Relativitat especiala

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Istòria</span> </button> <ul id="toc-Istòria-sublist" class="vector-toc-list"> <li id="toc-Lei_problemas_de_la_fisica_dau_sègle_XIX" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lei_problemas_de_la_fisica_dau_sègle_XIX"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Lei problemas de la fisica dau sègle XIX</span> </div> </a> <ul id="toc-Lei_problemas_de_la_fisica_dau_sègle_XIX-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-La_formulacion_de_la_relativitat_especiala" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_formulacion_de_la_relativitat_especiala"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>La formulacion de la relativitat especiala</span> </div> </a> <ul id="toc-La_formulacion_de_la_relativitat_especiala-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Postulats_e_otís_de_la_relativitat_especiala" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Postulats_e_otís_de_la_relativitat_especiala"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Postulats e otís de la relativitat especiala</span> </div> </a> <button aria-controls="toc-Postulats_e_otís_de_la_relativitat_especiala-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>Commuta la subsecció Postulats e otís de la relativitat especiala</span> </button> <ul id="toc-Postulats_e_otís_de_la_relativitat_especiala-sublist" class="vector-toc-list"> <li id="toc-Formulacion_dei_postulats" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formulacion_dei_postulats"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Formulacion dei postulats</span> </div> </a> <ul id="toc-Formulacion_dei_postulats-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-La_relativitat_de_la_simultaneïtat" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_relativitat_de_la_simultaneïtat"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>La relativitat de la simultaneïtat</span> </div> </a> <ul id="toc-La_relativitat_de_la_simultaneïtat-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-La_relativitat_de_la_distància_espaciala" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_relativitat_de_la_distància_espaciala"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>La relativitat de la distància espaciala</span> </div> </a> <ul id="toc-La_relativitat_de_la_distància_espaciala-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-La_transformacion_de_Lorentz" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_transformacion_de_Lorentz"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>La transformacion de Lorentz</span> </div> </a> <ul id="toc-La_transformacion_de_Lorentz-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Consequéncias_de_la_relativitat_especiala" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Consequéncias_de_la_relativitat_especiala"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Consequéncias de la relativitat especiala</span> </div> </a> <button aria-controls="toc-Consequéncias_de_la_relativitat_especiala-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>Commuta la subsecció Consequéncias de la relativitat especiala</span> </button> <ul id="toc-Consequéncias_de_la_relativitat_especiala-sublist" class="vector-toc-list"> <li id="toc-La_dilatacion_dau_temps" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_dilatacion_dau_temps"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>La dilatacion dau temps</span> </div> </a> <ul id="toc-La_dilatacion_dau_temps-sublist" class="vector-toc-list"> <li id="toc-Principi" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Principi"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Principi</span> </div> </a> <ul id="toc-Principi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experiéncia_teorica_de_dilatacion_dau_temps" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Experiéncia_teorica_de_dilatacion_dau_temps"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Experiéncia teorica de dilatacion dau temps</span> </div> </a> <ul id="toc-Experiéncia_teorica_de_dilatacion_dau_temps-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experiéncias_realas_de_dilatacion_dau_temps" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Experiéncias_realas_de_dilatacion_dau_temps"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span>Experiéncias realas de dilatacion dau temps</span> </div> </a> <ul id="toc-Experiéncias_realas_de_dilatacion_dau_temps-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-La_contraccion_dei_longors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_contraccion_dei_longors"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>La contraccion dei longors</span> </div> </a> <ul id="toc-La_contraccion_dei_longors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-La_paradòxa_dei_bessons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_paradòxa_dei_bessons"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>La paradòxa dei bessons</span> </div> </a> <ul id="toc-La_paradòxa_dei_bessons-sublist" class="vector-toc-list"> <li id="toc-Descripcion" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Descripcion"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.1</span> <span>Descripcion</span> </div> </a> <ul id="toc-Descripcion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solucion_de_la_paradòxa" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Solucion_de_la_paradòxa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.2</span> <span>Solucion de la paradòxa</span> </div> </a> <ul id="toc-Solucion_de_la_paradòxa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experiéncias_sus_la_paradòxa" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Experiéncias_sus_la_paradòxa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.3</span> <span>Experiéncias sus la paradòxa</span> </div> </a> <ul id="toc-Experiéncias_sus_la_paradòxa-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-La_composicion_dei_velocitats" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_composicion_dei_velocitats"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>La composicion dei velocitats</span> </div> </a> <ul id="toc-La_composicion_dei_velocitats-sublist" class="vector-toc-list"> <li id="toc-Generalitats" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Generalitats"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.1</span> <span>Generalitats</span> </div> </a> <ul id="toc-Generalitats-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experiéncia_de_Fizeau" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Experiéncia_de_Fizeau"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.2</span> <span>Experiéncia de Fizeau</span> </div> </a> <ul id="toc-Experiéncia_de_Fizeau-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Velocitat_limita" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Velocitat_limita"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.3</span> <span>Velocitat limita</span> </div> </a> <ul id="toc-Velocitat_limita-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-L'equivaléncia_massa-energia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#L'equivaléncia_massa-energia"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>L'equivaléncia massa-energia</span> </div> </a> <ul id="toc-L'equivaléncia_massa-energia-sublist" class="vector-toc-list"> <li id="toc-Generalitats_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Generalitats_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5.1</span> <span>Generalitats</span> </div> </a> <ul id="toc-Generalitats_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Particula_de_massa_nulla" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Particula_de_massa_nulla"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5.2</span> <span>Particula de massa nulla</span> </div> </a> <ul id="toc-Particula_de_massa_nulla-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experiéncias_sus_l'energia_relativista" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Experiéncias_sus_l'energia_relativista"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5.3</span> <span>Experiéncias sus l'energia relativista</span> </div> </a> <ul id="toc-Experiéncias_sus_l'energia_relativista-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Consequéncias_en_electromagnetisme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Consequéncias_en_electromagnetisme"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Consequéncias en electromagnetisme</span> </div> </a> <ul id="toc-Consequéncias_en_electromagnetisme-sublist" class="vector-toc-list"> <li id="toc-Fòrça_de_Lorentz_e_invariància_de_la_carga" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Fòrça_de_Lorentz_e_invariància_de_la_carga"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6.1</span> <span>Fòrça de Lorentz e invariància de la carga</span> </div> </a> <ul id="toc-Fòrça_de_Lorentz_e_invariància_de_la_carga-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Camps_electric_e_magnetic" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Camps_electric_e_magnetic"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6.2</span> <span>Camps electric e magnetic</span> </div> </a> <ul id="toc-Camps_electric_e_magnetic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Camp_electric_creat_per_una_carga_ponctuala_mobila" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Camp_electric_creat_per_una_carga_ponctuala_mobila"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6.3</span> <span>Camp electric creat per una carga ponctuala mobila</span> </div> </a> <ul id="toc-Camp_electric_creat_per_una_carga_ponctuala_mobila-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Liames_intèrnes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Liames_intèrnes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Liames intèrnes</span> </div> </a> <ul id="toc-Liames_intèrnes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liames_extèrnes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Liames_extèrnes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Liames extèrnes</span> </div> </a> <ul id="toc-Liames_extèrnes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nòtas_e_referéncias" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Nòtas_e_referéncias"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Nòtas e referéncias</span> </div> </a> <ul id="toc-Nòtas_e_referéncias-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="Somari" 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="Commuta la taula de continguts." > <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">Commuta la taula de continguts.</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">Relativitat especiala</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="Vés a un article en una altra llengua. Disponible en 110 llengües" > <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-110" 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">110 lengas</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 - aleman de Soïssa" lang="gsw" hreflang="gsw" data-title="Spezielle Relativitätstheorie" data-language-autonym="Alemannisch" data-language-local-name="aleman de Soïssa" 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 - amaric" lang="am" hreflang="am" data-title="ልዩ አንጻራዊነት" data-language-autonym="አማርኛ" data-language-local-name="amaric" 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 - aragonés" lang="an" hreflang="an" data-title="Relatividat especial" data-language-autonym="Aragonés" data-language-local-name="aragonés" 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 - arabi" lang="ar" hreflang="ar" data-title="النسبية الخاصة" data-language-autonym="العربية" data-language-local-name="arabi" 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 - àrab egipci" lang="arz" hreflang="arz" data-title="نسبيه خاصه" data-language-autonym="مصرى" data-language-local-name="àrab egipci" 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 - assamès" lang="as" hreflang="as" data-title="বিশেষ আপেক্ষিকতাবাদ তত্ত্ব" data-language-autonym="অসমীয়া" data-language-local-name="assamès" 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 - asturian" lang="ast" hreflang="ast" data-title="Teoría de la relatividá especial" data-language-autonym="Asturianu" data-language-local-name="asturian" 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 - azerbaijani" lang="az" hreflang="az" data-title="Xüsusi nisbilik nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijani" 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 - baixkir" lang="ba" hreflang="ba" data-title="Махсус сағыштырмалыҡ теорияһы" data-language-autonym="Башҡортса" data-language-local-name="baixkir" 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 - balinés" lang="ban" hreflang="ban" data-title="Rélativitas khusus" data-language-autonym="Basa Bali" data-language-local-name="balinés" 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 - bavarès" lang="bar" hreflang="bar" data-title="Spezieje Relativitetstheorie" data-language-autonym="Boarisch" data-language-local-name="bavarès" 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 - samogitien" lang="sgs" hreflang="sgs" data-title="Specēliuojė relētīvoma teuorėjė" data-language-autonym="Žemaitėška" data-language-local-name="samogitien" 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 - belarús" lang="be" hreflang="be" data-title="Спецыяльная тэорыя адноснасці" data-language-autonym="Беларуская" data-language-local-name="belarús" 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 - bulgar" lang="bg" hreflang="bg" data-title="Специална теория на относителността" data-language-autonym="Български" data-language-local-name="bulgar" 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 - bengalin" lang="bn" hreflang="bn" data-title="বিশেষ আপেক্ষিকতা" data-language-autonym="বাংলা" data-language-local-name="bengalin" 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 - bosniac" lang="bs" hreflang="bs" data-title="Posebna teorija relativnosti" data-language-autonym="Bosanski" data-language-local-name="bosniac" 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 - catalan" lang="ca" hreflang="ca" data-title="Relativitat especial" data-language-autonym="Català" data-language-local-name="catalan" 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 - kurd central" lang="ckb" hreflang="ckb" data-title="ڕێژەییی تایبەت" data-language-autonym="کوردی" data-language-local-name="kurd central" 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 - chèc" lang="cs" hreflang="cs" data-title="Speciální teorie relativity" data-language-autonym="Čeština" data-language-local-name="chèc" 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 - chovash" lang="cv" hreflang="cv" data-title="Танлаштарулăхăн ятарлă теорийĕ" data-language-autonym="Чӑвашла" data-language-local-name="chovash" 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 - gal·lès" lang="cy" hreflang="cy" data-title="Perthnasedd arbennig" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" 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 - danés" lang="da" hreflang="da" data-title="Speciel relativitetsteori" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="bons articles"><a href="https://de.wikipedia.org/wiki/Spezielle_Relativit%C3%A4tstheorie" title="Spezielle Relativitätstheorie - alemand" lang="de" hreflang="de" data-title="Spezielle Relativitätstheorie" data-language-autonym="Deutsch" data-language-local-name="alemand" 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 - grèc" lang="el" hreflang="el" data-title="Ειδική σχετικότητα" data-language-autonym="Ελληνικά" data-language-local-name="grèc" 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 - anglés" lang="en" hreflang="en" data-title="Special relativity" data-language-autonym="English" data-language-local-name="anglés" 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 - espanhòl" lang="es" hreflang="es" data-title="Teoría de la relatividad especial" data-language-autonym="Español" data-language-local-name="espanhòl" 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 - estonian" lang="et" hreflang="et" data-title="Erirelatiivsusteooria" data-language-autonym="Eesti" data-language-local-name="estonian" 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 - basc" lang="eu" hreflang="eu" data-title="Erlatibitate berezia" data-language-autonym="Euskara" data-language-local-name="basc" 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 - perse" lang="fa" hreflang="fa" data-title="نسبیت خاص" data-language-autonym="فارسی" data-language-local-name="perse" 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 - finlandés" lang="fi" hreflang="fi" data-title="Erityinen suhteellisuusteoria" data-language-autonym="Suomi" data-language-local-name="finlandés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Erirelatiivsusteooria" title="Erirelatiivsusteooria - võro" lang="vro" hreflang="vro" data-title="Erirelatiivsusteooria" data-language-autonym="Võro" data-language-local-name="võro" class="interlanguage-link-target"><span>Võro</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 - francés" lang="fr" hreflang="fr" data-title="Relativité restreinte" data-language-autonym="Français" data-language-local-name="francés" 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 - gaelic escossés" lang="gd" hreflang="gd" data-title="Teòirig shònraichte na dàimheachd" data-language-autonym="Gàidhlig" data-language-local-name="gaelic escossés" 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 - galician" lang="gl" hreflang="gl" data-title="Relatividade especial" data-language-autonym="Galego" data-language-local-name="galician" 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 - guaraní" lang="gn" hreflang="gn" data-title="Mba'ekuaarã joguerahaviárava ijapýva" data-language-autonym="Avañe'ẽ" data-language-local-name="guaraní" 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 - ebrèu" lang="he" hreflang="he" data-title="תורת היחסות הפרטית" data-language-autonym="עברית" data-language-local-name="ebrèu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><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 - Indi" lang="hi" hreflang="hi" data-title="विशिष्ट आपेक्षिकता" data-language-autonym="हिन्दी" data-language-local-name="Indi" 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 - hindi de Fiji" lang="hif" hreflang="hif" data-title="Special relativity" data-language-autonym="Fiji Hindi" data-language-local-name="hindi de Fiji" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://hr.wikipedia.org/wiki/Posebna_teorija_relativnosti" title="Posebna teorija relativnosti - croat" lang="hr" hreflang="hr" data-title="Posebna teorija relativnosti" data-language-autonym="Hrvatski" data-language-local-name="croat" 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 - ongrés" lang="hu" hreflang="hu" data-title="Speciális relativitáselmélet" data-language-autonym="Magyar" data-language-local-name="ongrés" 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 - armèni" lang="hy" hreflang="hy" data-title="Հարաբերականության հատուկ տեսություն" data-language-autonym="Հայերեն" data-language-local-name="armèni" 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 - indonesian" lang="id" hreflang="id" data-title="Relativitas khusus" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-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 - islandés" lang="is" hreflang="is" data-title="Takmarkaða afstæðiskenningin" data-language-autonym="Íslenska" data-language-local-name="islandés" 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 - italian" lang="it" hreflang="it" data-title="Relatività ristretta" data-language-autonym="Italiano" data-language-local-name="italian" 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 - japonés" lang="ja" hreflang="ja" data-title="特殊相対性理論" data-language-autonym="日本語" data-language-local-name="japonés" 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 - georgian" lang="ka" hreflang="ka" data-title="ფარდობითობის სპეციალური თეორია" data-language-autonym="ქართული" data-language-local-name="georgian" 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 - cazac" lang="kk" hreflang="kk" data-title="Арнайы салыстырмалылық теориясы" data-language-autonym="Қазақша" data-language-local-name="cazac" 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 - corean" lang="ko" hreflang="ko" data-title="특수 상대성이론" data-language-autonym="한국어" data-language-local-name="corean" 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 - kirguís" lang="ky" hreflang="ky" data-title="Атайын салыштырмалуулук теориясы" data-language-autonym="Кыргызча" data-language-local-name="kirguís" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://la.wikipedia.org/wiki/Relativitas_specialis" title="Relativitas specialis - latin" lang="la" hreflang="la" data-title="Relativitas specialis" data-language-autonym="Latina" data-language-local-name="latin" 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 - lituan" lang="lt" hreflang="lt" data-title="Specialioji reliatyvumo teorija" data-language-autonym="Lietuvių" data-language-local-name="lituan" 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 - leton" lang="lv" hreflang="lv" data-title="Speciālā relativitātes teorija" data-language-autonym="Latviešu" data-language-local-name="leton" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><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 - macedonian" lang="mk" hreflang="mk" data-title="Специјална теорија за релативноста" data-language-autonym="Македонски" data-language-local-name="macedonian" 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 - malaiàlam" lang="ml" hreflang="ml" data-title="വിശിഷ്ട ആപേക്ഷികതാ സിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><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 - mongòl" lang="mn" hreflang="mn" data-title="Харьцангуйн тусгай онол" data-language-autonym="Монгол" data-language-local-name="mongòl" 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 - malai" lang="ms" hreflang="ms" data-title="Kerelatifan khas" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" 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 - maltés" lang="mt" hreflang="mt" data-title="Relattività ristretta" data-language-autonym="Malti" data-language-local-name="maltés" 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 - birman" lang="my" hreflang="my" data-title="အထူးနှိုင်းရသီအိုရီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birman" 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 - baix alemany" lang="nds" hreflang="nds" data-title="Spetschale Relativitätstheorie" data-language-autonym="Plattdüütsch" data-language-local-name="baix alemany" 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 - neerlandés" lang="nl" hreflang="nl" data-title="Speciale relativiteitstheorie" data-language-autonym="Nederlands" data-language-local-name="neerlandés" 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 - norvegian nynorsk" lang="nn" hreflang="nn" data-title="Den spesielle relativitetsteorien" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegian 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 - norvegian bokmål" lang="nb" hreflang="nb" data-title="Den spesielle relativitetsteorien" data-language-autonym="Norsk bokmål" data-language-local-name="norvegian bokmål" class="interlanguage-link-target"><span>Norsk bokmål</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 - oriya" lang="or" hreflang="or" data-title="ବିଶେଷ ଆପେକ୍ଷିକ ତତ୍ତ୍ୱ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="oriya" 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 - polonés" lang="pl" hreflang="pl" data-title="Szczególna teoria względności" data-language-autonym="Polski" data-language-local-name="polonés" 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 - piemontès" lang="pms" hreflang="pms" data-title="Teorìa dla relatività limità" data-language-autonym="Piemontèis" data-language-local-name="piemontès" 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 - pashto" lang="ps" hreflang="ps" data-title="ځانګړی نسبيت" data-language-autonym="پښتو" data-language-local-name="pashto" 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 - portugués" lang="pt" hreflang="pt" data-title="Relatividade restrita" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse" title="Teoria relativității restrânse - romanés" lang="ro" hreflang="ro" data-title="Teoria relativității restrânse" data-language-autonym="Română" data-language-local-name="romanés" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%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 - rus" lang="ru" hreflang="ru" data-title="Специальная теория относительности" data-language-autonym="Русский" data-language-local-name="rus" 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 - sicilian" lang="scn" hreflang="scn" data-title="Tiurìa di la rilativitati spiciali" data-language-autonym="Sicilianu" data-language-local-name="sicilian" 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 - escossés" lang="sco" hreflang="sco" data-title="Special relativity" data-language-autonym="Scots" data-language-local-name="escossés" 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 - sindi" lang="sd" hreflang="sd" data-title="خاص نسبت جو نظريو" data-language-autonym="سنڌي" data-language-local-name="sindi" 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 - serbocroat" lang="sh" hreflang="sh" data-title="Specijalna teorija relativnosti" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroat" 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 - singalès" lang="si" hreflang="si" data-title="විශේෂ සාපේක්ෂතාවාදය" data-language-autonym="සිංහල" data-language-local-name="singalès" 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="articles de qualitat"><a href="https://sk.wikipedia.org/wiki/%C5%A0peci%C3%A1lna_te%C3%B3ria_relativity" title="Špeciálna teória relativity - eslovac" lang="sk" hreflang="sk" data-title="Špeciálna teória relativity" data-language-autonym="Slovenčina" data-language-local-name="eslovac" 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 - eslovèn" lang="sl" hreflang="sl" data-title="Posebna teorija relativnosti" data-language-autonym="Slovenščina" data-language-local-name="eslovèn" 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 - albanés" lang="sq" hreflang="sq" data-title="Teoria speciale e relativitetit" data-language-autonym="Shqip" data-language-local-name="albanés" 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 - serbi" lang="sr" hreflang="sr" data-title="Specijalna teorija relativnosti" data-language-autonym="Српски / srpski" data-language-local-name="serbi" 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 - sondanès" lang="su" hreflang="su" data-title="Teori Relativitas Khusus" data-language-autonym="Sunda" data-language-local-name="sondanès" 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 - suedés" lang="sv" hreflang="sv" data-title="Speciella relativitetsteorin" data-language-autonym="Svenska" data-language-local-name="suedés" 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 - tamol" lang="ta" hreflang="ta" data-title="சிறப்புச் சார்புக் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="tamol" 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 - tai" lang="th" hreflang="th" data-title="ทฤษฎีสัมพัทธภาพพิเศษ" data-language-autonym="ไทย" data-language-local-name="tai" 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 - tagal" lang="tl" hreflang="tl" data-title="Teorya ng natatanging relatibidad" data-language-autonym="Tagalog" data-language-local-name="tagal" 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 - turc" lang="tr" hreflang="tr" data-title="Özel görelilik" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><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 - tatar" lang="tt" hreflang="tt" data-title="Maxsus çağıştırmalılıq teoriäse" data-language-autonym="Татарча / tatarça" data-language-local-name="tatar" 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 - ucrainés" lang="uk" hreflang="uk" data-title="Спеціальна теорія відносності" data-language-autonym="Українська" data-language-local-name="ucrainés" 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 - ordó" lang="ur" hreflang="ur" data-title="اضافیت مخصوصہ" data-language-autonym="اردو" data-language-local-name="ordó" 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 - ozbèc" lang="uz" hreflang="uz" data-title="Maxsus nisbiylik nazariyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ozbèc" 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 - vepse" lang="vep" hreflang="vep" data-title="Specialine relätivižusen teorii" data-language-autonym="Vepsän kel’" data-language-local-name="vepse" 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 - vietnamian" lang="vi" hreflang="vi" data-title="Thuyết tương đối hẹp" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamian" 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 - xinès wu" lang="wuu" hreflang="wuu" data-title="狭义相对论" data-language-autonym="吴语" data-language-local-name="xinès 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 - yiddish" lang="yi" hreflang="yi" data-title="ספעציעלע טעאריע פון רעלאטיוויטעט" data-language-autonym="ייִדיש" data-language-local-name="yiddish" 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 - 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title="Tièra de 1000 articles que totas las Wikipèdias deurián aver."><span class="mw-default-size mw-image-border" typeof="mw:File"><a href="//oc.wikipedia.org/wiki/Wikip%C3%A8dia:Ti%C3%A8ra_de_1000_articles_que_totas_las_Wikip%C3%A8dias_deuri%C3%A1n_aver"><img alt="Tièra de 1000 articles que totas las Wikipèdias deurián aver." src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/1000F.png/24px-1000F.png" decoding="async" width="24" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/1000F.png/36px-1000F.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/1000F.png/49px-1000F.png 2x" data-file-width="1001" data-file-height="908" /></a></span></span></div></div> <div id="mw-indicator-dialecte-provençau" class="mw-indicator"><div class="mw-parser-output"><span title="Aqueste article es redigit en provençau."><span class="mw-default-size mw-image-border" typeof="mw:File"><a href="//oc.wikipedia.org/wiki/Proven%C3%A7au"><img alt="Aqueste article es redigit en provençau." src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Flag_of_Provence.svg/30px-Flag_of_Provence.svg.png" decoding="async" width="30" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Flag_of_Provence.svg/45px-Flag_of_Provence.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Flag_of_Provence.svg/60px-Flag_of_Provence.svg.png 2x" data-file-width="1125" data-file-height="750" /></a></span></span></div></div> </div> <div id="siteSub" class="noprint">Un article de Wikipèdia, l'enciclopèdia liura.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="oc" dir="ltr"><p class="mw-empty-elt"> </p><p>La <b>relativitat especiala</b> es una teoria fisica d'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> (<a href="/wiki/1879" class="mw-redirect" title="1879">1879</a>-<a href="/wiki/1955" class="mw-redirect" title="1955">1955</a>) pareguda en <a href="/wiki/1905" class="mw-redirect" title="1905">1905</a>. Remplaçant la <a href="/wiki/Mecanica_classica" title="Mecanica classica">mecanica classica</a> fondada sus lei teorias d'<a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> (<a href="/wiki/1642" class="mw-redirect" title="1642">1642</a>-<a href="/wiki/1727" class="mw-redirect" title="1727">1727</a>), es una teoria essenciala dau modèl estandard actuau de la <a href="/wiki/Fisica" title="Fisica">fisica</a> actuala. Es basada sus dos postulats fondamentaus edictant : </p> <ul><li>lei lèis de totei lei fenomèns fisics an la meteissa forma dins totei lei referenciaus galileans.</li> <li>la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a> dins lo vuege es egala a <i>c</i> dins totei lei referenciaus galileans.</li></ul> <p>Aqueleis enonciats donèron de relacions novèlas permetent de passar d'un referenciau galilean a un autre. Aquò aguèt de consequéncias importantas coma la descubèrta de la <a href="/w/index.php?title=Parad%C3%B2xa_dei_bessons&action=edit&redlink=1" class="new" title="Paradòxa dei bessons (la pagina existís pas)">paradòxa dei bessons</a> ò l'impossibilitat teorica d'agantar una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> superiora a <i>c</i>. Pasmens, aguèron de limits per considerar la <a href="/wiki/Fisica" title="Fisica">fisica</a> dins de referenciaus non galileans, çò que menèt a la publicacion de la <a href="/wiki/Relativitat_generala" title="Relativitat generala">relativitat generala</a> en <a href="/wiki/1915" class="mw-redirect" title="1915">1915</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Istòria"><span id="Ist.C3.B2ria"></span>Istòria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=1" title="Modificar la seccion : Istòria" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=1" title="Edita el codi de la secció: Istòria"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Lei_problemas_de_la_fisica_dau_sègle_XIX"><span id="Lei_problemas_de_la_fisica_dau_s.C3.A8gle_XIX"></span>Lei problemas de la fisica dau sègle XIX</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=2" title="Modificar la seccion : Lei problemas de la fisica dau sègle XIX" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=2" title="Edita el codi de la secció: Lei problemas de la fisica dau sègle XIX"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A la fin dau sègle XIX, lei domenis principaus de la <a href="/wiki/Fisica" title="Fisica">fisica</a> èran la <a href="/w/index.php?title=Mecanica&action=edit&redlink=1" class="new" title="Mecanica (la pagina existís pas)">mecanica</a>, la <a href="/wiki/Termodinamica" title="Termodinamica">termodinamica</a>, l'<a href="/wiki/Electricitat" title="Electricitat">electricitat</a>, lo <a href="/w/index.php?title=Magnetisme&action=edit&redlink=1" class="new" title="Magnetisme (la pagina existís pas)">magnetisme</a> e l'<a href="/wiki/Optica" title="Optica">optica</a>. La <a href="/w/index.php?title=Mecanica&action=edit&redlink=1" class="new" title="Mecanica (la pagina existís pas)">mecanica</a> èra basada sus l'òbra d'<a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>, lei <i><a href="/wiki/Philosophiae_naturalis_principia_mathematica" class="mw-redirect" title="Philosophiae naturalis principia mathematica">Philosophiae naturalis principia mathematica</a></i>, qu'aviá introduch la teoria de l'<a href="/wiki/Gravitacion" title="Gravitacion">atraccion universala</a> e pausat lei principis generaus de la disciplina. Vèrs <a href="/wiki/1871" class="mw-redirect" title="1871">1871</a>, <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a> (<a href="/wiki/1844" class="mw-redirect" title="1844">1844</a>-<a href="/wiki/1906" class="mw-redirect" title="1906">1906</a>) capitèt de la liar a la <a href="/wiki/Termodinamica" title="Termodinamica">termodinamica</a> après la descubèrta d'una <a href="/w/index.php?title=Teoria_cinetica_dei_gas&action=edit&redlink=1" class="new" title="Teoria cinetica dei gas (la pagina existís pas)">teoria cinetica dei gas</a>. </p><p>En parallèl, en <a href="/wiki/1864" class="mw-redirect" title="1864">1864</a>, <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a> (<a href="/wiki/1831" class="mw-redirect" title="1831">1831</a>-<a href="/wiki/1879" class="mw-redirect" title="1879">1879</a>) expausèt sa teoria <a href="/wiki/Electromagnetisme" title="Electromagnetisme">electromagnetica</a> de la <a href="/wiki/Lutz" title="Lutz">lutz</a> e donèt leis <a href="/w/index.php?title=Eq%C3%BCacions_de_Maxwell&action=edit&redlink=1" class="new" title="Eqüacions de Maxwell (la pagina existís pas)">eqüacions generalas</a> dau camp electromagnetic. Segon aquela teoria, la <a href="/wiki/Lutz" title="Lutz">lutz</a> es una onda formada d'un <a href="/wiki/Camp_electric" title="Camp electric">camp electric</a> e d'un <a href="/wiki/Camp_magnetic" title="Camp magnetic">camp magnetic</a>. Aqueu liame foguèt experimentalament observat en <a href="/wiki/1888" class="mw-redirect" title="1888">1888</a> per <a href="/w/index.php?title=Heinrich_Hertz&action=edit&redlink=1" class="new" title="Heinrich Hertz (la pagina existís pas)">Heinrich Hertz</a> (<a href="/wiki/1857" class="mw-redirect" title="1857">1857</a>-<a href="/wiki/1894" class="mw-redirect" title="1894">1894</a>), çò que permetèt d'unificar l'<a href="/wiki/Electricitat" title="Electricitat">electricitat</a>, lo <a href="/w/index.php?title=Magnetisme&action=edit&redlink=1" class="new" title="Magnetisme (la pagina existís pas)">magnetisme</a> e l'<a href="/wiki/Optica" title="Optica">optica</a>. </p><p>Ansin, au començament dau sègle XX, èra possible de redurre la <a href="/wiki/Fisica" title="Fisica">fisica</a> a l'estudi de dos ensembles de fenomèns : lei fenomèns <a href="/w/index.php?title=Mecanica&action=edit&redlink=1" class="new" title="Mecanica (la pagina existís pas)">mecanicas</a> e lei fenomèns <a href="/wiki/Electromagnetisme" title="Electromagnetisme">electromagnetics</a>. Pasmens, aquela situacion pausava un problema per lei <a href="/wiki/Fisica" title="Fisica">fisicians</a> dau periòde. D'efiech, lo premier ensemble èra fondat sus leis eqüacions de Newton que supausan d'accions instantanèas quinei que sigan lei distàncias consideradas. Au contrari, en <a href="/wiki/Electromagnetisme" title="Electromagnetisme">electromagnetica</a>, l'informacion se desplaça a la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a>, es a dire 300 000 m/s. Redurre lei contradiccions aparentas entre aquelei teorias èra donc un objectiu major. </p> <div class="mw-heading mw-heading3"><h3 id="La_formulacion_de_la_relativitat_especiala">La formulacion de la relativitat especiala</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=3" title="Modificar la seccion : La formulacion de la relativitat especiala" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=3" title="Edita el codi de la secció: La formulacion de la relativitat especiala"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fichi%C3%A8r:Einstein_1921_by_F_Schmutzer_-_restoration.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Einstein_1921_by_F_Schmutzer_-_restoration.jpg/220px-Einstein_1921_by_F_Schmutzer_-_restoration.jpg" decoding="async" width="220" height="289" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Einstein_1921_by_F_Schmutzer_-_restoration.jpg/330px-Einstein_1921_by_F_Schmutzer_-_restoration.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Einstein_1921_by_F_Schmutzer_-_restoration.jpg/440px-Einstein_1921_by_F_Schmutzer_-_restoration.jpg 2x" data-file-width="2523" data-file-height="3313" /></a><figcaption><a href="/wiki/Fotografia" title="Fotografia">Fotografia</a> d'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> en <a href="/wiki/1921" class="mw-redirect" title="1921">1921</a>.</figcaption></figure> <p>La teoria de la relativament d'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> foguèt formulada dins l'encastre d'un movement pus larg assaiant de resòuvre lei problemas de la fisica dau sègle XIX. <a href="/wiki/Hendrik_Lorentz" class="mw-redirect" title="Hendrik Lorentz">Hendrik Lorentz</a> (<a href="/wiki/1853" class="mw-redirect" title="1853">1853</a>-<a href="/wiki/1928" class="mw-redirect" title="1928">1928</a>) e <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> (<a href="/wiki/1854" class="mw-redirect" title="1854">1854</a>-<a href="/wiki/1912" class="mw-redirect" title="1912">1912</a>) ne'n foguèron lei doas autrei figuras majoras e sei trabalhs permetèron de completar leis idèas d'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a>. </p><p>Dins sei recèrcas, Einstein s'interessèt inicialament ai sistèmas animats d'un <a href="/w/index.php?title=Movement_rectilin%C3%A8u_unif%C3%B2rme&action=edit&redlink=1" class="new" title="Movement rectilinèu unifòrme (la pagina existís pas)">movement rectilinèu e unifòrme</a> avans d'estendre ai fenomèns <a href="/wiki/Electromagnetisme" title="Electromagnetisme">electromagnetics</a> lo principi de la relativitat galileana dei fenomèns mecanics. Puei, gràcias a una analisi dei <a href="/wiki/F%C3%B2r%C3%A7a" title="Fòrça">fòrças</a> de <a href="/wiki/Gravitacion" title="Gravitacion">gravitacion</a>, poguèt alargar son domeni de trabalh a totei lei sistèmas animats d'un movement. </p><p>La teoria de la relativitat especiala foguèt publicada en <a href="/wiki/1905" class="mw-redirect" title="1905">1905</a> e foguèt completada en <a href="/wiki/1915" class="mw-redirect" title="1915">1915</a> per la <a href="/wiki/Relativitat_generala" title="Relativitat generala">relativitat generala</a>. En despiech de divèrsei contestacions, obtenguèt un succès important e foguèt adoptada per la màger part de la comunautat scientifica. La meteissa annada, Einstein prepausèt a partir de sei teorias una solucion a l'anomalia de l'<a href="/wiki/Orbita" title="Orbita">orbita</a> de <a href="/wiki/Mercuri_(planeta)" title="Mercuri (planeta)">Mercuri</a>. Calculèt tanben la desviacion de la <a href="/wiki/Lutz" title="Lutz">lutz</a> deis <a href="/wiki/Est%C3%A8la" class="mw-redirect mw-disambig" title="Estèla">estèla</a> per lo <a href="/wiki/Solelh" class="mw-redirect" title="Solelh">Soleu</a> e una verificacion experimentala aguèt luòc en <a href="/wiki/1919" class="mw-redirect" title="1919">1919</a>. Aquò permetèt de validar l'ensemble de la relativitat qu'es totjorn una teoria en vigor a l'ora d'ara. </p> <div class="mw-heading mw-heading2"><h2 id="Postulats_e_otís_de_la_relativitat_especiala"><span id="Postulats_e_ot.C3.ADs_de_la_relativitat_especiala"></span>Postulats e otís de la relativitat especiala</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=4" title="Modificar la seccion : Postulats e otís de la relativitat especiala" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=4" title="Edita el codi de la secció: Postulats e otís de la relativitat especiala"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Formulacion_dei_postulats">Formulacion dei postulats</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=5" title="Modificar la seccion : Formulacion dei postulats" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=5" title="Edita el codi de la secció: Formulacion dei postulats"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-section bandeau-niveau-detail loupe">Article detalhat: <a href="/w/index.php?title=Premier_postulat_de_la_relativitat_especiala&action=edit&redlink=1" class="new" title="Premier postulat de la relativitat especiala (la pagina existís pas)">Premier postulat de la relativitat especiala</a>.</div> <p>Tre lei fondaments de la relativitat, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a> abandonèt lo concèpte d'<a href="/wiki/Et%C3%A8r_(fisica)" title="Etèr (fisica)">etèr</a> (e donc de referenciau absolut) e estendiguèt lo principi de la relativitat galileana a totei lei fenomèns. Ansin, lo <a href="/w/index.php?title=Premier_postulat_de_la_relativitat_especiala&action=edit&redlink=1" class="new" title="Premier postulat de la relativitat especiala (la pagina existís pas)">premier postulat de la relativitat especiala</a> foguèt formulat de la maniera seguenta : <i>« lei lèis de totei lei fenomèns fisics dèvon aver la meteissa forma dins totei lei sistèmas en translacion unifòrma entre elei »</i><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>. Aquò significa qu'una experiéncia de <a href="/wiki/Fisica" title="Fisica">fisica</a> permet pas d'afiermar que lo sistèma de referéncia utilizada per descriure lo movement es au repaus ò en movement de translacion unifòrma. </p> <div class="bandeau-section bandeau-niveau-detail loupe">Article detalhat: <a href="/w/index.php?title=Segond_postulat_de_la_relativitat_especiala&action=edit&redlink=1" class="new" title="Segond postulat de la relativitat especiala (la pagina existís pas)">Segond postulat de la relativitat especiala</a>.</div> <p>Lo <a href="/w/index.php?title=Second_postulat_de_la_relativitat_especiala&action=edit&redlink=1" class="new" title="Second postulat de la relativitat especiala (la pagina existís pas)">second postulat de la relativitat especiala</a> es la traduccion de l'abandon de l'<a href="/wiki/Et%C3%A8r_(fisica)" title="Etèr (fisica)">etèr</a>. Es egalament dich principi de la constància de la velocitat de la lutz. Son enonciat es : <i>« la lutz se propaga dins lo vuege dins totei lei direccions amb la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat <i>c</i></a> qu'a totjorn la meteissa valor quin movement de l'observator e de la fònt que siegue »</i><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>. Aqueu principi es en contradiccion amb la lèi de composicion dei velocitats de la <a href="/wiki/Mecanica_classica" title="Mecanica classica">mecanica classica</a>, principi que permet, per exemple, d'afiermar que la velocitat <i>V</i> d'un passatgier caminant a la velocitat <i>u</i> dins un <a href="/wiki/Tren" title="Tren">tren</a> circulant a la velocitat <i>v</i> es egala a <i>V</i> = <i>v</i> ± <i>u</i>. Pasmens, existís divèrseis experiéncias que permèton de lo validar<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>. </p><p>Per exemple, foguèt lo cas de mesuras realizadas sus de <a href="/wiki/Particula_element%C3%A0ria" title="Particula elementària">particulas elementàrias</a> per <a href="/w/index.php?title=Alfred_H._Joy&action=edit&redlink=1" class="new" title="Alfred H. Joy (la pagina existís pas)">Alfred H. Joy</a> e <a href="/w/index.php?title=Roscoe_F._Sanford&action=edit&redlink=1" class="new" title="Roscoe F. Sanford (la pagina existís pas)">Roscoe F. Sanford</a> en <a href="/wiki/1926" class="mw-redirect" title="1926">1926</a>. Per aquò, produguèron de <a href="/w/index.php?title=Pion_(particula)&action=edit&redlink=1" class="new" title="Pion (particula) (la pagina existís pas)">pions</a> neutres <i>π<sup>0</sup></i> dins un <a href="/wiki/Accelerator_de_particulas" title="Accelerator de particulas">accelerator</a> d'<a href="/wiki/Energia" title="Energia">energia</a> auta. Aquelei particulas, emesas a una velocitat superiora a 99,98% de la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a>, avián una durada de vida de 10<sup>-14</sup> <a href="/wiki/Segonda" title="Segonda">s</a> e se desintegravan en dos <a href="/wiki/Foton" title="Foton">fotons</a>. La <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> d'aquelei fotons foguèt mesurada egala a <i>c</i>, çò que laissava gaire de dobtes quant a la validitat dau segond postulat<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>. </p> <div class="mw-heading mw-heading3"><h3 id="La_relativitat_de_la_simultaneïtat"><span id="La_relativitat_de_la_simultane.C3.AFtat"></span>La relativitat de la simultaneïtat</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=6" title="Modificar la seccion : La relativitat de la simultaneïtat" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=6" title="Edita el codi de la secció: La relativitat de la simultaneïtat"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichi%C3%A8r:Relativitat_especiala_-_Relativitat_de_la_simultane%C3%AFtat.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Relativitat_especiala_-_Relativitat_de_la_simultane%C3%AFtat.png/220px-Relativitat_especiala_-_Relativitat_de_la_simultane%C3%AFtat.png" decoding="async" width="220" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Relativitat_especiala_-_Relativitat_de_la_simultane%C3%AFtat.png/330px-Relativitat_especiala_-_Relativitat_de_la_simultane%C3%AFtat.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Relativitat_especiala_-_Relativitat_de_la_simultane%C3%AFtat.png/440px-Relativitat_especiala_-_Relativitat_de_la_simultane%C3%AFtat.png 2x" data-file-width="784" data-file-height="363" /></a><figcaption>Illustracion de la simultaneïtat en relativitat especiala</figcaption></figure> <p>La nocion de simultaneïtat presenta quauquei particularitats dins l'encastre de la relativitat especiala. Per exemple, supausem un <a href="/wiki/Tren" title="Tren">tren</a> fòrça lòng se desplaçant lòng d'un <a href="/wiki/Camin_de_f%C3%A8rre" title="Camin de fèrre">camin de fèrre</a> amb una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> constanta. Tot eveniment qu'a luòc lòng de la via ferrada a donc tanben luòc dins un ponch determinat dau tren. Normalament, lei viatjaires utilizaràn lo <a href="/wiki/Tren" title="Tren">tren</a> coma referenciau e un observator exterior adoptarà lo <a href="/w/index.php?title=Ralh&action=edit&redlink=1" class="new" title="Ralh (la pagina existís pas)">ralh</a>. </p><p>Se dos ulhauç tòcan d'un biais simultanèu dos ponchs A e B dau <a href="/wiki/Camin_de_f%C3%A8rre" title="Camin de fèrre">camin de fèrre</a>, aquò significa que lei rais eissits dei ponchs A e B se rescòntran dins un ponch M situat au mitan de la distància AB sus lo ralh. S'aqueleis eveniments correspondon tanben a dos eveniments dins lo tren, lo ponch es ben situat au mitan dau segment AB au moment de la formacion dau tròn. Pasmens, en causa dau movement dau tren, lo ponch de rescòntre M' dei rais se desplaça a la velocitat dau tren. Ansin, lei viatjaires diràn que l'ulhauç en avans dau tren a agut luòc avans l'ulhauç aparegut a l'arrier. Dos eveniments simultanèus a respècte dau camin de fèrre son donc pas simultanèus a respècte dau tren, e invèrsament. </p><p>Ansin, cada sistèma de referéncia a son <a href="/wiki/Temps" title="Temps">temps</a> pròpri e una indicacion de temps a un sens unicament se se precisa lo referenciau d'aquela mesura. </p> <div class="mw-heading mw-heading3"><h3 id="La_relativitat_de_la_distància_espaciala"><span id="La_relativitat_de_la_dist.C3.A0ncia_espaciala"></span>La relativitat de la distància espaciala</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=7" title="Modificar la seccion : La relativitat de la distància espaciala" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=7" title="Edita el codi de la secció: La relativitat de la distància espaciala"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se gardam l'exemple dau <a href="/wiki/Tren" title="Tren">tren</a> presentat dins lo paragraf precedent, podèm i considerar dos ponchs determinats A e B e se questionar sus la distància que lei separan. Per aquò, es necessari d'utilizar un sistèma de <a href="/w/index.php?title=Coordenadas&action=edit&redlink=1" class="new" title="Coordenadas (la pagina existís pas)">coordenadas</a> e lo pus simple, es d'utilizar aqueu dau <a href="/wiki/Tren" title="Tren">tren</a>. Un observator plaçat dins lei <a href="/w/index.php?title=Vagon&action=edit&redlink=1" class="new" title="Vagon (la pagina existís pas)">vagons</a> pòu i mesurar aquela distància en linha drecha gràcias a una règla de mesura. </p><p>Pasmens, es tanben possible de mesurar la distància entre lei dos ponchs dins lo referenciau dau <a href="/wiki/Camin_de_f%C3%A8rre" title="Camin de fèrre">camin de fèrre</a>. Dins aqueu cas, pòu utilizar lo metòde seguent : pòu determinar lei ponchs A’ e B’ dau <a href="/w/index.php?title=Ralh&action=edit&redlink=1" class="new" title="Ralh (la pagina existís pas)">ralh</a> situats au nivèu dei ponchs A e B dau <a href="/wiki/Tren" title="Tren">tren</a> a un instant <i>t</i>. Puei, mesura la distància entre A’ e B’ dins son referenciau. <i>A priori</i>, i a ges de rason per que lei distàncias AB e A’B’ sigan egalas. </p> <div class="mw-heading mw-heading3"><h3 id="La_transformacion_de_Lorentz">La transformacion de Lorentz</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=8" title="Modificar la seccion : La transformacion de Lorentz" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=8" title="Edita el codi de la secció: La transformacion de Lorentz"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-section bandeau-niveau-detail loupe">Article detalhat: <a href="/w/index.php?title=Transformacion_de_Lorentz&action=edit&redlink=1" class="new" title="Transformacion de Lorentz (la pagina existís pas)">Transformacion de Lorentz</a>.</div> <p>L'utilizacion dei <a href="/w/index.php?title=Transformacion_de_Lorentz&action=edit&redlink=1" class="new" title="Transformacion de Lorentz (la pagina existís pas)">transformacions de Lorentz</a> es l'otís que permet de resòuvre la contradiccion aparenta entre lo <a href="/w/index.php?title=Principi_de_la_composicion_dei_velocitats&action=edit&redlink=1" class="new" title="Principi de la composicion dei velocitats (la pagina existís pas)">principi de la composicion dei velocitats</a> e lo <a href="/w/index.php?title=Segond_postulat_de_la_relativitat_especiala&action=edit&redlink=1" class="new" title="Segond postulat de la relativitat especiala (la pagina existís pas)">segond postulat de la relativitat especiala</a>. D'efiech, permet de mostrar que la composicion dei velocitats classica utilizava doas <a href="/wiki/Ipot%C3%A8si" title="Ipotèsi">ipotèsis</a> non justificadas : </p> <ul><li>la durada de temps entre dos eveniments èra independenta dau movement dau sistèma de referéncia.</li> <li>la distància espaciala entre dos ponchs d'un còrs rigid èra independenta dau movement dau sistèma de referéncia.</li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichi%C3%A8r:Relativitat_especiala_-_Sist%C3%A8mas_de_referenciaus_S_e_S%27.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Relativitat_especiala_-_Sist%C3%A8mas_de_referenciaus_S_e_S%27.png/220px-Relativitat_especiala_-_Sist%C3%A8mas_de_referenciaus_S_e_S%27.png" decoding="async" width="220" height="136" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Relativitat_especiala_-_Sist%C3%A8mas_de_referenciaus_S_e_S%27.png/330px-Relativitat_especiala_-_Sist%C3%A8mas_de_referenciaus_S_e_S%27.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Relativitat_especiala_-_Sist%C3%A8mas_de_referenciaus_S_e_S%27.png/440px-Relativitat_especiala_-_Sist%C3%A8mas_de_referenciaus_S_e_S%27.png 2x" data-file-width="797" data-file-height="494" /></a><figcaption>Sistèmas de referenciaus S e S' amb S', referenciau se desplaçant amb una velocitat v constanta</figcaption></figure> <p>Totjorn amb l'exemple dau <a href="/wiki/Tren" title="Tren">tren</a> se desplaçant amb una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v</i> constanta lòng d'un <a href="/wiki/Camin_de_f%C3%A8rre" title="Camin de fèrre">camin de fèrre</a>, es possible de designar per <i>S</i> lo sistèma de referéncia liat au <a href="/w/index.php?title=Ralh&action=edit&redlink=1" class="new" title="Ralh (la pagina existís pas)">ralh</a> e per <i>S’</i> aqueu dau <a href="/wiki/Tren" title="Tren">tren</a>. Un eveniment quin que siga es determinat dins l'espaci a respècte de <i>S</i> per lei coordenadas (<i>x</i> ; <i>y</i> ; <i>z</i>) e dins lo temps per la valor <i>t</i>. Dins lo referenciau S’, lo meteis eveniment es reperat per lei coordenadas (<i>x’</i> ; <i>y’</i> ; <i>z’</i> ; <i>t’</i>). Segon lei principis de relativitat expausats dins lei dos paragrafs precedents, lei (<i>x</i> ; <i>y</i> ; <i>z</i> ; <i>t</i>) e (<i>x’</i> ; <i>y’</i> ; <i>z’</i> ; <i>t’</i>) son normalament diferentas. </p><p>Per assaiar d'establir un liame entre lei dos referenciaus <i>S</i> e <i>S’</i>, es necessari de respectar lei lèis de propagacion d'un rai luminós. Dins lo nòstre cas, aqueu problema es resolut per leis eqüacions seguentas : </p> <center> <p><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'={\frac {x-vt}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mi>v</mi> <mi>t</mi> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x'={\frac {x-vt}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8981b8cd54d2285b4f5e76af1e5422f5360369b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:17.681ex; height:6.509ex;" alt="{\displaystyle x'={\frac {x-vt}{\sqrt {1-v^{2}/c^{2}}}}}"></span> </p><p><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> </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/e6239f12a70a7f715303934acf9dbae208fceb80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.099ex; height:2.843ex;" alt="{\displaystyle y'=y}"></span> </p><p><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> </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/80bfd939a15c0857a6b1df928f061d0e8973c342" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.962ex; height:2.509ex;" alt="{\displaystyle z'=z}"></span> </p><p><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'={\frac {t-vx/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>t</mi> <mo>−</mo> <mi>v</mi> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <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 t'={\frac {t-vx/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7be8be8ec20afd0bf3902bfcf669372dbcf38391" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:17.191ex; height:7.176ex;" alt="{\displaystyle t'={\frac {t-vx/c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}"></span> </p> </center> <p>Es aqueu sistèma d'<a href="/wiki/Eq%C3%BCacion" class="mw-redirect" title="Eqüacion">eqüacions</a> qu'es dicha « <a href="/w/index.php?title=Transformacion_de_Lorentz&action=edit&redlink=1" class="new" title="Transformacion de Lorentz (la pagina existís pas)">transformacion de Lorentz</a> ». Permet de verificar la validitat dau segond postulat, es a dire que de rais luminós arribant dins una direccion quina que siga an la meteissa velocitat dins lei referenciaus <i>S</i> e <i>S’</i>. </p><p>Per aquò, supausam qu'un rai de <a href="/wiki/Lutz" title="Lutz">lutz</a> es emés dau ponch <i>O</i>, fònt dau referenciau <i>S</i>, a l'instant <i>t</i> = 0. Sa propagacion a luòc conformament a la relacion : </p> <center> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\sqrt {x^{2}+y^{2}+z^{2}}}=ct}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>=</mo> <mi>c</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\sqrt {x^{2}+y^{2}+z^{2}}}=ct}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ef368e657822db11241afff8548eafdf2af3a85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:23.84ex; height:4.843ex;" alt="{\displaystyle r={\sqrt {x^{2}+y^{2}+z^{2}}}=ct}"></span> </p> </center> <p>Dins lo referenciau <i>S’</i>, la propagacion a luòc segon una relacion similara : </p> <center> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r'={\sqrt {x'^{2}+y'^{2}+z'^{2}}}=ct'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>r</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </msqrt> </mrow> <mo>=</mo> <mi>c</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r'={\sqrt {x'^{2}+y'^{2}+z'^{2}}}=ct'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e11d7625cc8bda0aade4b1390341b5ca6ceaf806" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:26.567ex; height:4.843ex;" alt="{\displaystyle r'={\sqrt {x'^{2}+y'^{2}+z'^{2}}}=ct'}"></span> </p> </center> <p>Es possible de transformar lei doas eqüacions en lei portant au carrat : </p> <center> <p><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^{2}+z^{2}-c^{2}t^{2}=0}"> <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> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d993f20a1aba94295f9c379c7e0431a91df46f4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.48ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}=0}"></span> </p><p><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'^{2}+z'^{2}-c^{2}t'^{2}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x'^{2}+y'^{2}+z'^{2}-c^{2}t'^{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24d31004c1dbf670e54767b11fb11265b0a4cc0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.29ex; height:3.009ex;" alt="{\displaystyle x'^{2}+y'^{2}+z'^{2}-c^{2}t'^{2}=0}"></span> </p> </center> <p>Puei, amb <i>α</i>, una constanta, aquò permet d'escriure l'egalitat seguenta : </p> <center> <p><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^{2}+z^{2}-c^{2}t^{2}=\alpha (x'^{2}+y'^{2}+z'^{2}-c^{2}t'^{2})}"> <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> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>α</mi> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}=\alpha (x'^{2}+y'^{2}+z'^{2}-c^{2}t'^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a36e8526f702be4590f3b24a2323084266148ea9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:46.644ex; height:3.176ex;" alt="{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}=\alpha (x'^{2}+y'^{2}+z'^{2}-c^{2}t'^{2})}"></span> </p> </center> <p>La transformacion de Lorentz permet aisament de respòndre a aquela eqüacion dins lo cas <i>α</i> = 0. Dins aquò, aqueu resultat pòu èsser generalizat se leis aisses de <i>S</i> e <i>S’</i> son pas parallèls<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="Consequéncias_de_la_relativitat_especiala"><span id="Consequ.C3.A9ncias_de_la_relativitat_especiala"></span>Consequéncias de la relativitat especiala</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=9" title="Modificar la seccion : Consequéncias de la relativitat especiala" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=9" title="Edita el codi de la secció: Consequéncias de la relativitat especiala"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="La_dilatacion_dau_temps">La dilatacion dau temps</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=10" title="Modificar la seccion : La dilatacion dau temps" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=10" title="Edita el codi de la secció: La dilatacion dau temps"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Principi">Principi</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=11" title="Modificar la seccion : Principi" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=11" title="Edita el codi de la secció: Principi"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Considerem un <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> au repaus d'un biais permanent a l'origina <i>x’</i> = 0 de <i>S’</i> e siá <i>t'<sub>1</sub></i> = 0 e <i>t'<sub>2</sub></i> = 1 s dos batements consecutius d'aqueu <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a>. La <a href="/w/index.php?title=Transformacion_de_Lorentz&action=edit&redlink=1" class="new" title="Transformacion de Lorentz (la pagina existís pas)">transformacion de Lorentz</a> permet de determinar leis instants <i>t<sub>1</sub></i> e <i>t<sub>2</sub></i> que correspondon a aqueleis eveniments dins lo referenciau <i>S</i> : </p> <center> <p><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_{1}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{1}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/827bf5c54cdc99abfe6483bd4702e2ea7f6da128" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.155ex; height:2.509ex;" alt="{\displaystyle t_{1}=0}"></span> </p> <ul><li><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_{2}={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <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 t_{2}={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a5f3ef389fc25e3bd610fb9133f5f512eb81c06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:17.56ex; height:6.509ex;" alt="{\displaystyle t_{2}={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"></span></li></ul> </center> <p>Dins aqueleis expressions, <i>v</i> representa la <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> dau <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> a respècte de <i>S</i>. Dins aqueu referenciau, lo batement dau mecanisme es superior a una <a href="/wiki/Segonda" title="Segonda">segonda</a>. Ansin, lo <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> i fonciona pus lentament, situacion de còps qualificada de « movement retardant »<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>. </p><p>Se la durada dau batejament dau relòtge es Δt' dins lo referenciau ont es au repaus e Δt dins aqueu ont es en movement a la velocitat <i>v</i>, la forma precedenta pòu se generalizar : </p> <center> <p><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={\frac {\Delta t'}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t={\frac {\Delta t'}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc9d8ba5b68ea44731cfe854322610ddf87d1e57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.442ex; height:6.843ex;" alt="{\displaystyle \Delta t={\frac {\Delta t'}{\sqrt {1-v^{2}/c^{2}}}}}"></span> </p> </center> <div class="mw-heading mw-heading4"><h4 id="Experiéncia_teorica_de_dilatacion_dau_temps"><span id="Experi.C3.A9ncia_teorica_de_dilatacion_dau_temps"></span>Experiéncia teorica de dilatacion dau temps</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=12" title="Modificar la seccion : Experiéncia teorica de dilatacion dau temps" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=12" title="Edita el codi de la secció: Experiéncia teorica de dilatacion dau temps"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per comprendre lei consequéncias de la dilatacion dau temps, es possible d'estudiar una <a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experiéncia</a> teorica implicant un aparelh constituït per una boita portant una fònt de rais <a href="/wiki/Lutz" title="Lutz">luminós</a> <i>S</i>, un <a href="/wiki/Mirau" class="mw-redirect" title="Mirau">mirau</a> <i>M</i> e un <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a>. L'objectiu es de mesurar la durada mesa per la <a href="/wiki/Lutz" title="Lutz">lutz</a> per anar de la fònt <i>S</i> au <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> (plaçat au nivèu de <i>S</i>) après aver subit una reflexion sus lo <a href="/wiki/Mirau" class="mw-redirect" title="Mirau">mirau</a>. La distància entre la fònt e lo mirau es marcada <i>L</i>. Un aparelh <a href="/wiki/Fotografia" title="Fotografia">fotografic</a> es plaçat a proximitat dau <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> per enregistrar un imatge permanent dau quadrant<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>. </p> <figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Fichi%C3%A8r:Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps_(partida_immobila).png" class="mw-file-description" title="Aparelh experimentau format d'una fònt de rais luminós, d'un mirau e d'un relòtge."><img alt="Aparelh experimentau format d'una fònt de rais luminós, d'un mirau e d'un relòtge." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps_%28partida_immobila%29.png/200px-Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps_%28partida_immobila%29.png" decoding="async" width="200" height="178" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps_%28partida_immobila%29.png/300px-Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps_%28partida_immobila%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps_%28partida_immobila%29.png/400px-Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps_%28partida_immobila%29.png 2x" data-file-width="426" data-file-height="380" /></a><figcaption>Aparelh experimentau format d'una fònt de rais luminós, d'un mirau e d'un relòtge.</figcaption></figure> <p>Se totei lei partidas de l'experiéncia son immobilas, lo rai de <a href="/wiki/Lutz" title="Lutz">lutz</a> percor dos còps la distància <i>L</i> per arribar au <a href="/wiki/Mirau" class="mw-redirect" title="Mirau">mirau</a> e per agantar lo <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a>. Lei <a href="/wiki/Fotografia" title="Fotografia">fotografias</a> permèton de mesurar una durada de 2<i>L</i>/<i>c</i> entre la partença e lo retorn dau rai. D'un biais pus precís, coma aquel interval de temps es estat mesurat amb lo meteis relòtge, es dich « interval de temps pròpri ». </p> <figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Fichi%C3%A8r:Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps.png" class="mw-file-description" title="Experiéncia teorica de dilatacion dau temps en relativitat especiala."><img alt="Experiéncia teorica de dilatacion dau temps en relativitat especiala." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps.png/500px-Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps.png" decoding="async" width="500" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps.png/750px-Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps.png/1000px-Relativitat_especiala_-_Experi%C3%A9ncia_teorica_de_dilatacion_dau_temps.png 2x" data-file-width="1257" data-file-height="428" /></a><figcaption>Experiéncia teorica de dilatacion dau temps en relativitat especiala.</figcaption></figure> <p>Considerem aquela <a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experiéncia</a> dau ponch de vista d'un observator se desplaçant vèrs la senèstra amb la <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v</i>. Dins lo referenciau <i>S</i> estacat a aquel individú, lo dispositiu experimentau se desplaça vèrs la drecha a la velocitat <i>v</i>. Supausem que lo rai quita la fònt quand l'aparelh es en posicion (a). La <a href="/wiki/Lutz" title="Lutz">lutz</a> arriba fins au <a href="/wiki/Mirau" class="mw-redirect" title="Mirau">mirau</a> e s'entorna a la fònt. Pasmens, durant aqueu trajècte, l'aparelh s'es desplaçat en posicion (b) e (c). Ansin, lo trajècte seguit per la <a href="/wiki/Lutz" title="Lutz">lutz</a> es lo camin S<sub>1</sub>M<sub>2</sub>S<sub>3</sub>. Se sa durada es egala a <i>Δt</i>, la distància S<sub>1</sub>S<sub>3</sub> es alora egala a <i>v</i>.<i>Δt</i>. Avèm donc : </p> <center> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M_{1}S_{2}M_{3}=2{\sqrt {L^{2}+({\frac {v\Delta t}{2}})^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{1}S_{2}M_{3}=2{\sqrt {L^{2}+({\frac {v\Delta t}{2}})^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec12521196d1d8f6b2544bdb785913916fe6069d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.761ex; height:6.343ex;" alt="{\displaystyle M_{1}S_{2}M_{3}=2{\sqrt {L^{2}+({\frac {v\Delta t}{2}})^{2}}}}"></span> </p> </center> <p>Dins lo referenciau <i>S</i>, la lutz se propaga amb la velocitat <i>c</i>, çò qu'entraïna <i>S<sub>1</sub>M<sub>2</sub>S<sub>3</sub></i> = <i>c</i>.<i>Δt</i>. L'eqüacion precedenta vèn alora : </p> <center> <p><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={\frac {\frac {2L}{c}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <mrow> <mn>2</mn> <mi>L</mi> </mrow> <mi>c</mi> </mfrac> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t={\frac {\frac {2L}{c}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1627730dfeb94cb0842d44a464398c0952fe1d25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:15.502ex; height:9.176ex;" alt="{\displaystyle \Delta t={\frac {\frac {2L}{c}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}"></span> </p> </center> <p>Avèm ansin mesurat l'interval de <a href="/wiki/Temps" title="Temps">temps</a> entre l'emission e la recepcion dau rai luminós dins lo sistèma de referéncia onte l'aparelh experimentau es en movement a la <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v</i>, valent a dire dins un referenciau onte lei dos eveniments an luòc a d'endrechs diferents. Un tal interval de temps es dich « interval de temps impròpri ». Se notam <i>Δt</i> aquel interval e <i>Δt’</i> l'interval de temps pròpri, tornam aver la relacion de dilatacion dau temps presentada au paragraf precedent : </p> <center> <p><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={\frac {\Delta t'}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t={\frac {\Delta t'}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b723cffccfe55a74f4738ca5405a6bbd7efa59f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:15.502ex; height:8.343ex;" alt="{\displaystyle \Delta t={\frac {\Delta t'}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}"></span> </p> </center> <p>Segon aqueu resultat, la conclusion es que lo relòtge mobil retarda. Aquò es pas faus mai entraïna un problema logic car sembla en contradiccion amb lo premier postulat. S'un <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> <i>A</i> se desplaça a respècte d'un relòtge <i>B</i> alora <i>A</i> retarda a respècte de <i>B</i>. Pasmens, vist dempuei lo sistèma de referéncia ont <i>A</i> es au repaus, es <i>B</i> qu'es en movement. Dins aqueu cas, es <i>B</i> que dèu retardar a respècte de <i>A</i>. </p><p>Per resòuvre aquela contradiccion, es necessari de perpensar a la causa mesurada per lei <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtges</a> : mesuran pas una quantitat dicha « temps » mai un interval de temps entre dos eveniments. Dins lo cas de l'experiéncia teorica, èran la partença e l'arribada d'un rai luminós e i aviá unicament un referenciau ont aqueleis eveniments avián luòc au meteis ponch : lo referenciau de l'aparelh. Òr, es dins aqueu referenciau que lo camin percórrer per la <a href="/wiki/Lutz" title="Lutz">lutz</a> es lo cort. </p> <div class="mw-heading mw-heading4"><h4 id="Experiéncias_realas_de_dilatacion_dau_temps"><span id="Experi.C3.A9ncias_realas_de_dilatacion_dau_temps"></span>Experiéncias realas de dilatacion dau temps</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=13" title="Modificar la seccion : Experiéncias realas de dilatacion dau temps" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=13" title="Edita el codi de la secció: Experiéncias realas de dilatacion dau temps"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-section bandeau-niveau-detail loupe">Article detalhat: <a href="/w/index.php?title=Experi%C3%A9ncia_d%27Ives-Stilwell&action=edit&redlink=1" class="new" title="Experiéncia d'Ives-Stilwell (la pagina existís pas)">Experiéncia d'Ives-Stilwell</a>.</div> <p>Considerada coma una consequéncia fòrça susprenent de la relativitat especiala, la dilatacion dau temps foguèt l'objècte d'<a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experiéncias</a> realas per assaiar de'n observar la veracitat. La premiera foguèt conducha per <a href="/w/index.php?title=Herbert_Eugene_Ives&action=edit&redlink=1" class="new" title="Herbert Eugene Ives (la pagina existís pas)">Herbert Eugene Ives</a> e <a href="/w/index.php?title=G._R._Stilwell&action=edit&redlink=1" class="new" title="G. R. Stilwell (la pagina existís pas)">G. R. Stilwell</a> en <a href="/wiki/1938" class="mw-redirect" title="1938">1938</a>. Son principi foguèt de mesurar lei cambiaments de <a href="/wiki/Frequ%C3%A9ncia" title="Frequéncia">frequéncia</a> dei radiacions emesas per d'<a href="/wiki/At%C3%B2m" title="Atòm">atòms</a> en movement rapid. Pasmens, leis efiechs observats èran febles car la velocitat deis <a href="/wiki/At%C3%B2m" title="Atòm">atòms</a> utilizats agantava solament 0,5% de la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a>. Lo concèpte de l'experiéncia foguèt donc melhorat per <a href="/w/index.php?title=Bruno_Rossi&action=edit&redlink=1" class="new" title="Bruno Rossi (la pagina existís pas)">Bruno Rossi</a> e <a href="/w/index.php?title=David_B._Hall&action=edit&redlink=1" class="new" title="David B. Hall (la pagina existís pas)">David B. Hall</a> en <a href="/wiki/1941" class="mw-redirect" title="1941">1941</a> e per <a href="/w/index.php?title=David_H._Frisch&action=edit&redlink=1" class="new" title="David H. Frisch (la pagina existís pas)">David H. Frisch</a> e <a href="/w/index.php?title=James_H._Smith_(fisician)&action=edit&redlink=1" class="new" title="James H. Smith (fisician) (la pagina existís pas)">James H. Smith</a> en <a href="/wiki/1963" class="mw-redirect" title="1963">1963</a>. Per aquò, utilizèron lei <a href="/wiki/Muon" title="Muon">muons</a> dau <a href="/wiki/Rai_cosmic" title="Rai cosmic">raionament cosmic</a>. </p><p>D'efiech, aquelei <a href="/wiki/Particula_element%C3%A0ria" title="Particula elementària">particulas elementàrias</a> an una massa egala a 200 còps la massa de l'<a href="/wiki/Electron" title="Electron">electron</a> e se desintegran en formant un <a href="/wiki/Electron" title="Electron">electron</a>, un <a href="/wiki/Neutrino" class="mw-redirect" title="Neutrino">neutrino</a> e un <a href="/w/index.php?title=Antineutrino&action=edit&redlink=1" class="new" title="Antineutrino (la pagina existís pas)">antineutrino</a> amb una <a href="/wiki/Semivida" class="mw-redirect" title="Semivida">semivida</a> <i>t<sub>1</sub></i> = 1,53.10<sup>-6</sup> s. La conoissença d'aquela durada permet d'utilizar lei muons coma relòtge<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>. A quauquei <a href="/wiki/Quilom%C3%A8tre" title="Quilomètre">quilomètres</a> d'<a href="/wiki/Altitud" title="Altitud">altitud</a>, lei <a href="/wiki/Muon" title="Muon">muons</a> dau raionament cosmic son relativament aisats de detectar car passan amb una trajectòria verticala amb una velocitat pròcha d'aquela de la <a href="/wiki/Lutz" title="Lutz">lutz</a>. Dins l'<a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experiéncia</a>, s'assaia de mesurar lo temps necessari per que lei <a href="/wiki/Muon" title="Muon">muons</a> percorran una distància d'aperaquí 2 000 <a href="/wiki/M%C3%A8tre" title="Mètre">m</a> gràcias a de <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtges</a> liats au sòu e au relòtge constituït per lei <a href="/wiki/Muon" title="Muon">muons</a> elei meteissei. </p><p>Durant de mesuras realizadas a la cima dau <a href="/wiki/Mont_Washington_(New_Hampshire)" title="Mont Washington (New Hampshire)">Mont Washington</a> (1 910 m), un comptaire de <a href="/wiki/Muon" title="Muon">muons</a> comptava lo nombre de muons aguent una velocitat compresa entre 99,50% e 99,54% de la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a> (aperaquí 563 ± 10 <a href="/wiki/Muon" title="Muon">muons</a>/h). Puei, lo sistèma de mesura foguèt desplaçat au nivèu de la <a href="/wiki/Mar" title="Mar">mar</a> a una <a href="/wiki/Altitud" title="Altitud">altitud</a> de 3 m. I enregistrèt un flux pus feble (408 ± 9 <a href="/wiki/Muon" title="Muon">muons</a>/h)<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>. </p><p>Leis experimentators assaièron de comparar lei temps de trajècte dei muons dins lei dos referenciaus estudiats. Dins lo cas dei duradas mesuradas per lei <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtges</a> liats a la <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>, trobèron premier que la velocitat dei muons mesurats èra en realitat de 99,2% de la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a> en causa d'un efiech de frenatge engendrat per l'<a href="/wiki/Atmosf%C3%A8ra" class="mw-disambig" title="Atmosfèra">atmosfèra</a>. Puei, mesusèron entre lei ponchs situats a 1 910 e 3 m d'<a href="/wiki/Altitud" title="Altitud">altitud</a> una durada egala a : </p> <center> <p><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={\frac {1910-3}{0,992\times 3.10^{6}}}=6,4.10^{-6}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1910</mn> <mo>−</mo> <mn>3</mn> </mrow> <mrow> <mn>0</mn> <mo>,</mo> <mn>992</mn> <mo>×</mo> <msup> <mn>3.10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>6</mn> <mo>,</mo> <msup> <mn>4.10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t={\frac {1910-3}{0,992\times 3.10^{6}}}=6,4.10^{-6}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c775282c33877acaabecc645fb5a86657a2fa0bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:32.765ex; height:6.176ex;" alt="{\displaystyle \Delta t={\frac {1910-3}{0,992\times 3.10^{6}}}=6,4.10^{-6}\ }"></span>s </p> </center> <p>Realizèron tanben lo meteis calcul en utilizant lo relòtge estacat ai <a href="/wiki/Muon" title="Muon">muons</a> e la formula permetent de calcular lo nombre de particulas N dins un flux comportant un nombre iniciau N<sub>0</sub> de particulas en foncion dau temps <i>t</i> : </p> <center> <p><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 N=N_{0}.e^{-\lambda .t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>λ</mi> <mo>.</mo> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=N_{0}.e^{-\lambda .t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc6e9cb84be93e16c6bd01bc70701367078fab53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.72ex; height:3.009ex;" alt="{\displaystyle N=N_{0}.e^{-\lambda .t}}"></span> </p> </center> <p>La constanta <i>λ</i> es egala a ln2/<i>t<sub>1</sub></i>. L'aplicacion numerica permetent de trobar lo temps <i>Δt</i> necessari au percors dei <a href="/wiki/Muon" title="Muon">muons</a> donèt alora : </p> <p><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 408=565.e^{\frac {-\Delta t.ln2}{1,53.10^{-6}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>408</mn> <mo>=</mo> <mn>565.</mn> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>.</mo> <mi>l</mi> <mi>n</mi> <mn>2</mn> </mrow> <mrow> <mn>1</mn> <mo>,</mo> <msup> <mn>53.10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 408=565.e^{\frac {-\Delta t.ln2}{1,53.10^{-6}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a24d815e728df8b3da8cae9ed52c6877f25f8849" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.79ex; height:4.343ex;" alt="{\displaystyle 408=565.e^{\frac {-\Delta t.ln2}{1,53.10^{-6}}}}"></span> siá un temps <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=0,715.10^{-6}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <msup> <mn>715.10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t=0,715.10^{-6}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d2e82125456c025ef5e7c37fe3d4e3e07c46e55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.443ex; height:3.009ex;" alt="{\displaystyle \Delta t=0,715.10^{-6}\ }"></span>s. </p> <p>L'interval de temps pròpri es egau a la durada <i>t<sub>p</sub></i> = 0,715.10sup>-6 s e es donc fòrça diferent de l'interval de temps impròpri <i>t<sub>i</sub></i> = 6,4.10sup>-6 s calculat dins lo referenciau terrèstre. Pasmens, lo rapòrt <i>t<sub>p</sub></i>/<i>t<sub>i</sub></i> a una valor quasi identica a la prediccion teorica (0,11 en practica còntra 0,13). Aquò permetèt ansin de demostrar la validitat experimentala de la teoria. </p> <div class="mw-heading mw-heading3"><h3 id="La_contraccion_dei_longors">La contraccion dei longors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=14" title="Modificar la seccion : La contraccion dei longors" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=14" title="Edita el codi de la secció: La contraccion dei longors"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Coma leis intervals de <a href="/wiki/Temps" title="Temps">temps</a>, lei <a href="/w/index.php?title=Longor&action=edit&redlink=1" class="new" title="Longor (la pagina existís pas)">longors</a> subisson d'efiechs susprenents dins lo quadre de la <a href="/wiki/Fisica" title="Fisica">fisica</a> relativista. Per aquò, se pòu estudiar lo movement d'una particula se desplaçant amb una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v</i> entre dos ponchs <i>A</i> e <i>B</i>, fixs dins lo referenciau dau <a href="/wiki/Laborat%C3%B2ri" title="Laboratòri">laboratòri</a> e separats per la distància <i>L’</i>. Dins aqueu sistèma de referéncia, la particula percor la distància <i>AB</i> en una durada L’/v. Pasmens, segon lo paragraf precedent, aquò es un interval de temps impròpri. </p><p>Lo <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> liat a la particula mesurariá una durada diferenta e egala 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 {\frac {L'}{v}}.{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>L</mi> <mo>′</mo> </msup> <mi>v</mi> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {L'}{v}}.{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86aea019e28e96cbe5df57952f00ca881ca444bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.482ex; height:7.509ex;" alt="{\displaystyle {\frac {L'}{v}}.{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}"></span>. </p><p>Ansin, dins lo referenciau de la particula, la longor <i>L</i> entre lei dos ponchs <i>A</i> e <i>B</i> es egala <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 L=L'.{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <msup> <mi>L</mi> <mo>′</mo> </msup> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=L'.{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fc69c204fe3ad68a7ee2e7eafe20393fa595f14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:17.327ex; height:7.509ex;" alt="{\displaystyle L=L'.{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}"></span>. </p><p>Aqueu resultat exprimís lo fenomèn de contraccion dei longors que mena necessiarament a aqueu de dilatacion dau <a href="/wiki/Temps" title="Temps">temps</a> : la longor d'una règla se desplaçant a una velocitat <i>v</i> demenís d'un factor <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 {1-{\frac {v^{2}}{c^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6e1b5d7b224a53dd554c45cd2c708e5bc77abfc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:9.345ex; height:7.509ex;" alt="{\displaystyle {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="La_paradòxa_dei_bessons"><span id="La_parad.C3.B2xa_dei_bessons"></span>La paradòxa dei bessons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=15" title="Modificar la seccion : La paradòxa dei bessons" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=15" title="Edita el codi de la secció: La paradòxa dei bessons"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-section bandeau-niveau-detail loupe">Article detalhat: <a href="/w/index.php?title=Parad%C3%B2xa_dei_bessons&action=edit&redlink=1" class="new" title="Paradòxa dei bessons (la pagina existís pas)">Paradòxa dei bessons</a>.</div> <p>La <a href="/w/index.php?title=Parad%C3%B2xa_dei_bessons&action=edit&redlink=1" class="new" title="Paradòxa dei bessons (la pagina existís pas)">paradòxa dei bessons</a> es una <a href="/wiki/Experi%C3%A9ncia_de_pensada" title="Experiéncia de pensada">experiéncia de pensada</a> fòrça famosa d'aplicacion dei principis de la relativitat especiala. Foguèt presentada per lo premier còp en <a href="/wiki/1911" class="mw-redirect" title="1911">1911</a> per <a href="/w/index.php?title=Paul_Langevin&action=edit&redlink=1" class="new" title="Paul Langevin (la pagina existís pas)">Paul Langevin</a> (<a href="/wiki/1872" class="mw-redirect" title="1872">1872</a>-<a href="/wiki/1946" class="mw-redirect" title="1946">1946</a>). </p> <div class="mw-heading mw-heading4"><h4 id="Descripcion">Descripcion</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=16" title="Modificar la seccion : Descripcion" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=16" title="Edita el codi de la secció: Descripcion"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se considera dos bessons, inicialament au repaus sus la <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>. Lo premier realiza un viatge fins a una <a href="/wiki/Planeta" title="Planeta">planeta</a> vesina a una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> fòrça auta avans de s'entornar sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>. A l'anar, lo besson demorat sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a> vetz totei lei <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtges</a> de la fusada de son fraire retardar. Òr, entre aquelei <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtges</a>, se tròba lo <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> biologic dau passatgier. La meteissa situacion se repetís durant lo viatge de retorn e, au finau, lo besson de la fusada vèn pus jove que lo besson demorat sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>. </p><p>La <a href="/w/index.php?title=Parad%C3%B2xa&action=edit&redlink=1" class="new" title="Paradòxa (la pagina existís pas)">paradòxa</a> apareis se consideram lo ponch de vista dau besson embarcat dins la <a href="/wiki/Fusada" title="Fusada">fusada</a>. Per eu, son lei <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtges</a> terrèstres que retardan e, a son retorn sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>, dèu pensar que son fraire es vengut pus jove. Dins aquò, aquela solucion sembla faussa car lo viatge es pas <a href="/wiki/Simetria" title="Simetria">simetric</a> per lei dos bessons. En particular, a respècte de son fraire demorat sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>, lo besson de la <a href="/wiki/Fusada" title="Fusada">fusada</a> subís una <a href="/wiki/Acceleracion" title="Acceleracion">acceleracion</a> a la fin de l'anar per s'entornar a son ponch d'origina. Ansin, es present a tres eveniments (partença, mieg torn, retorn) còntra dos (partença, retorn) e, per la màger part dei <a href="/wiki/Fisica" title="Fisica">fisicians</a> actuaus, la solucion corrècta de la paradòxa es donc la premiera. </p> <div class="mw-heading mw-heading4"><h4 id="Solucion_de_la_paradòxa"><span id="Solucion_de_la_parad.C3.B2xa"></span>Solucion de la paradòxa</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=17" title="Modificar la seccion : Solucion de la paradòxa" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=17" title="Edita el codi de la secció: Solucion de la paradòxa"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per explicar la solucion de la <a href="/w/index.php?title=Parad%C3%B2xa_dei_bessons&action=edit&redlink=1" class="new" title="Paradòxa dei bessons (la pagina existís pas)">paradòxa dei bessons</a>, s'utiliza generalament una simplificacion dau trajècte. Lo besson que quita la <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a> viatge a la velocitat <i>v</i> dins una premiera fusada s'alunchant de la <a href="/wiki/Planeta" title="Planeta">planeta</a>. Puei, a la fin d'aquela premiera etapa, sauta sus una segonda fusada que s'entorna vèrs la <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a> amb la meteissa <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v</i>. Desenant, avèm tres observators dau movement que son lo besson demorat sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a> e lei pilòts dei doas <a href="/wiki/Fusada" title="Fusada">fusadas</a>. </p><p>Dau ponch de vista dau besson restat sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>, lo viatge a una durada <i>T</i>. L'anar dura <i>T/2</i> e lo venir <i>T/2</i>. Pasmens, en parallèl, pòu observar lo retard dei <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtges</a> dei vaissèus. Per lo pilòt de la premiera fusada, la durada de l'anar es aquela de l'interval de temps pròpri, es a dire <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 {T}{2}}.{\sqrt {1-{v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <mn>2</mn> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <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> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {T}{2}}.{\sqrt {1-{v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53f78d9f9fc43a85840d6a12d8764d4baf859ee2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.238ex; height:5.176ex;" alt="{\displaystyle {\frac {T}{2}}.{\sqrt {1-{v^{2}/c^{2}}}}}"></span>. Idèm per lo pilòt de la segonda fusada per la durada dau retorn. Se lo besson que viatge calcula la durada totala dau trajècte a partir dei declaracions dei pilòts, arribarà a una durada totala 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 T.{\sqrt {1-{v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <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> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T.{\sqrt {1-{v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22f27b8eed0e8a0e12f88204a338c78eccd87b0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:14.402ex; height:4.843ex;" alt="{\displaystyle T.{\sqrt {1-{v^{2}/c^{2}}}}}"></span>. Coma lo besson demorat sus <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a> aurà vist lei relòtges dei fusadas retardar, serà d'acòrdi amb aquela valor maugrat son impression d'una durada de <i>T</i>. </p> <div class="mw-heading mw-heading4"><h4 id="Experiéncias_sus_la_paradòxa"><span id="Experi.C3.A9ncias_sus_la_parad.C3.B2xa"></span>Experiéncias sus la paradòxa</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=18" title="Modificar la seccion : Experiéncias sus la paradòxa" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=18" title="Edita el codi de la secció: Experiéncias sus la paradòxa"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lo resultat presentat au paragraf precedent es acceptat per la màger part dei <a href="/wiki/Fisica" title="Fisica">fisicians</a>. Pasmens, una minoritat o refusa, principalament per de rasons <a href="/wiki/Filosofia" title="Filosofia">filosoficas</a>. La figura principala d'aqueu corrent foguèt probablament <a href="/w/index.php?title=Herbert_Dingle&action=edit&redlink=1" class="new" title="Herbert Dingle (la pagina existís pas)">Herbert Dingle</a> (<a href="/wiki/1890" class="mw-redirect" title="1890">1890</a>-<a href="/wiki/1978" title="1978">1978</a>) que considerèt l'ensemble de la relativitat especiala coma faussa en causa d'aqueu resultat. Ansin, divèrseis experiéncias foguèron concebudas per assaiar de verificar la conclusion usuala dau besson viatjaire pus jove. </p><p>La pus vièlha es fondada sus la compatibilitat d'un certan nombre d'<a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experiéncias</a> independentas e es sovent presentada coma una <a href="/wiki/Experi%C3%A9ncia_de_pensada" title="Experiéncia de pensada">experiéncia de pensada</a>. Considerem un faissèu de <a href="/wiki/Particula_element%C3%A0ria" title="Particula elementària">particulas elementàrias</a> d'<a href="/wiki/Energia" title="Energia">energia</a> febla que seriá devesit en dos faissèus (representant lei dos bessons). Supausem qu'un dei faissèus siegue arrestat per una placa de matèria absorbenta onte se desintegran en formant d'autrei particulas (representacion dau besson que vielhís). L'autre faissèu viatja fins a una buta onte lei particulas son rebatudas (representacion de l'anar) e dirigits vèrs una segonda placa de matèria absorbenta situada a costat de la premiera (representacion dau retorn e dei retrobadas entre lei dos bessons). Experimentalament, lo faissèu representant lo besson que viatja es mesurat coma pus important que lo premier, çò que pareis confiermar la conclusion de la paradòxa. </p><p>Una segonda verificacion es obtenguda en comparant lei resultats de mesuras finas utilizant l'<a href="/w/index.php?title=Efiech_M%C3%B6ssbauer&action=edit&redlink=1" class="new" title="Efiech Mössbauer (la pagina existís pas)">efiech Mössbauer</a>. Dins aqueu cas, se considera dos bessons que realizan l'anar e lo venir a de <a href="/wiki/Velocitat" title="Velocitat">velocitats</a> diferentas. Lo besson pus rapid es representat per un grop d'<a href="/wiki/At%C3%B2m" title="Atòm">atòms</a> excitats de <a href="/wiki/Temperatura" title="Temperatura">temperatura</a> auta. Lo besson lent es simulat per un grop similar de <a href="/wiki/Temperatura" title="Temperatura">temperatura</a> bassa. Dins aqueu cas, lo besson rapid vielhís tanben pus lentament que lo besson lent dins la mesura que la frequéncia emesa per leis atòms cauds es pus febla qu'aquela deis atòmes fregs. </p><p>Enfin, existís una tresena verificacion que foguèt realizada durant una experiéncia dau <a href="/wiki/CERN" class="mw-redirect" title="CERN">CERN</a> sus de <a href="/wiki/Muon" title="Muon">muons</a> se desplaçant a una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> de 99,65% de la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a>. Aquelei particulas èran plaçadas sus una trajectòria circulara, çò que permetiá de comparar son temps a cada passatge a l'origina. La durada de vida d'aquelei muons foguèt mesurada 12 còps superiora a aquela de <a href="/wiki/Muon" title="Muon">muons</a> immobils coma lo tèrme <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}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cb427e2513b76fee3f323fbbd04554eae9e886c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:9.628ex; height:8.009ex;" alt="{\displaystyle {\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}"></span> permetiá d'o preveire. </p> <div class="mw-heading mw-heading3"><h3 id="La_composicion_dei_velocitats">La composicion dei velocitats</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=19" title="Modificar la seccion : La composicion dei velocitats" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=19" title="Edita el codi de la secció: La composicion dei velocitats"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Generalitats">Generalitats</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=20" title="Modificar la seccion : Generalitats" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=20" title="Edita el codi de la secció: Generalitats"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Considerem un ponch <i>M</i> se desplaçant dins un referenciau <i>S</i> amb una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v<sub>1</sub></i> parallèla a <i>Ox</i>. Dins lo referenciau <i>S’</i>, sa velocitat es <i>v’<sub>1</sub></i> parallèla a <i>Ox’</i>. La <a href="/w/index.php?title=Transformacion_de_Lorentz&action=edit&redlink=1" class="new" title="Transformacion de Lorentz (la pagina existís pas)">transformacion de Lorentz</a> mòstra alora que la composicion dei velocitats s'escriu : </p> <center> <p><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'_{1}={\frac {v+v_{1}}{1+{\frac {v.v_{1}}{c^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mo>+</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mo>.</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v'_{1}={\frac {v+v_{1}}{1+{\frac {v.v_{1}}{c^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01b4832a04837deb47cee4c6f43bca22276c8b52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:13.839ex; height:6.843ex;" alt="{\displaystyle v'_{1}={\frac {v+v_{1}}{1+{\frac {v.v_{1}}{c^{2}}}}}}"></span> </p> </center> <p>Se lei velocitats <i>v</i> e <i>v<sub>1</sub></i> son feblas a respècte de <i>c</i>, se torna trobar la composicion dei velocitats de la <a href="/wiki/Mecanica_classica" title="Mecanica classica">mecanica classica</a> : <i>v'<sub>1</sub></i> = <i>v</i> + <i>v<sub>1</sub></i>. </p> <div class="mw-heading mw-heading4"><h4 id="Experiéncia_de_Fizeau"><span id="Experi.C3.A9ncia_de_Fizeau"></span>Experiéncia de Fizeau</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=21" title="Modificar la seccion : Experiéncia de Fizeau" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=21" title="Edita el codi de la secció: Experiéncia de Fizeau"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La lèi de composicion dei <a href="/wiki/Velocitat" title="Velocitat">velocitats</a> foguèt un dei premiereis aspèctes possibles de verificar d'un biais experimentau per validar la teoria. D'efiech, tre <a href="/wiki/1850" class="mw-redirect" title="1850">1850</a>, lo <a href="/wiki/Fisica" title="Fisica">fisician</a> <a href="/wiki/Fran%C3%A7a" title="França">francés</a> <a href="/w/index.php?title=Hippolyte_Fizeau&action=edit&redlink=1" class="new" title="Hippolyte Fizeau (la pagina existís pas)">Hippolyte Fizeau</a> (<a href="/wiki/1819" class="mw-redirect" title="1819">1819</a>-<a href="/wiki/1896" class="mw-redirect" title="1896">1896</a>) aviá realizat una <a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experiéncia</a> permetent de la verificar. Son projècte èra d'estudiar la propagacion de la <a href="/wiki/Lutz" title="Lutz">lutz</a> dins de mitans materiaus immobils e mobils. </p><p>Per aquò, <a href="/w/index.php?title=Hippolyte_Fizeau&action=edit&redlink=1" class="new" title="Hippolyte Fizeau (la pagina existís pas)">Fizeau</a> trabalhèt amb un faissèu monocromatic emés per un <a href="/w/index.php?title=Lume_de_mercuri&action=edit&redlink=1" class="new" title="Lume de mercuri (la pagina existís pas)">lume de mercuri</a>. La radiacion utilizada èra dirigida vèrs una lama de vèire cubèrta d'un film d'<a href="/wiki/Argent_(metal)" title="Argent (metal)">argent</a> d'una espessor precisa permetent de rebatre la mitat dau faissèu vèrs un <a href="/wiki/Mirau" class="mw-redirect" title="Mirau">mirau</a> e de laissar passar lo rèsta. Aquò permetèt de crear dos faissèus sincròns e parallèls de meteissa intensitat. Puei, aquelei faissèus passavan dins dos tubes emplits d'<a href="/wiki/Aiga" title="Aiga">aiga</a> avans d'arribar sus un segond mirau permetent de lei rebatre vèrs l'<a href="/wiki/Uelh" class="mw-redirect" title="Uelh">uelh</a> de l'observator. </p><p>Se l'<a href="/wiki/Aiga" title="Aiga">aiga</a> es immobila dins lei tubes, leis intensitats dei dos faissèus s'addicionan e l'observator vetz unicament lo faissèu iniciau. En revènge, se l'<a href="/wiki/Aiga" title="Aiga">aiga</a> dei tubes se desplaça dins de sens opausats e « entraïnan » lei rais luminós, lei rais passant dins lo tube aguent una velocitat orientada dins lo meteis que la propagacion de la radiacion, arribaràn premier a l'observator. Se lei velocitats son chausidas per crear una diferéncia de <a href="/w/index.php?title=Camin_optic&action=edit&redlink=1" class="new" title="Camin optic (la pagina existís pas)">camin optic</a> entre lei dos faissèus egala a una mieja <a href="/wiki/Longor_d%27onda" title="Longor d'onda">longor d'onda</a>, s'obtèn alora un fenomèn d'<a href="/w/index.php?title=Interfer%C3%A9ncia&action=edit&redlink=1" class="new" title="Interferéncia (la pagina existís pas)">interferéncias luminosas</a>. Òr, aqueu fenomèn es ben previst per la lèi de la composicion dei velocitats relativista. </p> <div class="mw-heading mw-heading4"><h4 id="Velocitat_limita">Velocitat limita</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=22" title="Modificar la seccion : Velocitat limita" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=22" title="Edita el codi de la secció: Velocitat limita"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La relacion de la composicion dei velocitats relativista mòstra l'existéncia d'una velocitat limita, impossibla de passar, qu'es la <a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">velocitat de la lutz</a> <i>c</i>. Aqueu resultat foguèt observat dins mai d'una experiéncia dins d'<a href="/wiki/Accelerator_de_particulas" title="Accelerator de particulas">accelerators de particulas</a>. </p> <div class="mw-heading mw-heading3"><h3 id="L'equivaléncia_massa-energia"><span id="L.27equival.C3.A9ncia_massa-energia"></span>L'equivaléncia massa-energia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=23" title="Modificar la seccion : L'equivaléncia massa-energia" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=23" title="Edita el codi de la secció: L'equivaléncia massa-energia"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Generalitats_2">Generalitats</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=24" title="Modificar la seccion : Generalitats" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=24" title="Edita el codi de la secció: Generalitats"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Una autra consequéncia dei postulats de la relativitat especiala es l'equivaléncia <a href="/wiki/Massa" title="Massa">massa</a>-<a href="/wiki/Energia" title="Energia">energia</a> qu'es sovent resumida per la formula famosa <i>E</i> = <i>m</i>.<i>c</i>². Pasmens, la formula complèta de l'<a href="/wiki/Energia_cinetica" title="Energia cinetica">energia cinetica</a> donada per la relativitat especiala es<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> : </p> <center> <p><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={\frac {m.c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mo>.</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {m.c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/022d5317615c01c1bcec93c194bfc415d4304039" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:17.442ex; height:7.009ex;" alt="{\displaystyle E={\frac {m.c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}"></span> </p> </center> <p>Aquela eqüacion permetèt d'unificar dos principis importants de la <a href="/wiki/Mecanica_classica" title="Mecanica classica">mecanica classica</a> qu'èran la <a href="/wiki/Conservacion_de_l%27energia" title="Conservacion de l'energia">conservacion de l'energia</a> e la <a href="/w/index.php?title=Conservacion_de_la_massa&action=edit&redlink=1" class="new" title="Conservacion de la massa (la pagina existís pas)">conservacion de la massa</a>. De mai, a partir deis <a href="/w/index.php?title=Eq%C3%BCacions_de_Maxwell&action=edit&redlink=1" class="new" title="Eqüacions de Maxwell (la pagina existís pas)">eqüacions de Maxwell</a>, es possible de determinar l'aumentacion d'energia d'un objècte de <a href="/wiki/Massa" title="Massa">massa</a> <i>m</i> se desplaçant a la <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v'</i> e absorbissent una quantitat d'<a href="/wiki/Energia" title="Energia">energia</a> <i>E<sub>0</sub></i> sota forma de radiacions <a href="/wiki/Electromagnetisme" title="Electromagnetisme">electromagneticas</a> : </p> <center> <p><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 {E_{0}}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <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 {\frac {E_{0}}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6906fd89708a7aa6116ffdbdfd8f2128fc80e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:12.568ex; height:6.676ex;" alt="{\displaystyle {\frac {E_{0}}{\sqrt {1-v^{2}/c^{2}}}}}"></span> </p> </center> <p>Segon la definicion de l'<a href="/wiki/Energia_cinetica" title="Energia cinetica">energia cinetica</a>, l'<a href="/wiki/Energia" title="Energia">energia</a> de l'objècte es alora : </p> <center> <p><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 {(m+{\frac {E_{0}}{c^{2}}}).c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo stretchy="false">)</mo> <mo>.</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {(m+{\frac {E_{0}}{c^{2}}}).c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59cc561755262117cc603c38b85658206ecf5289" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.502ex; height:8.343ex;" alt="{\displaystyle {\frac {(m+{\frac {E_{0}}{c^{2}}}).c^{2}}{\sqrt {1-v^{2}/c^{2}}}}}"></span> </p> </center> <div class="mw-heading mw-heading4"><h4 id="Particula_de_massa_nulla">Particula de massa nulla</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=25" title="Modificar la seccion : Particula de massa nulla" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=25" title="Edita el codi de la secció: Particula de massa nulla"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Una consequéncia deis eqüacions presentadas dins lo paragraf precedentas es de considerar l'existéncia de particulas de <a href="/wiki/Massa" title="Massa">massa</a> nulla per poder aplicar la relativitat a la <a href="/wiki/Lutz" title="Lutz">lutz</a>. Dichas <a href="/wiki/Foton" title="Foton">fotons</a>, aquelei particulas son lei constituents deis ondas electromagneticas<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>. </p> <div class="mw-heading mw-heading4"><h4 id="Experiéncias_sus_l'energia_relativista"><span id="Experi.C3.A9ncias_sus_l.27energia_relativista"></span>Experiéncias sus l'energia relativista</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=26" title="Modificar la seccion : Experiéncias sus l'energia relativista" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=26" title="Edita el codi de la secció: Experiéncias sus l'energia relativista"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Divèrseis <a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experiéncias</a> an permés de verificar lei consequéncias <a href="/w/index.php?title=Teoria&action=edit&redlink=1" class="new" title="Teoria (la pagina existís pas)">teoricas</a> previstas per leis <a href="/wiki/Eq%C3%BCacion" class="mw-redirect" title="Eqüacion">eqüacions</a> sus l'<a href="/wiki/Energia" title="Energia">energia</a> relativista. Per exemple, se pòu considerar l'exemple de la <a href="/wiki/Reaccion_quimica" title="Reaccion quimica">reaccion quimica</a> :<br /> </p> <center>CO + O<sub>2</sub> → CO<sub>2</sub></center> <p>Aquela reaccion es acompanhada per una liberacion de calor de 94 kcal/mol que correspond a la diferéncia de massa entre lei reactius e lo produch. Pasmens, aquela diferéncia es fòrça febla, de l'òrdre de 4.10^<sup>-9</sup> g/mol, çò que complica sa deteccion experimentala. En revènge, dins lo cas de <a href="/wiki/Radioactivitat" title="Radioactivitat">reaccion nucleara</a>, lo defaut de massa es pus important e mesurable. Aquò es la basa dei reaccions de <a href="/wiki/Fission_nucleara" title="Fission nucleara">fission nucleara</a> utilizada dins lei <a href="/wiki/Centrala_nucleara" title="Centrala nucleara">centralas nuclearas</a>. Per exemple, es lo cas de la desintegracion seguenta de l'<a href="/wiki/Urani" title="Urani">urani</a>-239 que desgatja una energia de 221 MeV/mol : </p> <center><sup>239</sup>U → <sup>149</sup>Ce + <sup>99</sup>Ru</center> <div class="mw-heading mw-heading3"><h3 id="Consequéncias_en_electromagnetisme"><span id="Consequ.C3.A9ncias_en_electromagnetisme"></span>Consequéncias en electromagnetisme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=27" title="Modificar la seccion : Consequéncias en electromagnetisme" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=27" title="Edita el codi de la secció: Consequéncias en electromagnetisme"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se la relativitat especiala es subretot famosa per seis aplicacions <a href="/w/index.php?title=Mecanica&action=edit&redlink=1" class="new" title="Mecanica (la pagina existís pas)">mecanicas</a>, son origina se situa dins l'estudi de l'<a href="/wiki/Electromagnetisme" title="Electromagnetisme">electromagnetisme</a><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>. La teoria permet donc de produrre un quadre eficaç per explicar lo foncionament dei camps electrics e magnetics. </p> <div class="mw-heading mw-heading4"><h4 id="Fòrça_de_Lorentz_e_invariància_de_la_carga"><span id="F.C3.B2r.C3.A7a_de_Lorentz_e_invari.C3.A0ncia_de_la_carga"></span>Fòrça de Lorentz e invariància de la carga</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=28" title="Modificar la seccion : Fòrça de Lorentz e invariància de la carga" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=28" title="Edita el codi de la secció: Fòrça de Lorentz e invariància de la carga"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-section bandeau-niveau-detail loupe">Article detalhat: <a href="/wiki/F%C3%B2r%C3%A7a_de_Lorentz" title="Fòrça de Lorentz">Fòrça de Lorentz</a>.</div> <p>Considerem un faissèu de particulas cargadas, per exemple d'<a href="/wiki/Electron" title="Electron">electrons</a> emés per un <a href="/w/index.php?title=Tube_catodic&action=edit&redlink=1" class="new" title="Tube catodic (la pagina existís pas)">tube catodic</a>. S'aprocham d'aqueu faissèu un fieu percorrut per un <a href="/wiki/Corrent_electric" title="Corrent electric">corrent electric</a>, observam una desviacion dau faissèu. Aquela interaccion es descricha amb l'introduccion de la nocion de <a href="/wiki/Camp_magnetic" title="Camp magnetic">camp magnetic</a> en disent que tot corrent electric engendra la formacion d'un camp magnetic. Tota particula cargada plaçada dins un camp magnetic proporcionala a l'intensitat dau camp magnetic au ponch ont es situada la particula. </p><p>Per una particula de carga <i>q</i> e de velocitat <i>v</i> situada dins un <a href="/wiki/Camp_electric" title="Camp electric">camp electric</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 {\vec {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc18ae485a72f148e85ccbeff2b3dcdd4f5f3f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.843ex;" alt="{\displaystyle {\vec {E}}}"></span> e dins un <a href="/wiki/Camp_magnetic" title="Camp magnetic">camp magnetic</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 {\vec {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83ae7d80cab55b606de217162280b2279142bbb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.843ex;" alt="{\displaystyle {\vec {B}}}"></span>, la <a href="/wiki/F%C3%B2r%C3%A7a" title="Fòrça">fòrça</a> totala <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}}}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> aplicada sus la particula es egala a : </p> <center> <p><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}}=q{\vec {E}}+q{\vec {v}}\wedge {\vec {B}}}"> <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>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <mi>q</mi> <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>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=q{\vec {E}}+q{\vec {v}}\wedge {\vec {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c69099e907e2f48901d61acd8ae438fad449a729" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.146ex; height:3.176ex;" alt="{\displaystyle {\vec {F}}=q{\vec {E}}+q{\vec {v}}\wedge {\vec {B}}}"></span> </p> </center> <p>Una question importanta de la <a href="/wiki/Fisica" title="Fisica">fisica</a> de la fin dau sègle XIX e dau començament dau sègle XX èra de comprendre l'origina dau segond tèrme d'aquela lèi. Per i respòndre , la premiera etapa de la reflexion dei <a href="/wiki/Fisica" title="Fisica">fisicians</a> foguèt d'estudiar l'efiech dau movement d'una particula sus sa carga. Plusors experiéncias demostrèron l'abséncia de liames entre lei doas proprietats, çò que foguèt resumit per la conclusion : <i>« La carga totala d'un sistèma es pas afectada per lo movement dei portaires de carga »</i>. Divèrsei verificacions <a href="/wiki/Experi%C3%A9ncia" title="Experiéncia">experimentalas</a> d'aqueu resultat existisson coma, per exemple, la neutralitat electrica dei <a href="/wiki/Molecula" title="Molecula">moleculas</a> e deis <a href="/wiki/At%C3%B2m" title="Atòm">atòms</a> en movement. De mesuras pus precisas foguèron tanben menadas sus d'<a href="/wiki/At%C3%B2m" title="Atòm">atòms</a> d'<a href="/wiki/Idrog%C3%A8n" title="Idrogèn">idrogèn</a> e d'<a href="/wiki/%C3%88li" title="Èli">èli</a> amb de resultats identics<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>. </p> <div class="mw-heading mw-heading4"><h4 id="Camps_electric_e_magnetic">Camps electric e magnetic</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=29" title="Modificar la seccion : Camps electric e magnetic" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=29" title="Edita el codi de la secció: Camps electric e magnetic"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La teoria de la relativitat establís que lei camps electric e magnetics son d'aspèctes diferents d'un meteis fenomèn. Se consideram un <a href="/wiki/Condensator" class="mw-redirect" title="Condensator">condensator</a> plan immobil format d'armaduras parallèlas portant lei cargas +<i>Q</i> e –<i>Q</i>, lo <a href="/wiki/Camp_electric" title="Camp electric">camp electric</a> entre leis armaduras de <a href="/wiki/Largor" title="Largor">largor</a> <i>a</i> e de <a href="/w/index.php?title=Longor&action=edit&redlink=1" class="new" title="Longor (la pagina existís pas)">longor</a> <i>b</i> es parallèl a l'aisse <i>Oy</i> e egau a : </p> <center> <p><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_{y}={\frac {Q}{\epsilon _{0}.a.b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <mrow> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> <mi>a</mi> <mo>.</mo> <mi>b</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{y}={\frac {Q}{\epsilon _{0}.a.b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2a47b22fb29b35ecf85979fd37644035c675af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.993ex; height:5.843ex;" alt="{\displaystyle E_{y}={\frac {Q}{\epsilon _{0}.a.b}}}"></span> </p> </center> <p>Amb <i>ε<sub>0</sub></i> la <a href="/w/index.php?title=Permitivitat_dielectrica&action=edit&redlink=1" class="new" title="Permitivitat dielectrica (la pagina existís pas)">permitivitat dielectrica</a> dau mitan considerat. </p><p>Dins un referenciau <i>S’</i> se desplaçant vèrs lei <i>x</i> positius amb una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v</i>, lei cargas se desplaçan vèrs la senèstra amb la meteissa velocitat <i>v</i>. Lei cargas mobilas produson alora un <a href="/wiki/Camp_magnetic" title="Camp magnetic">camp magnetic</a> entre leis armaduras. Pasmens, lo <a href="/wiki/Condensator" class="mw-redirect" title="Condensator">condensator</a> es identic dins lei dos cas. Ansin, lo fach que lo camp siegue purament electric ò associat a un camp magnetic despend dau referenciau d'estudi. En particular, dins <i>S’</i>, es possible de mostrar que le camp magnetic <i>B’</i> es dirigit vèrs lei <i>x</i> negatius e qu'es egau a : </p> <center> <p><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 B'_{x}=-{\frac {v}{c^{2}}}.E_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>.</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B'_{x}=-{\frac {v}{c^{2}}}.E_{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9517c5aa5d8977f6b6055179078ac47e036a22e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.539ex; height:5.009ex;" alt="{\displaystyle B'_{x}=-{\frac {v}{c^{2}}}.E_{y}}"></span> </p> </center> <p>Ansin, dins lo referenciau onte lo condensator es en movement, i a aparicion d'un <a href="/wiki/Camp_magnetic" title="Camp magnetic">camp magnetic</a> e aumentacion dau <a href="/wiki/Camp_electric" title="Camp electric">camp electric</a> car lo fenomèn de contraccion dei longors entraïna una demenicion de la distància entre lei doas armaduras e de la superficia deis armaduras elei meteissei. Es possible d'exprimir la valor dau camp electric <i>E’</i> dins aqueu referenciau : </p> <center> <p><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'_{y}={\frac {E_{y}}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <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 E'_{y}={\frac {E_{y}}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cea1ab30d24e3a132d31c7acd562049055c3d052" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.431ex; height:6.843ex;" alt="{\displaystyle E'_{y}={\frac {E_{y}}{\sqrt {1-v^{2}/c^{2}}}}}"></span> </p> </center> <p>Lo <a href="/wiki/Camp_electric" title="Camp electric">camp electric</a> dins la direccion perpendiculària au movement es donc aumentat d'un factor <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}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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 {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58b3cc4ef77227f9da7b7d981cdbea9fbf1f35b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:12.568ex; height:6.509ex;" alt="{\displaystyle {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"></span>. </p><p>Se lo condensator es basculat d'un angle de 90° per plaçar leis armaduras d'un biais parallèl au plan <i>Oyz</i>, lo camp seriá parallèl a <i>Ox</i>. Dins aqueu cas, la contraccion dei longors regarda unicament la distància entre leis armaduras. Òr, lo camp electric es independent d'aquela longor. Ansin, seriá identic dins lo referenciau iniciau (au repaus) e dins lo referenciau <i>S’</i>. </p><p>Es possible de generalizar aqueu resultat dins lei cas onte son presents un <a href="/wiki/Camp_electric" title="Camp electric">camp electric</a> <i>E</i> e un <a href="/wiki/Camp_magnetic" title="Camp magnetic">camp magnetic</a> <i>B</i> : </p> <center> <p><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{cases}E'_{x}=E_{x}\\E'_{y}={\frac {E_{y}-v.B_{z}}{\sqrt {1-v^{2}/c^{2}}}}\\E'_{z}={\frac {E_{z}-v.B_{y}}{\sqrt {1-v^{2}/c^{2}}}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>−</mo> <mi>v</mi> <mo>.</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>−</mo> <mi>v</mi> <mo>.</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}E'_{x}=E_{x}\\E'_{y}={\frac {E_{y}-v.B_{z}}{\sqrt {1-v^{2}/c^{2}}}}\\E'_{z}={\frac {E_{z}-v.B_{y}}{\sqrt {1-v^{2}/c^{2}}}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5229974ab4b19fe525d74bbf9d3572db18198bc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.838ex; width:17.255ex; height:14.843ex;" alt="{\displaystyle {\begin{cases}E'_{x}=E_{x}\\E'_{y}={\frac {E_{y}-v.B_{z}}{\sqrt {1-v^{2}/c^{2}}}}\\E'_{z}={\frac {E_{z}-v.B_{y}}{\sqrt {1-v^{2}/c^{2}}}}\end{cases}}}"></span> </p> </center> <center> <p><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{cases}c.B'_{x}=c.B_{x}\\c.B'_{y}={\frac {c.B_{y}+{\frac {v}{c}}.E_{z}}{\sqrt {1-v^{2}/c^{2}}}}\\c.B'_{z}={\frac {c.B_{z}+{\frac {v}{c}}.E_{y}}{\sqrt {1-v^{2}/c^{2}}}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>c</mi> <mo>.</mo> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mi>c</mi> <mo>.</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> <mo>.</mo> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mo>.</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mi>c</mi> </mfrac> </mrow> <mo>.</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> <mo>.</mo> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> <mo>′</mo> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mo>.</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mi>c</mi> </mfrac> </mrow> <mo>.</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}c.B'_{x}=c.B_{x}\\c.B'_{y}={\frac {c.B_{y}+{\frac {v}{c}}.E_{z}}{\sqrt {1-v^{2}/c^{2}}}}\\c.B'_{z}={\frac {c.B_{z}+{\frac {v}{c}}.E_{y}}{\sqrt {1-v^{2}/c^{2}}}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db9604fccc8bf8326620c932f7107c283f9d71af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:20.071ex; height:15.843ex;" alt="{\displaystyle {\begin{cases}c.B'_{x}=c.B_{x}\\c.B'_{y}={\frac {c.B_{y}+{\frac {v}{c}}.E_{z}}{\sqrt {1-v^{2}/c^{2}}}}\\c.B'_{z}={\frac {c.B_{z}+{\frac {v}{c}}.E_{y}}{\sqrt {1-v^{2}/c^{2}}}}\end{cases}}}"></span> </p> </center> <p>Aquelei relacions mòstran coma lo <a href="/wiki/Camp_electric" title="Camp electric">camp electric</a> se transforma en <a href="/wiki/Camp_magnetic" title="Camp magnetic">camp magnetic</a>, e invèrsament, segon lo referenciau considerat. Ansin, lei camps electric e magnetic correspòndon en realitat a una meteissa quantitat qu'es dicha <a href="/w/index.php?title=Tensor_de_camp_electromagnetic&action=edit&redlink=1" class="new" title="Tensor de camp electromagnetic (la pagina existís pas)">tensor de camp electromagnetic</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Camp_electric_creat_per_una_carga_ponctuala_mobila">Camp electric creat per una carga ponctuala mobila</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=30" title="Modificar la seccion : Camp electric creat per una carga ponctuala mobila" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=30" title="Edita el codi de la secció: Camp electric creat per una carga ponctuala mobila"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Una consequéncia deis <a href="/wiki/Eq%C3%BCacion" class="mw-redirect" title="Eqüacion">eqüacions</a> precedentas regarda lo camp electric engendrat per una carga ponctuala mobila. D'efiech, se se considera una particula immobila de carga <i>q</i> en un ponch (x ; y ; z), congreda un camp electric radiau centrat sus la particula : </p> <center> <p><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{cases}E_{x}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {x}{(x^{2}+y^{2}+z^{2})^{3/2}}}\\E_{y}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {y}{(x^{2}+y^{2}+z^{2})^{3/2}}}\\E_{z}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {z}{(x^{2}+y^{2}+z^{2})^{3/2}}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <mrow> <mn>4.</mn> <mi>π</mi> <mo>.</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <mrow> <mn>4.</mn> <mi>π</mi> <mo>.</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <mrow> <mn>4.</mn> <mi>π</mi> <mo>.</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>z</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}E_{x}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {x}{(x^{2}+y^{2}+z^{2})^{3/2}}}\\E_{y}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {y}{(x^{2}+y^{2}+z^{2})^{3/2}}}\\E_{z}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {z}{(x^{2}+y^{2}+z^{2})^{3/2}}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f8c851edac10f8618b94e35ff70020ad62288e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.338ex; width:26.717ex; height:13.843ex;" alt="{\displaystyle {\begin{cases}E_{x}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {x}{(x^{2}+y^{2}+z^{2})^{3/2}}}\\E_{y}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {y}{(x^{2}+y^{2}+z^{2})^{3/2}}}\\E_{z}={\frac {q}{4.\pi .\epsilon _{0}}}.{\frac {z}{(x^{2}+y^{2}+z^{2})^{3/2}}}\end{cases}}}"></span> </p> </center> <p>Dins un referenciau <i>S’</i> se desplaçant vèrs la drecha amb una <a href="/wiki/Velocitat" title="Velocitat">velocitat</a> <i>v</i>, l'expression dau <a href="/wiki/Camp_electric" title="Camp electric">camp electric</a> a <i>t’</i> = 0 es egala a : </p> <center> <p><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{cases}E_{x}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {x}{({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\\E_{y}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {y}{({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\\E_{z}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {z}{(({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <mrow> <mn>4.</mn> <mi>π</mi> <mo>.</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <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> </mrow> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <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> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <mrow> <mn>4.</mn> <mi>π</mi> <mo>.</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <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> </mrow> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <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> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <mrow> <mn>4.</mn> <mi>π</mi> <mo>.</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <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> </mrow> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>z</mi> <mrow> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <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> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}E_{x}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {x}{({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\\E_{y}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {y}{({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\\E_{z}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {z}{(({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfcdb646675b5f84629174cfb1288a9e3192dfc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.836ex; margin-bottom: -0.335ex; width:40.979ex; height:21.343ex;" alt="{\displaystyle {\begin{cases}E_{x}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {x}{({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\\E_{y}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {y}{({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\\E_{z}={\frac {q}{4.\pi .\epsilon _{0}.{\sqrt {1-v^{2}/c^{2}}}}}.{\frac {z}{(({\frac {x^{2}}{\sqrt {1-v^{2}/c^{2}}}}+y^{2}+z^{2})^{3/2}}}\end{cases}}}"></span> </p> </center> <p>S'aqueu camp es encara radiau, a plus la meteissa valor dins totei lei direccions. En particular, apareis pus fòrt d'un factor <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 (1-v^{2}/c^{2})^{3/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <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> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1-v^{2}/c^{2})^{3/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9c1a2515bbfa5600150f561a62d659fd8ba8e3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.916ex; height:3.343ex;" alt="{\displaystyle (1-v^{2}/c^{2})^{3/2}}"></span> dins leis aisses perpendiculars au movement. Ansin, se consideram la forma generala dau camp, lei linhas de camp son pus cortas dins l'aisse dau movement e pus lòngas dins lei direccions que li son perpendicularas. </p> <div class="mw-heading mw-heading2"><h2 id="Liames_intèrnes"><span id="Liames_int.C3.A8rnes"></span>Liames intèrnes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=31" title="Modificar la seccion : Liames intèrnes" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=31" title="Edita el codi de la secció: Liames intèrnes"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>.</li> <li><a href="/wiki/Electromagnetisme" title="Electromagnetisme">Electromagnetisme</a>.</li> <li><a href="/wiki/Fisica" title="Fisica">Fisica</a>.</li> <li><a href="/wiki/Hendrik_Lorentz" class="mw-redirect" title="Hendrik Lorentz">Hendrik Lorentz</a>.</li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a>.</li> <li><a href="/wiki/Lutz" title="Lutz">Lutz</a>.</li> <li><a href="/wiki/Mecanica_classica" title="Mecanica classica">Mecanica classica</a>.</li> <li><a href="/wiki/Relativitat_generala" title="Relativitat generala">Relativitat generala</a>.</li> <li><a href="/w/index.php?title=Transformacion_de_Lorentz&action=edit&redlink=1" class="new" title="Transformacion de Lorentz (la pagina existís pas)">Transformacion de Lorentz</a>.</li> <li><a href="/wiki/Velocitat_de_la_lutz" title="Velocitat de la lutz">Velocitat de la lutz</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Liames_extèrnes"><span id="Liames_ext.C3.A8rnes"></span>Liames extèrnes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=32" title="Modificar la seccion : Liames extèrnes" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=32" title="Edita el codi de la secció: Liames extèrnes"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En catalan">(<abbr title="">ca</abbr>)</span> <a rel="nofollow" class="external text" href="http://www.traduccionssimoneweil.cat/pdf/reflexionsapropositdelateoriadelsquanta.pdf">Reflexions sobre les teories de la relativitat i dels quanta (Simone Weil)</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=33" title="Modificar la seccion : Bibliografia" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=33" title="Edita el codi de la secció: Bibliografia"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Nòtas_e_referéncias"><span id="N.C3.B2tas_e_refer.C3.A9ncias"></span>Nòtas e referéncias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relativitat_especiala&veaction=edit&section=34" title="Modificar la seccion : Nòtas e referéncias" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relativitat_especiala&action=edit&section=34" title="Edita el codi de la secció: Nòtas e referéncias"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Amb una formulacion pus modèrna, aquò pòu s'escriure <i>« lei lèis de la fisica an la meteissa forma dins totei lei <a href="/w/index.php?title=Referenciau_galilean&action=edit&redlink=1" class="new" title="Referenciau galilean (la pagina existís pas)">referenciaus galileans</a> »</i>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Amb una formulacion pus modèrna, aquò pòu s'escriure <i>« la velocitat de la lutz dins lo vuege a la meteissa valor dins totei lei <a href="/w/index.php?title=Referenciau_galilean&action=edit&redlink=1" class="new" title="Referenciau galilean (la pagina existís pas)">referenciaus galileans</a> »</i>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Se fau nòtar qu'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> formulèt lo segond postulat per necessitat logica. D'efiech, a la publicacion de la teoria en <a href="/wiki/1905" class="mw-redirect" title="1905">1905</a>, i aviá encara ges de pròva de sa pertinéncia.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">D'efiech, se lo segond postulat èra faus, lo vam fenomau donat ai fotons per la velocitat iniciala fòrça auta dei pions auriá normalament permés de mesurar de velocitats superioras a <i>c</i>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">De mai, pòu s'observar que se la velocitat <i>v</i> es fòrça febla a respècte de <i>c</i>, leis eqüacions de la transformacion de Lorentz se simplifican per venir : <center> <p><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'=x-vt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>x</mi> <mo>−</mo> <mi>v</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x'=x-vt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/750ef5412025d2ea242170bb04644aaeed88dd7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.25ex; height:2.676ex;" alt="{\displaystyle x'=x-vt}"></span> </p><p><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> </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/e6239f12a70a7f715303934acf9dbae208fceb80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.099ex; height:2.843ex;" alt="{\displaystyle y'=y}"></span> </p><p><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> </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/80bfd939a15c0857a6b1df928f061d0e8973c342" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.962ex; height:2.509ex;" alt="{\displaystyle z'=z}"></span> </p><p><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'=t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t'=t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7827fb8419fde60614213d775219698ef599c39d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.462ex; height:2.509ex;" alt="{\displaystyle t'=t}"></span> </p> </center> <p>Aquò es la lèi de composicion dei velocitats de la <a href="/wiki/Mecanica_classica" title="Mecanica classica">mecanica classica</a>, çò que permet d'afiermar que la mecanica newtoniana es un cas simplificat de la mecanica relativista, valable per lei movements amb de velocitats feblas a respècte de <i>c</i>. </p> </span></li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Se fau remarcar que se <i>v</i> = <i>c</i>, lo tèrme 1 - v²/c² es egau a 0 e l'interval de temps entre dos batejaments dau <a href="/wiki/Rel%C3%B2tge" title="Relòtge">relòtge</a> es plus definit. Ansin, en relativitat, la velocitat <i>c</i> es un limit impossible d'agantar e de passar.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">En practica, aquela experiéncia es impossibla de realizar en causa dei limits <a href="/wiki/Tecnologia" title="Tecnologia">tecnologics</a> actuaus que permetèron pas de dispausar de sistèmas capables d'agantar de <a href="/wiki/Velocitat" title="Velocitat">velocitats</a> pròchas de la valor de <i>c</i>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text">D'efiech, s'avèm 1 000 muons a l'instant <i>t</i> = 0, n'avèm 500 a l'instant <i>t</i> = <i>t<sub>1</sub></i>, 250 a l'instant <i>t</i> = 2.<i>t<sub>1</sub></i>... etc. Ansin, en mesurant lo taus de muons, es possible de mesurar un interval de temps entre dos </span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">De segur, foguèt pas lo meteis flux de <a href="/wiki/Muon" title="Muon">muons</a> que foguèt mesurat dins lei dos cas. Pasmens, l'intensitat dau <a href="/w/index.php?title=Raionament_cosmic&action=edit&redlink=1" class="new" title="Raionament cosmic (la pagina existís pas)">raionament cosmic</a> recebut a la superficia de la <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a> es constanta.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text">Segon aquela expression, <i>E</i> = <i>m</i>.<i>c</i>² es donc una simplificacion per lei situacions amb una velocitat <i>v</i> fòrça inferiora a <i>c</i>.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text">Aquela expression vèn infinida se <i>v</i> = <i>c</i></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text">Dins lo <a href="/w/index.php?title=Mod%C3%A8l_estandard_de_la_fisica_dei_particulas&action=edit&redlink=1" class="new" title="Modèl estandard de la fisica dei particulas (la pagina existís pas)">modèl estandard de la fisica dei particulas</a>, lei <a href="/wiki/Neutrino" class="mw-redirect" title="Neutrino">neutrinos</a> son una autra particula dotada d'una massa nulla. Pasmens, d'experiéncias recentas indican l'existéncia probabla d'una massa fòrça febla.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">En particular, l'article de <a href="/wiki/1905" class="mw-redirect" title="1905">1905</a> d'<a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> aviá per títol « Sus l'electrodinamica dei còrs en movement »</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text">J.C. Zorn, G.E. Chamberlain e V.W. Hughes, <i>Physical Review</i>, 1963, '<i>129</i>, p. 2566.</span> </li> </ol>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Recuperada de « <a dir="ltr" href="https://oc.wikipedia.org/w/index.php?title=Relativitat_especiala&oldid=2258289">https://oc.wikipedia.org/w/index.php?title=Relativitat_especiala&oldid=2258289</a> »</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categorias de la pagina</a> : <ul><li><a href="/w/index.php?title=Categoria:P%C3%A0gines_amb_mides_d%27imatge_que_contenen_px_addicionals&action=edit&redlink=1" class="new" title="Categoria:Pàgines amb mides d'imatge que contenen px addicionals (la pagina existís pas)">Pàgines amb mides d'imatge que contenen px addicionals</a></li><li><a href="/wiki/Categoria:Article_redigit_en_proven%C3%A7au" title="Categoria:Article redigit en provençau">Article redigit en provençau</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Aquela pagina es estada modificada pel darrièr còp lo 7 abril de 2021 a 20.24.</li> <li id="footer-info-copyright"><span style="white-space: normal"><a href="/wiki/Wikip%C3%A8dia:Drech_d%27autor" title="Wikipèdia:Drech d'autor">Drech d'autor</a> : Los tèxtes son disponibles jos <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.fr">licéncia Creative Commons paternitat pertatge a l’identic</a> ; d’autras condicions se pòdon aplicar. 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