Teoria relativității restrânse

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href="#Origini"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Origini</span> </div> </a> <ul id="toc-Origini-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Semnificație" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Semnificație"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Semnificație</span> </div> </a> <ul id="toc-Semnificație-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Postulate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Postulate"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Postulate</span> </div> </a> <ul id="toc-Postulate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lipsa_unui_sistem_de_referință_absolut" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lipsa_unui_sistem_de_referință_absolut"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Lipsa unui sistem de referință absolut</span> </div> </a> <ul id="toc-Lipsa_unui_sistem_de_referință_absolut-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Consecințe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Consecințe"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Consecințe</span> </div> </a> <ul id="toc-Consecințe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sisteme_de_referință,_coordonate_și_transformarea_Lorentz" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sisteme_de_referință,_coordonate_și_transformarea_Lorentz"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Sisteme de referință, coordonate și transformarea Lorentz</span> </div> </a> <ul id="toc-Sisteme_de_referință,_coordonate_și_transformarea_Lorentz-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simultaneitatea" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Simultaneitatea"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Simultaneitatea</span> </div> </a> <ul id="toc-Simultaneitatea-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dilatarea_timpului_și_contracția_lungimilor" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dilatarea_timpului_și_contracția_lungimilor"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Dilatarea timpului și contracția lungimilor</span> </div> </a> <ul id="toc-Dilatarea_timpului_și_contracția_lungimilor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cauzalitatea_și_imposibilitatea_depășirii_vitezei_luminii" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cauzalitatea_și_imposibilitatea_depășirii_vitezei_luminii"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Cauzalitatea și imposibilitatea depășirii vitezei luminii</span> </div> </a> <ul id="toc-Cauzalitatea_și_imposibilitatea_depășirii_vitezei_luminii-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Compunerea_vitezelor" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Compunerea_vitezelor"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Compunerea vitezelor</span> </div> </a> <ul id="toc-Compunerea_vitezelor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Masa,_impulsul_și_energia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Masa,_impulsul_și_energia"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Masa, impulsul și energia</span> </div> </a> <ul id="toc-Masa,_impulsul_și_energia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Masa_relativistă" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Masa_relativistă"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Masa relativistă</span> </div> </a> <ul id="toc-Masa_relativistă-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Forța" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Forța"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Forța</span> </div> </a> <ul id="toc-Forța-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometria_spațiu-timpului" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geometria_spațiu-timpului"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Geometria spațiu-timpului</span> </div> </a> <ul id="toc-Geometria_spațiu-timpului-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fizica_spațiu-timpului" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fizica_spațiu-timpului"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>Fizica spațiu-timpului</span> </div> </a> <button aria-controls="toc-Fizica_spațiu-timpului-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 Fizica spațiu-timpului subsection</span> </button> <ul id="toc-Fizica_spațiu-timpului-sublist" class="vector-toc-list"> <li id="toc-Metrica_și_transformările_de_coordonate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Metrica_și_transformările_de_coordonate"> <div class="vector-toc-text"> <span class="vector-toc-numb">15.1</span> <span>Metrica și transformările de coordonate</span> </div> </a> <ul id="toc-Metrica_și_transformările_de_coordonate-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Statutul_teoriei" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Statutul_teoriei"> <div class="vector-toc-text"> <span class="vector-toc-numb">16</span> <span>Statutul teoriei</span> </div> </a> <button aria-controls="toc-Statutul_teoriei-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 Statutul teoriei subsection</span> </button> <ul id="toc-Statutul_teoriei-sublist" class="vector-toc-list"> <li id="toc-Experimente_fondatoare" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Experimente_fondatoare"> <div class="vector-toc-text"> <span class="vector-toc-numb">16.1</span> <span>Experimente fondatoare</span> </div> </a> <ul id="toc-Experimente_fondatoare-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experimente_testare_teorii_alternative" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Experimente_testare_teorii_alternative"> <div class="vector-toc-text"> <span class="vector-toc-numb">16.2</span> <span>Experimente testare teorii alternative</span> </div> </a> <ul id="toc-Experimente_testare_teorii_alternative-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Oponenți_notabili" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Oponenți_notabili"> <div class="vector-toc-text"> <span class="vector-toc-numb">17</span> <span>Oponenți notabili</span> </div> </a> <ul id="toc-Oponenți_notabili-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">18</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legături_externe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legături_externe"> <div class="vector-toc-text"> <span class="vector-toc-numb">19</span> <span>Legături externe</span> </div> </a> <ul id="toc-Legături_externe-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="Cuprins" 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="Comută cuprinsul" > <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">Comută cuprinsul</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"><span class="mw-page-title-main">Teoria relativității restrânse</span></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="Mergeți la un articol în altă limbă. Disponibil în 109 limbi" > <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-109" 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">109 limbi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Spesiale_relatiwiteit" title="Spesiale relatiwiteit – afrikaans" lang="af" hreflang="af" data-title="Spesiale relatiwiteit" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Spezielle_Relativit%C3%A4tstheorie" title="Spezielle Relativitätstheorie – germană (Elveția)" lang="gsw" hreflang="gsw" data-title="Spezielle Relativitätstheorie" data-language-autonym="Alemannisch" data-language-local-name="germană (Elveția)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%8D%E1%8B%A9_%E1%8A%A0%E1%8A%95%E1%8C%BB%E1%88%AB%E1%8B%8A%E1%8A%90%E1%89%B5" title="ልዩ አንጻራዊነት – amharică" lang="am" hreflang="am" data-title="ልዩ አንጻራዊነት" data-language-autonym="አማርኛ" data-language-local-name="amharică" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Relatividat_especial" title="Relatividat especial – aragoneză" lang="an" hreflang="an" data-title="Relatividat especial" data-language-autonym="Aragonés" data-language-local-name="aragoneză" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D9%86%D8%B3%D8%A8%D9%8A%D8%A9_%D8%A7%D9%84%D8%AE%D8%A7%D8%B5%D8%A9" title="النسبية الخاصة – arabă" lang="ar" hreflang="ar" data-title="النسبية الخاصة" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%86%D8%B3%D8%A8%D9%8A%D9%87_%D8%AE%D8%A7%D8%B5%D9%87" title="نسبيه خاصه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="نسبيه خاصه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%B6%E0%A7%87%E0%A6%B7_%E0%A6%86%E0%A6%AA%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%BF%E0%A6%95%E0%A6%A4%E0%A6%BE%E0%A6%AC%E0%A6%BE%E0%A6%A6_%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="বিশেষ আপেক্ষিকতাবাদ তত্ত্ব – asameză" lang="as" hreflang="as" data-title="বিশেষ আপেক্ষিকতাবাদ তত্ত্ব" data-language-autonym="অসমীয়া" data-language-local-name="asameză" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Teor%C3%ADa_de_la_relativid%C3%A1_especial" title="Teoría de la relatividá especial – asturiană" lang="ast" hreflang="ast" data-title="Teoría de la relatividá especial" data-language-autonym="Asturianu" data-language-local-name="asturiană" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/X%C3%BCsusi_nisbilik_n%C9%99z%C9%99riyy%C9%99si" title="Xüsusi nisbilik nəzəriyyəsi – azeră" lang="az" hreflang="az" data-title="Xüsusi nisbilik nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="azeră" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D8%A4%D8%B2%D9%84_%D9%86%DB%8C%D8%B3%D8%A8%DB%8C%D8%AA" title="اؤزل نیسبیت – South Azerbaijani" lang="azb" hreflang="azb" data-title="اؤزل نیسبیت" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%B0%D1%85%D1%81%D1%83%D1%81_%D1%81%D0%B0%D2%93%D1%8B%D1%88%D1%82%D1%8B%D1%80%D0%BC%D0%B0%D0%BB%D1%8B%D2%A1_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Махсус сағыштырмалыҡ теорияһы – bașkiră" lang="ba" hreflang="ba" data-title="Махсус сағыштырмалыҡ теорияһы" data-language-autonym="Башҡортса" data-language-local-name="bașkiră" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/R%C3%A9lativitas_khusus" title="Rélativitas khusus – balineză" lang="ban" hreflang="ban" data-title="Rélativitas khusus" data-language-autonym="Basa Bali" data-language-local-name="balineză" class="interlanguage-link-target"><span>Basa Bali</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Spezieje_Relativitetstheorie" title="Spezieje Relativitetstheorie – Bavarian" lang="bar" hreflang="bar" data-title="Spezieje Relativitetstheorie" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Spec%C4%93liuoj%C4%97_rel%C4%93t%C4%ABvoma_teuor%C4%97j%C4%97" title="Specēliuojė relētīvoma teuorėjė – Samogitian" lang="sgs" hreflang="sgs" data-title="Specēliuojė relētīvoma teuorėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B0%D0%B4%D0%BD%D0%BE%D1%81%D0%BD%D0%B0%D1%81%D1%86%D1%96" title="Спецыяльная тэорыя адноснасці – belarusă" lang="be" hreflang="be" data-title="Спецыяльная тэорыя адноснасці" data-language-autonym="Беларуская" data-language-local-name="belarusă" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A1%D0%BF%D1%8D%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B0%D0%B4%D0%BD%D0%BE%D1%81%D0%BD%D0%B0%D1%81%D1%8C%D1%86%D1%96" title="Спэцыяльная тэорыя адноснасьці – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Спэцыяльная тэорыя адноснасьці" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%BE%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D0%BD%D0%BE%D1%81%D1%82%D1%82%D0%B0" title="Специална теория на относителността – bulgară" lang="bg" hreflang="bg" data-title="Специална теория на относителността" data-language-autonym="Български" data-language-local-name="bulgară" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AC%E0%A4%BF%E0%A4%B6%E0%A5%87%E0%A4%B8_%E0%A4%B8%E0%A4%BE%E0%A4%AA%E0%A5%87%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%A4%E0%A4%BE" title="बिशेस सापेक्षता – Bhojpuri" lang="bh" hreflang="bh" data-title="बिशेस सापेक्षता" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%B6%E0%A7%87%E0%A6%B7_%E0%A6%86%E0%A6%AA%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%BF%E0%A6%95%E0%A6%A4%E0%A6%BE" title="বিশেষ আপেক্ষিকতা – bengaleză" lang="bn" hreflang="bn" data-title="বিশেষ আপেক্ষিকতা" data-language-autonym="বাংলা" data-language-local-name="bengaleză" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Posebna_teorija_relativnosti" title="Posebna teorija relativnosti – bosniacă" lang="bs" hreflang="bs" data-title="Posebna teorija relativnosti" data-language-autonym="Bosanski" data-language-local-name="bosniacă" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A5%D0%B0%D1%80%D0%B8%D1%81%D0%B0%D0%BD%D0%B3%D1%8B_%D0%B1%D0%B0%D0%B9%D0%B4%D0%B0%D0%BB%D0%B0%D0%B9_%D1%82%D1%83%D1%81%D1%85%D0%B0%D0%B9_%D0%BE%D0%BD%D0%BE%D0%BB" title="Харисангы байдалай тусхай онол – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Харисангы байдалай тусхай онол" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Relativitat_especial" title="Relativitat especial – catalană" lang="ca" hreflang="ca" data-title="Relativitat especial" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%95%DB%8E%DA%98%DB%95%DB%8C%DB%8C%DB%8C_%D8%AA%D8%A7%DB%8C%D8%A8%DB%95%D8%AA" title="ڕێژەییی تایبەت – kurdă centrală" lang="ckb" hreflang="ckb" data-title="ڕێژەییی تایبەت" data-language-autonym="کوردی" data-language-local-name="kurdă centrală" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Speci%C3%A1ln%C3%AD_teorie_relativity" title="Speciální teorie relativity – cehă" lang="cs" hreflang="cs" data-title="Speciální teorie relativity" data-language-autonym="Čeština" data-language-local-name="cehă" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D0%B0%D0%BD%D0%BB%D0%B0%D1%88%D1%82%D0%B0%D1%80%D1%83%D0%BB%C4%83%D1%85%C4%83%D0%BD_%D1%8F%D1%82%D0%B0%D1%80%D0%BB%C4%83_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B9%C4%95" title="Танлаштарулăхăн ятарлă теорийĕ – ciuvașă" lang="cv" hreflang="cv" data-title="Танлаштарулăхăн ятарлă теорийĕ" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Perthnasedd_arbennig" title="Perthnasedd arbennig – galeză" lang="cy" hreflang="cy" data-title="Perthnasedd arbennig" data-language-autonym="Cymraeg" data-language-local-name="galeză" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Speciel_relativitetsteori" title="Speciel relativitetsteori – daneză" lang="da" hreflang="da" data-title="Speciel relativitetsteori" data-language-autonym="Dansk" data-language-local-name="daneză" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="articol bun"><a href="https://de.wikipedia.org/wiki/Spezielle_Relativit%C3%A4tstheorie" title="Spezielle Relativitätstheorie – germană" lang="de" hreflang="de" data-title="Spezielle Relativitätstheorie" data-language-autonym="Deutsch" data-language-local-name="germană" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Teoriya_Relatifiya_X%C4%B1susiye" title="Teoriya Relatifiya Xısusiye – Zazaki" lang="diq" hreflang="diq" data-title="Teoriya Relatifiya Xısusiye" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CE%AE_%CF%83%CF%87%CE%B5%CF%84%CE%B9%CE%BA%CF%8C%CF%84%CE%B7%CF%84%CE%B1" title="Ειδική σχετικότητα – greacă" lang="el" hreflang="el" data-title="Ειδική σχετικότητα" data-language-autonym="Ελληνικά" data-language-local-name="greacă" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Special_relativity" title="Special relativity – engleză" lang="en" hreflang="en" data-title="Special relativity" data-language-autonym="English" data-language-local-name="engleză" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Speciala_teorio_de_relativeco" title="Speciala teorio de relativeco – esperanto" lang="eo" hreflang="eo" data-title="Speciala teorio de relativeco" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_de_la_relatividad_especial" title="Teoría de la relatividad especial – spaniolă" lang="es" hreflang="es" data-title="Teoría de la relatividad especial" data-language-autonym="Español" data-language-local-name="spaniolă" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Erirelatiivsusteooria" title="Erirelatiivsusteooria – estonă" lang="et" hreflang="et" data-title="Erirelatiivsusteooria" data-language-autonym="Eesti" data-language-local-name="estonă" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erlatibitate_berezia" title="Erlatibitate berezia – bască" lang="eu" hreflang="eu" data-title="Erlatibitate berezia" data-language-autonym="Euskara" data-language-local-name="bască" 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/%D9%86%D8%B3%D8%A8%DB%8C%D8%AA_%D8%AE%D8%A7%D8%B5" title="نسبیت خاص – persană" lang="fa" hreflang="fa" data-title="نسبیت خاص" data-language-autonym="فارسی" data-language-local-name="persană" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Erityinen_suhteellisuusteoria" title="Erityinen suhteellisuusteoria – finlandeză" lang="fi" hreflang="fi" data-title="Erityinen suhteellisuusteoria" data-language-autonym="Suomi" data-language-local-name="finlandeză" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Relativit%C3%A9_restreinte" title="Relativité restreinte – franceză" lang="fr" hreflang="fr" data-title="Relativité restreinte" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Te%C3%B2irig_sh%C3%B2nraichte_na_d%C3%A0imheachd" title="Teòirig shònraichte na dàimheachd – gaelică scoțiană" lang="gd" hreflang="gd" data-title="Teòirig shònraichte na dàimheachd" data-language-autonym="Gàidhlig" data-language-local-name="gaelică scoțiană" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Relatividade_especial" title="Relatividade especial – galiciană" lang="gl" hreflang="gl" data-title="Relatividade especial" data-language-autonym="Galego" data-language-local-name="galiciană" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Mba%27ekuaar%C3%A3_joguerahavi%C3%A1rava_ijap%C3%BDva" title="Mba'ekuaarã joguerahaviárava ijapýva – guarani" lang="gn" hreflang="gn" data-title="Mba'ekuaarã joguerahaviárava ijapýva" data-language-autonym="Avañe'ẽ" data-language-local-name="guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%99%D7%97%D7%A1%D7%95%D7%AA_%D7%94%D7%A4%D7%A8%D7%98%D7%99%D7%AA" title="תורת היחסות הפרטית – ebraică" lang="he" hreflang="he" data-title="תורת היחסות הפרטית" data-language-autonym="עברית" data-language-local-name="ebraică" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B6%E0%A4%BF%E0%A4%B7%E0%A5%8D%E0%A4%9F_%E0%A4%86%E0%A4%AA%E0%A5%87%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%BF%E0%A4%95%E0%A4%A4%E0%A4%BE" title="विशिष्ट आपेक्षिकता – hindi" lang="hi" hreflang="hi" data-title="विशिष्ट आपेक्षिकता" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Special_relativity" title="Special relativity – Fiji Hindi" lang="hif" hreflang="hif" data-title="Special relativity" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://hr.wikipedia.org/wiki/Posebna_teorija_relativnosti" title="Posebna teorija relativnosti – croată" lang="hr" hreflang="hr" data-title="Posebna teorija relativnosti" data-language-autonym="Hrvatski" data-language-local-name="croată" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Speci%C3%A1lis_relativit%C3%A1selm%C3%A9let" title="Speciális relativitáselmélet – maghiară" lang="hu" hreflang="hu" data-title="Speciális relativitáselmélet" data-language-autonym="Magyar" data-language-local-name="maghiară" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D6%80%D5%A1%D5%A2%D5%A5%D6%80%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%A1%D5%B6_%D5%B0%D5%A1%D5%BF%D5%B8%D6%82%D5%AF_%D5%BF%D5%A5%D5%BD%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Հարաբերականության հատուկ տեսություն – armeană" lang="hy" hreflang="hy" data-title="Հարաբերականության հատուկ տեսություն" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Relativitate_special" title="Relativitate special – interlingua" lang="ia" hreflang="ia" data-title="Relativitate special" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Relativitas_khusus" title="Relativitas khusus – indoneziană" lang="id" hreflang="id" data-title="Relativitas khusus" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Specala_relativeso" title="Specala relativeso – ido" lang="io" hreflang="io" data-title="Specala relativeso" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Takmarka%C3%B0a_afst%C3%A6%C3%B0iskenningin" title="Takmarkaða afstæðiskenningin – islandeză" lang="is" hreflang="is" data-title="Takmarkaða afstæðiskenningin" data-language-autonym="Íslenska" data-language-local-name="islandeză" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Relativit%C3%A0_ristretta" title="Relatività ristretta – italiană" lang="it" hreflang="it" data-title="Relatività ristretta" data-language-autonym="Italiano" data-language-local-name="italiană" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%89%B9%E6%AE%8A%E7%9B%B8%E5%AF%BE%E6%80%A7%E7%90%86%E8%AB%96" title="特殊相対性理論 – japoneză" lang="ja" hreflang="ja" data-title="特殊相対性理論" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A4%E1%83%90%E1%83%A0%E1%83%93%E1%83%9D%E1%83%91%E1%83%98%E1%83%97%E1%83%9D%E1%83%91%E1%83%98%E1%83%A1_%E1%83%A1%E1%83%9E%E1%83%94%E1%83%AA%E1%83%98%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90" title="ფარდობითობის სპეციალური თეორია – georgiană" lang="ka" hreflang="ka" data-title="ფარდობითობის სპეციალური თეორია" data-language-autonym="ქართული" data-language-local-name="georgiană" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%80%D0%BD%D0%B0%D0%B9%D1%8B_%D1%81%D0%B0%D0%BB%D1%8B%D1%81%D1%82%D1%8B%D1%80%D0%BC%D0%B0%D0%BB%D1%8B%D0%BB%D1%8B%D2%9B_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Арнайы салыстырмалылық теориясы – kazahă" lang="kk" hreflang="kk" data-title="Арнайы салыстырмалылық теориясы" data-language-autonym="Қазақша" data-language-local-name="kazahă" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8A%B9%EC%88%98_%EC%83%81%EB%8C%80%EC%84%B1%EC%9D%B4%EB%A1%A0" title="특수 상대성이론 – coreeană" lang="ko" hreflang="ko" data-title="특수 상대성이론" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%82%D0%B0%D0%B9%D1%8B%D0%BD_%D1%81%D0%B0%D0%BB%D1%8B%D1%88%D1%82%D1%8B%D1%80%D0%BC%D0%B0%D0%BB%D1%83%D1%83%D0%BB%D1%83%D0%BA_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Атайын салыштырмалуулук теориясы – kârgâză" lang="ky" hreflang="ky" data-title="Атайын салыштырмалуулук теориясы" data-language-autonym="Кыргызча" data-language-local-name="kârgâză" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://la.wikipedia.org/wiki/Relativitas_specialis" title="Relativitas specialis – latină" lang="la" hreflang="la" data-title="Relativitas specialis" data-language-autonym="Latina" data-language-local-name="latină" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Specialioji_reliatyvumo_teorija" title="Specialioji reliatyvumo teorija – lituaniană" lang="lt" hreflang="lt" data-title="Specialioji reliatyvumo teorija" data-language-autonym="Lietuvių" data-language-local-name="lituaniană" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Speci%C4%81l%C4%81_relativit%C4%81tes_teorija" title="Speciālā relativitātes teorija – letonă" lang="lv" hreflang="lv" data-title="Speciālā relativitātes teorija" data-language-autonym="Latviešu" data-language-local-name="letonă" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B7%D0%B0_%D1%80%D0%B5%D0%BB%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D0%B0" title="Специјална теорија за релативноста – macedoneană" lang="mk" hreflang="mk" data-title="Специјална теорија за релативноста" data-language-autonym="Македонски" data-language-local-name="macedoneană" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B4%BF%E0%B4%B6%E0%B4%BF%E0%B4%B7%E0%B5%8D%E0%B4%9F_%E0%B4%86%E0%B4%AA%E0%B5%87%E0%B4%95%E0%B5%8D%E0%B4%B7%E0%B4%BF%E0%B4%95%E0%B4%A4%E0%B4%BE_%E0%B4%B8%E0%B4%BF%E0%B4%A6%E0%B5%8D%E0%B4%A7%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%82" title="വിശിഷ്ട ആപേക്ഷികതാ സിദ്ധാന്തം – malayalam" lang="ml" hreflang="ml" data-title="വിശിഷ്ട ആപേക്ഷികതാ സിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D0%B0%D1%80%D1%8C%D1%86%D0%B0%D0%BD%D0%B3%D1%83%D0%B9%D0%BD_%D1%82%D1%83%D1%81%D0%B3%D0%B0%D0%B9_%D0%BE%D0%BD%D0%BE%D0%BB" title="Харьцангуйн тусгай онол – mongolă" lang="mn" hreflang="mn" data-title="Харьцангуйн тусгай онол" data-language-autonym="Монгол" data-language-local-name="mongolă" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B6%E0%A5%87%E0%A4%B7_%E0%A4%B8%E0%A4%BE%E0%A4%AA%E0%A5%87%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%A4%E0%A4%BE" title="विशेष सापेक्षता – marathi" lang="mr" hreflang="mr" data-title="विशेष सापेक्षता" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kerelatifan_khas" title="Kerelatifan khas – malaeză" lang="ms" hreflang="ms" data-title="Kerelatifan khas" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Relattivit%C3%A0_ristretta" title="Relattività ristretta – malteză" lang="mt" hreflang="mt" data-title="Relattività ristretta" data-language-autonym="Malti" data-language-local-name="malteză" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%91%E1%80%B0%E1%80%B8%E1%80%94%E1%80%BE%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9B%E1%80%9E%E1%80%AE%E1%80%A1%E1%80%AD%E1%80%AF%E1%80%9B%E1%80%AE" title="အထူးနှိုင်းရသီအိုရီ – birmană" lang="my" hreflang="my" data-title="အထူးနှိုင်းရသီအိုရီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmană" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Spetschale_Relativit%C3%A4tstheorie" title="Spetschale Relativitätstheorie – germana de jos" lang="nds" hreflang="nds" data-title="Spetschale Relativitätstheorie" data-language-autonym="Plattdüütsch" data-language-local-name="germana de jos" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Speciale_relativiteitstheorie" title="Speciale relativiteitstheorie – neerlandeză" lang="nl" hreflang="nl" data-title="Speciale relativiteitstheorie" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Den_spesielle_relativitetsteorien" title="Den spesielle relativitetsteorien – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Den spesielle relativitetsteorien" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Den_spesielle_relativitetsteorien" title="Den spesielle relativitetsteorien – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Den spesielle relativitetsteorien" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Relativitat_especiala" title="Relativitat especiala – occitană" lang="oc" hreflang="oc" data-title="Relativitat especiala" data-language-autonym="Occitan" data-language-local-name="occitană" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AC%E0%AC%BF%E0%AC%B6%E0%AD%87%E0%AC%B7_%E0%AC%86%E0%AC%AA%E0%AD%87%E0%AC%95%E0%AD%8D%E0%AC%B7%E0%AC%BF%E0%AC%95_%E0%AC%A4%E0%AC%A4%E0%AD%8D%E0%AC%A4%E0%AD%8D%E0%AD%B1" title="ବିଶେଷ ଆପେକ୍ଷିକ ତତ୍ତ୍ୱ – odia" lang="or" hreflang="or" data-title="ବିଶେଷ ଆପେକ୍ଷିକ ତତ୍ତ୍ୱ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A8%BF%E0%A8%B8%E0%A8%BC%E0%A9%87%E0%A8%B8%E0%A8%BC_%E0%A8%B8%E0%A8%BE%E0%A8%AA%E0%A9%87%E0%A8%96%E0%A8%A4%E0%A8%BE" title="ਵਿਸ਼ੇਸ਼ ਸਾਪੇਖਤਾ – punjabi" lang="pa" hreflang="pa" data-title="ਵਿਸ਼ੇਸ਼ ਸਾਪੇਖਤਾ" 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/Szczeg%C3%B3lna_teoria_wzgl%C4%99dno%C5%9Bci" title="Szczególna teoria względności – poloneză" lang="pl" hreflang="pl" data-title="Szczególna teoria względności" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Teor%C3%ACa_dla_relativit%C3%A0_limit%C3%A0" title="Teorìa dla relatività limità – Piedmontese" lang="pms" hreflang="pms" data-title="Teorìa dla relatività limità" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B3%D9%BE%DB%8C%D8%B4%D9%84_%D8%B1%DB%8C%D9%84%DB%8C%D9%B9%DB%8C%D9%88%D9%B9%DB%8C" title="سپیشل ریلیٹیوٹی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="سپیشل ریلیٹیوٹی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DA%81%D8%A7%D9%86%DA%AB%DA%93%DB%8C_%D9%86%D8%B3%D8%A8%D9%8A%D8%AA" title="ځانګړی نسبيت – paștună" lang="ps" hreflang="ps" data-title="ځانګړی نسبيت" data-language-autonym="پښتو" data-language-local-name="paștună" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Relatividade_restrita" title="Relatividade restrita – portugheză" lang="pt" hreflang="pt" data-title="Relatividade restrita" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BE%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Специальная теория относительности – rusă" lang="ru" hreflang="ru" data-title="Специальная теория относительности" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Tiur%C3%ACa_di_la_rilativitati_spiciali" title="Tiurìa di la rilativitati spiciali – siciliană" lang="scn" hreflang="scn" data-title="Tiurìa di la rilativitati spiciali" data-language-autonym="Sicilianu" data-language-local-name="siciliană" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Special_relativity" title="Special relativity – scots" lang="sco" hreflang="sco" data-title="Special relativity" data-language-autonym="Scots" data-language-local-name="scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%AE%D8%A7%D8%B5_%D9%86%D8%B3%D8%A8%D8%AA_%D8%AC%D9%88_%D9%86%D8%B8%D8%B1%D9%8A%D9%88" title="خاص نسبت جو نظريو – sindhi" lang="sd" hreflang="sd" data-title="خاص نسبت جو نظريو" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Specijalna_teorija_relativnosti" title="Specijalna teorija relativnosti – sârbo-croată" lang="sh" hreflang="sh" data-title="Specijalna teorija relativnosti" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="sârbo-croată" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%9A%E0%B7%82_%E0%B7%83%E0%B7%8F%E0%B6%B4%E0%B7%9A%E0%B6%9A%E0%B7%8A%E0%B7%82%E0%B6%AD%E0%B7%8F%E0%B7%80%E0%B7%8F%E0%B6%AF%E0%B6%BA" title="විශේෂ සාපේක්ෂතාවාදය – singhaleză" lang="si" hreflang="si" data-title="විශේෂ සාපේක්ෂතාවාදය" data-language-autonym="සිංහල" data-language-local-name="singhaleză" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Special_relativity" title="Special relativity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Special relativity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://sk.wikipedia.org/wiki/%C5%A0peci%C3%A1lna_te%C3%B3ria_relativity" title="Špeciálna teória relativity – slovacă" lang="sk" hreflang="sk" data-title="Špeciálna teória relativity" data-language-autonym="Slovenčina" data-language-local-name="slovacă" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Posebna_teorija_relativnosti" title="Posebna teorija relativnosti – slovenă" lang="sl" hreflang="sl" data-title="Posebna teorija relativnosti" data-language-autonym="Slovenščina" data-language-local-name="slovenă" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Teoria_speciale_e_relativitetit" title="Teoria speciale e relativitetit – albaneză" lang="sq" hreflang="sq" data-title="Teoria speciale e relativitetit" data-language-autonym="Shqip" data-language-local-name="albaneză" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Specijalna_teorija_relativnosti" title="Specijalna teorija relativnosti – sârbă" lang="sr" hreflang="sr" data-title="Specijalna teorija relativnosti" data-language-autonym="Српски / srpski" data-language-local-name="sârbă" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Teori_Relativitas_Khusus" title="Teori Relativitas Khusus – sundaneză" lang="su" hreflang="su" data-title="Teori Relativitas Khusus" data-language-autonym="Sunda" data-language-local-name="sundaneză" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Speciella_relativitetsteorin" title="Speciella relativitetsteorin – suedeză" lang="sv" hreflang="sv" data-title="Speciella relativitetsteorin" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Uhusianifu_maalumu" title="Uhusianifu maalumu – swahili" lang="sw" hreflang="sw" data-title="Uhusianifu maalumu" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BF%E0%AE%B1%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="சிறப்புச் சார்புக் கோட்பாடு – tamilă" lang="ta" hreflang="ta" data-title="சிறப்புச் சார்புக் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="tamilă" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%AA%E0%B8%B1%E0%B8%A1%E0%B8%9E%E0%B8%B1%E0%B8%97%E0%B8%98%E0%B8%A0%E0%B8%B2%E0%B8%9E%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9" title="ทฤษฎีสัมพัทธภาพพิเศษ – thailandeză" lang="th" hreflang="th" data-title="ทฤษฎีสัมพัทธภาพพิเศษ" data-language-autonym="ไทย" data-language-local-name="thailandeză" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Teorya_ng_natatanging_relatibidad" title="Teorya ng natatanging relatibidad – tagalog" lang="tl" hreflang="tl" data-title="Teorya ng natatanging relatibidad" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96zel_g%C3%B6relilik" title="Özel görelilik – turcă" lang="tr" hreflang="tr" data-title="Özel görelilik" data-language-autonym="Türkçe" data-language-local-name="turcă" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://tt.wikipedia.org/wiki/Maxsus_%C3%A7a%C4%9F%C4%B1%C5%9Ft%C4%B1rmal%C4%B1l%C4%B1q_teori%C3%A4se" title="Maxsus çağıştırmalılıq teoriäse – tătară" lang="tt" hreflang="tt" data-title="Maxsus çağıştırmalılıq teoriäse" data-language-autonym="Татарча / tatarça" data-language-local-name="tătară" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D1%96%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B2%D1%96%D0%B4%D0%BD%D0%BE%D1%81%D0%BD%D0%BE%D1%81%D1%82%D1%96" title="Спеціальна теорія відносності – ucraineană" lang="uk" hreflang="uk" data-title="Спеціальна теорія відносності" data-language-autonym="Українська" data-language-local-name="ucraineană" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%B6%D8%A7%D9%81%DB%8C%D8%AA_%D9%85%D8%AE%D8%B5%D9%88%D8%B5%DB%81" title="اضافیت مخصوصہ – urdu" lang="ur" hreflang="ur" data-title="اضافیت مخصوصہ" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Maxsus_nisbiylik_nazariyasi" title="Maxsus nisbiylik nazariyasi – uzbecă" lang="uz" hreflang="uz" data-title="Maxsus nisbiylik nazariyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Specialine_rel%C3%A4tivi%C5%BEusen_teorii" title="Specialine relätivižusen teorii – Veps" lang="vep" hreflang="vep" data-title="Specialine relätivižusen teorii" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Thuy%E1%BA%BFt_t%C6%B0%C6%A1ng_%C4%91%E1%BB%91i_h%E1%BA%B9p" title="Thuyết tương đối hẹp – vietnameză" lang="vi" hreflang="vi" data-title="Thuyết tương đối hẹp" data-language-autonym="Tiếng Việt" data-language-local-name="vietnameză" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Pinaurog_nga_relatibidad" title="Pinaurog nga relatibidad – waray" lang="war" hreflang="war" data-title="Pinaurog nga relatibidad" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%8B%AD%E4%B9%89%E7%9B%B8%E5%AF%B9%E8%AE%BA" title="狭义相对论 – chineză wu" lang="wuu" hreflang="wuu" data-title="狭义相对论" data-language-autonym="吴语" data-language-local-name="chineză wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A1%D7%A4%D7%A2%D7%A6%D7%99%D7%A2%D7%9C%D7%A2_%D7%98%D7%A2%D7%90%D7%A8%D7%99%D7%A2_%D7%A4%D7%95%D7%9F_%D7%A8%D7%A2%D7%9C%D7%90%D7%98%D7%99%D7%95%D7%95%D7%99%D7%98%D7%A2%D7%98" title="ספעציעלע טעאריע פון רעלאטיוויטעט – idiș" lang="yi" hreflang="yi" data-title="ספעציעלע טעאריע פון רעלאטיוויטעט" data-language-autonym="ייִדיש" data-language-local-name="idiș" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%8B%AD%E4%B9%89%E7%9B%B8%E5%AF%B9%E8%AE%BA" title="狭义相对论 – chineză" lang="zh" hreflang="zh" data-title="狭义相对论" data-language-autonym="中文" data-language-local-name="chineză" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%8B%B9%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="狹義相對論 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="狹義相對論" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%8B%B9%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="狹義相對論 – cantoneză" lang="yue" hreflang="yue" data-title="狹義相對論" data-language-autonym="粵語" data-language-local-name="cantoneză" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11455#sitelinks-wikipedia" title="Modifică legăturile interlinguale" class="wbc-editpage">Modifică legăturile</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Spații de nume"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon 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0.2em;padding-top:0;font-size:145%;line-height:1.2em"><a href="/wiki/Relativitate_general%C4%83" class="mw-redirect" title="Relativitate generală">Relativitate generală</a></th></tr><tr><td style="padding:0.2em 0 0.4em"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier: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 style="padding-top:0.2em;line-height:1.2em;padding:0.5em 0.2em 0.6em;border-bottom:1px solid #aaa; display:block;margin-bottom:0.1em;"><a href="/w/index.php?title=Einstein_field_equations&action=edit&redlink=1" class="new" title="Einstein field equations — pagină inexistentă"><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 }={8\pi G \over c^{4}}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"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </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 }={8\pi G \over c^{4}}T_{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/021a494922172bfe1c9fa4e80d25ac90228d72cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.286ex; height:5.676ex;" alt="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }}"></span></a></div></td></tr><tr><td style="padding:0 0.1em 0.4em;padding-bottom:0.75em;"> <ul><li><div class="hlist" style="margin-left:0em;"><div class="plainlist"><ul style=""><li style=""><a href="/w/index.php?title=Istoria_relativit%C4%83%C8%9Bii_generale&action=edit&redlink=1" class="new" title="Istoria relativității generale — pagină inexistentă">Istoric</a> </li><li style=""> <a href="/wiki/Teste_experimentale_ale_relativit%C4%83%C8%9Bii_generale" class="mw-redirect" title="Teste experimentale ale relativității generale">Teste</a></li></ul></div></div></li> <li><a href="/w/index.php?title=Matematica_relativit%C4%83%C8%9Bii_generale&action=edit&redlink=1" class="new" title="Matematica relativității generale — pagină inexistentă">Formulare matematică</a></li> <li><div class="hlist" style="margin-left:0em;"></div></li></ul></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:#ddf; text-align:center;">Concepte fundamentale</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Principiul_relativit%C4%83%C8%9Bii" title="Principiul relativității">Principiul relativității</a></li> <li><a href="/wiki/Teoria_relativit%C4%83%C8%9Bii" title="Teoria relativității">Teoria relativității</a></li> <li><a href="/wiki/Sistem_de_referin%C8%9B%C4%83" title="Sistem de referință">Sistem de referință</a></li> <li><a href="/wiki/Sistem_de_referin%C8%9B%C4%83_iner%C8%9Bial" title="Sistem de referință inerțial">Sistem de referință inerțial</a></li> <li><a href="/wiki/Principiul_echivalen%C8%9Bei" title="Principiul echivalenței">Principiul echivalenței</a></li> <li><a href="/wiki/Echivalen%C8%9B%C4%83_mas%C4%83%E2%80%93energie" class="mw-redirect" title="Echivalență masă–energie">Echivalență masă–energie</a></li> <li><a class="mw-selflink selflink">Relativitatea restrânsă</a></li> <li><a href="/w/index.php?title=Geometrie_riemannian%C4%83&action=edit&redlink=1" class="new" title="Geometrie riemanniană — pagină inexistentă">Geometrie riemanniană</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:#ddf; text-align:center;">Fenomenologie</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;color:var(--color-base, #000) !important;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td style="padding:0 0.1em 0.4em"> <ul><li><a href="/w/index.php?title=Gravitoelectromagnetism&action=edit&redlink=1" class="new" title="Gravitoelectromagnetism — pagină inexistentă">Gravitoelectromagnetism</a></li> <li><a href="/wiki/Gravita%C8%9Bie" title="Gravitație">Gravitație</a></li> <li><a href="/wiki/C%C3%A2mp_gravita%C8%9Bional" title="Câmp gravitațional">Câmp gravitațional</a></li> <li><a href="/wiki/Lentil%C4%83_gravita%C8%9Bional%C4%83" title="Lentilă gravitațională">Lentilă gravitațională</a></li> <li><a href="/wiki/Und%C4%83_gravita%C8%9Bional%C4%83" title="Undă gravitațională">Undă gravitațională</a></li> <li><a href="/wiki/Deplasarea_spre_ro%C8%99u" class="mw-redirect" title="Deplasarea spre roșu">Deplasarea spre roșu</a></li> <li><a href="/w/index.php?title=Deplasarea_spre_albastru&action=edit&redlink=1" class="new" title="Deplasarea spre albastru — pagină inexistentă">Deplasarea spre albastru</a></li> <li><a href="/wiki/Dilatarea_timpului" title="Dilatarea timpului">Dilatarea timpului</a></li> <li><a href="/wiki/Dilatare_temporal%C4%83_gravita%C8%9Bional%C4%83" title="Dilatare temporală gravitațională">Dilatare temporală gravitațională</a></li> <li><a href="/wiki/%C3%8Ent%C3%A2rzierea_Shapiro" title="Întârzierea Shapiro">Întârzierea Shapiro</a></li> <li><a href="/w/index.php?title=Poten%C8%9Bial_gravita%C8%9Bional&action=edit&redlink=1" class="new" title="Potențial gravitațional — pagină inexistentă">Potențial gravitațional</a></li> <li><a href="/wiki/Compresie_gravita%C8%9Bional%C4%83" title="Compresie gravitațională">Compresie gravitațională</a></li> <li><a href="/wiki/Colaps_gravita%C8%9Bional" title="Colaps gravitațional">Colaps gravitațional</a></li> <li><a href="/wiki/Orizont_de_evenimente" title="Orizont de evenimente">Orizont de evenimente</a></li> <li><a href="/wiki/Singularitate_gravita%C8%9Bional%C4%83" title="Singularitate gravitațională">Singularitate gravitațională</a></li> <li><a href="/w/index.php?title=Singularitate_nud%C4%83&action=edit&redlink=1" class="new" title="Singularitate nudă — pagină inexistentă">Singularitate nudă</a></li> <li><a href="/wiki/Gaur%C4%83_neagr%C4%83" title="Gaură neagră">Gaură neagră</a></li> <li><a href="/wiki/Gaur%C4%83_alb%C4%83" title="Gaură albă">Gaură albă</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#ececff; font-style:italic;font-weight:normal;"> <a href="/wiki/Spa%C8%9Biu-timp" title="Spațiu-timp">Spațiu-timp</a></th></tr><tr><td style="padding:0 0.1em 0.4em"> <ul><li><a href="/wiki/Spa%C8%9Biu" title="Spațiu">Spațiu</a></li> <li><a href="/wiki/Timp" title="Timp">Timp</a></li> <li><a href="/w/index.php?title=Diagrama_Minkowski&action=edit&redlink=1" class="new" title="Diagrama Minkowski — pagină inexistentă">Diagrama Minkowski</a></li> <li><a href="/wiki/Spa%C8%9Biu_Minkowski" title="Spațiu Minkowski">Spațiu Minkowski</a></li> <li><a href="/wiki/Gaur%C4%83_de_vierme" title="Gaură de vierme">Gaură de vierme</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:#ddf; text-align:center;">Ecuații și teorii</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;color:var(--color-base, #000) !important;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;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 style="padding:0.1em;font-style:italic;font-weight:normal;padding-bottom:0;"> Ecuații</th></tr><tr><td style="padding:0 0.1em 0.4em;padding-top:0;"> <ul><li><a href="/wiki/Ecua%C8%9Biile_lui_Einstein" title="Ecuațiile lui Einstein">Ecuațiile lui Einstein</a></li> <li><a href="/w/index.php?title=Ecua%C8%9Biile_lui_Friedmann&action=edit&redlink=1" class="new" title="Ecuațiile lui Friedmann — pagină inexistentă">Friedmann</a></li> <li><a href="/w/index.php?title=Ecua%C8%9Biile_Mathisson%E2%80%93Papapetrou%E2%80%93Dixon&action=edit&redlink=1" class="new" title="Ecuațiile Mathisson–Papapetrou–Dixon — pagină inexistentă">Mathisson–Papapetrou–Dixon</a></li> <li><a href="/w/index.php?title=Ecua%C8%9Bia_Hamilton%E2%80%93Jacobi%E2%80%93Einstein&action=edit&redlink=1" class="new" title="Ecuația Hamilton–Jacobi–Einstein — pagină inexistentă">Hamilton–Jacobi–Einstein</a></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;font-weight:normal;padding-bottom:0;"> Formalism</th></tr><tr><td style="padding:0 0.1em 0.4em;padding-top:0;"> <ul><li><a href="/w/index.php?title=Formalism_ADM&action=edit&redlink=1" class="new" title="Formalism ADM — pagină inexistentă">ADM</a></li> <li><a href="/w/index.php?title=Formalism_BSSN&action=edit&redlink=1" class="new" title="Formalism BSSN — pagină inexistentă">BSSN</a></li> <li><a href="/w/index.php?title=Formalism_Newman%E2%80%93Penrose&action=edit&redlink=1" class="new" title="Formalism Newman–Penrose — pagină inexistentă">Newman-Penrose</a></li> <li><a href="/w/index.php?title=Formalism_parametric_post-newtonian&action=edit&redlink=1" class="new" title="Formalism parametric post-newtonian — pagină inexistentă">Post-Newtonian</a></li></ul></td> </tr><tr><th style="padding:0.1em;font-style:italic;font-weight:normal;padding-bottom:0;"> Teorii avansate</th></tr><tr><td style="padding:0 0.1em 0.4em;padding-top:0;"> <ul><li><a href="/wiki/Teoria_Kaluza%E2%80%93Klein" title="Teoria Kaluza–Klein">Teoria Kaluza–Klein</a></li> <li><a href="/wiki/Gravita%C8%9Bie_cuantic%C4%83" title="Gravitație cuantică">Gravitație cuantică</a></li> <li><a href="/wiki/Supergravita%C8%9Bie" title="Supergravitație">Supergravitație</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:#ddf; text-align:center;"><a href="/wiki/Solu%C8%9Bii_exacte_%C3%AEn_relativitatea_general%C4%83" title="Soluții exacte în relativitatea generală">Soluții</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Solu%C8%9Bia_Schwarzschild" title="Soluția Schwarzschild">Schwarzschild</a></li> <li><a href="/w/index.php?title=Solu%C8%9Bia_Reissner%E2%80%93Nordstr%C3%B6m&action=edit&redlink=1" class="new" title="Soluția Reissner–Nordström — pagină inexistentă">Reissner–Nordström</a></li> <li><a href="/w/index.php?title=Solu%C8%9Bia_G%C3%B6del&action=edit&redlink=1" class="new" title="Soluția Gödel — pagină inexistentă">Gödel</a></li> <li><a href="/w/index.php?title=Solu%C8%9Bia_Kerr&action=edit&redlink=1" class="new" title="Soluția Kerr — pagină inexistentă">Kerr</a></li> <li><a href="/w/index.php?title=Solu%C8%9Bia_Kerr%E2%80%93Newman&action=edit&redlink=1" class="new" title="Soluția Kerr–Newman — pagină inexistentă">Kerr–Newman</a></li> <li><a href="/w/index.php?title=Solu%C8%9Bia_Kasner&action=edit&redlink=1" class="new" title="Soluția Kasner — pagină inexistentă">Kasner</a></li> <li><a href="/w/index.php?title=Solu%C8%9Bia_Lema%C3%AEtre%E2%80%93Tolman&action=edit&redlink=1" class="new" title="Soluția Lemaître–Tolman — pagină inexistentă">Lemaître–Tolman</a></li> <li><a href="/w/index.php?title=Solu%C8%9Bia_Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker&action=edit&redlink=1" class="new" title="Soluția Friedmann–Lemaître–Robertson–Walker — pagină inexistentă">Robertson–Walker</a></li> <li><a href="/wiki/Praful_lui_van_Stockum" title="Praful lui van Stockum">Praful lui van Stockum</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:#ddf; text-align:center;">Oameni de știință</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <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="/w/index.php?title=Hans_Reissner&action=edit&redlink=1" class="new" title="Hans Reissner — pagină inexistentă">Reissner</a></li> <li><a href="/w/index.php?title=Gunnar_Nordstr%C3%B6m&action=edit&redlink=1" class="new" title="Gunnar Nordström — pagină inexistentă">Nordström</a></li> <li><a href="/w/index.php?title=Hermann_Weyl&action=edit&redlink=1" class="new" title="Hermann Weyl — pagină inexistentă">Weyl</a></li> <li><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Eddington</a></li> <li><a href="/wiki/Alexander_Friedmann" class="mw-redirect" title="Alexander Friedmann">Friedman</a></li> <li><a href="/w/index.php?title=Edward_Arthur_Milne&action=edit&redlink=1" class="new" title="Edward Arthur Milne — pagină inexistentă">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/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="/w/index.php?title=Howard_P._Robertson&action=edit&redlink=1" class="new" title="Howard P. Robertson — pagină inexistentă">Robertson</a></li> <li><a href="/w/index.php?title=James_M._Bardeen&action=edit&redlink=1" class="new" title="James M. Bardeen — pagină inexistentă">Bardeen</a></li> <li><a href="/w/index.php?title=Arthur_Geoffrey_Walker&action=edit&redlink=1" class="new" title="Arthur Geoffrey Walker — pagină inexistentă">Walker</a></li> <li><a href="/w/index.php?title=Roy_Kerr&action=edit&redlink=1" class="new" title="Roy Kerr — pagină inexistentă">Kerr</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/w/index.php?title=J%C3%BCrgen_Ehlers&action=edit&redlink=1" class="new" title="Jürgen Ehlers — pagină inexistentă">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="/w/index.php?title=Amal_Kumar_Raychaudhuri&action=edit&redlink=1" class="new" title="Amal Kumar Raychaudhuri — pagină inexistentă">Raychaudhuri</a></li> <li><a href="/wiki/Joseph_Hooton_Taylor_Jr." class="mw-redirect" 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="/w/index.php?title=Willem_Jacob_van_Stockum&action=edit&redlink=1" class="new" title="Willem Jacob van Stockum — pagină inexistentă">van Stockum</a></li> <li><a href="/w/index.php?title=Abraham_H._Taub&action=edit&redlink=1" class="new" title="Abraham H. Taub — pagină inexistentă">Taub</a></li> <li><a href="/w/index.php?title=Ezra_T._Newman&action=edit&redlink=1" class="new" title="Ezra T. Newman — pagină inexistentă">Newman</a></li> <li><a href="/w/index.php?title=Shing-Tung_Yau&action=edit&redlink=1" class="new" title="Shing-Tung Yau — pagină inexistentă">Yau</a></li> <li><a href="/wiki/Kip_Thorne" title="Kip Thorne">Thorne</a></li> <li><a href="/w/index.php?title=List_of_contributors_to_general_relativity&action=edit&redlink=1" class="new" title="List of contributors to general relativity — pagină inexistentă"><i>alții</i></a></li></ul></div></div></td> </tr><tr><td style="text-align:right;font-size:115%;padding-top: 0.6em;"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Format:Relativitate_general%C4%83" title="Format:Relativitate generală"><abbr title="Vizualizează acest format">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Discu%C8%9Bie_Format:Relativitate_general%C4%83&action=edit&redlink=1" class="new" title="Discuție Format:Relativitate generală — pagină inexistentă"><abbr title="Discută acest format">d</abbr></a></li><li class="nv-edit"><a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Format:Relativitate_general%C4%83&action=edit"><abbr title="Modifică acest format">m</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Relativitatea restrânsă</b> (<b>Teoria relativității restrânse</b> sau <b>teoria restrânsă a relativității</b>), denumită ulterior <b>teoria specială a relativității</b> sau <b>relativitatea specială</b>, este <a href="/wiki/Fizic%C4%83_teoretic%C4%83" title="Fizică teoretică">teoria fizică</a> a <a href="/wiki/M%C4%83surare" title="Măsurare">măsurării</a> în <a href="/wiki/Sistem_de_referin%C8%9B%C4%83_iner%C8%9Bial" title="Sistem de referință inerțial">sistemele de referință inerțiale</a> propusă în <a href="/wiki/1905" title="1905">1905</a> de către <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> în articolul său <b>Despre electrodinamica corpurilor în mișcare</b>. Ea generalizează <a href="/w/index.php?title=Invarian%C8%9Ba_galielean%C4%83&action=edit&redlink=1" class="new" title="Invarianța galieleană — pagină inexistentă">principiul relativității al lui Galilei</a> — care spunea că toate <a href="/wiki/Sistem_de_referin%C8%9B%C4%83_iner%C8%9Bial" title="Sistem de referință inerțial">mișcările uniforme</a> sunt relative, și că nu există stare de repaus absolută și <a href="/wiki/Expresie_bine_definit%C4%83" title="Expresie bine definită">bine definită</a> (nu există sistem de referință privilegiat) — de la <a href="/wiki/Mecanic%C4%83" title="Mecanică">mecanică</a> la toate <a href="/w/index.php?title=Legile_fizicii&action=edit&redlink=1" class="new" title="Legile fizicii — pagină inexistentă">legile fizicii</a>, inclusiv <a href="/wiki/Electrodinamic%C4%83" title="Electrodinamică">electrodinamica</a>. </p><p>Pentru a evidenția acest lucru, Einstein nu s-a oprit la a lărgi postulatul relativității, ci a adăugat un al doilea postulat: acela că toți observatorii vor obține aceeași valoare pentru <a href="/wiki/Viteza_luminii" title="Viteza luminii">viteza luminii</a> indiferent de starea lor de mișcare uniformă și rectilinie.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Această teorie are o serie de consecințe surprinzătoare și contraintuitive, dar care au fost de atunci <a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html">verificate pe cale experimentală</a>. Relativitatea restrânsă modifică <a href="/wiki/Fizic%C4%83_newtonian%C4%83" class="mw-redirect" title="Fizică newtoniană">noțiunile newtoniene de spațiu și timp</a> afirmând că <a href="/wiki/Timp" title="Timp">timpul</a> și <a href="/wiki/Spa%C8%9Biu" title="Spațiu">spațiul</a> sunt percepute diferit în sensul că măsurătorile privind lungimea și intervalele de timp depind de starea de mișcare a observatorului. Rezultă de aici echivalența dintre <a href="/wiki/Materie" title="Materie">materie</a> și <a href="/wiki/Energie" title="Energie">energie</a>, exprimată în formula <a href="/wiki/Echivalen%C8%9B%C4%83_mas%C4%83-energie" title="Echivalență masă-energie">de echivalență a masei și energiei</a> <i>E</i> = <i>mc</i><sup>2</sup>, unde <i>c</i> este viteza luminii în vid. Relativitatea restrânsă este o generalizare a mecanicii newtoniene, aceasta din urmă fiind o aproximație a relativității restrânse pentru experimente în care vitezele sunt mici în comparație cu viteza luminii. </p><p>Teoria a fost numită "restrânsă" deoarece aplică <a href="/wiki/Principiul_relativit%C4%83%C8%9Bii" title="Principiul relativității">principiul relativității</a> doar la <a href="/wiki/Sisteme_iner%C8%9Biale" class="mw-redirect" title="Sisteme inerțiale">sisteme inerțiale</a>. Einstein a dezvoltat <a href="/wiki/Relativitatea_generalizat%C4%83" class="mw-redirect" title="Relativitatea generalizată">relativitatea generalizată</a> care aplică principiul general, oricărui sistem de referință, și acea teorie include și efectele <a href="/wiki/Gravita%C8%9Bie" title="Gravitație">gravitației</a>. Relativitatea restrânsă nu ține cont de gravitație, dar tratează <a href="/wiki/Accelera%C8%9Bie" title="Accelerație">accelerația</a>. </p><p>Deși teoria relativității restrânse face anumite cantități relative, cum ar fi timpul, pe care ni l-am fi imaginat ca fiind absolut, pe baza experienței de zi cu zi, face absolute unele cantități pe care le-am fi crezut altfel relative. În particular, se spune în teoria relativității că viteza luminii este aceeași pentru toți observatorii, chiar dacă ei sunt în mișcare unul față de celălalt. Relativitatea restrânsă dezvăluie faptul că <i>c</i> nu este doar viteza unui anumit fenomen - propagarea luminii - ci o trăsătură fundamentală a felului în care sunt legate între ele spațiul și timpul. În particular, relativitatea restrânsă afirmă că este imposibil ca un obiect material să fie accelerat până la viteza luminii. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Origini">Origini</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=1" title="Modifică secțiunea: Origini" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=1" title="Edit section's source code: Origini"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Această teorie a fost formulată pentru a explica aspecte legate de <b>electrodinamica corpurilor în mișcare</b>, acesta fiind titlul articolului original al lui Einstein de la care a pornit formularea teoriei. Până când Einstein nu a dezvoltat relativitatea generală, introducând un spațiu-timp curbat pentru a încorpora gravitația, sintagma „relativitate specială” nu a fost folosită. O traducere folosită uneori este „relativitate restrânsă”; „special” înseamnă cu adevărat „caz special”.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Einstein însuși, în <i>The Foundations of the General Theory of Relativity</i>, , Ann. Phys. 49 (1916), scrie „Cuvântul „special” este menit să specifice că principiul este limitat la caz...”<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> </p> <div class="mw-heading mw-heading2"><h2 id="Semnificație"><span id="Semnifica.C8.9Bie"></span>Semnificație</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=2" title="Modifică secțiunea: Semnificație" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=2" title="Edit section's source code: Semnificație"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Teoria specială a relativității a fost inițial propusă de <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> într-o lucrare publicată la 26 septembrie 1905 intitulată "<i>Despre electrodinamica corpurilor în mișcare</i>".<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 id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Inconsecvența mecanicii newtoniene cu <a href="/wiki/Ecua%C8%9Biile_lui_Maxwell" title="Ecuațiile lui Maxwell">ecuațiile lui Maxwell</a> ale <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetismului</a> și lipsa confirmării experimentale a unui <a href="/wiki/Eter_luminifer" title="Eter luminifer">eter luminifer</a> ipotetic au dus la dezvoltarea relativității speciale, care corectează <a href="/wiki/Mecanic%C4%83" title="Mecanică">mecanica</a> pentru a face față situațiilor care implică mișcări la o fracțiune semnificativă din <a href="/wiki/Viteza_luminii" title="Viteza luminii">viteza luminii</a> (cunoscută ca viteză relativistă). Astăzi, relativitatea specială este cel mai precis model de mișcare la orice viteză atunci când efectele gravitaționale sunt neglijabile.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><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> Chiar și așa, modelul mecanicii newtoniene este încă util (datorită simplității și preciziei sale înalte) ca o aproximare la viteze mici în raport cu viteza luminii. </p><p>Înainte de formularea relativității speciale, <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a> și alții au remarcat deja că electromagnetismul diferă de <a href="/wiki/Fizica_newtonian%C4%83" class="mw-redirect" title="Fizica newtoniană">fizica newtoniană</a> prin aceea că observațiile unui aceluiași fenomen pot fi diferite pentru o persoană care se deplasează în raport cu altă persoană la viteze apropiate de <a href="/wiki/Viteza_luminii" title="Viteza luminii">viteza luminii</a>. De exemplu, una din persoane poate observa că nu există niciun <a href="/wiki/C%C3%A2mp_magnetic" title="Câmp magnetic">câmp magnetic</a>, în timp ce cealaltă observă un câmp magnetic în aceeași zonă fizică. Lorentz a sugerat o teorie a eterului, în care obiectele și observatorii care călătoresc față de un eter staționar suferă o contracție fizică (<i><a href="/wiki/Contrac%C8%9Bia_Lorentz" title="Contracția Lorentz">contracția Lorentz</a> -Fitzgerald</i>) și o modificare a timpului (<i><a href="/wiki/Dilatarea_timpului" title="Dilatarea timpului">dilatarea timpului</a></i>). Acest lucru a permis reconcilierea parțială a electromagnetismului cu <a href="/wiki/Fizica_newtonian%C4%83" class="mw-redirect" title="Fizica newtoniană">fizica newtoniană</a>. Când vitezele implicate sunt mult mai mici decât viteza luminii, legile rezultate se simplifică la <a href="/wiki/Legile_lui_Newton" title="Legile lui Newton">legile lui Newton</a>. Teoria, cunoscut sub numele de <i>Teoria Eterului Lorentz</i>, a fost criticată (chiar și de către Lorentz însuși), din cauza naturii sale neelaborate. <sup id="cite_ref-Teoria_10-0" class="reference"><a href="#cite_note-Teoria-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>În timp ce Lorentz sugera ecuațiile de transformare Lorentz ca o descriere matematică cu exactitate a rezultatelor măsurătorilor, contribuția lui Einstein a fost de a obține aceste ecuații pornind de la o teorie mai fundamentală. Einstein a vrut să afle ce este invariant (neschimbat) pentru toți observatorii. Titlul său original pentru teoria sa a fost (tradus din germană), "<i>Teoria invarianților</i>". <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> a propus termenul de "relativitate", pentru a sublinia ideea că legile fizicii se schimbă pentru observatori în mișcare unul față de celălalt. </p><p>După ce Einstein a dezvoltat <a href="/wiki/Relativitatea_general%C4%83" class="mw-redirect" title="Relativitatea generală">relativitatea generală</a>, pentru a încorpora cadre generale (sau accelerate) de referință și gravitație, a fost folosită expresia "relativitate specială". </p><p>O caracteristică definitorie a relativității speciale este înlocuirea transformărilor galileene ale mecanicii newtoniene cu <a href="/wiki/Transform%C4%83rile_Lorentz" class="mw-redirect" title="Transformările Lorentz">transformările Lorentz</a>. Timpul și spațiul nu pot fi definite separat unele de altele. Mai degrabă <a href="/wiki/Spa%C8%9Biu" title="Spațiu">spațiul</a> și <a href="/wiki/Timp" title="Timp">timpul</a> sunt interconectate într-un singur continuum cunoscut sub numele de <a href="/wiki/Spa%C8%9Biu-timp" title="Spațiu-timp">spațiu-timp</a>. Evenimente care apar simultan pentru un singur observator pot avea loc la momente diferite pentru altul. </p><p>Teoria este "specială" prin faptul că se aplică numai în cazul special în care <a href="/wiki/Curbur%C4%83" title="Curbură">curbura</a> <a href="/wiki/Spa%C8%9Biu-timp" title="Spațiu-timp">spațiu-timpului</a> datorită <a href="/wiki/Gravita%C8%9Bie" title="Gravitație">gravitației</a> este neglijabilă.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Pentru a include gravitația, Einstein a formulat <a href="/wiki/Relativitatea_general%C4%83" class="mw-redirect" title="Relativitatea generală">relativitatea generală</a> în 1915. Relativitatea specială, contrar unor descrieri depășite, este capabilă de includerea accelerațiilor, precum și a cadrelor de referință accelerate.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Așa cum relativitatea galileană este acum considerată o aproximare a relativității speciale care este valabilă pentru viteze reduse, relativitatea specială este considerată o aproximare a relativității generale care este valabilă pentru câmpurile gravitaționale slabe, adică la o scară suficient de mică și în condiții de cădere liberă. În timp ce relativitatea generală incorporează geometria noneuclideană pentru a reprezenta efectele gravitaționale ca curbură geometrică a spațiului, relativitatea specială este limitată la spațiu-timpul plat, cunoscut ca spațiul Minkowski. Un cadru local invariant Lorentz care respectă relativitatea specială poate fi definit la scări suficient de mici, chiar și în spațiu-timpul curbat.<sup id="cite_ref-Teoria_10-1" class="reference"><a href="#cite_note-Teoria-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a> afirmase deja că nu există o stare de repaus absolut și bine definit (nu există cadre de referință privilegiate), un principiu numit acum principiul de relativitate al lui Galileo. Einstein a extins acest principiu astfel încât acesta a reprezentat viteza constantă a luminii,<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> fenomen care a fost observat în <a href="/wiki/Experimentul_Michelson-Morley" title="Experimentul Michelson-Morley">experimentul Michelson-Morley</a>. El a afirmat, de asemenea, că este valabil pentru toate legile fizicii, inclusiv legile mecanicii și ale electrodinamicii.<sup id="cite_ref-Rindler0_16-0" class="reference"><a href="#cite_note-Rindler0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Postulate">Postulate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=3" title="Modifică secțiunea: Postulate" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=3" title="Edit section's source code: Postulate"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Primul <a href="/wiki/Postulat" class="mw-redirect" title="Postulat">postulat</a> - <b><a href="/wiki/Principiul_relativit%C4%83%C8%9Bii" title="Principiul relativității">Principiul relativității</a> restrânse</b> - Legile <a href="/wiki/Fizic%C4%83" title="Fizică">fizicii</a> sunt aceleași în orice <a href="/wiki/Sistem_de_referin%C8%9B%C4%83_iner%C8%9Bial" title="Sistem de referință inerțial">sistem de referință inerțial</a>. Cu alte cuvinte, nu există sistem de referință inerțial privilegiat.</li> <li>Al doilea postulat - <b>Invarianța lui <i>c</i></b> - Viteza luminii în <a href="/wiki/Vid" title="Vid">vid</a> este o <a href="/wiki/Constant%C4%83_universal%C4%83" class="mw-redirect" title="Constantă universală">constantă universală</a>, <i>c</i>, independentă de mișcarea sursei de <a href="/wiki/Lumin%C4%83" title="Lumină">lumină</a>.</li></ul> <p>Puterea argumentului lui Einstein reiese din maniera în care a dedus niște rezultate surprinzătoare și aparent incredibile din două presupuneri simple bazate pe analiza observațiilor. Un observator care încearcă să măsoare viteza de propagare a luminii va obține exact același rezultat indiferent de cum se mișcă componentele sistemului. </p> <div class="mw-heading mw-heading2"><h2 id="Lipsa_unui_sistem_de_referință_absolut"><span id="Lipsa_unui_sistem_de_referin.C8.9B.C4.83_absolut"></span>Lipsa unui sistem de referință absolut</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=4" title="Modifică secțiunea: Lipsa unui sistem de referință absolut" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=4" title="Edit section's source code: Lipsa unui sistem de referință absolut"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Principiul_relativit%C4%83%C8%9Bii" title="Principiul relativității">Principiul relativității</a>, care afirmă că nu există sistem de referință staționar, datează de pe vremea lui <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a>, și a fost inclus în fizica newtoniană. Însă, spre sfârșitul secolului al XIX-lea, existența <a href="/wiki/Radia%C8%9Bie_electromagnetic%C4%83" title="Radiație electromagnetică">undelor electromagnetice</a> a condus unii fizicieni să sugereze că universul este umplut cu o substanță numită "<a href="/wiki/Eter_luminifer" title="Eter luminifer">eter</a>", care ar acționa ca mediu de propagare al acestor unde. Se credea că eterul constituie un sistem de referință absolut față de care se pot măsura vitezele. Cu alte cuvinte, eterul era singurul lucru fix și nemișcat din univers. Se presupunea că eterul are niște proprietăți extraordinare: era destul de elastic pentru a suporta unde electromagetice, iar aceste unde puteau interacționa cu materia, dar același eter nu opunea rezistență <a href="/wiki/Corp_(fizic%C4%83)" title="Corp (fizică)">corpurilor</a> care treceau prin el. Rezultatele diferitelor experimente, în special <a href="/wiki/Experien%C8%9Ba_Michelson-Morley" class="mw-redirect" title="Experiența Michelson-Morley">experiența Michelson-Morley</a>, au indicat că Pământul este mereu în repaus în raport cu eterul — ceva dificil de explicat, deoarece Pământul era pe orbită în jurul Soarelui. Soluția elegantă dată de Einstein avea să elimine noțiunea de eter și de stare de repaus absolută. Relativitatea restrânsă este formulată de așa natură încât să nu presupună că vreun sistem de referință este special; în schimb, în relativitate, orice sistem de referință în mișcare uniformă va respecta aceleași legi ale fizicii. În particular, viteza luminii în vid este mereu măsurată ca fiind <i>c</i>, chiar și măsurată din sisteme multiple, mișcându-se cu viteze diferite, dar constante. </p> <div class="mw-heading mw-heading2"><h2 id="Consecințe"><span id="Consecin.C8.9Be"></span>Consecințe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=5" title="Modifică secțiunea: Consecințe" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=5" title="Edit section's source code: Consecințe"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Einstein a spus că toate consecințele relativității restrânse pot fi derivate din examinarea <a href="/wiki/Transform%C4%83rile_Lorentz" class="mw-redirect" title="Transformările Lorentz">transformărilor Lorentz</a>. </p><p>Aceste transformări, și deci teoria relativității restrânse, a condus la predicții fizice diferite de cele date de mecanica newtoniană atunci când vitezele relative se apropie de viteza luminii. Viteza luminii este atât de mult mai mare decât orice viteză întâlnită de oameni încât unele efecte ale relativității sunt la început contraintuitive: </p> <ul><li><b><a href="/wiki/Dilatarea_temporal%C4%83" class="mw-redirect" title="Dilatarea temporală">Dilatarea temporală</a></b> — timpul scurs între două evenimente nu este invariant de la un observator la altul, ci depinde de mișcarea relativă a sistemelor de referință ale observatorilor (ca în <a href="/wiki/Paradoxul_gemenilor" title="Paradoxul gemenilor">paradoxul gemenilor</a> care implică plecarea unui frate geamăn cu o navă spațială care se deplasează la viteză aproape de cea a luminii și faptul că la întoarcere constată că fratele său geamăn a îmbătrânit mai mult).</li> <li><b><a href="/wiki/Relativitatea_simultaneit%C4%83%C8%9Bii" title="Relativitatea simultaneității">Relativitatea simultaneității</a></b> — două evenimente ce au loc în două locații diferite, care au loc simultan pentru un observator, ar putea apărea ca având loc la momente diferite pentru un alt observator (lipsa <a href="/w/index.php?title=Simultaneitate_absolut%C4%83&action=edit&redlink=1" class="new" title="Simultaneitate absolută — pagină inexistentă">simultaneității absolute</a>).</li> <li><b><a href="/wiki/Contrac%C8%9Bia_Lorentz" title="Contracția Lorentz">Contracția Lorentz</a></b> — dimensiunile (de exemplu lungimea) unui obiect măsurate de un observator pot fi mai mici decât rezultatele acelorași măsurători efectuate de un alt observator (de exemplu, <a href="/w/index.php?title=Paradoxul_sc%C4%83rii&action=edit&redlink=1" class="new" title="Paradoxul scării — pagină inexistentă">paradoxul scării</a> implică o scară lungă care se deplasează cu viteză apropiată de cea a luminii și ținută într-un garaj mai mic).</li> <li><b><a href="/w/index.php?title=Formula_adun%C4%83rii_vitezelor&action=edit&redlink=1" class="new" title="Formula adunării vitezelor — pagină inexistentă">Compunerea vitezelor</a></b> — vitezele nu se adună pur și simplu, de exemplu dacă o rachetă se mișcă la ⅔ din viteza luminii pentru un observator, și din ea pleacă o altă rachetă la ⅔ din viteza luminii relativ la racheta inițială, a doua rachetă nu depășește viteza luminii în raport cu observatorul. (În acest exemplu, observatorul vede racheta a doua ca deplasându-se cu 12/13 din viteza luminii.)</li> <li><b><a href="/wiki/Iner%C8%9Bie_(fizic%C4%83)" title="Inerție (fizică)">Inerția</a> și <a href="/wiki/Impuls" title="Impuls">impulsul</a></b> — când viteza unui obiect se apropie de cea a luminii din punctul de vedere al unui observator, masa obiectului pare să crească făcând astfel mai dificilă accelerarea sa în sistemul de referință al observatorului.</li> <li><b>Echivalența <a href="/wiki/Mas%C4%83" title="Masă">masei</a> și <a href="/wiki/Energie" title="Energie">energiei</a>, <a href="/wiki/Echivalen%C8%9B%C4%83_mas%C4%83-energie" title="Echivalență masă-energie"><i>E</i> = <i>mc</i><sup>2</sup></a></b> — Energia înmagazinată de un obiect în repaus cu masa m este egală cu <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 mc^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mc^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68e4e95f7216bad6eab483ef0072d531a965962b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.101ex; height:2.676ex;" alt="{\displaystyle mc^{2}}"></span>. Conservarea energiei implică faptul că în orice reacție, o scădere a sumei maselor particulelor trebuie să fie însoțită de o creștere a energiilor cinetice ale particulelor după reacție. Similar, masa unui obiect poate fi mărită prin absorbția de către acesta de energie cinetică.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Sisteme_de_referință,_coordonate_și_transformarea_Lorentz"><span id="Sisteme_de_referin.C8.9B.C4.83.2C_coordonate_.C8.99i_transformarea_Lorentz"></span>Sisteme de referință, coordonate și transformarea Lorentz</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=6" title="Modifică secțiunea: Sisteme de referință, coordonate și transformarea Lorentz" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=6" title="Edit section's source code: Sisteme de referință, coordonate și transformarea Lorentz"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/Fi%C8%99ier:Lorentz_transform_of_world_line.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e4/Lorentz_transform_of_world_line.gif" decoding="async" width="200" height="200" class="mw-file-element" data-file-width="200" data-file-height="200" /></a><figcaption>Diagrama 1. Modificarea percepției spațiu-timpului de-a lungul <a href="/w/index.php?title=Linie_de_univers&action=edit&redlink=1" class="new" title="Linie de univers — pagină inexistentă">liniei de univers</a> a unui observator care accelerează rapid.<br /><br />În această animație, direcția verticală indică timpul iar cea orizontală indică distanța, linia punctată este traiectoria spațiu-timp ("linia de univers") a observatorului. Sfertul inferior al diagramei arată evenimentele vizibile pentru observator, iar sfertul superior arată <a href="/w/index.php?title=Con_de_lumin%C4%83&action=edit&redlink=1" class="new" title="Con de lumină — pagină inexistentă">conul de lumină</a>- cei care pot vedea observatorul. Punctele mici sunt evenimente arbitrare din spațiu-timp. <br /><br />Panta liniei de univers (deviația de la verticală) dă viteza relativă față de observator. De observat cum percepția spațiu-timpului se modifică atunci când observatorul accelerează.</figcaption></figure> <p>Teoria relativității depinde de "<a href="/wiki/Sisteme_de_referin%C8%9B%C4%83" class="mw-redirect" title="Sisteme de referință">sisteme de referință</a>". Un sistem de referință este o perspectivă observațională în spațiu în repaus sau în mișcare uniformă, de unde se poate măsura o poziție de-a lungul a 3 axe spațiale. În plus, un sistem de referință are abilitatea de a determina măsurătorile evenimentelor în timp, folosind un 'ceas' (orice dispozitiv de referință cu periodicitate uniformă). </p><p>Un eveniment este un lucru căruia i se poate asigna un moment în timp și un loc în spațiu unice în raport cu un sistem de referință: este un "punct" în <a href="/wiki/Spa%C8%9Biu-timp" title="Spațiu-timp">spațiu-timp</a>. Deoarece viteza luminii este constantă în teoria relativității în orice sistem de referință, impulsurile luminoase pot fi folosite pentru a măsura neambiguu distanțele și a da timpul la care evenimentele au avut loc pentru ceasul sistemului, deși lumina are nevoie de timp pentru a ajunge la ceas după ce evenimentul a trecut. </p><p>De exemplu, explozia unei petarde poate fi considerată un "eveniment". Putem specifica complet un eveniment prin cele patru coordonate spațiu-timp: Momentul la care a avut loc și poziția spațială în 3 dimensiuni definesc un punct de referință. Să numim acest sistem de referință S. </p><p>În teoria relativității se dorește adesea calcularea poziției unui punct dintr-un alt sistem de referință. </p><p>Să presupunem că avem un al doilea sistem de referință S', ale cărui axe spațiale și ceas coincid exact cu ale lui S la momentul zero, dar care se mișcă cu o viteză constantă <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 v\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b67d1fd725a759a151374b793113d7a78a65da4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.515ex; height:1.676ex;" alt="{\displaystyle v\,}"></span> în raport cu S în jurul axei <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 x\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab34739435d9d9d99cddf4041740b107343b1398" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.717ex; height:1.676ex;" alt="{\displaystyle x\,}"></span>. </p><p>Deoarece nu există sistem de referință absolut în teoria relativității, conceptul de "în mișcare" nu există în sens strict, întrucât toate sunt mereu în mișcare în raport cu alte sisteme de referință. </p><p>Să definim evenimentul de coordonate spațiu-timp <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 (t,x,y,z)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (t,x,y,z)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e9bb5fbde6e1e0edd674676f7c7ab3c65cfbcae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.711ex; height:2.843ex;" alt="{\displaystyle (t,x,y,z)\,}"></span> în sistemul S și <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 (t',x',y',z')\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (t',x',y',z')\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5badaeba2fceb2eb0d8f483976838d4cfe48564" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.457ex; height:3.009ex;" alt="{\displaystyle (t',x',y',z')\,}"></span> în S'. Atunci <a href="/wiki/Transform%C4%83rile_Lorentz" class="mw-redirect" title="Transformările Lorentz">transformările Lorentz</a> specifică faptul că aceste coordonate sunt legate în felul următor: </p> <dl><dd><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 t'=\gamma \left(t-{\frac {vx}{c^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mrow> <mo>(</mo> <mrow> <mi>t</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi>x</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t'=\gamma \left(t-{\frac {vx}{c^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a8a590569fa24f6d516f5dfa70d57a5195f4dbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.667ex; height:6.176ex;" alt="{\displaystyle t'=\gamma \left(t-{\frac {vx}{c^{2}}}\right)}"></span></dd> <dd><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 x'=\gamma (x-vt)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>v</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x'=\gamma (x-vt)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5383ec7545787725887aed10f8f92ae402ada08c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.709ex; height:3.009ex;" alt="{\displaystyle x'=\gamma (x-vt)\,}"></span></dd> <dd><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 y'=y\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>y</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y'=y\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c14836c0a537d408ca839276c44ee0fb4781658e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.486ex; height:2.843ex;" alt="{\displaystyle y'=y\,}"></span></dd> <dd><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 z'=z\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>z</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z'=z\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e29e0271747c2c9629aa0752cd2ac080742c183" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.349ex; height:2.509ex;" alt="{\displaystyle z'=z\,}"></span></dd></dl> <p>unde <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 \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b130ec5e5e9586833b7888f7cbe2433f1e295e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:16.929ex; height:6.509ex;" alt="{\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"></span> se numește <a href="/wiki/Factor_Lorentz" title="Factor Lorentz">factor Lorentz</a> și <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 c\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}"></span> este <a href="/wiki/Viteza_luminii" title="Viteza luminii">viteza luminii</a> în vid. </p><p>Coordonatele <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 y\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c8c233e7cc39fac816991250d86e09b515d02e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.543ex; height:2.009ex;" alt="{\displaystyle y\,}"></span> și <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 z\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/624faa61961bd63f364dee3e97dec7dd48694600" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.475ex; height:1.676ex;" alt="{\displaystyle z\,}"></span> nu sunt afectate, dar axele <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 x\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab34739435d9d9d99cddf4041740b107343b1398" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.717ex; height:1.676ex;" alt="{\displaystyle x\,}"></span> și <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 t\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/946383a7c6d1876177c662a95b369ced2ad99cd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.227ex; height:2.009ex;" alt="{\displaystyle t\,}"></span> sunt implicate în transformare. Într-un fel, această transformare poate fi înțeleasă ca o rotație hiperbolică. </p> <div class="mw-heading mw-heading2"><h2 id="Simultaneitatea">Simultaneitatea</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=7" title="Modifică secțiunea: Simultaneitatea" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=7" title="Edit section's source code: Simultaneitatea"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Din prima ecuație a transformărilor Lorentz în termeni de diferențe de coordonate </p> <dl><dd><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 \Delta t'=\gamma \left(\Delta t-{\frac {v\Delta x}{c^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t'=\gamma \left(\Delta t-{\frac {v\Delta x}{c^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1629f3d62a2d7beaf2c32de515509618608cf49b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.474ex; height:6.176ex;" alt="{\displaystyle \Delta t'=\gamma \left(\Delta t-{\frac {v\Delta x}{c^{2}}}\right)}"></span></dd></dl> <p>este clar că două evenimente care sunt simultane în sistemul de referință S (satisfăcând <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 \Delta t=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd37cbc735bfbf81aa7e380e1a345a932f08254d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.424ex; height:2.176ex;" alt="{\displaystyle \Delta t=0\,}"></span>), nu sunt neapărat simultane în alt sistem inerțial S' (satisfăcând <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 \Delta t'=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t'=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/789b0a983d87fdcd6bf775cdf36901e6e1fcc256" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.108ex; height:2.509ex;" alt="{\displaystyle \Delta t'=0\,}"></span>). Doar dacă aceste evenimente sunt colocale în sistemul S (satisfăcând <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 \Delta x=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bceb888e8a31e482a13a2da2044a87bd1373777" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.914ex; height:2.176ex;" alt="{\displaystyle \Delta x=0\,}"></span>), atunci ele vor fi simultane și în S'. </p> <div class="mw-heading mw-heading2"><h2 id="Dilatarea_timpului_și_contracția_lungimilor"><span id="Dilatarea_timpului_.C8.99i_contrac.C8.9Bia_lungimilor"></span>Dilatarea timpului și contracția lungimilor</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=8" title="Modifică secțiunea: Dilatarea timpului și contracția lungimilor" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=8" title="Edit section's source code: Dilatarea timpului și contracția lungimilor"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Scriind transformarea Lorentz și inversa sa în termenii diferențelor de coordonate, se obține </p> <dl><dd><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 \Delta t'=\gamma \left(\Delta t-{\frac {v\Delta x}{c^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t'=\gamma \left(\Delta t-{\frac {v\Delta x}{c^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1629f3d62a2d7beaf2c32de515509618608cf49b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.474ex; height:6.176ex;" alt="{\displaystyle \Delta t'=\gamma \left(\Delta t-{\frac {v\Delta x}{c^{2}}}\right)}"></span></dd> <dd><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 \Delta x'=\gamma (\Delta x-v\Delta t)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo>−</mo> <mi>v</mi> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x'=\gamma (\Delta x-v\Delta t)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ea798e2a957c0766e5c8ec6d695dce040ef0a8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.517ex; height:3.009ex;" alt="{\displaystyle \Delta x'=\gamma (\Delta x-v\Delta t)\,}"></span></dd></dl> <p>și </p> <dl><dd><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 \Delta t=\gamma \left(\Delta t'+{\frac {v\Delta x'}{c^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mi>γ</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi mathvariant="normal">Δ</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t=\gamma \left(\Delta t'+{\frac {v\Delta x'}{c^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d075709462881042b88236ebe091cbbd57dd6c21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.159ex; height:6.176ex;" alt="{\displaystyle \Delta t=\gamma \left(\Delta t'+{\frac {v\Delta x'}{c^{2}}}\right)}"></span></dd> <dd><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 \Delta x=\gamma (\Delta x'+v\Delta t')\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo>=</mo> <mi>γ</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>v</mi> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x=\gamma (\Delta x'+v\Delta t')\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74702f8533b30ab4420f2f47acdcf2f0deec1d0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.201ex; height:3.009ex;" alt="{\displaystyle \Delta x=\gamma (\Delta x'+v\Delta t')\,}"></span></dd></dl> <p>Să presupunem că avem un ceas în repaus în sistemul S. Două bătăi consecutive ale acestui ceas sunt caracterizate prin <b><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 \Delta x=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87d1101e37797b3fc4042e255aeafd1140c9def" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.526ex; height:2.176ex;" alt="{\displaystyle \Delta x=0}"></span></b>. Dacă vrem să știm relația dintre timpii dintre aceste bătăi măsurate în ambele sisteme, putem folosi prima ecuație și obținem: </p> <dl><dd><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 \Delta t'=\gamma \Delta t\qquad (\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mspace width="2em" /> <mo stretchy="false">(</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t'=\gamma \Delta t\qquad (\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65d2023db79569a91ad96248d0663c938dfc50c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.533ex; height:3.009ex;" alt="{\displaystyle \Delta t'=\gamma \Delta t\qquad (\,}"></span> pentru evenimentele care satisfac condiția <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 \Delta x=0)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x=0)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/501f56188cb7baf328723249c2d4bf6fbfe05b59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.818ex; height:2.843ex;" alt="{\displaystyle \Delta x=0)\,}"></span></dd></dl> <p>Aceasta arată că durata de timp <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 \Delta t'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50ea24905e052383d75e10e87e33a3d805d39b43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.46ex; height:2.509ex;" alt="{\displaystyle \Delta t'}"></span> între două bătăi ale ceasului, văzute în sistemul în mișcare S' este mai mare decât durata de timp <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 \Delta t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.775ex; height:2.176ex;" alt="{\displaystyle \Delta t}"></span> dintre aceleași bătăi măsurate în sistemul în care ceasul este în repaus. Acest fenomen se numește <a href="/wiki/Dilatare_temporal%C4%83" class="mw-redirect" title="Dilatare temporală">dilatare temporală</a>. </p><p>Similar, presupunem că avem un etalon de lungime în repaus în sistemul S. În acest sistem, lungimea etalonului este scrisă ca <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 \Delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.266ex; height:2.176ex;" alt="{\displaystyle \Delta x}"></span>. Dacă dorim să aflăm lungimea acestui etalon, ca măsurată în sistemul în mișcare S', trebuie să ne asigurăm că măsurăm distanțele <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 x'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac74959896052e160a5953102e4bc3850fe93b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.014ex; height:2.509ex;" alt="{\displaystyle x'}"></span> între capetele etalonului simultan în sistemul S'. Cu alte cuvinte, măsurarea este caracterizată prin <b><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 \Delta t'=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t'=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79312af2caef81493091b785626154e3b97c172c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.721ex; height:2.509ex;" alt="{\displaystyle \Delta t'=0}"></span></b>, pe care o putem combina cu a patra ecuație pentru a găsi relația dintre lungimile <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 \Delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.266ex; height:2.176ex;" alt="{\displaystyle \Delta x}"></span> și <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 \Delta x'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/996b22949cf5ae8c34f290c9ef364504d2447455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.95ex; height:2.509ex;" alt="{\displaystyle \Delta x'}"></span>: </p> <dl><dd><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 \Delta x'={\frac {\Delta x}{\gamma }}\qquad (\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> <mi>γ</mi> </mfrac> </mrow> <mspace width="2em" /> <mo stretchy="false">(</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x'={\frac {\Delta x}{\gamma }}\qquad (\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75c39c1cada4cd808e97106dafe78a1ada6c625a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.087ex; height:5.843ex;" alt="{\displaystyle \Delta x'={\frac {\Delta x}{\gamma }}\qquad (\,}"></span> pentru evenimente care satisfac <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 \Delta t'=0)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t'=0)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/621926bd8b971bbabcd57417dd94cd5180002da4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.013ex; height:3.009ex;" alt="{\displaystyle \Delta t'=0)\,}"></span></dd></dl> <p>Aceasta arată că lungimea <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 \Delta x'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/996b22949cf5ae8c34f290c9ef364504d2447455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.95ex; height:2.509ex;" alt="{\displaystyle \Delta x'}"></span> a etalonului măsurată în sistemul în mișcare S' este mai mică decât lungimea <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 \Delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.266ex; height:2.176ex;" alt="{\displaystyle \Delta x}"></span> în sistemul față de care se află în repaus. Acest fenomen se numește <i><a href="/wiki/Ipoteza_contrac%C8%9Biei_Lorentz-FitzGerald" class="mw-redirect" title="Ipoteza contracției Lorentz-FitzGerald">contracția lungimii</a></i> sau <i>contracție Lorentz</i>. </p><p>Aceste efect nu sunt doar aparente; ele sunt legate explicit de felul în care măsurăm <i>intervalele de timp</i> între evenimente care au loc în același loc într-un sistem de coordonate dat (numite evenimente "co-locale"). Aceste intervale de timp vor fi <i>diferite</i> într-un alt sistem de coordonate, în mișcare în raport cu primul, dacă evenimentele nu sunt simultane. Similar, aceste efecte leagă de distanțele măsurate între evenimente separate dar simultane într-un sistem de coordonate dat. Dacă aceste evenimente nu sunt co-locale, ci separate de distanță (spațiu), ele <i>nu</i> vor avea loc la aceeași <i>distanță spațială</i> unul de celălalt când vor fi văzute din alt sistem de coordonate în mișcare. </p> <div class="mw-heading mw-heading2"><h2 id="Cauzalitatea_și_imposibilitatea_depășirii_vitezei_luminii"><span id="Cauzalitatea_.C8.99i_imposibilitatea_dep.C4.83.C8.99irii_vitezei_luminii"></span>Cauzalitatea și imposibilitatea depășirii vitezei luminii</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=9" title="Modifică secțiunea: Cauzalitatea și imposibilitatea depășirii vitezei luminii" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=9" title="Edit section's source code: Cauzalitatea și imposibilitatea depășirii vitezei luminii"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Light_cone_ro.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Light_cone_ro.svg/220px-Light_cone_ro.svg.png" decoding="async" width="220" height="340" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Light_cone_ro.svg/330px-Light_cone_ro.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Light_cone_ro.svg/440px-Light_cone_ro.svg.png 2x" data-file-width="333" data-file-height="515" /></a><figcaption>Diagrama 2. <a href="/w/index.php?title=Conul_de_lumin%C4%83&action=edit&redlink=1" class="new" title="Conul de lumină — pagină inexistentă">Conul de lumină</a></figcaption></figure> <p>În diagrama 2, intervalul AB este <i>temporal</i>; cu alte cuvinte, există un sistem de referință în care evenimentul A și evenimentul B au loc în aceeași poziție în spațiu, și sunt separate doar de faptul că au loc la momente de timp diferite. Dacă A precede B în acel sistem de referință, atunci A precede B în toate sistemele de referință. Ipotetic, este posibil ca materia (sau informația) să călătorească de la A la B, astfel că poate exista o relație cauzală între ele (A fiind cauza, iar B efectul). </p><p>Intervalul AC din diagramă este 'spațial'; cu alte cuvinte, există un sistem de referință în care evenimentul A și evenimentul C au loc simultan, fiind separate doar de o distanță în spațiu. Însă există și sisteme în care A precede C (după cum se vede) și sisteme în care C precede A. Dacă ar fi posibilă o relație de tip cauză-efect între evenimentele A și C, atunci ar rezulta paradoxuri ale cauzalității. De exemplu, dacă A este cauza, iar C efectul, atunci ar exista sisteme de referință în care efectul precede cauza. Deși acest fapt singur nu dă naștere vreunui paradox, se poate arăta <sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> că se pot trimite semnalele cu viteză mai mare decât a luminii în trecut. Atunci se poate construi un paradox cauzal trimițând semnalul <a href="/wiki/Dac%C4%83_%C8%99i_numai_dac%C4%83" title="Dacă și numai dacă">dacă și numai dacă</a> anterior nu s-a primit niciun semnal. </p><p>Astfel, una din consecințele relativității restrânse este că (presupunând că se păstrează <a href="/wiki/Cauzalitate" title="Cauzalitate">cauzalitatea</a>), nicio informație și niciun obiect material nu pot călători mai repede decât lumina. Pe de altă parte, situația logică nu mai este așa de clară în cazul relativității generalizate, deci rămâne o întrebare deschisă dacă există vreun <a href="/w/index.php?title=Conjectura_protec%C8%9Biei_cronologiei&action=edit&redlink=1" class="new" title="Conjectura protecției cronologiei — pagină inexistentă">principiu fundamental</a> care păstrează cauzalitatea (și deci previne mișcarea cu viteză mai mare decât a luminii) în relativitatea generalizată. </p><p>Chiar fără a lua în calcul cauzalitatea, sunt alte motive puternice pentru care călătoria cu viteză peste cea a luminii este interzisă de relativitatea restrânsă. De exemplu, dacă se aplică o forță constantă asupra unui obiect pentru o perioadă nelimitată de timp, atunci integrând <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 F\,=\,{\frac {dp}{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>p</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\,=\,{\frac {dp}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e30c5f6b97d0fd6a8b035863192971678603ff9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.835ex; height:5.509ex;" alt="{\displaystyle F\,=\,{\frac {dp}{dt}}}"></span> rezultă un impuls care crește nelimitat, dar aceasta se întâmplă doar pentru că <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 p=m\gamma v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>m</mi> <mi>γ</mi> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=m\gamma v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b296776d9f129fec70e3696fc4fbc1255c3e287" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:8.788ex; height:2.176ex;" alt="{\displaystyle p=m\gamma v}"></span> tinde la infinit când <i>v</i> tinde la <i>c</i>. Pentru un observator care nu accelerează, pare că inerția obiectului crește, producând o accelerație mai mică pentru aceeași forță aplicată. Acest comportament este observat în <a href="/wiki/Accelerator_de_particule" title="Accelerator de particule">acceleratoarele de particule</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Compunerea_vitezelor">Compunerea vitezelor</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=10" title="Modifică secțiunea: Compunerea vitezelor" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=10" title="Edit section's source code: Compunerea vitezelor"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dacă observatorul din <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 S\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ebca8014cfb8a1cbd89f085a458f03bbc1c8c30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S\!}"></span> vede un obiect care se mișcă de-a lungul axei <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 x\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13b85d29899b2b2e4931388408d51f4fb086e7ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.271ex; width:1.214ex; height:1.676ex;" alt="{\displaystyle x\!}"></span> cu viteza <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 w\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6c66d9afac615bc5aaf52e96280caf61d4c5361" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.327ex; width:1.604ex; height:1.676ex;" alt="{\displaystyle w\!}"></span>, atunci observatorul din sistemul <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 S'\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1787a0e464c8da11ad3f980454d906c1477e43fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'\!}"></span>, un sistem de referință ce se mișcă la viteza <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 v\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.086ex; height:1.676ex;" alt="{\displaystyle v\!}"></span> în direcția <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 x\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13b85d29899b2b2e4931388408d51f4fb086e7ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.271ex; width:1.214ex; height:1.676ex;" alt="{\displaystyle x\!}"></span> în raport cu <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 S\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ebca8014cfb8a1cbd89f085a458f03bbc1c8c30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S\!}"></span>, va vedea obiectul mișcându-se cu viteza <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 w'\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mo>′</mo> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w'\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5ae2a742d253df69f20a8d1712aa1a24e5a0782" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.349ex; height:2.509ex;" alt="{\displaystyle w'\!}"></span> unde </p> <dl><dd><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 w'={\frac {w-v}{1-wv/c^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mi>v</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>w</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w'={\frac {w-v}{1-wv/c^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e06f485995d746b14166180be8f7805c9db81410" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.948ex; height:5.843ex;" alt="{\displaystyle w'={\frac {w-v}{1-wv/c^{2}}}.}"></span></dd></dl> <p>Această ecuație poate fi derivată din transformările spațială și temporală de mai sus. De observat că dacă obiectul s-ar mișca cu viteza luminii în sistemul <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 S\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ebca8014cfb8a1cbd89f085a458f03bbc1c8c30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S\!}"></span> (adică <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 w=c\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mi>c</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w=c\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1977723f846acb5b846e148581b470a4ba1f20b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.38ex; width:5.762ex; height:1.676ex;" alt="{\displaystyle w=c\!}"></span> ), atunci el s-ar mișca cu viteza luminii și în sistemul <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 S'\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1787a0e464c8da11ad3f980454d906c1477e43fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'\!}"></span>. De asemenea, dacă <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 w\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6c66d9afac615bc5aaf52e96280caf61d4c5361" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.327ex; width:1.604ex; height:1.676ex;" alt="{\displaystyle w\!}"></span> și <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 v\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.086ex; height:1.676ex;" alt="{\displaystyle v\!}"></span> sunt mici în raport cu viteza luminii, se recuperează transformările galileiene ale vitezelor: <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 w'\approx w-v\!.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mo>′</mo> </msup> <mo>≈</mo> <mi>w</mi> <mo>−</mo> <mi>v</mi> <mspace width="negativethinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w'\approx w-v\!.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01cc0b18cec7524a5096a90bdc07bc3efc5b67fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.339ex; height:2.676ex;" alt="{\displaystyle w'\approx w-v\!.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Masa,_impulsul_și_energia"><span id="Masa.2C_impulsul_.C8.99i_energia"></span>Masa, impulsul și energia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=11" title="Modifică secțiunea: Masa, impulsul și energia" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=11" title="Edit section's source code: Masa, impulsul și energia"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>În plus față de modificarea noțiunilor de spațiu și timp, relativitatea restrânsă forțează reconsiderarea conceptelor de <a href="/wiki/Mas%C4%83" title="Masă">masă</a>, <a href="/wiki/Impuls" title="Impuls">impuls</a> și <a href="/wiki/Energie" title="Energie">energie</a>, toate fiind concepte de bază în <a href="/wiki/Mecanica_newtonian%C4%83" class="mw-redirect" title="Mecanica newtoniană">mecanica newtoniană</a>. Relativitatea restrânsă arată că, de fapt, aceste concepte sunt toate diferite aspecte ale aceleiași cantități fizice cam în același fel în care arată că spațiul și timpul sunt interconectate. </p><p>Există câteva moduri echivalente de a defini impulsul și energia în relativitatea restrânsă. O metodă folosește <a href="/wiki/Lege_de_conservare" title="Lege de conservare">legile de conservare</a>. Dacă aceste legi rămân valide în teoria relativității restrânse, ele trebuie să fie adevărate în orice sistem de referință posibil. Însă, dacă se fac niște simple <a href="/w/index.php?title=Experimente_imaginare&action=edit&redlink=1" class="new" title="Experimente imaginare — pagină inexistentă">experimente imaginare</a> folosind definițiile newtoniene ale impulsului și energiei, se vede că aceste cantități nu se conservă în relativitatea restrânsă. Ideea de conservare se poate salva făcând câteva mici modificări ale definițiilor acestora pentru a ține cont de vitezele relativiste. În teoria relativității, aceste definiții sunt considerate definiții corecte pentru impuls și energie. </p><p>Dat fiind un obiect cu masa invariantă <i>m</i> călătorind cu viteza <i>v</i> energia și impulsul lui sunt date (și definite) de </p> <dl><dd><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 E=\gamma mc^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>γ</mi> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\gamma mc^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/789eacdb78b89d28514cb8e8acbb3f85d4c93f25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:10.625ex; height:3.176ex;" alt="{\displaystyle E=\gamma mc^{2}\,\!}"></span></dd></dl> <dl><dd><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 {\vec {p}}=\gamma m{\vec {v}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>γ</mi> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}=\gamma m{\vec {v}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c92e7084ba90a2d37c4db0ec94250e1afa3b0a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; margin-right: -0.387ex; width:9.378ex; height:2.843ex;" alt="{\displaystyle {\vec {p}}=\gamma m{\vec {v}}\,\!}"></span></dd></dl> <p>unde <i>γ</i> (<a href="/wiki/Factorul_Lorentz" class="mw-redirect" title="Factorul Lorentz">Factorul Lorentz</a>) este dat de </p> <dl><dd><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 \gamma ={\frac {1}{\sqrt {1-\beta ^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma ={\frac {1}{\sqrt {1-\beta ^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fb91924eaa6e5a593ba98cc7e2dfda04f764f07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.915ex; height:6.509ex;" alt="{\displaystyle \gamma ={\frac {1}{\sqrt {1-\beta ^{2}}}}}"></span></dd></dl> <p>unde <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 \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> raportul dintre viteză și viteza luminii. Termenul γ apare frecvent în relativitate, și vine din ecuațiile <a href="/wiki/Transform%C4%83rile_Lorentz" class="mw-redirect" title="Transformările Lorentz">transformărilor Lorentz</a>. </p><p>Energia relativistă și impulsul relativist sunt legate prin relația </p> <dl><dd><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 E^{2}-(pc)^{2}=(mc^{2})^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}-(pc)^{2}=(mc^{2})^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74d1ea28745778ca94539a36248cad47fb6747eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:21.179ex; height:3.176ex;" alt="{\displaystyle E^{2}-(pc)^{2}=(mc^{2})^{2}\,\!}"></span></dd></dl> <p>numită și <i>ecuația relativistă energie-impuls</i>. Este interesant de observat că în timp ce energia <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 E\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9123abddc2ec35f72035ec59f443c79ee052c9ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.163ex; height:2.176ex;" alt="{\displaystyle E\,}"></span> și impulsul <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 p\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4fa5f88a712eb9b03398066a0577fdcf33e02c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.646ex; height:2.009ex;" alt="{\displaystyle p\,}"></span> sunt dependente de observator (variază de la un sistem de referință la altul) cantitatea <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 E^{2}-(pc)^{2}=(mc^{2})^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}-(pc)^{2}=(mc^{2})^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74d1ea28745778ca94539a36248cad47fb6747eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:21.179ex; height:3.176ex;" alt="{\displaystyle E^{2}-(pc)^{2}=(mc^{2})^{2}\,\!}"></span> este independentă de observator. </p><p>Pentru viteze mult mai mici decât a luminii, γ poate fi aproximat folosind o <a href="/wiki/Serie_Taylor" title="Serie Taylor">dezvoltare în serie Taylor</a> din care rezultă </p> <dl><dd><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 E\approx mc^{2}+{\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>≈</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mi>m</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\approx mc^{2}+{\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/182f4d7818672fe4dc71760a2c2e6b3a81aacb94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.968ex; margin-right: -0.387ex; margin-bottom: -0.203ex; width:18.835ex; height:3.509ex;" alt="{\displaystyle E\approx mc^{2}+{\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}\,\!}"></span></dd></dl> <dl><dd><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 {\vec {p}}\approx m{\vec {v}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>≈</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}\approx m{\vec {v}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6b2a2e0f2e591ca82d577d8205da12300cc7d79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; margin-right: -0.387ex; width:8.116ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}\approx m{\vec {v}}\,\!}"></span></dd></dl> <p>Eliminând primul termen din expresia energiei, aceste formule sunt exact definițiile standard ale <a href="/wiki/Energie_cinetic%C4%83" title="Energie cinetică">energiei cinetice</a> și impulsului. Așa și trebuie să fie, deoarece mecanica newtoniană este o aproximație a relativității restrânse pentru viteze mici. </p><p>Privind formula de mai sus, a energiei, se vede că atunci când un obiect este în repaus (<i><b>v</b></i> = 0 și γ = 1) rămâne o energie diferită de zero: </p> <dl><dd><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 E_{rest}=mc^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{rest}=mc^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/572d673815365367a9aa3e895f5863cc5efdd8a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:12.407ex; height:3.009ex;" alt="{\displaystyle E_{rest}=mc^{2}\,\!}"></span></dd></dl> <p>Această energie este denumită <i>energia stării de repaus</i>. Energia stării de repaus nu cauzează niciun conflict cu teoria newtoniană deoarece este constantă și, din punctul de vedere al energiei cinetice, doar diferențele de energie au semnificație. </p><p>Interpretând această formulă, se poate concluziona că în teoria relativității <i>masa este doar o altă formă a energiei</i>. În 1927 Einstein a făcut următoarea remarcă privind relativitatea restrânsă: </p><p><i>În această teorie, masa nu este o mărime nealterabilă, ci o mărime dependentă de (și, într-adevăr, identică cu) cantitatea de energie.</i><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Această formulă devine importantă când se măsoară masele diferiților nuclei atomici. Privind diferențele de masă, se poate prezice care nuclei au energie suplimentară stocată și care poate fi eliberată prin <a href="/w/index.php?title=Reac%C8%9Bii_nucleare&action=edit&redlink=1" class="new" title="Reacții nucleare — pagină inexistentă">reacții nucleare</a>, oferind informații importante utile în dezvoltarea energiei nucleare și, în consecință, a <a href="/wiki/Bomb%C4%83_nuclear%C4%83" class="mw-redirect" title="Bombă nucleară">bombei nucleare</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Masa_relativistă"><span id="Masa_relativist.C4.83"></span>Masa relativistă</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=12" title="Modifică secțiunea: Masa relativistă" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=12" title="Edit section's source code: Masa relativistă"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;color:var(--color-base, #000) !important;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%"><tbody><tr><th style="padding:0.2em 0.4em 0.2em;font-size:145%;line-height:1.2em"><a href="/w/index.php?title=Fizica_modern%C4%83&action=edit&redlink=1" class="new" title="Fizica modernă — pagină inexistentă">Fizica modernă</a></th></tr><tr><td style="padding:0.2em 0 0.4em"><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 {\hat {H}}|\psi _{n}(t)\rangle =i\hbar {\frac {\partial }{\partial t}}|\psi _{n}(t)\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}|\psi _{n}(t)\rangle =i\hbar {\frac {\partial }{\partial t}}|\psi _{n}(t)\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03b24b7ca95f4810737a9b44ce50173911b134e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.129ex; height:5.509ex;" alt="{\displaystyle {\hat {H}}|\psi _{n}(t)\rangle =i\hbar {\frac {\partial }{\partial t}}|\psi _{n}(t)\rangle }"></span> <br /><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 {\frac {1}{{c}^{2}}}{\frac {{\partial }^{2}{\phi }_{n}}{{\partial t}^{2}}}-{{\nabla }^{2}{\phi }_{n}}+{\left({\frac {mc}{\hbar }}\right)}^{2}{\phi }_{n}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>ϕ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∇</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>ϕ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mi>c</mi> </mrow> <mi class="MJX-variant">ℏ</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>ϕ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{{c}^{2}}}{\frac {{\partial }^{2}{\phi }_{n}}{{\partial t}^{2}}}-{{\nabla }^{2}{\phi }_{n}}+{\left({\frac {mc}{\hbar }}\right)}^{2}{\phi }_{n}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c29e013d0d1fe7ad93e0ae91cac4c0a4121b406b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.587ex; height:6.676ex;" alt="{\displaystyle {\frac {1}{{c}^{2}}}{\frac {{\partial }^{2}{\phi }_{n}}{{\partial t}^{2}}}-{{\nabla }^{2}{\phi }_{n}}+{\left({\frac {mc}{\hbar }}\right)}^{2}{\phi }_{n}=0}"></span><div style="padding-top:0.2em;line-height:1.2em;font-size:90%;padding-top:0.4em;font-style:italic;"><a href="/wiki/Ecua%C8%9Bia_lui_Schr%C3%B6dinger" title="Ecuația lui Schrödinger">Ecuația lui Schrödinger</a> și <a href="/w/index.php?title=Ecua%C8%9Bia_Klein%E2%80%93Gordon&action=edit&redlink=1" class="new" title="Ecuația Klein–Gordon — pagină inexistentă">Ecuația Klein–Gordon</a></div></td></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:transparent;border-top:1px solid #aaa;text-align:center;">Fondatori</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Max_Born" title="Max Born">Max Born</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Pascual Jordan</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">Louis de Broglie</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Satyendra Nath Bose</a></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:transparent;border-top:1px solid #aaa;text-align:center;">Concepte</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><a href="/wiki/Spa%C8%9Biu" title="Spațiu">Spațiu</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Timp" title="Timp">Timp</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Energie" title="Energie">Energie</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Materie" title="Materie">Materie</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Lucru_mecanic" title="Lucru mecanic">Lucru mecanic</a> <br /> <a href="/wiki/Aleatoriu" title="Aleatoriu">Aleatoriu</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Informa%C8%9Bie" title="Informație">Informație</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Entropie" title="Entropie">Entropie</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Minte" title="Minte">Minte</a> <br /> <a href="/wiki/Lumin%C4%83" title="Lumină">Lumină</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Particul%C4%83" title="Particulă">Particulă</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Und%C4%83" title="Undă">Undă</a></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:transparent;border-top:1px solid #aaa;text-align:center;">Ramuri</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><a href="/wiki/Fizic%C4%83_aplicat%C4%83" title="Fizică aplicată">Aplicată</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Fizic%C4%83_experimental%C4%83" title="Fizică experimentală">Experimentală</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Fizic%C4%83_teoretic%C4%83" title="Fizică teoretică">Teoretică</a> <br /> <a href="/wiki/Filosofia_%C8%99tiin%C8%9Bei" class="mw-redirect" title="Filosofia științei">Filosofia științei</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Filosofia_fizicii" class="mw-redirect" title="Filosofia fizicii">Filosofia fizicii</a> <br /> <a href="/wiki/Logic%C4%83_matematic%C4%83" title="Logică matematică">Logică matematică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Fizic%C4%83_matematic%C4%83" title="Fizică matematică">Fizică matematică</a> <br /> <a href="/wiki/Supersimetrie" title="Supersimetrie">Supersimetrie</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Teoria_coardelor" title="Teoria coardelor">Teoria coardelor</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Teoria_M" title="Teoria M">Teoria M</a><br /> <a href="/w/index.php?title=Marea_teorie_unificat%C4%83&action=edit&redlink=1" class="new" title="Marea teorie unificată — pagină inexistentă">Marea teorie unificată</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Modelul_standard" title="Modelul standard">Modelul standard</a> <br /> <a href="/wiki/Mecanic%C4%83_cuantic%C4%83" title="Mecanică cuantică">Mecanică cuantică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Teoria_cuantic%C4%83_a_c%C3%A2mpurilor" title="Teoria cuantică a câmpurilor">Teoria cuantică a câmpurilor</a> <br /> <a href="/wiki/Antiparticul%C4%83" title="Antiparticulă">Antiparticulă</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Antimaterie" title="Antimaterie">Antimaterie</a> <br /> <a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Electrodinamic%C4%83_cuantic%C4%83" title="Electrodinamică cuantică">Electrodinamică cuantică</a> <br /> <a href="/wiki/Interac%C8%9Biune_slab%C4%83" title="Interacțiune slabă">Interacțiune slabă</a> <span style="font-weight:bold;">·</span> <a href="/w/index.php?title=Interac%C8%9Biune_electroslab%C4%83&action=edit&redlink=1" class="new" title="Interacțiune electroslabă — pagină inexistentă">Interacțiune electroslabă</a> <br /> <a href="/wiki/Interac%C8%9Biune_tare" title="Interacțiune tare">Interacțiune tare</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Cromodinamic%C4%83_cuantic%C4%83" title="Cromodinamică cuantică">Cromodinamică cuantică</a> <br /> <a href="/wiki/Fizic%C4%83_atomic%C4%83" title="Fizică atomică">Fizică atomică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Fizica_particulelor_elementare" title="Fizica particulelor elementare">Fizica particulelor elementare</a><br /><a href="/wiki/Fizic%C4%83_nuclear%C4%83" title="Fizică nucleară">Fizică nucleară</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Materie_exotic%C4%83" title="Materie exotică">Materie exotică</a><br /><a href="/wiki/Bosonul_Higgs" title="Bosonul Higgs">Bosonul Higgs</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Fizic%C4%83_atomic%C4%83_%C8%99i_molecular%C4%83" title="Fizică atomică și moleculară">Fizică atomică și moleculară</a> <br /> <a href="/wiki/Fizica_materiei_condensate" title="Fizica materiei condensate">Fizica materiei condensate</a> <br /><a href="/w/index.php?title=Informa%C8%9Bie_cuantic%C4%83&action=edit&redlink=1" class="new" title="Informație cuantică — pagină inexistentă">Informație cuantică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Calculator_cuantic" title="Calculator cuantic">Calculator cuantic</a> <br /> <a href="/w/index.php?title=Spintronic%C4%83&action=edit&redlink=1" class="new" title="Spintronică — pagină inexistentă">Spintronică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Superconductivitate" class="mw-redirect" title="Superconductivitate">Superconductivitate</a> <br /> <a href="/wiki/Sistem_dinamic" title="Sistem dinamic">Sistem dinamic</a> <span style="font-weight:bold;">·</span> <a href="/w/index.php?title=Fotonic%C4%83&action=edit&redlink=1" class="new" title="Fotonică — pagină inexistentă">Fotonică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Biofizic%C4%83" title="Biofizică">Biofizică</a> <br /> <a href="/w/index.php?title=Neurofizic%C4%83&action=edit&redlink=1" class="new" title="Neurofizică — pagină inexistentă">Neurofizică</a> <span style="font-weight:bold;">·</span> <a href="/w/index.php?title=Minte_cuantic%C4%83&action=edit&redlink=1" class="new" title="Minte cuantică — pagină inexistentă">Minte cuantică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Plasm%C4%83" title="Plasmă">Plasmă</a><br /> <a class="mw-selflink selflink">Relativitate restrânsă</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Teoria_relativit%C4%83%C8%9Bii_generale" title="Teoria relativității generale">Relaivitate generală</a> <br /><a href="/wiki/Materie_%C3%AEntunecat%C4%83" class="mw-redirect" title="Materie întunecată">Materie întunecată</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Energie_%C3%AEntunecat%C4%83" title="Energie întunecată">Energie întunecată</a> <br /> <a href="/w/index.php?title=Haos_cuantic&action=edit&redlink=1" class="new" title="Haos cuantic — pagină inexistentă">Haos cuantic</a> <span style="font-weight:bold;">·</span>  <a href="/w/index.php?title=Emergen%C8%9B%C4%83&action=edit&redlink=1" class="new" title="Emergență — pagină inexistentă">Emergență</a> <span style="font-weight:bold;">·</span> <a href="/w/index.php?title=Sistem_complex&action=edit&redlink=1" class="new" title="Sistem complex — pagină inexistentă">Sistem complex</a> <br /> <a href="/wiki/Gaur%C4%83_neagr%C4%83" title="Gaură neagră">Gaură neagră</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Principiul_holografic" title="Principiul holografic">Principiul holografic</a> <br /> <a href="/wiki/Astrofizic%C4%83" title="Astrofizică">Astrofizică</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Univers_observabil" title="Univers observabil">Univers observabil</a> <br /> <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Cosmologie" title="Cosmologie">Cosmologie</a> <br /><a href="/wiki/Gravita%C8%9Bie" title="Gravitație">Gravitație</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Gravita%C8%9Bie_cuantic%C4%83" title="Gravitație cuantică">Gravitație cuantică</a><br /><a href="/wiki/Teoria_%C3%AEntregului" title="Teoria întregului">Teoria întregului</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Multivers" title="Multivers">Multivers</a></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:transparent;border-top:1px solid #aaa;text-align:center;">Oameni de știință</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><a href="/w/index.php?title=Edward_Witten&action=edit&redlink=1" class="new" title="Edward Witten — pagină inexistentă">Witten</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Wilhelm_R%C3%B6ntgen" title="Wilhelm Röntgen">Röntgen</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Henri_Becquerel" class="mw-redirect" title="Henri Becquerel">Becquerel</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Hendrik_Lorentz" title="Hendrik 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W. Anderson</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a> <span style="font-weight:bold;">·</span>  <a href="/w/index.php?title=Sir_George_Paget_Thomson&action=edit&redlink=1" class="new" title="Sir George Paget Thomson — pagină inexistentă">Thomson</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a> <span style="font-weight:bold;">·</span> <a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a> <span style="font-weight:bold;">·</span> <a href="/w/index.php?title=Robert_A._Millikan&action=edit&redlink=1" class="new" title="Robert A. Millikan — pagină inexistentă">Millikan</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Yoichiro_Nambu" title="Yoichiro Nambu">Nambu</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Peter_Higgs" title="Peter Higgs">Higgs</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Otto_Hahn" title="Otto Hahn">Hahn</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman</a> <span style="font-weight:bold;">·</span>  <a href="/w/index.php?title=Yang_Chen-Ning&action=edit&redlink=1" class="new" title="Yang Chen-Ning — pagină inexistentă">Yang</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Tsung-Dao_Lee" title="Tsung-Dao Lee">Lee</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Philipp_Lenard" title="Philipp Lenard">Lenard</a> <span style="font-weight:bold;">·</span> <a href="/wiki/Abdus_Salam" title="Abdus Salam">Salam</a> <span style="font-weight:bold;">·</span>  <a href="/w/index.php?title=Gerard_%27t_Hooft&action=edit&redlink=1" class="new" title="Gerard 't Hooft — pagină inexistentă">'t Hooft</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">Bell</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Murray_Gell-Mann" title="Murray Gell-Mann">Gell-Mann</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/J._J._Thomson" class="mw-redirect" title="J. J. Thomson">J. J. Thomson</a>  <span style="font-weight:bold;">·</span>  <a href="/wiki/C._V._Raman" class="mw-redirect" title="C. V. Raman">Raman</a> <span style="font-weight:bold;">·</span>  <a href="/w/index.php?title=Lawrence_Bragg&action=edit&redlink=1" class="new" title="Lawrence Bragg — pagină inexistentă">Bragg</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/John_Bardeen" title="John Bardeen">Bardeen</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/William_Shockley" class="mw-redirect" title="William Shockley">Shockley</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/James_Chadwick" title="James Chadwick">Chadwick</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Ernest_O._Lawrence" class="mw-redirect" title="Ernest O. Lawrence">Lawrence</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Zeilinger</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/Samuel_Goudsmit" title="Samuel Goudsmit">Goudsmit</a> <span style="font-weight:bold;">·</span>  <a href="/wiki/George_Uhlenbeck" title="George Uhlenbeck">Uhlenbeck</a></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:inherit;color:var(--color-base, #000) !important;text-align:left;background:transparent;border-top:1px solid #aaa;text-align:center;">Categorii</div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><div class="CategoryTreeTag" data-ct-options="{"mode":0,"hideprefix":20,"showcount":false,"namespaces":false,"notranslations":false}"><span class="CategoryTreeNotice">Categoria <i>Fizică modernă</i> nu a fost găsită</span></div></div></div></td> </tr><tr><td style="text-align:right;font-size:115%;padding-top: 0.6em;"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Format:Fizica_modern%C4%83" title="Format:Fizica modernă"><abbr title="Vizualizează acest format">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Discu%C8%9Bie_Format:Fizica_modern%C4%83&action=edit&redlink=1" class="new" title="Discuție Format:Fizica modernă — pagină inexistentă"><abbr title="Discută acest format">d</abbr></a></li><li class="nv-edit"><a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Format:Fizica_modern%C4%83&action=edit"><abbr title="Modifică acest format">m</abbr></a></li></ul></div></td></tr></tbody></table> <p>Cursurile de fizică introductivă, precum și unele manuale mai vechi despre teoria relativității restrânse definesc o <i><a href="/w/index.php?title=Mas%C4%83_relativist%C4%83&action=edit&redlink=1" class="new" title="Masă relativistă — pagină inexistentă">masă relativistă</a></i> care crește cu creșterea vitezei unui corp. Conform interpretării geometrice a relativității restrânse, această definiție nu se mai folosește, iar termenul "masă" este limitat la noțiunea de <a href="/wiki/Mas%C4%83_de_repaus" title="Masă de repaus">masă de repaus</a> fiind astfel independentă de sistemul de referință. </p><p>Folosind definiția relativistă a masei, masa unui obiect poate varia în funcție de sistemul de referință inerțial al observatorului, în același fel în care alte proprietăți ale sale, cum ar fi lungimea, fac același lucru. Definirea unei astfel de cantități poate fi uneori utilă prin faptul că această definire simplifică un calcul restricționându-l la un anumit sistem de referință. De exemplu, considerând un corp cu masa de repaus m care se mișcă la o anumită viteză relativ la un sistem de referință al observatorului. Acel observator definește <i>masa relativistă</i> a corpului ca fiind: </p> <dl><dd><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=\gamma m\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mi>γ</mi> <mi>m</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=\gamma m\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b42ab72db553b75bd4cab4c7e6d0041b18c2b4e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.338ex; width:8.795ex; height:2.676ex;" alt="{\displaystyle M=\gamma m\!}"></span></dd></dl> <p>"Masa relativistă" nu trebuie să fie confundată cu "masa longitudinală" și cea "transversală", definite și utilizate în preajma anului 1900 și bazate pe o aplicare inconsistentă a legilor lui Newton: acestea foloseau <i>f=ma</i> pentru o masă variabilă, pe când masa relativistă corespunde masei dinamice a lui Newton în care <i>p=Mv</i> și <i>f=dp/dt</i>. </p><p>Se observă și faptul că corpul <i>nu</i> devine mai masiv în sistemul său <i>propriu</i> de referință, deoarece masa relativistă este diferită doar pentru un observator dintr-un alt sistem. <i>Singura</i> masă independentă de sistemul de referință este masa de repaus. Când se folosește masa relativistă, trebuie să se specifice și sistemul de referință aplicabil dacă nu este evident, sau dedus implicit din formularea problemei. Este evident și că creșterea de masă relativistă nu rezultă din creșterea numărului de atomi al obiectului. În schimb, masa relativistă a fiecărui atom și particulă subatomică crește ea însăși. </p><p>Manualele de fizică folosesc uneori masa relativistă, deoarece ea permite studenților să utilizeze cunoștințele lor de fizică newtoniană pentru a face mai intuitive anumite concepte, restrângându-le la anumite sisteme de referință alese. "Masa relativistă" este consistentă și cu conceptele de "dilatare temporală" și "contracție a lungimii". </p> <div class="mw-heading mw-heading2"><h2 id="Forța"><span id="For.C8.9Ba"></span>Forța</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=13" title="Modifică secțiunea: Forța" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=13" title="Edit section's source code: Forța"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Definiția clasică a forței f este dată de <a href="/wiki/Legile_lui_Newton" title="Legile lui Newton">Legea a doua a lui Newton</a> în forma ei originală: </p> <dl><dd><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 {\vec {f}}={\frac {d{\vec {p}}}{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {f}}={\frac {d{\vec {p}}}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2c849c8ed3d93fcaacf1c0b2edc9fe21ee8c10d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.14ex; height:5.676ex;" alt="{\displaystyle {\vec {f}}={\frac {d{\vec {p}}}{dt}}}"></span></dd></dl> <p>și aceasta este valabilă în teoria relativității. </p><p>Multe manuale moderne rescriu Legea a doua a lui Newton sub forma </p> <dl><dd><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 {\vec {f}}=M{\vec {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {f}}=M{\vec {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ccd53feaed4180366aa5d76314f21215729e65a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.435ex; height:3.343ex;" alt="{\displaystyle {\vec {f}}=M{\vec {a}}}"></span></dd></dl> <p>Această formă nu este valabilă în teoria relativității sau în alte situații în care masa relativistă <i>M</i> este variabilă. </p><p>Această formulă poate fi înlocuită în cazul relativist cu </p> <dl><dd><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 {\vec {f}}=\gamma m{\vec {a}}+\gamma ^{3}m{\frac {{\vec {v}}\cdot {\vec {a}}}{c^{2}}}{\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>γ</mi> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {f}}=\gamma m{\vec {a}}+\gamma ^{3}m{\frac {{\vec {v}}\cdot {\vec {a}}}{c^{2}}}{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5af613ee62c24a316ad8944c7f009dfa4a9c1b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:22.606ex; height:5.676ex;" alt="{\displaystyle {\vec {f}}=\gamma m{\vec {a}}+\gamma ^{3}m{\frac {{\vec {v}}\cdot {\vec {a}}}{c^{2}}}{\vec {v}}}"></span></dd></dl> <p>După cum se vede din ecuație, vectorii clasici forță și accelerație nu mai sunt neapărat paraleli în teoria relativității. </p><p>Totuși expresia tetradimensională care leagă <a href="/w/index.php?title=Tetrafor%C8%9Ba&action=edit&redlink=1" class="new" title="Tetraforța — pagină inexistentă">tetraforța</a> <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 F^{\mu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6588144b8e662613b074bdcd17a4d97efa89535" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.425ex; height:2.343ex;" alt="{\displaystyle F^{\mu }\,}"></span> cu <a href="/w/index.php?title=Masa_de_repaus&action=edit&redlink=1" class="new" title="Masa de repaus — pagină inexistentă">masa de repaus</a> m și <a href="/w/index.php?title=Tetraaccelera%C8%9Bia&action=edit&redlink=1" class="new" title="Tetraaccelerația — pagină inexistentă">tetraaccelerația</a> <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 A^{\mu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\mu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d7bc47b5640fde0eaafbade66c82869288f4e30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.354ex; height:2.343ex;" alt="{\displaystyle A^{\mu }\,}"></span> restaurează aceeași formă a ecuației </p> <dl><dd><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 F^{\mu }=mA^{\mu }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>=</mo> <mi>m</mi> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F^{\mu }=mA^{\mu }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21f53f07ad910bc811f2f2bd5daf2b84bf1ad469" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.531ex; height:2.343ex;" alt="{\displaystyle F^{\mu }=mA^{\mu }\,}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Geometria_spațiu-timpului"><span id="Geometria_spa.C8.9Biu-timpului"></span>Geometria spațiu-timpului</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=14" title="Modifică secțiunea: Geometria spațiu-timpului" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=14" title="Edit section's source code: Geometria spațiu-timpului"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Spa%C8%9Biu_Minkowski" title="Spațiu Minkowski">Spațiu Minkowski</a>.</div><style data-mw-deduplicate="TemplateStyles:r16505893">@media screen{html.skin-theme-clientpref-night .mw-parser-output .rellink{display:flex}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .rellink{display:flex}}</style> <p>În teoria relativității se folosește un spațiu Minkowski tetradimensional <i>plat</i>, care este un exemplu de <a href="/wiki/Spa%C8%9Biu-timp" title="Spațiu-timp">spațiu-timp</a>. Acest spațiu, însă, este foarte similar cu <a href="/wiki/Spa%C8%9Biu_tridimensional" title="Spațiu tridimensional">spațiul tridimensional</a> <a href="/wiki/Spa%C8%9Biu_euclidian" title="Spațiu euclidian">euclidian</a> standard, și astfel este ușor de lucrat cu el. </p><p><a href="/w/index.php?title=Diferen%C8%9Biala&action=edit&redlink=1" class="new" title="Diferențiala — pagină inexistentă">Diferențiala</a> distanței (<i>ds</i>) în spațiul <a href="/w/index.php?title=Cartezian&action=edit&redlink=1" class="new" title="Cartezian — pagină inexistentă">cartezian</a> 3D este definită ca: </p> <dl><dd><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 ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00c415168f3fc1aba9d7ab37612e89b292dec428" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.939ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}}"></span></dd></dl> <p>unde <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 (dx_{1},dx_{2},dx_{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (dx_{1},dx_{2},dx_{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e47ac80c2c3878788204410b04853d08e4c5f275" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.677ex; height:2.843ex;" alt="{\displaystyle (dx_{1},dx_{2},dx_{3})}"></span> sunt diferențialele celor trei dimensiuni spațiale. În geometria relativității restrânse, se adaugă o a patra dimensiune, derivată din timp, și astfel ecuația diferențialei distanței devine: </p> <dl><dd><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 ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19f2b2d91c3ca8c2c1070c37b9fab369e127abf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:30.95ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"></span></dd></dl> <p>Dacă se dorește să se facă și coordonata timpului să arate ca și cele spațiale, se poate trata timpul ca fiind <a href="/wiki/Num%C4%83r_imaginar" title="Număr imaginar">imaginar</a>: <i>x<sub>4</sub> = ict</i>. În acest caz, ecuația de mai sus devine <a href="/wiki/Func%C8%9Bie_simetric%C4%83" title="Funcție simetrică">simetrică</a>: </p> <dl><dd><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 ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+dx_{4}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+dx_{4}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9aaeb88bf3153cc07210fba803437118da4beba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.379ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+dx_{4}^{2}}"></span></dd></dl> <p>Aceasta sugerează ceea ce de fapt este o concluzie teoretică profundă, care arată că teoria relativitățiieste doar o <a href="/wiki/Simetrie_de_rota%C8%9Bie" title="Simetrie de rotație">simetrie de rotație</a> a <a href="/wiki/Spa%C8%9Biu-timp" title="Spațiu-timp">spațiu-timpului</a> nostru, foarte simialră cu simetria de rotație a <a href="/wiki/Spa%C8%9Biu_euclidian" title="Spațiu euclidian">spațiului euclidian</a>. Așa cum spațiul euclidian folosește o <a href="/w/index.php?title=Metric%C4%83_euclidian%C4%83&action=edit&redlink=1" class="new" title="Metrică euclidiană — pagină inexistentă">metrică euclidiană</a>, și spațiul timpul folosește o <a href="/w/index.php?title=Metric%C4%83_Minkowski&action=edit&redlink=1" class="new" title="Metrică Minkowski — pagină inexistentă">metrică Minkowski</a>. În esență, relativitatea restrânsă poate fi enunțată în termenii invarianței intervalului spațiu-timp (dintre oricare două evenimente) ca văzut din orice sistem de referință inerțial. Toate ecuațiile și efectele relativității restrânse pot fi deduse din această simetrie de rotație (<a href="/wiki/Grup_Poincar%C3%A9" title="Grup Poincaré">grup Poincaré</a>) a spațiu-timpului Minkowski. Misner (1971 §2.3), În cele din urmă, profunda înțelegere a relativității restrânse și a celei generale vor veni din studiul metricii Minkowski (descrisă mai jos) și nu din cel al unei metrici euclidiene "deghizate" folosind <i>ict</i> drept coordonată temporală. </p><p>Dacă reducem la 2 numărul dimensiunilor spațiale, pentru a putea reprezenta fizica într-un spațiu 3D </p> <dl><dd><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 ds^{2}=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85f5ce7255168d8385a507de9595924994f96690" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.51ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"></span></dd></dl> <p>vedem că liniile <a href="/wiki/Geodezic%C4%83" title="Geodezică">geodezice</a> <a href="/w/index.php?title=Geodezic%C4%83_nul%C4%83&action=edit&redlink=1" class="new" title="Geodezică nulă — pagină inexistentă">nule</a> se află de-a lungul unui con definit de ecuația </p> <dl><dd><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 ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e43aa213a6206f390257013d99ba7b7c2a33fe2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.771ex; height:3.343ex;" alt="{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"></span></dd></dl> <p>sau </p> <dl><dd><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 dx_{1}^{2}+dx_{2}^{2}=c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx_{1}^{2}+dx_{2}^{2}=c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f13e83090ebdfe1e9378dded386e629543fe2739" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.309ex; height:3.343ex;" alt="{\displaystyle dx_{1}^{2}+dx_{2}^{2}=c^{2}dt^{2}}"></span></dd></dl> <p>Adică ecuația unui cerc de rază <i>r=c×dt</i>. Dacă extindem aceasta la dimensiuni spațiale 3D, geodezicele nule se află pe un con tetradimensional: </p> <dl><dd><span class="mw-default-size" typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Null_spherical_space_(special_relativity).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/39/Null_spherical_space_%28special_relativity%29.jpg" decoding="async" width="140" height="110" class="mw-file-element" data-file-width="140" data-file-height="110" /></a></span></dd></dl> <dl><dd><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 ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/651ec5a5c69df295c86316d566133dfec28b076f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:35.211ex; height:3.343ex;" alt="{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"></span></dd></dl> <dl><dd><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 dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}=c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}=c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9de9a20458007959615dc7a86a89e861fd939a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.749ex; height:3.343ex;" alt="{\displaystyle dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}=c^{2}dt^{2}}"></span></dd></dl> <p>Acest con dual reprezintă "raza vizuală" a unui punct din spațiu. Adică atunci când privim <a href="/wiki/Stea" title="Stea">stelele</a> și spunem "Lumina pe care o recepționez de la stea este veche de X ani", privim până la limita acestei raze vizuale: o geodezică nulă. Privim un eveniment la o distanță de <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 d={\sqrt {x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d={\sqrt {x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54abac3f97536607ca02acedebccac4fa59d1e1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.471ex; height:4.843ex;" alt="{\displaystyle d={\sqrt {x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}}}"></span> metri ce a avut loc cu <i>d/c</i> secunde în urmă. Din acest motiv, conul dual nul este numit și 'con de lumină'. </p><p>Conul din regiunea <i>-t</i> este informația pe care acel punct o primește, iar conul din secțiunea <i>+t</i> este informația pe care acel punct o trimite. </p><p>Geometria spațiului Minkowski poate fi descrisă printr-o <a href="/w/index.php?title=Diagram%C4%83_Minkowski&action=edit&redlink=1" class="new" title="Diagramă Minkowski — pagină inexistentă">diagramă Minkowski</a>, utilă în înțelegerea multor experimente imaginare din teoria relativității restrânse. </p> <div class="mw-heading mw-heading2"><h2 id="Fizica_spațiu-timpului"><span id="Fizica_spa.C8.9Biu-timpului"></span>Fizica spațiu-timpului</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=15" title="Modifică secțiunea: Fizica spațiu-timpului" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=15" title="Edit section's source code: Fizica spațiu-timpului"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poziția unui eveniment în spațiu-timp este dată de un cuadrivector <a href="/w/index.php?title=Contravariant&action=edit&redlink=1" class="new" title="Contravariant — pagină inexistentă">contravariant</a> ale cărui componente sunt: </p> <dl><dd><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 x^{\nu }=\left(t,x,y,z\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{\nu }=\left(t,x,y,z\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dd6ed07afbe6e9268bac06020dfac9eb55c0ed8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.856ex; height:2.843ex;" alt="{\displaystyle x^{\nu }=\left(t,x,y,z\right)}"></span></dd></dl> <p>Adică, <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 x^{0}=t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>=</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{0}=t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6075a833d5c830ee4c29dadb30300b0cf5213f8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.322ex; height:2.676ex;" alt="{\displaystyle x^{0}=t}"></span>, <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 x^{1}=x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{1}=x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/989591a51a17a5e50b3d75801710adb76aeea684" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.812ex; height:2.676ex;" alt="{\displaystyle x^{1}=x}"></span>, <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 x^{2}=y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}=y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdd1f6dcf78d5d1dc0f92f69e76736a81f73b124" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.638ex; height:3.009ex;" alt="{\displaystyle x^{2}=y}"></span> și <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 x^{3}=z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}=z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62cc0d304c051d6767d2b7383ca2c1bef7c15701" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.571ex; height:2.676ex;" alt="{\displaystyle x^{3}=z}"></span>. La exponent sunt indicii contravarianți și nu puteri. La indice sunt indicii <a href="/w/index.php?title=Covariant&action=edit&redlink=1" class="new" title="Covariant — pagină inexistentă">covarianți</a>, de la zero la trei. Gradientul în spațiu-timp al unui câmp φ este: </p> <dl><dd><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 \partial _{0}\phi ={\frac {\partial \phi }{\partial t}},\quad \partial _{1}\phi ={\frac {\partial \phi }{\partial x}},\quad \partial _{2}\phi ={\frac {\partial \phi }{\partial y}},\quad \partial _{3}\phi ={\frac {\partial \phi }{\partial z}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ϕ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ϕ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ϕ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ϕ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{0}\phi ={\frac {\partial \phi }{\partial t}},\quad \partial _{1}\phi ={\frac {\partial \phi }{\partial x}},\quad \partial _{2}\phi ={\frac {\partial \phi }{\partial y}},\quad \partial _{3}\phi ={\frac {\partial \phi }{\partial z}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/deb92eb645cb3278316f0229773434ef776b4475" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:51.965ex; height:6.176ex;" alt="{\displaystyle \partial _{0}\phi ={\frac {\partial \phi }{\partial t}},\quad \partial _{1}\phi ={\frac {\partial \phi }{\partial x}},\quad \partial _{2}\phi ={\frac {\partial \phi }{\partial y}},\quad \partial _{3}\phi ={\frac {\partial \phi }{\partial z}}.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Metrica_și_transformările_de_coordonate"><span id="Metrica_.C8.99i_transform.C4.83rile_de_coordonate"></span>Metrica și transformările de coordonate</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=16" title="Modifică secțiunea: Metrica și transformările de coordonate" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=16" title="Edit section's source code: Metrica și transformările de coordonate"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>După ce a fost identificată natura tetradimensională a spațiu-timpului, se folosește metrica Minkowski, η, dată pe componente (valide în orice <a href="/wiki/Sistem_de_referin%C8%9B%C4%83_iner%C8%9Bial" title="Sistem de referință inerțial">sistem de referință inerțial</a>) ca: </p> <dl><dd><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 _{\alpha \beta }={\begin{pmatrix}-c^{2}&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta _{\alpha \beta }={\begin{pmatrix}-c^{2}&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35a857de1a10e753659c40af205c12c3ace99d2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:25.623ex; height:12.509ex;" alt="{\displaystyle \eta _{\alpha \beta }={\begin{pmatrix}-c^{2}&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}"></span></dd></dl> <p>Inversa ei este: </p> <dl><dd><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 ^{\alpha \beta }={\begin{pmatrix}-1/c^{2}&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta ^{\alpha \beta }={\begin{pmatrix}-1/c^{2}&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27b782e487a77b6a86189db5f034963b945af4ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.838ex; margin-top: -0.286ex; width:27.966ex; height:12.843ex;" alt="{\displaystyle \eta ^{\alpha \beta }={\begin{pmatrix}-1/c^{2}&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}"></span></dd></dl> <p>Transformările de coordonate între sisteme de referință inerțiale sunt date de <a href="/wiki/Tensor" title="Tensor">tensorul</a> <a href="/wiki/Transformare_Lorentz" class="mw-redirect" title="Transformare Lorentz">transformărilor Lorentz</a> Λ. Pentru cazul special al mișcării de-a lungul axei x, avem: </p> <dl><dd><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 \Lambda ^{\mu '}{}_{\nu }={\begin{pmatrix}\gamma &-\beta \gamma /c&0&0\\-\beta \gamma c&\gamma &0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>μ</mi> <mo>′</mo> </msup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>γ</mi> </mtd> <mtd> <mo>−</mo> <mi>β</mi> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>β</mi> <mi>γ</mi> <mi>c</mi> </mtd> <mtd> <mi>γ</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda ^{\mu '}{}_{\nu }={\begin{pmatrix}\gamma &-\beta \gamma /c&0&0\\-\beta \gamma c&\gamma &0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2740c8dd45fb36146f5ab67a74faaff59e9002e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.838ex; width:33.662ex; height:12.843ex;" alt="{\displaystyle \Lambda ^{\mu '}{}_{\nu }={\begin{pmatrix}\gamma &-\beta \gamma /c&0&0\\-\beta \gamma c&\gamma &0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}"></span></dd></dl> <p>adică matricea de rotație de la coordonatele <i>x</i> la <i>t</i>. μ' indică rândul și ν indică coloana. De asemenea, β și γ sunt definite ca: </p> <dl><dd><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 \beta ={\frac {v}{c}},\ \gamma ={\frac {1}{\sqrt {1-\beta ^{2}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mi>c</mi> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <mi>γ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta ={\frac {v}{c}},\ \gamma ={\frac {1}{\sqrt {1-\beta ^{2}}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30a9664445e8c168dac883023bbe31b746f6d30e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:22.57ex; height:6.509ex;" alt="{\displaystyle \beta ={\frac {v}{c}},\ \gamma ={\frac {1}{\sqrt {1-\beta ^{2}}}}.}"></span></dd></dl> <p>Mai general, o transformare de la un sistem inerțial (ignorând translațiile, pentru simplitate) la un altul trebuie să satisfacă condiția: </p> <dl><dd><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 _{\alpha \beta }=\eta _{\mu '\nu '}\Lambda ^{\mu '}{}_{\alpha }\Lambda ^{\nu '}{}_{\beta }\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mi>β</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>μ</mi> <mo>′</mo> </msup> <msup> <mi>ν</mi> <mo>′</mo> </msup> </mrow> </msub> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>μ</mi> <mo>′</mo> </msup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>ν</mi> <mo>′</mo> </msup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msub> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta _{\alpha \beta }=\eta _{\mu '\nu '}\Lambda ^{\mu '}{}_{\alpha }\Lambda ^{\nu '}{}_{\beta }\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/112da67c612e26df3ffb0e61437c2f95bb2d6d69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:19.903ex; height:3.509ex;" alt="{\displaystyle \eta _{\alpha \beta }=\eta _{\mu '\nu '}\Lambda ^{\mu '}{}_{\alpha }\Lambda ^{\nu '}{}_{\beta }\!}"></span></dd></dl> <p>unde este implicită suma lui <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 \mu '\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>μ</mi> <mo>′</mo> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu '\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb476cdc985efe434c60315fc4731c6b7e5b5e4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:2.086ex; height:3.009ex;" alt="{\displaystyle \mu '\!}"></span> și <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 \nu '\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ν</mi> <mo>′</mo> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu '\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f7a06de10e09980391ac17139237ce0f4812853" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.942ex; height:2.509ex;" alt="{\displaystyle \nu '\!}"></span> de la 0 la 3 în partea dreaptă a ecuației, conform <a href="/w/index.php?title=Nota%C8%9Bia_Einstein&action=edit&redlink=1" class="new" title="Notația Einstein — pagină inexistentă">notației Einstein pentru sume</a>. <a href="/wiki/Grup_Poincar%C3%A9" title="Grup Poincaré">Grupul Poincaré</a> este cel mai general grup de transformări care păstrează <a href="/w/index.php?title=Metrica_Minkowski&action=edit&redlink=1" class="new" title="Metrica Minkowski — pagină inexistentă">metrica Minkowski</a> și reprezintă simetria fizică ce stă la baza relativității restrânse. </p><p>Toate cantitățile fizice sunt date ca tensori. Pentru a trece dintr-un sistem în altul, se folosește <a href="/wiki/Tensor" title="Tensor">legea transformărilor tensoriale</a> </p> <dl><dd><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 T_{\left[j_{1}',j_{2}',...j_{q}'\right]}^{\left[i_{1}',i_{2}',...i_{p}'\right]}=\Lambda ^{i_{1}'}{}_{i_{1}}\Lambda ^{i_{2}'}{}_{i_{2}}...\Lambda ^{i_{p}'}{}_{i_{p}}\Lambda _{j_{1}'}{}^{j_{1}}\Lambda _{j_{2}'}{}^{j_{2}}...\Lambda _{j_{q}'}{}^{j_{q}}T_{\left[j_{1},j_{2},...j_{q}\right]}^{\left[i_{1},i_{2},...i_{p}\right]}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mrow> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> <mo>,</mo> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mo>′</mo> </msubsup> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> <mo>′</mo> </msubsup> </mrow> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mrow> <msubsup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> <mo>,</mo> <msubsup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mo>′</mo> </msubsup> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msubsup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> <mo>′</mo> </msubsup> </mrow> <mo>]</mo> </mrow> </mrow> </msubsup> <mo>=</mo> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mo>′</mo> </msubsup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> <mo>′</mo> </msubsup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mrow> </msub> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msup> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mo>′</mo> </msubsup> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msup> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> <mo>′</mo> </msubsup> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> </mrow> </msup> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mrow> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> </mrow> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mrow> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mrow> <mo>]</mo> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\left[j_{1}',j_{2}',...j_{q}'\right]}^{\left[i_{1}',i_{2}',...i_{p}'\right]}=\Lambda ^{i_{1}'}{}_{i_{1}}\Lambda ^{i_{2}'}{}_{i_{2}}...\Lambda ^{i_{p}'}{}_{i_{p}}\Lambda _{j_{1}'}{}^{j_{1}}\Lambda _{j_{2}'}{}^{j_{2}}...\Lambda _{j_{q}'}{}^{j_{q}}T_{\left[j_{1},j_{2},...j_{q}\right]}^{\left[i_{1},i_{2},...i_{p}\right]}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9eb24f5ef857f15d66b924e9616a97b60c32c5c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:58.65ex; height:5.176ex;" alt="{\displaystyle T_{\left[j_{1}',j_{2}',...j_{q}'\right]}^{\left[i_{1}',i_{2}',...i_{p}'\right]}=\Lambda ^{i_{1}'}{}_{i_{1}}\Lambda ^{i_{2}'}{}_{i_{2}}...\Lambda ^{i_{p}'}{}_{i_{p}}\Lambda _{j_{1}'}{}^{j_{1}}\Lambda _{j_{2}'}{}^{j_{2}}...\Lambda _{j_{q}'}{}^{j_{q}}T_{\left[j_{1},j_{2},...j_{q}\right]}^{\left[i_{1},i_{2},...i_{p}\right]}}"></span></dd></dl> <p>unde <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 \Lambda _{j_{k}'}{}^{j_{k}}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <mo>′</mo> </msubsup> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda _{j_{k}'}{}^{j_{k}}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36621fbdc7fcd138daa00da29907d480cff73026" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; margin-right: -0.387ex; width:5.152ex; height:3.676ex;" alt="{\displaystyle \Lambda _{j_{k}'}{}^{j_{k}}\!}"></span> este matricea inversă a lui <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 \Lambda ^{j_{k}'}{}_{j_{k}}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <mo>′</mo> </msubsup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </msub> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda ^{j_{k}'}{}_{j_{k}}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6924ff799e4cc5c2b0824b67150582cb37e664da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:5.152ex; height:3.509ex;" alt="{\displaystyle \Lambda ^{j_{k}'}{}_{j_{k}}\!}"></span>. </p><p>Pentru a vedea utilitatea acesteia, transformăm poziția unui eveniment de la un sistem de coordonate <i>S</i> la un sistem <i>S'</i>, calculând </p> <dl><dd><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 {\begin{pmatrix}t'\\x'\\y'\\z'\end{pmatrix}}=x^{\mu '}=\Lambda ^{\mu '}{}_{\nu }x^{\nu }={\begin{pmatrix}\gamma &-\beta \gamma /c&0&0\\-\beta \gamma c&\gamma &0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}{\begin{pmatrix}t\\x\\y\\z\end{pmatrix}}={\begin{pmatrix}\gamma t-\gamma \beta x/c\\\gamma x-\beta \gamma ct\\y\\z\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msup> <mi>t</mi> <mo>′</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>x</mi> <mo>′</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>y</mi> <mo>′</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>z</mi> <mo>′</mo> </msup> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>μ</mi> <mo>′</mo> </msup> </mrow> </msup> <mo>=</mo> <msup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>μ</mi> <mo>′</mo> </msup> </mrow> </msup> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>γ</mi> </mtd> <mtd> <mo>−</mo> <mi>β</mi> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>β</mi> <mi>γ</mi> <mi>c</mi> </mtd> <mtd> <mi>γ</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>t</mi> </mtd> </mtr> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>γ</mi> <mi>t</mi> <mo>−</mo> <mi>γ</mi> <mi>β</mi> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <mi>γ</mi> <mi>x</mi> <mo>−</mo> <mi>β</mi> <mi>γ</mi> <mi>c</mi> <mi>t</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{pmatrix}t'\\x'\\y'\\z'\end{pmatrix}}=x^{\mu '}=\Lambda ^{\mu '}{}_{\nu }x^{\nu }={\begin{pmatrix}\gamma &-\beta \gamma /c&0&0\\-\beta \gamma c&\gamma &0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}{\begin{pmatrix}t\\x\\y\\z\end{pmatrix}}={\begin{pmatrix}\gamma t-\gamma \beta x/c\\\gamma x-\beta \gamma ct\\y\\z\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e2ded5182dbb5aa4da0dc608ea085c05bf0ab5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.838ex; width:77.31ex; height:12.843ex;" alt="{\displaystyle {\begin{pmatrix}t'\\x'\\y'\\z'\end{pmatrix}}=x^{\mu '}=\Lambda ^{\mu '}{}_{\nu }x^{\nu }={\begin{pmatrix}\gamma &-\beta \gamma /c&0&0\\-\beta \gamma c&\gamma &0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}{\begin{pmatrix}t\\x\\y\\z\end{pmatrix}}={\begin{pmatrix}\gamma t-\gamma \beta x/c\\\gamma x-\beta \gamma ct\\y\\z\end{pmatrix}}}"></span></dd></dl> <p>care este chiar transformarea Lorentz dată mai sus. Toți tensorii se transformă după aceeași regulă. </p><p>Tetravectorul pătratelor diferențialelor distanțelor <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 dx^{\mu }\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx^{\mu }\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1026a8fc586e9ee58cce0866eed79c3d978c6279" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:3.769ex; height:2.343ex;" alt="{\displaystyle dx^{\mu }\!}"></span> construit folosind </p> <dl><dd><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 \mathbf {dx} ^{2}=\eta _{\mu \nu }dx^{\mu }dx^{\nu }=-(c\cdot dt)^{2}+(dx)^{2}+(dy)^{2}+(dz)^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mi>d</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mi>d</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi>c</mi> <mo>⋅</mo> <mi>d</mi> <mi>t</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>d</mi> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>d</mi> <mi>y</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>d</mi> <mi>z</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {dx} ^{2}=\eta _{\mu \nu }dx^{\mu }dx^{\nu }=-(c\cdot dt)^{2}+(dx)^{2}+(dy)^{2}+(dz)^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/197cd608dc66523adb50ff927f2c714f53ce0120" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:54.949ex; height:3.343ex;" alt="{\displaystyle \mathbf {dx} ^{2}=\eta _{\mu \nu }dx^{\mu }dx^{\nu }=-(c\cdot dt)^{2}+(dx)^{2}+(dy)^{2}+(dz)^{2}\,}"></span></dd></dl> <p>este invariant. Faptul că este invariant înseamnă că are aceeași valoare în toate sistemele inerțiale, deoarece este un scalar (tensor de rang 0), și astfel Λ nu apare în transformarea sa trivială. De observat că atunci când elementul <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 \mathbf {dx} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {dx} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82b24f984c80a9eef902bb17cc45b55d0472e020" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.951ex; height:2.676ex;" alt="{\displaystyle \mathbf {dx} ^{2}}"></span> este negativ, <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 d\tau ={\sqrt {-\mathbf {dx} ^{2}}}/c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>τ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\tau ={\sqrt {-\mathbf {dx} ^{2}}}/c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/342bd305b4cab0b41ed5727ec4cc30d7a2f67289" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.768ex; height:3.843ex;" alt="{\displaystyle d\tau ={\sqrt {-\mathbf {dx} ^{2}}}/c}"></span> este diferențiala <a href="/w/index.php?title=Timp_propriu&action=edit&redlink=1" class="new" title="Timp propriu — pagină inexistentă">timpului propriu</a>, iar când <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 \mathbf {dx} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {dx} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82b24f984c80a9eef902bb17cc45b55d0472e020" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.951ex; height:2.676ex;" alt="{\displaystyle \mathbf {dx} ^{2}}"></span> este pozitiv, <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 {\sqrt {\mathbf {dx} ^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {\mathbf {dx} ^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3e191c87b707407e0fbac37d31f00a3059ee10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.274ex; height:3.509ex;" alt="{\displaystyle {\sqrt {\mathbf {dx} ^{2}}}}"></span> este diferențiala <a href="/w/index.php?title=Distan%C8%9B%C4%83_proprie&action=edit&redlink=1" class="new" title="Distanță proprie — pagină inexistentă">distanței proprii</a>. </p><p>Utilitatea principală a exprimării ecuațiilor fizicii în formă tensorială este că atunci sunt invariante în raport cu grupul Poincaré, astfel că nu avem de-a face cu un calcul special și dificil pentru a verifica aceasta. De asemenea, la construirea acestor ecuații adesea găsim că alte ecuații despre care anterior credeam că nu au nicio legătură cu ele sunt, de fapt, strâns legate, ca făcând parte din aceeași ecuație tensorială. </p> <div class="mw-heading mw-heading2"><h2 id="Statutul_teoriei">Statutul teoriei</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=17" title="Modifică secțiunea: Statutul teoriei" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=17" title="Edit section's source code: Statutul teoriei"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Relativitatea restrânsă este exactă doar când <a href="/w/index.php?title=Poten%C8%9Bial_gravita%C8%9Bional&action=edit&redlink=1" class="new" title="Potențial gravitațional — pagină inexistentă">potențialul gravitațional</a> este mult mai mic ca c<sup>2</sup>; într-un câmp gravitațional puternic trebuie să se folosească <a href="/wiki/Teoria_relativit%C4%83%C8%9Bii_generalizate" class="mw-redirect" title="Teoria relativității generalizate">teoria relativității generalizate</a> (care este, la limită, echivalentă cu cea restrânsă pentru câmpuri gravitaționale slabe). La scară foarte mică (la lungimi de ordinul <a href="/w/index.php?title=Distan%C8%9Ba_Planck&action=edit&redlink=1" class="new" title="Distanța Planck — pagină inexistentă">distanței Planck</a> și mai mici) trebuie să fie luate în calcul și efectele cuantice, de unde rezultă <a href="/wiki/Gravita%C8%9Bia_cuantic%C4%83" class="mw-redirect" title="Gravitația cuantică">gravitația cuantică</a>. Totuși, la nivel macroscopic și în absența câmpurilor gravitaționale puternice, relativitatea restrânsă a fost testată experimental, obținându-se un grad extrem de înalt de precizie (10<sup>−20</sup>) <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> <sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> și astfel este acceptată de comunitatea fizicienilor. Rezultatele experimentale care par să o contrazică nu sunt reproductibile și sunt considerate a se datora erorilor experimentale. </p><p>Datorită libertății pe care o acordă teoria de a alege cum să se definească unitățile de distanță și timp în fizică, este posibil să se facă unul din postulatele relativității consecință <a href="/wiki/Tautologie" title="Tautologie">tautologică</a> a definițiilor, dar acest lucru nu poate fi făcut pentru ambele postulate simultan, deoarece, împreună, ele au consecințe independente de alegerea definițiilor pentru distanță și timp. </p><p>Relativitatea restrânsă este consistentă cu ea însăși din punct de vedere matematic, și este parte organică din toate teoriile fizice moderne, în primul rând din <a href="/w/index.php?title=Teoria_cuantic%C4%83_de_c%C3%A2mp&action=edit&redlink=1" class="new" title="Teoria cuantică de câmp — pagină inexistentă">teoria cuantică de câmp</a>, <a href="/wiki/Teoria_coardelor" title="Teoria coardelor">teoria coardelor</a> și <a href="/wiki/Teoria_relativit%C4%83%C8%9Bii_generalizate" class="mw-redirect" title="Teoria relativității generalizate">teoria relativității generalizate</a> (pentru cazul câmpurilor gravitaționale neglijabile). </p><p>Mecanica newtoniană derivă matematic din teoria relativității restrânse pentru viteze mici față de cea a luminii - astfel mecanica newtoniană poate fi considerată o relativitate restrânsă a corpurilor lente. </p> <div class="mw-heading mw-heading3"><h3 id="Experimente_fondatoare">Experimente fondatoare</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=18" title="Modifică secțiunea: Experimente fondatoare" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=18" title="Edit section's source code: Experimente fondatoare"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Câteva experimente-cheie au condus la elaborarea teoriei relativității restrânse: </p> <ul><li><a href="/w/index.php?title=Experimentul_Trouton%E2%80%93Noble&action=edit&redlink=1" class="new" title="Experimentul Trouton–Noble — pagină inexistentă">Experimentul Trouton–Noble</a> a arătat că momentul unui condensator este independent de poziția sa și de sistemul de referință inerțial</li> <li>Celebrul <a href="/wiki/Experien%C8%9Ba_Michelson-Morley" class="mw-redirect" title="Experiența Michelson-Morley">experiment Michelson-Morley</a> a dat mai mult suport postulatului privind imposibilitatea detectării unei viteze absolute<span class="citationNeeded skin-invert"></span><sup class="noprint"><span style="color:red;">[<a href="/wiki/Wikipedia:Citarea_surselor" title="Wikipedia:Citarea surselor"><i>necesită citare</i></a>]</span></sup><style data-mw-deduplicate="TemplateStyles:r16584850">.mw-parser-output .citationNeeded{background-color:#ffeaea;color:#444444}</style>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Experimente_testare_teorii_alternative">Experimente testare teorii alternative</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=19" title="Modifică secțiunea: Experimente testare teorii alternative" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=19" title="Edit section's source code: Experimente testare teorii alternative"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O serie de experimente au fost efectuate cu scopul de a testa teoria relativității restrânse în raport cu alte teorii rivale. Printre acestea se numără: </p> <ul><li>Experimentul lui <a href="/w/index.php?title=Walter_Kaufmann&action=edit&redlink=1" class="new" title="Walter Kaufmann — pagină inexistentă">Kaufmann</a> — devierea electronilor conform predicției Lorentz-Einstein</li> <li><a href="/w/index.php?title=Experimentul_Hamar&action=edit&redlink=1" class="new" title="Experimentul Hamar — pagină inexistentă">Experimentul Hamar</a> — absența obstrucției fluxului de eter</li> <li><a href="/w/index.php?title=Experimentul_Kennedy%E2%80%93Thorndike&action=edit&redlink=1" class="new" title="Experimentul Kennedy–Thorndike — pagină inexistentă">Experimentul Kennedy–Thorndike</a> — dilatarea temporală conform cu transformările Lorentz</li> <li><a href="/w/index.php?title=Experimentul_Rossi-Hall&action=edit&redlink=1" class="new" title="Experimentul Rossi-Hall — pagină inexistentă">Experimentul Rossi-Hall</a> — efecte relativiste asupra timpului de înjumătățire a unei particule de mare viteză</li> <li>Experimentele de test ale <a href="/w/index.php?title=Teoria_emisiei&action=edit&redlink=1" class="new" title="Teoria emisiei — pagină inexistentă">teoriei emisiei</a> au demonstrat că viteza luminii este independentă de viteza sursei acesteia.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Oponenți_notabili"><span id="Oponen.C8.9Bi_notabili"></span>Oponenți notabili</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=20" title="Modifică secțiunea: Oponenți notabili" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=20" title="Edit section's source code: Oponenți notabili"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Joseph Larmor</li> <li>Nicola Tesla</li></ul> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=21" title="Modifică secțiunea: Note" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=21" title="Edit section's source code: Note"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><cite class="citation book">Taylor, Edwin F.; Wheeler, John Archibald (<time datetime="1992">1992</time>). <i>Spacetime Physics: Introduction to Special Relativity</i>. W. H. Freeman.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Spacetime+Physics%3A+Introduction+to+Special+Relativity&rft.pub=W.+H.+Freeman&rft.date=1992&rft.aulast=Taylor&rft.aufirst=Edwin+F.&rft.au=Wheeler%2C+John+Archibald&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span> <span style="font-size:100%" class="error citation-comment">Text "ISBN:0-7167-2327-1" ignorat (<a href="/wiki/Ajutor:Erori_CS1#text_ignored" title="Ajutor:Erori CS1">ajutor</a>)</span><style data-mw-deduplicate="TemplateStyles:r16236537">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"„""”""«""»"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style></span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text">"Science and Common Sense", P. W. Bridgman, <i>The Scientific Monthly</i>, Vol. 79, No. 1 (Jul. 1954), pp. 32–39.</span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text">The Electromagnetic Mass and Momentum of a Spinning Electron, G. Breit, Proceedings of the National Academy of Sciences, Vol. 12, p.451, 1926</span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text">Kinematics of an electron with an axis. Phil. Mag. 3:1-22. L. H. Thomas.]</span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><cite class="citation book">Einstein, A., Lorentz, H. A., Minkowski, H., & Weyl, H. (<time datetime="1952">1952</time>). <a rel="nofollow" class="external text" href="https://books.google.com/?id=yECokhzsJYIC&pg=PA111"><i>The Principle of Relativity: a collection of original memoirs on the special and general theory of relativity</i></a>. Courier Dover Publications. p. 111. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/978-0-486-60081-9" title="Special:Referințe în cărți/978-0-486-60081-9">978-0-486-60081-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Principle+of+Relativity%3A+a+collection+of+original+memoirs+on+the+special+and+general+theory+of+relativity&rft.pages=111&rft.pub=Courier+Dover+Publications&rft.date=1952&rft.isbn=978-0-486-60081-9&rft.au=Einstein%2C+A.%2C+Lorentz%2C+H.+A.%2C+Minkowski%2C+H.%2C+%26+Weyl%2C+H.&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3DyECokhzsJYIC%26pg%3DPA111&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">Mentenanță CS1: Nume multiple: lista autorilor (<a href="/wiki/Categorie:Mentenan%C8%9B%C4%83_CS1:_Nume_multiple:_lista_autorilor" title="Categorie:Mentenanță CS1: Nume multiple: lista autorilor">link</a>) </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-6"><b><a href="#cite_ref-6">^</a></b> <span class="reference-text"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> (1905) "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20050220050316/http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf"><i>Zur Elektrodynamik bewegter Körper</i></a>", <i>Annalen der Physik</i> 17: 891.</span> </li> <li id="cite_note-7"><b><a href="#cite_ref-7">^</a></b> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://www.telework.ro/ro/relativitatea-speciala/">„Relativitatea specială”</a>. <i>SetThings.com</i>. <time datetime="2014-06-21">21 iunie 2014</time><span class="reference-accessdate">. Accesat în <time datetime="2020-10-12">12 octombrie 2020</time></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=SetThings.com&rft.atitle=Relativitatea+special%C4%83&rft.date=2014-06-21&rft_id=https%3A%2F%2Fwww.telework.ro%2Fro%2Frelativitatea-speciala%2F&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-8"><b><a href="#cite_ref-8">^</a></b> <span class="reference-text"><cite class="citation book"><a href="/wiki/Herbert_Goldstein" title="Herbert Goldstein">Goldstein, Herbert</a> (<time datetime="1980">1980</time>). „Chapter 7: Special Relativity in Classical Mechanics”. <i>Classical Mechanics</i> (ed. 2nd). Addison-Wesley Publishing Company. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/0-201-02918-9" title="Special:Referințe în cărți/0-201-02918-9">0-201-02918-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+7%3A+Special+Relativity+in+Classical+Mechanics&rft.btitle=Classical+Mechanics&rft.edition=2nd&rft.pub=Addison-Wesley+Publishing+Company&rft.date=1980&rft.isbn=0-201-02918-9&rft.aulast=Goldstein&rft.aufirst=Herbert&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-9"><b><a href="#cite_ref-9">^</a></b> <span class="reference-text"><cite class="citation book">Lanczos, Cornelius (<time datetime="1970">1970</time>). „Chapter IX: Relativistic Mechanics”. <i>The Variational Principles of Mechanics</i> (ed. 4th). Dover Publications. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/978-0-486-65067-8" title="Special:Referințe în cărți/978-0-486-65067-8">978-0-486-65067-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+IX%3A+Relativistic+Mechanics&rft.btitle=The+Variational+Principles+of+Mechanics&rft.edition=4th&rft.pub=Dover+Publications&rft.date=1970&rft.isbn=978-0-486-65067-8&rft.aulast=Lanczos&rft.aufirst=Cornelius&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-Teoria-10">^ <a href="#cite_ref-Teoria_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Teoria_10-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text"><cite class="citation book">Sfetcu, Nicolae (<time datetime="2018">2018</time>). <a rel="nofollow" class="external text" href="https://books.google.ro/books?id=hslKDwAAQBAJ"><i>Teoria specială a relativității</i></a>. MultiMedia Publishing. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/978-606-9016-44-2" title="Special:Referințe în cărți/978-606-9016-44-2">978-606-9016-44-2</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Teoria+special%C4%83+a+relativit%C4%83%C8%9Bii&rft.pub=MultiMedia+Publishing&rft.date=2018&rft.isbn=978-606-9016-44-2&rft.aulast=Sfetcu&rft.aufirst=Nicolae&rft_id=https%3A%2F%2Fbooks.google.ro%2Fbooks%3Fid%3DhslKDwAAQBAJ&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-11"><b><a href="#cite_ref-11">^</a></b> <span class="reference-text">Sean Carroll, Lecture Notes on General Relativity, ch. 1, "Special relativity and flat spacetime," <a rel="nofollow" class="external free" href="http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll1.html">http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll1.html</a></span> </li> <li id="cite_note-12"><b><a href="#cite_ref-12">^</a></b> <span class="reference-text">Wald, General Relativity, p. 60: "... the special theory of relativity asserts that spacetime is the manifold ℝ<sup>4</sup> with a flat metric of Lorentz signature defined on it. Conversely, the entire content of special relativity ... is contained in this statement ..."</span> </li> <li id="cite_note-13"><b><a href="#cite_ref-13">^</a></b> <span class="reference-text"><cite class="citation book">Koks, Don (<time datetime="2006">2006</time>). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ObMb7l9-9loC"><i>Explorations in Mathematical Physics: The Concepts Behind an Elegant Language</i></a> (ed. illustrated). Springer Science & Business Media. p. 234. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/978-0-387-32793-8" title="Special:Referințe în cărți/978-0-387-32793-8">978-0-387-32793-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Explorations+in+Mathematical+Physics%3A+The+Concepts+Behind+an+Elegant+Language&rft.pages=234&rft.edition=illustrated&rft.pub=Springer+Science+%26+Business+Media&rft.date=2006&rft.isbn=978-0-387-32793-8&rft.aulast=Koks&rft.aufirst=Don&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DObMb7l9-9loC&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ObMb7l9-9loC&pg=PA234">Extract of page 234</a></span> </li> <li id="cite_note-14"><b><a href="#cite_ref-14">^</a></b> <span class="reference-text"><cite class="citation book">Steane, Andrew M. (<time datetime="2012">2012</time>). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=75rCErZkh7EC"><i>Relativity Made Relatively Easy</i></a> (ed. illustrated). OUP Oxford. p. 226. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/978-0-19-966286-9" title="Special:Referințe în cărți/978-0-19-966286-9">978-0-19-966286-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativity+Made+Relatively+Easy&rft.pages=226&rft.edition=illustrated&rft.pub=OUP+Oxford&rft.date=2012&rft.isbn=978-0-19-966286-9&rft.aulast=Steane&rft.aufirst=Andrew+M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D75rCErZkh7EC&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=75rCErZkh7EC&pg=PA226">Extract of page 226</a></span> </li> <li id="cite_note-15"><b><a href="#cite_ref-15">^</a></b> <span class="reference-text"><cite class="citation book">Edwin F. Taylor; John Archibald Wheeler (<time datetime="1992">1992</time>). <a rel="nofollow" class="external text" href="https://archive.org/details/spacetimephysics00edwi_0"><i>Spacetime Physics: Introduction to Special Relativity</i></a>. W. H. Freeman. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/978-0-7167-2327-1" title="Special:Referințe în cărți/978-0-7167-2327-1">978-0-7167-2327-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Spacetime+Physics%3A+Introduction+to+Special+Relativity&rft.pub=W.+H.+Freeman&rft.date=1992&rft.isbn=978-0-7167-2327-1&rft.au=Edwin+F.+Taylor&rft.au=John+Archibald+Wheeler&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fspacetimephysics00edwi_0&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-Rindler0-16"><b><a href="#cite_ref-Rindler0_16-0">^</a></b> <span class="reference-text"><cite class="citation book">Rindler, Wolfgang (<time datetime="1977">1977</time>). <a rel="nofollow" class="external text" href="https://books.google.com/?id=0J_dwCmQThgC&pg=PT148"><i>Essential Relativity: Special, General, and Cosmological</i></a> (ed. illustrated). Springer Science & Business Media. p. §1,11 p. 7. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/978-3-540-07970-5" title="Special:Referințe în cărți/978-3-540-07970-5">978-3-540-07970-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essential+Relativity%3A+Special%2C+General%2C+and+Cosmological&rft.pages=%C2%A71%2C11+p.+7&rft.edition=illustrated&rft.pub=Springer+Science+%26+Business+Media&rft.date=1977&rft.isbn=978-3-540-07970-5&rft.aulast=Rindler&rft.aufirst=Wolfgang&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3D0J_dwCmQThgC%26pg%3DPT148&rfr_id=info%3Asid%2Fro.wikipedia.org%3ATeoria+relativit%C4%83%C8%9Bii+restr%C3%A2nse" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-17"><b><a href="#cite_ref-17">^</a></b> <span class="reference-text">R. C. Tolman, <i>The theory of the Relativity of Motion</i>, (Berkeley 1917), p. 54</span> </li> <li id="cite_note-18"><b><a href="#cite_ref-18">^</a></b> <span class="reference-text">G. A. Benford, D. L. Book, and W. A. Newcomb, <i>The Tachyonic Antitelephone</i>, Phys. Rev. D <b>2</b>, 263 - 265 (1970) <a rel="nofollow" class="external text" href="http://link.aps.org/abstract/PRD/v2/p263">articol</a></span> </li> <li id="cite_note-19"><b><a href="#cite_ref-19">^</a></b> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.pbs.org/wgbh/nova/newton/einstein.html">Einstein despre Newton</a> 1927</span> </li> <li id="cite_note-20"><b><a href="#cite_ref-20">^</a></b> <span class="reference-text">Sidney Coleman, Sheldon L. Glashow, <i>Cosmic Ray and Neutrino Tests of Special Relativity</i>, Phys. Lett. B405 (1997) 249-252, <a rel="nofollow" class="external text" href="http://arxiv.org/abs/hep-ph/9703240">online</a></span> </li> <li id="cite_note-21"><b><a href="#cite_ref-21">^</a></b> <span class="reference-text"><a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html">Pagină a fizicianului</a> <a href="/w/index.php?title=John_Baez&action=edit&redlink=1" class="new" title="John Baez — pagină inexistentă">John Baez</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Legături_externe"><span id="Leg.C4.83turi_externe"></span>Legături externe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&veaction=edit&section=22" title="Modifică secțiunea: Legături externe" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse&action=edit&section=22" title="Edit section's source code: Legături externe"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint tright portal" style="border:solid #aaa 1px; margin:0.5em 0 0.5em 0.5em;"> <table style="background:var(--background-color-interactive-subtle, #f9f9f9); color:inherit; font-size:85%; line-height:110%; max-width:175px;"> <tbody><tr> <td style="text-align: center;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="Portal icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/25px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/37px-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/49px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </td> <td style="padding: 0 0.2em; vertical-align: middle; font-style: italic; font-weight: bold"><b><a href="/wiki/Portal:Fizic%C4%83" title="Portal:Fizică">Portal Fizică </a></b> </td></tr> </tbody></table></div> <ul><li><a rel="nofollow" class="external text" href="http://ziarullumina.ro/stiinta-si-tehnologie/noi-experimente-confirma-relativitatea-speciala">Noi experimente confirmă relativitatea specială</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140808142623/http://ziarullumina.ro/stiinta-si-tehnologie/noi-experimente-confirma-relativitatea-speciala">Arhivat</a> în <time datetime="2014-08-08">8 august 2014</time>, la <a href="/wiki/Wayback_Machine" class="mw-redirect" title="Wayback Machine">Wayback Machine</a>., 6 februarie 2009, Diac. 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