar ephemeris INPOP17a and its application to fundamental physics"</a>. <i>Monthly Notices of the Royal Astronomical Society</i>. <b>476</b> (2): 1877–1888. <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/1710.09167">1710.09167</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/2018MNRAS.476.1877V">2018MNRAS.476.1877V</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/10.1093%2Fmnras%2Fsty096">10.1093/mnras/sty096</a></span>. <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:119454879">119454879</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=The+new+lunar+ephemeris+INPOP17a+and+its+application+to+fundamental+physics&rft.volume=476&rft.issue=2&rft.pages=1877-1888&rft.date=2018-05&rft_id=info%3Aarxiv%2F1710.09167&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119454879%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1093%2Fmnras%2Fsty096&rft_id=info%3Abibcode%2F2018MNRAS.476.1877V&rft.aulast=Viswanathan&rft.aufirst=V&rft.au=Fienga%2C+A&rft.au=Minazzoli%2C+O&rft.au=Bernus%2C+L&rft.au=Laskar%2C+J&rft.au=Gastineau%2C+M&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fmnras%252Fsty096&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRansom2014" class="citation journal cs1">Ransom, Scott M.; et al. (2014). <a rel="nofollow" class="external text" href="http://www.nature.com/nature/journal/vaop/ncurrent/full/nature12917.html#ref7">"A millisecond pulsar in a stellar triple system"</a>. <i>Nature</i>. <b>505</b> (7484): 520–524. <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/1401.0535">1401.0535</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/2014Natur.505..520R">2014Natur.505..520R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature12917">10.1038/nature12917</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/24390352">24390352</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:4468698">4468698</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=A+millisecond+pulsar+in+a+stellar+triple+system&rft.volume=505&rft.issue=7484&rft.pages=520-524&rft.date=2014&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4468698%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2014Natur.505..520R&rft_id=info%3Aarxiv%2F1401.0535&rft_id=info%3Apmid%2F24390352&rft_id=info%3Adoi%2F10.1038%2Fnature12917&rft.aulast=Ransom&rft.aufirst=Scott+M.&rft_id=http%3A%2F%2Fwww.nature.com%2Fnature%2Fjournal%2Fvaop%2Fncurrent%2Ffull%2Fnature12917.html%23ref7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnne_M._Archibald2018" class="citation journal cs1"><a href="/wiki/Anne_Archibald" title="Anne Archibald">Anne M. Archibald</a>; et al. (4 July 2018). "Universality of free fall from the orbital motion of a pulsar in a stellar triple system". <i>Nature</i>. <b>559</b> (7712): 73–76. <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/1807.02059">1807.02059</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/2018Natur.559...73A">2018Natur.559...73A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41586-018-0265-1">10.1038/s41586-018-0265-1</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/29973733">29973733</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:49578025">49578025</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Universality+of+free+fall+from+the+orbital+motion+of+a+pulsar+in+a+stellar+triple+system&rft.volume=559&rft.issue=7712&rft.pages=73-76&rft.date=2018-07-04&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A49578025%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2018Natur.559...73A&rft_id=info%3Aarxiv%2F1807.02059&rft_id=info%3Apmid%2F29973733&rft_id=info%3Adoi%2F10.1038%2Fs41586-018-0265-1&rft.au=Anne+M.+Archibald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://public.nrao.edu/news/neutron-stars-fall/">"Even Phenomenally Dense Neutron Stars Fall like a Feather – Einstein Gets It Right Again"</a>. <i>Charles Blue, Paul Vosteen</i>. NRAO. 4 July 2018.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Charles+Blue%2C+Paul+Vosteen&rft.atitle=Even+Phenomenally+Dense+Neutron+Stars+Fall+like+a+Feather+%E2%80%93+Einstein+Gets+It+Right+Again&rft.date=2018-07-04&rft_id=https%3A%2F%2Fpublic.nrao.edu%2Fnews%2Fneutron-stars-fall%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVoisinCognardFreireWex2020" class="citation journal cs1">Voisin, G.; Cognard, I.; Freire, P. C. C.; Wex, N.; Guillemot, L.; Desvignes, G.; Kramer, M.; Theureau, G. (1 June 2020). <a rel="nofollow" class="external text" href="https://www.aanda.org/articles/aa/abs/2020/06/aa38104-20/aa38104-20.html">"An improved test of the strong equivalence principle with the pulsar in a triple star system"</a>. <i>Astronomy & Astrophysics</i>. <b>638</b>: A24. <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/2005.01388">2005.01388</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/2020A&A...638A..24V">2020A&A...638A..24V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%2F202038104">10.1051/0004-6361/202038104</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0004-6361">0004-6361</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:218486794">218486794</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+%26+Astrophysics&rft.atitle=An+improved+test+of+the+strong+equivalence+principle+with+the+pulsar+in+a+triple+star+system&rft.volume=638&rft.pages=A24&rft.date=2020-06-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A218486794%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2020A%26A...638A..24V&rft_id=info%3Aarxiv%2F2005.01388&rft.issn=0004-6361&rft_id=info%3Adoi%2F10.1051%2F0004-6361%2F202038104&rft.aulast=Voisin&rft.aufirst=G.&rft.au=Cognard%2C+I.&rft.au=Freire%2C+P.+C.+C.&rft.au=Wex%2C+N.&rft.au=Guillemot%2C+L.&rft.au=Desvignes%2C+G.&rft.au=Kramer%2C+M.&rft.au=Theureau%2C+G.&rft_id=https%3A%2F%2Fwww.aanda.org%2Farticles%2Faa%2Fabs%2F2020%2F06%2Faa38104-20%2Faa38104-20.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEquivalence+principle" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li>Dicke, Robert H.; "New Research on Old Gravitation", <i>Science</i> <b>129</b>, 3349 (1959). Explains the value of research on gravitation and distinguishes between the strong (later renamed "Einstein") and weak equivalence principles.</li> <li>Dicke, Robert H.; "Mach's Principle and Equivalence", in <i>Evidence for gravitational theories: proceedings of course 20 of the International School of Physics "Enrico Fermi"</i>, ed. C. Møller (Academic Press, New York, 1962). This article outlines the approach to precisely testing general relativity advocated by Dicke and pursued from 1959 onwards.</li> <li>Misner, Charles W.; Thorne, Kip S.; and Wheeler, John A.; <i>Gravitation</i>, New York: W. H. Freeman and Company, 1973, Chapter 16 discusses the equivalence principle.</li> <li>Ohanian, Hans; and Ruffini, Remo; <i>Gravitation and Spacetime 2nd edition</i>, New York: Norton, 1994, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-393-96501-5" title="Special:BookSources/0-393-96501-5">0-393-96501-5</a> Chapter 1 discusses the equivalence principle, but incorrectly, according to modern usage, states that the strong equivalence principle is wrong.</li> <li>Will, Clifford M.; <i>Theory and experiment in gravitational physics</i>, Cambridge, UK: Cambridge University Press, 1993. This is the standard technical reference for tests of general relativity.</li> <li>Will, Clifford M.; <i>Was Einstein Right?: Putting General Relativity to the Test</i>, Basic Books (1993). This is a popular account of tests of general relativity.</li> <li>Friedman, Michael; <i>Foundations of Space-Time Theories</i>, Princeton, New Jersey: Princeton University Press, 1983. Chapter V discusses the equivalence principle.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Equivalence_principle" class="extiw" title="q:Special:Search/Equivalence principle">Equivalence principle</a></b></i>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://feynmanlectures.caltech.edu/II_42.html#Ch42-S5">Gravity and the principle of equivalence – The Feynman Lectures on Physics</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080515172036/http://www.phy.syr.edu/courses/modules/LIGHTCONE/equivalence.html">Introducing The Einstein Principle of Equivalence</a> from Syracuse University</li> <li><a rel="nofollow" class="external text" href="http://www.mathpages.com/rr/s5-06/5-06.htm">The Equivalence Principle</a> at MathPages</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090329031728/http://emis.math.ecnu.edu.cn/journals/LRG/Articles/lrr-2001-4/node3.html">The Einstein Equivalence Principle</a> at Living Reviews on General Relativity</li> <li><a rel="nofollow" class="external text" href="https://physicsworld.com/a/equivalence-principle-passes-atomic-test/">"...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 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aria-labelledby="Albert_Einstein" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Albert_Einstein" title="Template:Albert Einstein"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Albert_Einstein" title="Template talk:Albert Einstein"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Albert_Einstein" title="Special:EditPage/Template:Albert Einstein"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Albert_Einstein" style="font-size:114%;margin:0 4em"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a> <ul><li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/General_relativity" title="General relativity">General relativity</a></li></ul></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/Brownian_motion" title="Brownian motion">Brownian motion</a></li> <li><a href="/wiki/Photoelectric_effect" title="Photoelectric effect">Photoelectric effect</a></li> <li><a href="/wiki/Einstein_coefficients" title="Einstein coefficients">Einstein coefficients</a></li> <li><a href="/wiki/Einstein_solid" title="Einstein solid">Einstein solid</a></li> <li><a class="mw-selflink selflink">Equivalence principle</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Einstein_radius" title="Einstein radius">Einstein radius</a></li> <li><a href="/wiki/Einstein_relation_(kinetic_theory)" title="Einstein relation (kinetic theory)">Einstein relation (kinetic theory)</a></li> <li><a href="/wiki/Cosmological_constant" title="Cosmological constant">Cosmological constant</a></li> <li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li> <li><a href="/wiki/Bose%E2%80%93Einstein_statistics" title="Bose–Einstein statistics">Bose–Einstein statistics</a></li> <li><a href="/wiki/Bose%E2%80%93Einstein_correlations" title="Bose–Einstein correlations">Bose–Einstein correlations</a></li> <li><a href="/wiki/Einstein%E2%80%93Cartan_theory" title="Einstein–Cartan theory">Einstein–Cartan theory</a></li> <li><a href="/wiki/Einstein%E2%80%93Infeld%E2%80%93Hoffmann_equations" title="Einstein–Infeld–Hoffmann equations">Einstein–Infeld–Hoffmann equations</a></li> <li><a href="/wiki/Einstein%E2%80%93de_Haas_effect" title="Einstein–de Haas effect">Einstein–de Haas effect</a></li> <li><a href="/wiki/EPR_paradox" class="mw-redirect" title="EPR paradox">EPR paradox</a></li> <li><a href="/wiki/Bohr%E2%80%93Einstein_debates" title="Bohr–Einstein debates">Bohr–Einstein debates</a></li> <li><a href="/wiki/Teleparallelism" title="Teleparallelism">Teleparallelism</a></li> <li><a href="/wiki/Einstein%27s_thought_experiments" title="Einstein's thought experiments">Thought experiments</a></li> <li><a href="/wiki/Einstein%27s_unsuccessful_investigations" title="Einstein's unsuccessful investigations">Unsuccessful investigations</a></li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li> <li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational wave</a></li> <li><a href="/wiki/Tea_leaf_paradox" title="Tea leaf paradox">Tea leaf paradox</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_scientific_publications_by_Albert_Einstein" title="List of scientific publications by Albert Einstein">Works</a></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/Annus_mirabilis_papers" title="Annus mirabilis papers"><i>Annus mirabilis</i> papers</a> (1905)</li> <li>"<a href="/wiki/%C3%9Cber_die_von_der_molekularkinetischen_Theorie_der_W%C3%A4rme_geforderte_Bewegung_von_in_ruhenden_Fl%C3%BCssigkeiten_suspendierten_Teilchen" title="Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen">Investigations on the Theory of Brownian Movement</a>" (1905)</li> <li><i><a href="/wiki/Relativity:_The_Special_and_the_General_Theory" title="Relativity: The Special and the General Theory">Relativity: The Special and the General Theory</a></i> (1916)</li> <li><i><a href="/wiki/The_Meaning_of_Relativity" title="The Meaning of Relativity">The Meaning of Relativity</a></i> (1922)</li> <li><i><a href="/wiki/The_World_as_I_See_It_(book)" title="The World as I See It (book)">The World as I See It</a></i> (1934)</li> <li><i><a href="/wiki/The_Evolution_of_Physics" title="The Evolution of Physics">The Evolution of Physics</a></i> (1938)</li> <li>"<a href="/wiki/Why_Socialism%3F" title="Why Socialism?">Why Socialism?</a>" (1949)</li> <li><a href="/wiki/Russell%E2%80%93Einstein_Manifesto" title="Russell–Einstein Manifesto">Russell–Einstein Manifesto</a> (1955)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Albert_Einstein_in_popular_culture" title="Albert Einstein in popular culture">In popular<br />culture</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Die_Grundlagen_der_Einsteinschen_Relativit%C3%A4ts-Theorie" title="Die Grundlagen der Einsteinschen Relativitäts-Theorie">Die Grundlagen der Einsteinschen Relativitäts-Theorie</a></i> (1922 documentary)</li> <li><i><a href="/wiki/The_Einstein_Theory_of_Relativity" title="The Einstein Theory of Relativity">The Einstein Theory of Relativity</a></i> (1923 documentary)</li> <li><i><a href="/wiki/Relics:_Einstein%27s_Brain" title="Relics: Einstein's Brain">Relics: Einstein's Brain</a></i> (1994 documentary)</li> <li><i><a href="/wiki/Insignificance_(film)" title="Insignificance (film)">Insignificance</a></i> (1985 film)</li> <li><i><a href="/wiki/Young_Einstein" title="Young Einstein">Young Einstein</a></i> (1988 film)</li> <li><i><a href="/wiki/Picasso_at_the_Lapin_Agile" title="Picasso at the Lapin Agile">Picasso at the Lapin Agile</a></i> (1993 play)</li> <li><i><a href="/wiki/I.Q._(film)" title="I.Q. (film)">I.Q.</a></i> (1994 film)</li> <li><i><a href="/wiki/Einstein%27s_Gift" title="Einstein's Gift">Einstein's Gift</a></i> (2003 play)</li> <li><i><a href="/wiki/Einstein_and_Eddington" title="Einstein and Eddington">Einstein and Eddington</a></i> (2008 TV film)</li> <li><i><a href="/wiki/Genius_(American_TV_series)" title="Genius (American TV series)">Genius</a></i> (2017 series)</li> <li><i><a href="/wiki/Oppenheimer_(film)" title="Oppenheimer (film)">Oppenheimer</a></i> (2023 film)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Prizes</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/Albert_Einstein_Award" title="Albert Einstein Award">Albert Einstein Award</a></li> <li><a href="/wiki/Albert_Einstein_Medal" title="Albert Einstein Medal">Albert Einstein Medal</a></li> <li><a href="/wiki/Kalinga_Prize" title="Kalinga Prize">Kalinga Prize</a></li> <li><a href="/wiki/Albert_Einstein_Peace_Prize" title="Albert Einstein Peace Prize">Albert Einstein Peace Prize</a></li> <li><a href="/wiki/Albert_Einstein_World_Award_of_Science" title="Albert Einstein World Award of Science">Albert Einstein World Award of Science</a></li> <li><a href="/wiki/Einstein_Prize_for_Laser_Science" title="Einstein Prize for Laser Science">Einstein Prize for Laser Science</a></li> <li><a href="/wiki/Einstein_Prize_(APS)" title="Einstein Prize (APS)">Einstein Prize (APS)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Books about<br />Einstein</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Albert_Einstein:_Creator_and_Rebel" title="Albert Einstein: Creator and Rebel">Albert Einstein: Creator and Rebel</a></i></li> <li><i><a href="/wiki/Einstein_and_Religion" title="Einstein and Religion">Einstein and Religion</a></i></li> <li><i><a href="/wiki/Einstein_for_Beginners" title="Einstein for Beginners">Einstein for Beginners</a></i></li> <li><i><a href="/wiki/Einstein:_His_Life_and_Universe" title="Einstein: His Life and Universe">Einstein: His Life and Universe</a></i></li> <li><i><a href="/wiki/Einstein%27s_Cosmos" title="Einstein's Cosmos">Einstein's Cosmos</a></i></li> <li><i><a href="/wiki/I_Am_Albert_Einstein" title="I Am Albert Einstein">I Am Albert Einstein</a></i></li> <li><i><a href="/wiki/Introducing_Relativity" title="Introducing Relativity">Introducing Relativity</a></i></li> <li><i><a href="/wiki/Subtle_is_the_Lord" title="Subtle is the Lord">Subtle is the Lord</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Einstein_family" title="Einstein family">Family</a></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/Mileva_Mari%C4%87" title="Mileva Marić">Mileva Marić</a> (first wife)</li> <li><a href="/wiki/Elsa_Einstein" title="Elsa Einstein">Elsa Einstein</a> (second wife; cousin)</li> <li><a href="/wiki/Lieserl_Einstein" class="mw-redirect" title="Lieserl Einstein">Lieserl Einstein</a> (daughter)</li> <li><a href="/wiki/Hans_Albert_Einstein" title="Hans Albert Einstein">Hans Albert Einstein</a> (son)</li> <li><a href="/wiki/Pauline_Koch" class="mw-redirect" title="Pauline Koch">Pauline Koch</a> (mother)</li> <li><a href="/wiki/Hermann_Einstein" class="mw-redirect" title="Hermann Einstein">Hermann Einstein</a> (father)</li> <li><a href="/wiki/Maja_Einstein" title="Maja Einstein">Maja Einstein</a> (sister)</li> <li><a href="/wiki/Einstein_family#Eduard_"Tete"_Einstein_(Albert's_second_son)" title="Einstein family">Eduard Einstein</a> (son)</li> <li><a href="/wiki/Murder_of_the_family_of_Robert_Einstein" title="Murder of the family of Robert Einstein">Robert Einstein</a> (cousin)</li> <li><a href="/wiki/Bernhard_Caesar_Einstein" title="Bernhard Caesar Einstein">Bernhard Caesar Einstein</a> (grandson)</li> <li><a href="/wiki/Evelyn_Einstein" title="Evelyn Einstein">Evelyn Einstein</a> (granddaughter)</li> <li><a href="/wiki/Thomas_Martin_Einstein" class="mw-redirect" title="Thomas Martin Einstein">Thomas Martin Einstein</a> (great-grandson)</li> <li><a href="/wiki/Siegbert_Einstein" title="Siegbert Einstein">Siegbert Einstein</a> (distant cousin)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_awards_and_honors_received_by_Albert_Einstein" title="List of awards and honors received by Albert Einstein">Awards and honors</a></li> <li><a href="/wiki/Brain_of_Albert_Einstein" title="Brain of Albert Einstein">Brain</a></li> <li><a href="/wiki/Albert_Einstein_House" title="Albert Einstein House">House</a></li> <li><a href="/wiki/Albert_Einstein_Memorial" title="Albert Einstein Memorial">Memorial</a></li> <li><a href="/wiki/Political_views_of_Albert_Einstein" title="Political views of Albert Einstein">Political views</a></li> <li><a href="/wiki/Religious_and_philosophical_views_of_Albert_Einstein" title="Religious and philosophical views of Albert Einstein">Religious views</a></li> <li><a href="/wiki/List_of_things_named_after_Albert_Einstein" title="List of things named after Albert Einstein">Things named after</a></li> <li><a href="/wiki/Einstein%E2%80%93Oppenheimer_relationship" title="Einstein–Oppenheimer relationship">Einstein–Oppenheimer relationship</a></li> <li><a href="/wiki/Albert_Einstein_Archives" title="Albert Einstein Archives">Albert Einstein Archives</a></li> <li><a href="/wiki/Einstein%27s_Blackboard" title="Einstein's Blackboard">Einstein's Blackboard</a></li> <li><a href="/wiki/Einstein_Papers_Project" title="Einstein Papers Project">Einstein Papers Project</a></li> <li><a href="/wiki/Einstein_refrigerator" title="Einstein refrigerator">Einstein refrigerator</a></li> <li><a href="/wiki/Einsteinhaus" title="Einsteinhaus">Einsteinhaus</a></li> <li><a href="/wiki/Einsteinium" title="Einsteinium">Einsteinium</a></li> <li><a href="/wiki/Max_Talmey" title="Max Talmey">Max Talmey</a></li> <li><a href="/wiki/Emergency_Committee_of_Atomic_Scientists" title="Emergency Committee of Atomic Scientists">Emergency Committee of Atomic Scientists</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div> <ul><li><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> <b><a href="/wiki/Category:Albert_Einstein" title="Category:Albert Einstein">Category</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Relativity" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Relativity" title="Template:Relativity"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Relativity" title="Template talk:Relativity"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Relativity" title="Special:EditPage/Template:Relativity"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Relativity" style="font-size:114%;margin:0 4em"><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Relativity</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a 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 href="/wiki/Relativity_of_simultaneity" title="Relativity of simultaneity">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 class="mw-selflink selflink">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. 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