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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Povijest_i_motivacija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Povijest_i_motivacija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Povijest i motivacija</span> </div> </a> <ul id="toc-Povijest_i_motivacija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Postulati" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Postulati"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Postulati</span> </div> </a> <ul id="toc-Postulati-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Status" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Status"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Status</span> </div> </a> <ul id="toc-Status-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zaključci" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zaključci"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Zaključci</span> </div> </a> <ul id="toc-Zaključci-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nedostatak_apsolutnog_referentnog_okvira" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nedostatak_apsolutnog_referentnog_okvira"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Nedostatak apsolutnog referentnog okvira</span> </div> </a> <ul id="toc-Nedostatak_apsolutnog_referentnog_okvira-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Prostor,_vrijeme_i_brzina" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Prostor,_vrijeme_i_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Prostor, vrijeme i brzina</span> </div> </a> <ul id="toc-Prostor,_vrijeme_i_brzina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Masa,_moment_i_energija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Masa,_moment_i_energija"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Masa, moment i energija</span> </div> </a> <button aria-controls="toc-Masa,_moment_i_energija-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>Sadržaj cjeline Masa, moment i energija</span> </button> <ul id="toc-Masa,_moment_i_energija-sublist" class="vector-toc-list"> <li id="toc-O_masi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#O_masi"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>O masi</span> </div> </a> <ul id="toc-O_masi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Simultanost_i_uzročnost" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Simultanost_i_uzročnost"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Simultanost i uzročnost</span> </div> </a> <ul id="toc-Simultanost_i_uzročnost-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometrija_prostorvremena" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geometrija_prostorvremena"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Geometrija prostorvremena</span> </div> </a> <ul id="toc-Geometrija_prostorvremena-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Povezane_teme_i_pojmovi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Povezane_teme_i_pojmovi"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Povezane teme i pojmovi</span> </div> </a> <ul id="toc-Povezane_teme_i_pojmovi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bilješke" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bilješke"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Bilješke</span> </div> </a> <ul id="toc-Bilješke-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vanjske_poveznice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vanjske_poveznice"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Vanjske poveznice</span> </div> </a> <ul id="toc-Vanjske_poveznice-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="Sadržaj" 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="Prikaz sadržaja stranice" > <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">Prikaz sadržaja stranice</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">Posebna teorija relativnosti</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="Idi na druge jezične varijante članka. Dostupan je na 110 jezika" > <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 jezika</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 – švicarski njemački" lang="gsw" hreflang="gsw" data-title="Spezielle Relativitätstheorie" data-language-autonym="Alemannisch" data-language-local-name="švicarski njemački" 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 – amharski" lang="am" hreflang="am" data-title="ልዩ አንጻራዊነት" data-language-autonym="አማርኛ" data-language-local-name="amharski" 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 – aragonski" lang="an" hreflang="an" data-title="Relatividat especial" data-language-autonym="Aragonés" data-language-local-name="aragonski" 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 – arapski" lang="ar" hreflang="ar" data-title="النسبية الخاصة" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%86%D8%B3%D8%A8%D9%8A%D9%87_%D8%AE%D8%A7%D8%B5%D9%87" title="نسبيه خاصه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="نسبيه خاصه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%B6%E0%A7%87%E0%A6%B7_%E0%A6%86%E0%A6%AA%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%BF%E0%A6%95%E0%A6%A4%E0%A6%BE%E0%A6%AC%E0%A6%BE%E0%A6%A6_%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="বিশেষ আপেক্ষিকতাবাদ তত্ত্ব – asamski" lang="as" hreflang="as" data-title="বিশেষ আপেক্ষিকতাবাদ তত্ত্ব" data-language-autonym="অসমীয়া" data-language-local-name="asamski" 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 – asturijski" lang="ast" hreflang="ast" data-title="Teoría de la relatividá especial" data-language-autonym="Asturianu" data-language-local-name="asturijski" 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 – azerbajdžanski" lang="az" hreflang="az" data-title="Xüsusi nisbilik nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanski" 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 – baškirski" lang="ba" hreflang="ba" data-title="Махсус сағыштырмалыҡ теорияһы" data-language-autonym="Башҡортса" data-language-local-name="baškirski" 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 – balijski" lang="ban" hreflang="ban" data-title="Rélativitas khusus" data-language-autonym="Basa Bali" data-language-local-name="balijski" class="interlanguage-link-target"><span>Basa Bali</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Spezieje_Relativitetstheorie" title="Spezieje Relativitetstheorie – Bavarian" lang="bar" hreflang="bar" data-title="Spezieje Relativitetstheorie" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Spec%C4%93liuoj%C4%97_rel%C4%93t%C4%ABvoma_teuor%C4%97j%C4%97" title="Specēliuojė relētīvoma teuorėjė – Samogitian" lang="sgs" hreflang="sgs" data-title="Specēliuojė relētīvoma teuorėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B0%D0%B4%D0%BD%D0%BE%D1%81%D0%BD%D0%B0%D1%81%D1%86%D1%96" title="Спецыяльная тэорыя адноснасці – bjeloruski" lang="be" hreflang="be" data-title="Спецыяльная тэорыя адноснасці" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" 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 – bugarski" lang="bg" hreflang="bg" data-title="Специална теория на относителността" data-language-autonym="Български" data-language-local-name="bugarski" 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 – bangla" lang="bn" hreflang="bn" data-title="বিশেষ আপেক্ষিকতা" data-language-autonym="বাংলা" data-language-local-name="bangla" 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 – bosanski" lang="bs" hreflang="bs" data-title="Posebna teorija relativnosti" data-language-autonym="Bosanski" data-language-local-name="bosanski" 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 – katalonski" lang="ca" hreflang="ca" data-title="Relativitat especial" data-language-autonym="Català" data-language-local-name="katalonski" 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 – soranski kurdski" lang="ckb" hreflang="ckb" data-title="ڕێژەییی تایبەت" data-language-autonym="کوردی" data-language-local-name="soranski kurdski" 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 – češki" lang="cs" hreflang="cs" data-title="Speciální teorie relativity" data-language-autonym="Čeština" data-language-local-name="češki" 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 – čuvaški" lang="cv" hreflang="cv" data-title="Танлаштарулăхăн ятарлă теорийĕ" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" 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 – velški" lang="cy" hreflang="cy" data-title="Perthnasedd arbennig" data-language-autonym="Cymraeg" data-language-local-name="velški" 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 – danski" lang="da" hreflang="da" data-title="Speciel relativitetsteori" data-language-autonym="Dansk" data-language-local-name="danski" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="dobri članak"><a href="https://de.wikipedia.org/wiki/Spezielle_Relativit%C3%A4tstheorie" title="Spezielle Relativitätstheorie – njemački" lang="de" hreflang="de" data-title="Spezielle Relativitätstheorie" data-language-autonym="Deutsch" data-language-local-name="njemački" 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 – grčki" lang="el" hreflang="el" data-title="Ειδική σχετικότητα" data-language-autonym="Ελληνικά" data-language-local-name="grčki" 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 – engleski" lang="en" hreflang="en" data-title="Special relativity" data-language-autonym="English" data-language-local-name="engleski" 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 – španjolski" lang="es" hreflang="es" data-title="Teoría de la relatividad especial" data-language-autonym="Español" data-language-local-name="španjolski" 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 – estonski" lang="et" hreflang="et" data-title="Erirelatiivsusteooria" data-language-autonym="Eesti" data-language-local-name="estonski" 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 – baskijski" lang="eu" hreflang="eu" data-title="Erlatibitate berezia" data-language-autonym="Euskara" data-language-local-name="baskijski" 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 – perzijski" lang="fa" hreflang="fa" data-title="نسبیت خاص" data-language-autonym="فارسی" data-language-local-name="perzijski" 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 – finski" lang="fi" hreflang="fi" data-title="Erityinen suhteellisuusteoria" data-language-autonym="Suomi" data-language-local-name="finski" 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 – francuski" lang="fr" hreflang="fr" data-title="Relativité restreinte" data-language-autonym="Français" data-language-local-name="francuski" 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 – škotski gaelski" lang="gd" hreflang="gd" data-title="Teòirig shònraichte na dàimheachd" data-language-autonym="Gàidhlig" data-language-local-name="škotski gaelski" 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 – galicijski" lang="gl" hreflang="gl" data-title="Relatividade especial" data-language-autonym="Galego" data-language-local-name="galicijski" 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 – gvaranski" lang="gn" hreflang="gn" data-title="Mba'ekuaarã joguerahaviárava ijapýva" data-language-autonym="Avañe'ẽ" data-language-local-name="gvaranski" 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 – hebrejski" lang="he" hreflang="he" data-title="תורת היחסות הפרטית" data-language-autonym="עברית" data-language-local-name="hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi badge-Q17437796 badge-featuredarticle mw-list-item" title="izabrani članak"><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 – hindski" lang="hi" hreflang="hi" data-title="विशिष्ट आपेक्षिकता" data-language-autonym="हिन्दी" data-language-local-name="hindski" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Special_relativity" title="Special relativity – Fiji Hindi" lang="hif" hreflang="hif" data-title="Special relativity" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Speci%C3%A1lis_relativit%C3%A1selm%C3%A9let" title="Speciális relativitáselmélet – mađarski" lang="hu" hreflang="hu" data-title="Speciális relativitáselmélet" data-language-autonym="Magyar" data-language-local-name="mađarski" 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 – armenski" lang="hy" hreflang="hy" data-title="Հարաբերականության հատուկ տեսություն" data-language-autonym="Հայերեն" data-language-local-name="armenski" 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 – indonezijski" lang="id" hreflang="id" data-title="Relativitas khusus" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" 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 – islandski" lang="is" hreflang="is" data-title="Takmarkaða afstæðiskenningin" data-language-autonym="Íslenska" data-language-local-name="islandski" 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 – talijanski" lang="it" hreflang="it" data-title="Relatività ristretta" data-language-autonym="Italiano" data-language-local-name="talijanski" 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 – japanski" lang="ja" hreflang="ja" data-title="特殊相対性理論" data-language-autonym="日本語" data-language-local-name="japanski" 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 – gruzijski" lang="ka" hreflang="ka" data-title="ფარდობითობის სპეციალური თეორია" data-language-autonym="ქართული" data-language-local-name="gruzijski" 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 – kazaški" lang="kk" hreflang="kk" data-title="Арнайы салыстырмалылық теориясы" data-language-autonym="Қазақша" data-language-local-name="kazaški" 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 – korejski" lang="ko" hreflang="ko" data-title="특수 상대성이론" data-language-autonym="한국어" data-language-local-name="korejski" 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 – kirgiski" lang="ky" hreflang="ky" data-title="Атайын салыштырмалуулук теориясы" data-language-autonym="Кыргызча" data-language-local-name="kirgiski" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="izabrani članak"><a href="https://la.wikipedia.org/wiki/Relativitas_specialis" title="Relativitas specialis – latinski" lang="la" hreflang="la" data-title="Relativitas specialis" data-language-autonym="Latina" data-language-local-name="latinski" 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 – litavski" lang="lt" hreflang="lt" data-title="Specialioji reliatyvumo teorija" data-language-autonym="Lietuvių" data-language-local-name="litavski" 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 – latvijski" lang="lv" hreflang="lv" data-title="Speciālā relativitātes teorija" data-language-autonym="Latviešu" data-language-local-name="latvijski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="izabrani članak"><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 – makedonski" lang="mk" hreflang="mk" data-title="Специјална теорија за релативноста" data-language-autonym="Македонски" data-language-local-name="makedonski" 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 – malajalamski" lang="ml" hreflang="ml" data-title="വിശിഷ്ട ആപേക്ഷികതാ സിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="malajalamski" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn badge-Q17437796 badge-featuredarticle mw-list-item" title="izabrani članak"><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 – mongolski" lang="mn" hreflang="mn" data-title="Харьцангуйн тусгай онол" data-language-autonym="Монгол" data-language-local-name="mongolski" 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 – marathski" lang="mr" hreflang="mr" data-title="विशेष सापेक्षता" data-language-autonym="मराठी" data-language-local-name="marathski" 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 – malajski" lang="ms" hreflang="ms" data-title="Kerelatifan khas" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" 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 – malteški" lang="mt" hreflang="mt" data-title="Relattività ristretta" data-language-autonym="Malti" data-language-local-name="malteški" 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 – burmanski" lang="my" hreflang="my" data-title="အထူးနှိုင်းရသီအိုရီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmanski" 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 – donjonjemački" lang="nds" hreflang="nds" data-title="Spetschale Relativitätstheorie" data-language-autonym="Plattdüütsch" data-language-local-name="donjonjemački" 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 – nizozemski" lang="nl" hreflang="nl" data-title="Speciale relativiteitstheorie" data-language-autonym="Nederlands" data-language-local-name="nizozemski" 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 – norveški nynorsk" lang="nn" hreflang="nn" data-title="Den spesielle relativitetsteorien" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški 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 – norveški bokmål" lang="nb" hreflang="nb" data-title="Den spesielle relativitetsteorien" data-language-autonym="Norsk bokmål" data-language-local-name="norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Relativitat_especiala" title="Relativitat especiala – okcitanski" lang="oc" hreflang="oc" data-title="Relativitat especiala" data-language-autonym="Occitan" data-language-local-name="okcitanski" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AC%E0%AC%BF%E0%AC%B6%E0%AD%87%E0%AC%B7_%E0%AC%86%E0%AC%AA%E0%AD%87%E0%AC%95%E0%AD%8D%E0%AC%B7%E0%AC%BF%E0%AC%95_%E0%AC%A4%E0%AC%A4%E0%AD%8D%E0%AC%A4%E0%AD%8D%E0%AD%B1" title="ବିଶେଷ ଆପେକ୍ଷିକ ତତ୍ତ୍ୱ – orijski" lang="or" hreflang="or" data-title="ବିଶେଷ ଆପେକ୍ଷିକ ତତ୍ତ୍ୱ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="orijski" 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 – pandžapski" lang="pa" hreflang="pa" data-title="ਵਿਸ਼ੇਸ਼ ਸਾਪੇਖਤਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžapski" 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 – poljski" lang="pl" hreflang="pl" data-title="Szczególna teoria względności" data-language-autonym="Polski" data-language-local-name="poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Teor%C3%ACa_dla_relativit%C3%A0_limit%C3%A0" title="Teorìa dla relatività limità – Piedmontese" lang="pms" hreflang="pms" data-title="Teorìa dla relatività limità" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B3%D9%BE%DB%8C%D8%B4%D9%84_%D8%B1%DB%8C%D9%84%DB%8C%D9%B9%DB%8C%D9%88%D9%B9%DB%8C" title="سپیشل ریلیٹیوٹی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="سپیشل ریلیٹیوٹی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DA%81%D8%A7%D9%86%DA%AB%DA%93%DB%8C_%D9%86%D8%B3%D8%A8%D9%8A%D8%AA" title="ځانګړی نسبيت – paštunski" lang="ps" hreflang="ps" data-title="ځانګړی نسبيت" data-language-autonym="پښتو" data-language-local-name="paštunski" 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 – portugalski" lang="pt" hreflang="pt" data-title="Relatividade restrita" data-language-autonym="Português" data-language-local-name="portugalski" 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 – rumunjski" lang="ro" hreflang="ro" data-title="Teoria relativității restrânse" data-language-autonym="Română" data-language-local-name="rumunjski" 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 – ruski" lang="ru" hreflang="ru" data-title="Специальная теория относительности" data-language-autonym="Русский" data-language-local-name="ruski" 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 – sicilijski" lang="scn" hreflang="scn" data-title="Tiurìa di la rilativitati spiciali" data-language-autonym="Sicilianu" data-language-local-name="sicilijski" 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 – škotski" lang="sco" hreflang="sco" data-title="Special relativity" data-language-autonym="Scots" data-language-local-name="škotski" 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 – sindski" lang="sd" hreflang="sd" data-title="خاص نسبت جو نظريو" data-language-autonym="سنڌي" data-language-local-name="sindski" 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 – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Specijalna teorija relativnosti" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" 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 – sinhaleški" lang="si" hreflang="si" data-title="විශේෂ සාපේක්ෂතාවාදය" data-language-autonym="සිංහල" data-language-local-name="sinhaleški" 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="izabrani članak"><a href="https://sk.wikipedia.org/wiki/%C5%A0peci%C3%A1lna_te%C3%B3ria_relativity" title="Špeciálna teória relativity – slovački" lang="sk" hreflang="sk" data-title="Špeciálna teória relativity" data-language-autonym="Slovenčina" data-language-local-name="slovački" 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 – slovenski" lang="sl" hreflang="sl" data-title="Posebna teorija relativnosti" data-language-autonym="Slovenščina" data-language-local-name="slovenski" 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 – albanski" lang="sq" hreflang="sq" data-title="Teoria speciale e relativitetit" data-language-autonym="Shqip" data-language-local-name="albanski" 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 – srpski" lang="sr" hreflang="sr" data-title="Specijalna teorija relativnosti" data-language-autonym="Српски / srpski" data-language-local-name="srpski" 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 – sundanski" lang="su" hreflang="su" data-title="Teori Relativitas Khusus" data-language-autonym="Sunda" data-language-local-name="sundanski" 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 – švedski" lang="sv" hreflang="sv" data-title="Speciella relativitetsteorin" data-language-autonym="Svenska" data-language-local-name="švedski" 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 – svahili" lang="sw" hreflang="sw" data-title="Uhusianifu maalumu" data-language-autonym="Kiswahili" data-language-local-name="svahili" 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 – tamilski" lang="ta" hreflang="ta" data-title="சிறப்புச் சார்புக் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="tamilski" 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 – tajlandski" lang="th" hreflang="th" data-title="ทฤษฎีสัมพัทธภาพพิเศษ" data-language-autonym="ไทย" data-language-local-name="tajlandski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Teorya_ng_natatanging_relatibidad" title="Teorya ng natatanging relatibidad – tagalog" lang="tl" hreflang="tl" data-title="Teorya ng natatanging relatibidad" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96zel_g%C3%B6relilik" title="Özel görelilik – turski" lang="tr" hreflang="tr" data-title="Özel görelilik" data-language-autonym="Türkçe" data-language-local-name="turski" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt badge-Q17437796 badge-featuredarticle mw-list-item" title="izabrani članak"><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 – tatarski" lang="tt" hreflang="tt" data-title="Maxsus çağıştırmalılıq teoriäse" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarski" 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 – ukrajinski" lang="uk" hreflang="uk" data-title="Спеціальна теорія відносності" data-language-autonym="Українська" data-language-local-name="ukrajinski" 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 – urdski" lang="ur" hreflang="ur" data-title="اضافیت مخصوصہ" data-language-autonym="اردو" data-language-local-name="urdski" 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 – uzbečki" lang="uz" hreflang="uz" data-title="Maxsus nisbiylik nazariyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Specialine_rel%C3%A4tivi%C5%BEusen_teorii" title="Specialine relätivižusen teorii – Veps" lang="vep" hreflang="vep" data-title="Specialine relätivižusen teorii" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Thuy%E1%BA%BFt_t%C6%B0%C6%A1ng_%C4%91%E1%BB%91i_h%E1%BA%B9p" title="Thuyết tương đối hẹp – vijetnamski" lang="vi" hreflang="vi" data-title="Thuyết tương đối hẹp" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" 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 – wu kineski" lang="wuu" hreflang="wuu" data-title="狭义相对论" data-language-autonym="吴语" data-language-local-name="wu kineski" 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 – jidiš" lang="yi" hreflang="yi" data-title="ספעציעלע טעאריע פון רעלאטיוויטעט" data-language-autonym="ייִדיש" data-language-local-name="jidiš" 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 – kineski" lang="zh" hreflang="zh" data-title="狭义相对论" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%8B%B9%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="狹義相對論 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="狹義相對論" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%8B%B9%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="狹義相對論 – kantonski" lang="yue" hreflang="yue" data-title="狹義相對論" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11455#sitelinks-wikipedia" title="Poveznice na druge jezike" class="wbc-editpage">Uredi poveznice</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Posebna_teorija_relativnosti" title="Pogledaj sadržaj [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Razgovor:Posebna_teorija_relativnosti" rel="discussion" title="Razgovorna stranica [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Promijeni jezičnu varijantu" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">hrvatski</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Pogledi"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Posebna_teorija_relativnosti"><span>Čitaj</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=history" title="Ranije izmjene na ovoj stranici [h]" accesskey="h"><span>Vidi povijest</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Pomagala" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Pomagala</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Pomagala</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">sakrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Više mogućnosti" > <div class="vector-menu-heading"> Radnje </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Posebna_teorija_relativnosti"><span>Čitaj</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=history"><span>Vidi povijest</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Razno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:%C5%A0to_vodi_ovamo/Posebna_teorija_relativnosti" title="Popis svih stranica koje sadrže poveznice na ovu stranicu [j]" accesskey="j"><span>Što vodi ovamo</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:Povezane_promjene/Posebna_teorija_relativnosti" rel="nofollow" title="Nedavne promjene na stranicama koje su povezane s navedenom stranicom [k]" accesskey="k"><span>Povezane promjene</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedija:Upload" title="Postavi datoteke [u]" accesskey="u"><span>Postavi datoteku</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:Posebne_stranice" title="Popis svih posebnih stranica [q]" accesskey="q"><span>Posebne stranice</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&oldid=6537866" title="Trajna poveznica na ovu verziju stranice"><span>Trajna poveznica</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=info" title="Više informacija o ovoj stranici"><span>Podatci o stranici</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Citiraj&page=Posebna_teorija_relativnosti&id=6537866&wpFormIdentifier=titleform" title="Informacije o tome kako citirati ovu stranicu"><span>Citiraj ovu stranicu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:Skra%C4%87iva%C4%8D_adresa&url=https%3A%2F%2Fhr.wikipedia.org%2Fwiki%2FPosebna_teorija_relativnosti"><span>Skraćeni URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrKodu&url=https%3A%2F%2Fhr.wikipedia.org%2Fwiki%2FPosebna_teorija_relativnosti"><span>Preuzmi QR kôd</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Ispis/izvoz </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Posebno:Zbirka&bookcmd=book_creator&referer=Posebna+teorija+relativnosti"><span>Stvori knjigu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Posebna_teorija_relativnosti&action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Posebna_teorija_relativnosti&printable=yes" title="Inačica za ispis ove stranice [p]" accesskey="p"><span>Inačica za ispis</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Wikimedijini projekti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Special_relativity" hreflang="en"><span>Zajednički poslužitelj</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11455" title="Poveznica na stavku na projektu Wikipodatci [g]" accesskey="g"><span>Stavka na Wikipodatcima</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-izdvojeni" class="mw-indicator"><div class="mw-parser-output"><span typeof="mw:File"><a href="/wiki/Wikipedija:Izabrani_%C4%8Dlanci" title="Ovo je izdvojeni članak – lipanj 2008. Kliknite ovdje za više informacija."><img alt="Ovo je izdvojeni članak – lipanj 2008. Kliknite ovdje za više informacija." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/20px-Cscr-featured.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/30px-Cscr-featured.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/40px-Cscr-featured.svg.png 2x" data-file-width="466" data-file-height="443" /></a></span></div></div> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</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="hr" dir="ltr"><p> <b>Posebna teorija relativnosti</b> je <a href="/wiki/Fizika" title="Fizika">fizikalna</a> teorija koju je <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> objavio<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> <a href="/wiki/1905." title="1905.">1905.</a> Ona je zamijenila <a href="/wiki/Isaac_Newton" title="Isaac Newton">njutnovsku</a> koncepciju prostora i vremena i inkorporirala <a href="/wiki/Elektromagnetizam" title="Elektromagnetizam">elektromagnetizam</a> reprezentiran <a href="/wiki/Maxwellove_jednad%C5%BEbe" title="Maxwellove jednadžbe">Maxwellovim jednadžbama</a>. Teorija je nazvana "specijalna" jer predstavlja poseban slučaj Einsteinove <a href="/wiki/Teorija_relativnosti" title="Teorija relativnosti">teorije relativnosti</a> u kojem se efekti <a href="/wiki/Ubrzanje" title="Ubrzanje">ubrzanja</a> i <a href="/wiki/Gravitacija" title="Gravitacija">gravitacije</a> mogu ignorirati. Deset godina kasnije, Einstein je objavio <a href="/wiki/Op%C4%87a_teorija_relativnosti" title="Opća teorija relativnosti">teoriju opće relativnosti</a> koja obuhvaća i gravitaciju. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Povijest_i_motivacija">Povijest i motivacija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=1" title="Uredi odlomak: Povijest i motivacija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=1" title="Uredi kôd odjeljka Povijest i motivacija"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Princip_relativnosti" class="mw-redirect" title="Princip relativnosti">Princip relativnosti</a> prvi je uveo <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a>. Za razliku od ranijeg, apsolutističkog, <a href="/wiki/Aristotel" title="Aristotel">Aristotelovog</a> stajališta, on je držao da kretanje, ili barem jednoliko kretanje po pravcu, može imati smisla samo u odnosu (relaciji) na nešto, te da stoga ne postoji apsolutni referentni okvir u kojem bi mogle biti mjerene sve pojave. </p><p>Činilo se da princip relativnosti funkcionira dobro kada su u pitanju svakidašnji fenomeni koji uključuju čvrste objekte, ali kada je u pitanju svjetlost, stvar je još uvijek bila problematična. Mehanički valovi putuju gibajući se kroz neki medij i isto je pretpostavljano i za svjetlost. Taj hipotetski medij nazvan je <i>"luminiferous aether"</i>. Izgledalo je da ideja etera ponovo uvodi ideju detektibilnog apsolutnog referentnog okvira, onoga stacionarnoga u odnosu na eter. </p><p>Nakon <a href="/wiki/James_Clark_Maxwell" class="mw-redirect" title="James Clark Maxwell"> Maxwellovog</a> objedinjavanja svjetlosti, elektriciteta i magnetizma te nakon eksperimentalnih dokaza kao što je <a href="/wiki/Michelson-Morleyev_pokus" class="mw-redirect" title="Michelson-Morleyev pokus">Michelson-Morleyev pokus</a>, postignut je opći dogovor da brzina svjetlosti ne varira obzirom na brzinu kretanja promatrača, te da brzina svjetlosti mora biti nepromjenjiva (ista, "invarijantna") za sve promatrače. Činilo se da to vodi daljnjem sukobu s principom relativiteta. <a href="/wiki/Hendrik_Lorentz" class="mw-redirect" title="Hendrik Lorentz">Hendrik Lorentz</a> predložio je rješenje postulirajući teoriju etera prema kojoj su objekti i promatrači koji se kreću u odnosu na statični eter podložni fizikalnom "skraćenju" (<a href="/wiki/Lorentz-Fitzgeraldova_kontrakcija" class="mw-redirect" title="Lorentz-Fitzgeraldova kontrakcija">Lorentz-Fitzgeraldova kontrakcija</a>) i promjeni vremenskog odnosa (<a href="/wiki/Vremenska_dilatacija" title="Vremenska dilatacija">vremenskoj dilataciji</a>). <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaréova</a> verzija principa relativiteta (1904) ustvrdila je da "Zakoni fizikalnih fenomena moraju biti isti bez obzira na to da li je promatrač u mirovanju ili se jednoliko giba, stoga ne postoji i ne može postojati nikakav način razlučivanja jesmo li ili nismo sudionici takvoga gibanja." </p><p>Einsteinov doprinos bio je, između ostaloga, da Lorenzove jednadžbe izvede iz još fundamentalnijeg principa, bez pretpostavljanja prisutnosti etera. Kao posebnu teoriju relativiteta, kompleksne Lorentzove i Fitzgeraldove transformacije izveo je čistije, iz jednostavne geometrije i <a href="/wiki/Pitagora#Dostignuća_Pitagorejske_škole" title="Pitagora">Pitagorinog poučka</a>. Originalni naslov njegove teorije bio je (prevedeno s njemačkog) "O elektrodinamici tijela u kretanju". <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> je prvi predložio termin <a href="/wiki/Relativnost" class="mw-disambig" title="Relativnost">relativnost</a> da bi naglasio koncepciju transformiranja fizikalnih zakona između promatrača koji su u relativnom kretanju, jedan u odnosu na drugoga. </p> <div class="mw-heading mw-heading2"><h2 id="Postulati">Postulati</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=2" title="Uredi odlomak: Postulati" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=2" title="Uredi kôd odjeljka Postulati"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>1. Prvi postulat (<a href="/wiki/Princip_relativnosti" class="mw-redirect" title="Princip relativnosti">princip relativnosti</a>) </p> <dl><dd>Zakoni <a href="/wiki/Elektrodinamika" title="Elektrodinamika">elektrodinamike</a> i <a href="/wiki/Optika" title="Optika">optike</a> vrijedit će u svim okvirima u kojima važe mehanički zakoni.</dd></dl> <dl><dd>Svaka fizikalna teorija mora matematički izgledati isto svakom inertnom promatraču.</dd></dl> <dl><dd>Fizikalni zakoni nezavisni su od prostorne ili vremenske lokacije.</dd></dl> <p>2. Drugi postulat (nepromjenjivost <i>c</i>) </p> <dl><dd><a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">Brzina svjetlosti</a> u <a href="/wiki/Vakuum" title="Vakuum">vakuumu</a>, uobičajeno označena s <i>c</i>, ista je za sve inertne promatrače, ista je u svim smjerovima i ne ovisi o brzini objekta koji emitira svjetlost. U kombinaciji s Prvim postulatom, ovaj Drugi postulat ekvivalentan je tvrđenju da svjetlost za širenje ne zahtijeva nikakav medij (kao što je primjerice "eter").</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Status">Status</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=3" title="Uredi odlomak: Status" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=3" title="Uredi kôd odjeljka Status"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Posebna relativnost korektna je kada su gravitacijski efekti zanemarivi ili vrlo slabi, u protivnom mora biti zamijenjena <a href="/wiki/Op%C4%87a_teorija_relativnosti" title="Opća teorija relativnosti">općom relativnošću</a>. Kod vrlo malih skala, kao što je Planckova dužina i ispod toga, također je moguće podbacivanje posebne relativnosti zbog efekata kvantne gravitacije. Bez obzira na to, za makroskopske skale i u odsutnosti jakih gravitacijskih polja, posebna relativnost danas je univerzalno prihvaćena od strane zajednice fizičara, a za eksperimentalne rezultate koji joj naizgled proturječe općenito se smatra da su plod neponovljive eksperimentalne greške. </p><p>Budući da u fizici postoji sloboda definiranja jedinica prostora i vremena, moguće je jedan od dva postulata relativnosti prikazati <a href="/wiki/Tautologija" class="mw-disambig" title="Tautologija">tautološkom</a> posljedicom definicije, no to nije moguće učiniti istovremeno s oba postulata, pa su, u kombinaciji, njihove posljedice nezavisne od individualnog izbora definicije prostora i vremena. </p><p>Posebna relativnost je matematički samodosljedna i kompatibilna sa svim modernim fizikalnim teorijama, od kojih su najznačajnije <a href="/w/index.php?title=Teorija_kvantnih_polja&action=edit&redlink=1" class="new" title="Teorija kvantnih polja (stranica ne postoji)">teorija kvantnih polja</a>, <a href="/wiki/Teorija_struna" title="Teorija struna">teorija struna</a> i opća relativnost (u graničnom slučaju zanemarivih gravitacijskih polja). Unatoč tome, posebna relativnost nekompatibilna je s nekoliko ranijih teorija, od kojih je najznačajnija njutnovska mehanika. </p><p>Provedeni su brojni pokusi kako bi se posebna relativnost testirala naspram konkurentnih teorija, uključujući: </p> <ul><li>Michelson-Morleyjev pokus - dokaz nemogućnosti širenja eterom i test nepromjenjivosti (invarijantnosti) brzine svjetlosti u odnosu na smjer</li> <li>Hamarov pokus – opstrukcija eterskog toka</li> <li>Trouton-Nobleov pokus</li> <li>Kennedy-Thorndikeov pokus – kontrakcija vremena</li> <li>Rossi-Hallov pokus – efekt prostorvremenske kontrakcije na poluživot brzokrećućih čestica</li> <li>pokusi koji testiraju teoriju emitera demonstrirali su da je brzina svjetlosti nezavisna od brzine emitera</li></ul> <div class="mw-heading mw-heading2"><h2 id="Zaključci"><span id="Zaklju.C4.8Dci"></span>Zaključci</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=4" title="Uredi odlomak: Zaključci" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=4" title="Uredi kôd odjeljka Zaključci"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kod relativnih brzina bliskih brzini svjetlosti, posebna relativnost vodi drugačijim fizikalnim predviđanjima nego galilejevska relativnost. </p> <ul><li>Vrijeme proteklo između dva događaja nije nepromjenjivo od promatrača do promatrača nego ovisi o relativnoj brzini promatračevog referentnog okvira (Lorentzove transformacije).</li> <li>Dva događaja koja se zbivaju simultano na različitim mjestima unutar jednog referentnog okvira mogu se zbivati u različita vremena unutar drugog referentnog okvira (nedostatak <a href="/wiki/Apsolutna_simultanost" title="Apsolutna simultanost">apsolutne simultanosti</a>).</li> <li>Dimenzije (npr. dužina) nekog objekta izmjerene od strane jednog promatrača mogu se razlikovati od izmjera istog objekta od strane drugog promatrača (Lorentzove transformacije).</li> <li>"<a href="/wiki/Paradoks_blizanaca" title="Paradoks blizanaca">Paradoks blizanaca</a>" – sitacija u kojoj jedan od blizanaca putuje svemirskim brodom brzinom bliskom brzini svjetlosti i po povratku otkriva da je drugi blizanac stario rapidno brže (ili sporije) nego on.</li> <li>"<a href="/wiki/Paradoks_ljestava" title="Paradoks ljestava">Paradoks ljestava</a>" – situacija u kojoj dugačke ljestve putuju brzinom bliskom brzini svjetlosti i bivaju uskladištene u manju garažu.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Nedostatak_apsolutnog_referentnog_okvira">Nedostatak apsolutnog referentnog okvira</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=5" title="Uredi odlomak: Nedostatak apsolutnog referentnog okvira" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=5" title="Uredi kôd odjeljka Nedostatak apsolutnog referentnog okvira"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Posebna relativnost odbija ideju postojanja bilo kakvog apsolutnog ('unikatnog' ili 'posebnog') referentnog okvira, umjesto toga fizika mora izgledati jednako <i><b>svim</b></i> promatračima koji se jednoliko gibaju (inercijski okvir). Ovaj, '<a href="/wiki/Princip_relativnosti" class="mw-redirect" title="Princip relativnosti">princip relativnosti</a>' datira unatrag do <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galilea</a> i utjelovljen je u njutnovsku fiziku. U kasnom devetnaestom stoljeću neki su fizičari sugerirali da je <a href="/wiki/Svemir" title="Svemir">svemir</a> ispunjen supstancom poznatom kao "eter" koja provodi elektromagnetske valove. Eter je tvorio apsolutni referentni okvir unutar kojeg mogu biti mjerene brzine. Imao je neka čudesna svojstva: dovoljnu elastičnost da može podržavati elektromagnetske valove tako da ti valovi mogu biti u interakciji s materijom, istodobno ne pružajući otpor tijelima koja kroz njega prolaze. Rezultati različitih pokusa, uključujući Michelson-Morleyjev pokus, sugerirali su da je Zemlja uvijek relativno 'statična' u odnosu na eter – nešto teško objašnjivo. Najelegantnije rješenje bilo je odbaciti nužnost etera i apsolutnog okvira i prihvatiti Einsteinove postulate. </p> <div class="mw-heading mw-heading2"><h2 id="Prostor,_vrijeme_i_brzina"><span id="Prostor.2C_vrijeme_i_brzina"></span>Prostor, vrijeme i brzina</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=6" title="Uredi odlomak: Prostor, vrijeme i brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=6" title="Uredi kôd odjeljka Prostor, vrijeme i brzina"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Događaj je pojava koja može biti označena jedinstvenim <a href="/wiki/Vrijeme_(fizika)" title="Vrijeme (fizika)">vremenom</a> i <a href="/wiki/Prostor" title="Prostor">prostornom</a> lokacijom - "točka" u <a href="/wiki/Prostorvrijeme" title="Prostorvrijeme">prostorvremenu</a>. Npr. eksplozija petarde je dobra aproksimacija "događaja". Neki događaj možemo u potpunosti specificirati pomoću četiri prostornovremenske koordinate: vremenu pojavljivanja i trodimenzionalnoj prostornoj lokaciji. Pretpostavimo da imamo dva sistema <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}"></span>, čije su prostorne osi jednako smještene, te da se jedan u odnosu na drugi kreću jednolikom brzinom (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span>) uzduž njihovih osi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>. Ako neki događaj ima prostornovremenske koordinate <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (t,x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (t,x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/899eb4e1d2776847a8a39f5a9e0354b2e1383c80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.324ex; height:2.843ex;" alt="{\displaystyle (t,x,y,z)}"></span> u sistemu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (t',x',y',z')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (t',x',y',z')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0570a0199bfae73e0e14346ad593034c49540343" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.07ex; height:3.009ex;" alt="{\displaystyle (t',x',y',z')}"></span> u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}"></span>, a njihova ishodišta se poklapaju (drugim riječima (0,0,0,0) u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> poklapa se sa (0,0,0,0) u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}"></span>), tada Lorentzove transformacije specificiraju da su njihove koordinate povezane na sljedeći način: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t'=\gamma \left(t-{\frac {vx}{c^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mrow> <mo>(</mo> <mrow> <mi>t</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mi>x</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t'=\gamma \left(t-{\frac {vx}{c^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a8a590569fa24f6d516f5dfa70d57a5195f4dbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.667ex; height:6.176ex;" alt="{\displaystyle t'=\gamma \left(t-{\frac {vx}{c^{2}}}\right)}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x'=\gamma (x-vt)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>v</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x'=\gamma (x-vt)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5383ec7545787725887aed10f8f92ae402ada08c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.709ex; height:3.009ex;" alt="{\displaystyle x'=\gamma (x-vt)\,}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y'=y\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>y</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y'=y\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c14836c0a537d408ca839276c44ee0fb4781658e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.486ex; height:2.843ex;" alt="{\displaystyle y'=y\,}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z'=z\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>z</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z'=z\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e29e0271747c2c9629aa0752cd2ac080742c183" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.349ex; height:2.509ex;" alt="{\displaystyle z'=z\,}"></span></dd></dl> <p>gdje je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma \equiv {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma \equiv {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a81435e92ffd41118fa16ab9dcc151efb821fd64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:16.929ex; height:6.509ex;" alt="{\displaystyle \gamma \equiv {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"></span> <a href="/wiki/Lorentzov_faktor" title="Lorentzov faktor">Lorentzov faktor</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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> <a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">brzina svjetlosti</a> u <a href="/wiki/Vakuum" title="Vakuum">vakuumu</a>. </p><p>Ako promatrač u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> vidi neki objekt koji se giba duž osi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> brzinom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> tada će promatrač u sistemu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}"></span> vidjeti objekt koji se kreće brzinom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98af407af5c02e29010c7563af95f8986026679c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.349ex; height:2.509ex;" alt="{\displaystyle w'}"></span> gdje je </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w'={\frac {w-v}{1-wv/c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mi>v</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>w</mi> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w'={\frac {w-v}{1-wv/c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7a867b3b599db55dd386644431fba72b39f91b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.302ex; height:5.843ex;" alt="{\displaystyle w'={\frac {w-v}{1-wv/c^{2}}}}"></span></dd></dl> <p>Ova jednadžba izvodi se iz gornjih prostornih i vremenskih transformacija. Zapazite da ako se objekt kreće brzinom svjetlosti u sistemu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> (tj. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ee50ffdda2874b77f62f49886b83d25968ef2d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.769ex; height:1.676ex;" alt="{\displaystyle w=c}"></span>), tada će se također kretati brzinom svjetlosti u sistemu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}"></span>. Dakle, ako su oboje, i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> dovoljno mali u odnosu na brzinu svjetlosti, otkrit ćemo intuitivnu Galilejevu transformaciju brzina: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w'=w-v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>w</mi> <mo>−</mo> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w'=w-v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcb4f85dec22ce142c69a6321cc2aafb0c6c18d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.079ex; height:2.676ex;" alt="{\displaystyle w'=w-v}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Masa,_moment_i_energija"><span id="Masa.2C_moment_i_energija"></span>Masa, moment i energija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=7" title="Uredi odlomak: Masa, moment i energija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=7" title="Uredi kôd odjeljka Masa, moment i energija"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Uz modifikaciju poimanja prostora i vremena, posebna relativnost prisiljava nas na ponovno razmatranje koncepata <a href="/wiki/Masa" title="Masa">mase</a>, <a href="/wiki/Moment" class="mw-redirect" title="Moment">momenta</a> i <a href="/wiki/Energija" title="Energija">energije</a>, sve važnih konstrukcijskih elemenata njutnovske mehanike. Posebna relativnost zapravo pokazuje da su svi ti koncepti tek različiti aspekti iste fizikalne kvantitete, upravo na isti način kao što pokazuje neodvojivost prostora i vremena. </p><p>Postoji nekoliko ekvivalentnih načina da se u specijalnoj relativnosti definiraju moment i energija. Jedna od metoda koristi se <a href="/wiki/Zakon_o%C4%8Duvanja_energije" title="Zakon očuvanja energije">zakonom očuvanja energije</a>. Ako taj zakon i nadalje vrijedi u posebnoj relativnosti, tada mora biti istinit za svaki mogući referentni okvir. Ako napravimo jednostavni <a href="/wiki/Misaoni_pokus" title="Misaoni pokus">misaoni pokus</a> koristeći njutnovske definicije momenta i energije vidjet ćemo da te kvantitete nisu očuvane u specijalnoj relativnosti. Ideja očuvanja može se spasiti malim modifikacijama definicija pri računanju s relativističkim brzinama. Upravo tako modificirane definicije uzimaju se kao korektne za moment i energiju u posebnoj relativnosti. </p><p>Za dani objekt mase u mirovanju <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a6ff51ee949104fe6fae553cfbdfba29d5fac1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.095ex; height:2.009ex;" alt="{\displaystyle m_{0}}"></span> koji se kreće brzinom <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 u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span>, energija i moment su dani sa: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\gamma m_{0}c^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>γ</mi> <msub> <mi>m</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> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\gamma m_{0}c^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf0c804d1370c181de9249e89b83ed4b77393e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:11.679ex; height:3.176ex;" alt="{\displaystyle E=\gamma m_{0}c^{2}\,\!}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\gamma m_{0}u\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>γ</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>u</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\gamma m_{0}u\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fc8566b1d47a515fc520daabaaad7e3cdf687fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; margin-right: -0.387ex; width:10.431ex; height:2.176ex;" alt="{\displaystyle p=\gamma m_{0}u\,\!}"></span></dd></dl> <p>gdje je <i>γ</i> (<a href="/wiki/Lorentzov_faktor" title="Lorentzov faktor">Lorentzov faktor</a>) dan sa </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma ={\frac {1}{\sqrt {1-u^{2}/c^{2}}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma ={\frac {1}{\sqrt {1-u^{2}/c^{2}}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1a4857cc0e40ff5bbb055d2d65f1e034396a4d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; margin-right: -0.387ex; width:17.518ex; height:6.509ex;" alt="{\displaystyle \gamma ={\frac {1}{\sqrt {1-u^{2}/c^{2}}}}\,\!}"></span>,</dd></dl> <p>a <i>c</i> <a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">brzina svjetlosti</a>. Termin <i>γ</i> često se pojavljuje u teoriji relativnosti, a dolazi iz jednadžbi Lorentzovih transformacija. Energija i moment mogu se povezati formulom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E^{2}-(pc)^{2}=(m_{0}c^{2})^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>m</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> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}-(pc)^{2}=(m_{0}c^{2})^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30e705b1b549bc6bef1bcb29fa1136c701b0a651" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:22.233ex; height:3.176ex;" alt="{\displaystyle E^{2}-(pc)^{2}=(m_{0}c^{2})^{2}\,\!}"></span></dd></dl> <p>koja se naziva <i>relativističkom jednadžbom energije-momenta</i>. Ove jednadžbe mogu biti konciznije postavljene korištenjem četveromomentnog <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/341a1bb56fdff644b4f49968bd9d08bc1e7bdfe1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.923ex; height:2.343ex;" alt="{\displaystyle P^{a}}"></span> i četverobrzinskog <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 U^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e56df777f9dae9020c1e12759b4641b935a74f2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.943ex; height:2.343ex;" alt="{\displaystyle U^{a}}"></span> kao </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P^{a}=m_{0}U^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P^{a}=m_{0}U^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0dd3e63772b5aa180bd32a137916cbdc3a06a0bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.06ex; height:2.676ex;" alt="{\displaystyle P^{a}=m_{0}U^{a}}"></span></dd></dl> <p>što je relativistička analogija Drugog njutnovog zakona. </p><p>Za brzine puno manje od brzine svjetlosti γ može biti aproksimiran korištenjem <a href="/wiki/Taylorov_red" title="Taylorov red">Taylorovog reda</a> i tada se pokazuje da je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E\approx m_{0}c^{2}+{\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{0}u^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>≈</mo> <msub> <mi>m</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> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\approx m_{0}c^{2}+{\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{0}u^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71be40efc21e5e782ec8bbc473354caa0406a284" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.968ex; margin-right: -0.387ex; margin-bottom: -0.203ex; width:21.145ex; height:3.509ex;" alt="{\displaystyle E\approx m_{0}c^{2}+{\begin{matrix}{\frac {1}{2}}\end{matrix}}m_{0}u^{2}\,\!}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p\approx m_{0}u\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>≈</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>u</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\approx m_{0}u\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c2d55697c18cf8ac8eef50f97019bd4bf2b9337" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; margin-right: -0.387ex; width:9.169ex; height:2.009ex;" alt="{\displaystyle p\approx m_{0}u\,\!}"></span></dd></dl> <p>Izuzevši prvi termin u izrazu za energiju, ove se formule u potpunosti slažu sa standardnim definicijama njutnovske <a href="/wiki/Kineti%C4%8Dka_energija" title="Kinetička energija">kinetičke energije</a> i momenta, što znači da je specijalna relativnost pri niskim brzinama u skladu s njutnovskom mehanikom. </p><p>Promatrajući gornje formule za energiju vidimo da, kada se objekt nalazi u mirovanju (<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 u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> = 0 and <i>γ</i> = 1), ima energiju različitu od nule: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=m_{0}c^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <msub> <mi>m</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> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=m_{0}c^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bed5e507c2e436981a896d2c29337e58293f2195" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:10.417ex; height:3.009ex;" alt="{\displaystyle E=m_{0}c^{2}\,\!}"></span></dd></dl> <p>Ova se energija naziva "energijom mirovanja". Ona nije kontradiktorna njutnovskoj teoriji jer je konstantna i značajne su jedino razlike u energiji. </p><p>Ono što je bitno kod ove formule je da pokazuje da je u relativnosti <i>masa jednostavno drugi oblik energije</i>. Ova formula postaje važna pri mjerenju masa različitih <a href="/wiki/Atom" title="Atom">atomskih jezgri</a>. Promatrajući razlike u njihovim masama moguće je predvidjeti koje jezgre imaju spremljenu posebnu energiju koja može biti otpuštena nuklearnom reakcijom, što je i iskorišteno u razvoju nuklearne bombe. Implikacije ove formule na život dvadesetog stoljeća učinile su je jednom od najčuvenijih formula u cjelokupnoj znanosti. </p> <div class="mw-heading mw-heading3"><h3 id="O_masi">O masi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=8" title="Uredi odlomak: O masi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=8" title="Uredi kôd odjeljka O masi"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Uvodni tečajevi fizike i neki stariji udžbenici o posebnoj teoriji relativnosti ponekad definiraju tzv. <i>relativističku masu</i>, što može dovesti do pogrešnog utiska da posebna relativnost implicira da se masa tijela povećava s povećanjem brzine. Ovo je, s teorijskog stajališta, tehnički nekorektno jer je <a class="mw-selflink-fragment" href="#Postulati">Prvi postulat</a> upotrijebljen da bi se konstruirala teorija u kojoj su svojstva objekta nezavisna (tj. nepromjenjiva; invarijantna) od bilo kojeg inercijalnog referentnog okvira. Unatoč tome, definiranje takve kvantitete ponekada može biti <i>korisno</i> jer pojednostavljuje izračunavanje restrikcijom u specifični okvir. Na primjer, razmotrimo promatrača koji sebe drži mirujućim i tijelo nepromjenjive mase <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{0}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{0}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c923c5b85557227d95b81e683879bfab069d5954" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.095ex; height:2.009ex;" alt="{\displaystyle m_{0}\!}"></span> koje se kreće nekom brzinom relativno u odnosu na promatrača. Promatrač će <i>relativističku masu</i> tog tijela definirati kao: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=\gamma m_{0}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>γ</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\gamma m_{0}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/775288f04b443fb9abee90e52d8f958d1affde64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:9.496ex; height:2.176ex;" alt="{\displaystyle m=\gamma m_{0}\!}"></span></dd></dl> <p>Zapazite da tijelo <i>ne</i> postaje uistinu masivnije, nego da je <a href="/w/index.php?title=Relativisti%C4%8Dka_masa&action=edit&redlink=1" class="new" title="Relativistička masa (stranica ne postoji)">relativistička masa</a> drugačija za promatrača u specifičnom okviru. <i> Jedino </i> masa koja je nezavisna od promatrača je nepromjenjiva masa. Kod korištenja relativističke mase uvijek se mora specificirati brzina relativna pojedinom promatraču. Ovo je također konzistentno s konceptima "dilatacije vremena" i "<a href="/wiki/Kontrakcija" class="mw-disambig" title="Kontrakcija">kontrakcije dužine</a>". </p> <div class="mw-heading mw-heading2"><h2 id="Simultanost_i_uzročnost"><span id="Simultanost_i_uzro.C4.8Dnost"></span>Simultanost i uzročnost</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=9" title="Uredi odlomak: Simultanost i uzročnost" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=9" title="Uredi kôd odjeljka Simultanost i uzročnost"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Light_cone.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Light_cone.png/220px-Light_cone.png" decoding="async" width="220" height="276" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Light_cone.png/330px-Light_cone.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Light_cone.png/440px-Light_cone.png 2x" data-file-width="557" data-file-height="698" /></a><figcaption>Svjetlosni stožac</figcaption></figure> <p>Posebna relativnost smatra da ono što je simultano u jednom referentnom okviru ne mora nužno biti simultano u drugom referentnom okviru. </p><p>Interval AB u desnom dijagramu je 'vremenolik' tj. postoji referentni okvir u kojem se događaj A i događaj B zbivaju na istoj prostornoj lokaciji, razdvojeni jedino pojavljivanjem u različitim vremenima. Ako A prethodi B u tom okviru, tada A prethodi B u svim okvirima. Hipotetski je moguće da materija (ili informacija) putuje od A do B, stoga je moguća uzročno-posljedična veza između njih (s A kao uzrokom i B kao posljedicom). </p><p>Interval AC u dijagramu je 'prostornolik' tj. postoji referentni okvir u kojem se događaj A i događaj C zbivaju simultano, razdvojeni jedino u prostoru. Zapravo postoje referentni okviri u kojima A prethodi C (kao što je prikazano) i referentni okviri u kojima C prethodi A. </p><p>Čak ni pri putovanju brzinom bržom od <a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">brzine svjetlosti</a>, nikakvoj materiji (ili informaciji) nije moguće putovati od A do C ili od C do A, stoga ne postoji uzročno-posljedična veza između A i C. </p> <div class="mw-heading mw-heading2"><h2 id="Geometrija_prostorvremena">Geometrija prostorvremena</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=10" title="Uredi odlomak: Geometrija prostorvremena" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=10" title="Uredi kôd odjeljka Geometrija prostorvremena"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Posebna relativnost koristi 'plošni' četverodimenzionalni 'Minkowskijev prostor' kao primjer <a href="/wiki/Prostorvrijeme" title="Prostorvrijeme">prostorvremena</a>. Ovaj prostor je vrlo sličan standardnom trodimenzionalnom Euklidovskom prostoru i sretna okolnost je da je s njime lako raditi. </p><p>Diferencijal dužine (<i>ds</i>) u Kartezijevom trodimenzionalnom prostoru definiran je kao: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00c415168f3fc1aba9d7ab37612e89b292dec428" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.939ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}}"></span></dd></dl> <p>gdje su <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (dx_{1},dx_{2},dx_{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mi>d</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (dx_{1},dx_{2},dx_{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e47ac80c2c3878788204410b04853d08e4c5f275" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.677ex; height:2.843ex;" alt="{\displaystyle (dx_{1},dx_{2},dx_{3})}"></span> diferencijali tri prostorne dimenzije. U geometriji posebne relativnosti dodana je četvrta dimenzija, vrijeme, s jedinicom <a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">c</a>, tako da jednadžba diferencijala dužine postaje: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19f2b2d91c3ca8c2c1070c37b9fab369e127abf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:30.95ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"></span></dd></dl> <p>U mnogim je situacijama prikladno tretirati vrijeme kao imaginarno (tj. to može pojednostavniti jednadžbe), u kojem slučaju se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> u gornjoj jednadžbi zamjenjuje sa <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 i.t'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>.</mo> <msup> <mi>t</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i.t'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6426c6c68b74b3fa8804e08add02799e6d61d90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.361ex; height:2.509ex;" alt="{\displaystyle i.t'}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+c^{2}(dt')^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>d</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+c^{2}(dt')^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d9d4aa1915f03c9af048283bcbe2447508b42f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:33.444ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+c^{2}(dt')^{2}}"></span></dd></dl> <p>Kada prostorne dimenzije reduciramo na dvije, fiziku možemo prikazati u trodimenzionalnom prostoru: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85f5ce7255168d8385a507de9595924994f96690" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.51ex; height:3.343ex;" alt="{\displaystyle ds^{2}=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"></span></dd></dl> <p>Vidimo da geodezici leže duž dualnog stošca: </p><p><span typeof="mw:File"><a href="/wiki/Datoteka:Sr1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Sr1.svg/200px-Sr1.svg.png" decoding="async" width="200" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Sr1.svg/300px-Sr1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Sr1.svg/400px-Sr1.svg.png 2x" data-file-width="401" data-file-height="312" /></a></span> </p><p>definiranog jednadžbom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e43aa213a6206f390257013d99ba7b7c2a33fe2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.771ex; height:3.343ex;" alt="{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}-c^{2}dt^{2}}"></span></dd></dl> <p>ili </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dx_{1}^{2}+dx_{2}^{2}=c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx_{1}^{2}+dx_{2}^{2}=c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f13e83090ebdfe1e9378dded386e629543fe2739" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.309ex; height:3.343ex;" alt="{\displaystyle dx_{1}^{2}+dx_{2}^{2}=c^{2}dt^{2}}"></span></dd></dl> <p>što je jednadžba kružnice polumjera <i>r=c*dt</i>. Ako ovo proširimo na tri prostorne dimenzije nulti geodezici su kontinuirane koncentrične sfere kojima je polumjer = dužina = c*± vrijeme. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/Datoteka:Null_spherical_space_(special_relativity).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/39/Null_spherical_space_%28special_relativity%29.jpg" decoding="async" width="140" height="110" class="mw-file-element" data-file-width="140" data-file-height="110" /></a></span> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/651ec5a5c69df295c86316d566133dfec28b076f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:35.211ex; height:3.343ex;" alt="{\displaystyle ds^{2}=0=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-c^{2}dt^{2}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}=c^{2}dt^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>d</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}=c^{2}dt^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9de9a20458007959615dc7a86a89e861fd939a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.749ex; height:3.343ex;" alt="{\displaystyle dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}=c^{2}dt^{2}}"></span></dd></dl> <p>Ovaj nulti dualni stožac predstavlja "pravac gledanja" iz neke točke u prostoru. Primjerice, kada gledamo u zvijezde i kažemo "Svjetlost s ove zvijezde koju vidimo je X godina stara", mi gledamo niz taj pravac gledanja: nulti geodezik. Gledamo događaj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d={\sqrt {x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d={\sqrt {x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54abac3f97536607ca02acedebccac4fa59d1e1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.471ex; height:4.843ex;" alt="{\displaystyle d={\sqrt {x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}}}"></span> metara udaljen i <i>d/c</i> sekundi u prošlosti. Iz tog razloga nulti dualni stožac je poznat kao 'svjetlosni stožac'. (Točka u donjem lijevom dijelu slike (ispod) predstavlja zvijezdu, ishodište predstavlja promatrača, a pravac provučen tim dvjema točkama nulti geodezik "pravca gledanja". </p><p><span typeof="mw:File"><a href="/wiki/Datoteka:Sr1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Sr1.svg/200px-Sr1.svg.png" decoding="async" width="200" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Sr1.svg/300px-Sr1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Sr1.svg/400px-Sr1.svg.png 2x" data-file-width="401" data-file-height="312" /></a></span> </p><p>"-t" područje stošca predstavlja područje iz kojeg točka ishodišta 'prima', a "+t" područje stošca područje u koje točka ishodišta 'odašilje'. </p><p>Geometrija Minkowskog prostora može biti prikazana korištenjem Minkowskijevih dijagrama koji su korisni u razumijevanju mnogih misaonih pokusa u posebnoj relativnosti. </p> <div class="mw-heading mw-heading2"><h2 id="Povezane_teme_i_pojmovi">Povezane teme i pojmovi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=11" title="Uredi odlomak: Povezane teme i pojmovi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=11" title="Uredi kôd odjeljka Povezane teme i pojmovi"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><b>Osobe</b>: <a href="/w/index.php?title=Arthur_Eddington&action=edit&redlink=1" class="new" title="Arthur Eddington (stranica ne postoji)">Arthur Eddington</a> | <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> | <a href="/wiki/Hendrik_Antoon_Lorentz" title="Hendrik Antoon Lorentz">Hendrik Antoon Lorentz</a> | <a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Hermann Minkowski</a> | <a href="/w/index.php?title=Hernhard_Riemann&action=edit&redlink=1" class="new" title="Hernhard Riemann (stranica ne postoji)">Hernhard Riemann</a> | <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> | <a href="/w/index.php?title=Alexander_MacFarlane&action=edit&redlink=1" class="new" title="Alexander MacFarlane (stranica ne postoji)">Alexander MacFarlane</a> | <a href="/w/index.php?title=Harry_Bateman&action=edit&redlink=1" class="new" title="Harry Bateman (stranica ne postoji)">Harry Bateman</a> | <a href="/w/index.php?title=Robert_S._Shankland&action=edit&redlink=1" class="new" title="Robert S. Shankland (stranica ne postoji)">Robert S. Shankland</a></dd> <dd><b>Relativnost</b>: <a href="/wiki/Teorija_relativnosti" title="Teorija relativnosti">Teorija relativnosti</a> | <a href="/wiki/Princip_relativnosti" class="mw-redirect" title="Princip relativnosti">princip relativnosti</a> | <a href="/wiki/Op%C4%87a_relativnost" class="mw-redirect" title="Opća relativnost">opća relativnost</a> | <a href="/wiki/Referentni_okvir" class="mw-redirect" title="Referentni okvir">referentni okvir</a> | <a href="/wiki/Inercijski_referentni_okvir" title="Inercijski referentni okvir">inercijski referentni okvir</a> | <a href="/wiki/Lorentzove_transformacije" title="Lorentzove transformacije">Lorentzove transformacije</a></dd> <dd><b>Fizika</b>: <a href="/w/index.php?title=Njutnovska_mehanika&action=edit&redlink=1" class="new" title="Njutnovska mehanika (stranica ne postoji)">njutnovska mehanika</a> | <a href="/wiki/Prostorvrijeme" title="Prostorvrijeme">prostorvrijeme</a> | <a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">brzina svjetlosti</a> | <a href="/wiki/Apsolutna_simultanost" title="Apsolutna simultanost">apsolutna simultanost</a> | <a href="/wiki/Kozmologija" title="Kozmologija">kozmologija</a> | <a href="/wiki/Dopplerov_efekt" title="Dopplerov efekt">Dopplerov efekt</a> | <a href="/w/index.php?title=Relativisti%C4%8Dke_Eulerove_jednad%C5%BEbe&action=edit&redlink=1" class="new" title="Relativističke Eulerove jednadžbe (stranica ne postoji)">relativističke Eulerove jednadžbe</a></dd> <dd><b>Matematika</b>: <a href="/w/index.php?title=Prostor_Minkovskog&action=edit&redlink=1" class="new" title="Prostor Minkovskog (stranica ne postoji)">prostor Minkovskog</a> | <a href="/w/index.php?title=Svjetlosni_sto%C5%BEac&action=edit&redlink=1" class="new" title="Svjetlosni stožac (stranica ne postoji)">svjetlosni stožac</a> | <a href="/w/index.php?title=Lorentzova_grupa&action=edit&redlink=1" class="new" title="Lorentzova grupa (stranica ne postoji)">Lorentzova grupa</a> | <a href="/w/index.php?title=Poincar%C3%A9ova_grupa&action=edit&redlink=1" class="new" title="Poincaréova grupa (stranica ne postoji)">Poincaréova grupa</a> | <a href="/wiki/Geometrija" title="Geometrija">geometrija</a> | <a href="/wiki/Tenzor" title="Tenzor">tenzori</a></dd></dl> <dl><dd><b>Pokusi</b>: <a href="/w/index.php?title=Pokus_Hafelea_i_Keatinga&action=edit&redlink=1" class="new" title="Pokus Hafelea i Keatinga (stranica ne postoji)">pokus Hafelea i Keatinga</a></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Bilješke"><span id="Bilje.C5.A1ke"></span>Bilješke</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=12" title="Uredi odlomak: Bilješke" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=12" title="Uredi kôd odjeljka Bilješke"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.fourmilab.ch/etexts/einstein/specrel/www/">[1]</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Vanjske_poveznice">Vanjske poveznice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Posebna_teorija_relativnosti&veaction=edit&section=13" title="Uredi odlomak: Vanjske poveznice" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Posebna_teorija_relativnosti&action=edit&section=13" title="Uredi kôd odjeljka Vanjske poveznice"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.phys.unsw.edu.au/einsteinlight">Einstein Light - uvod sastavljen od filmova i prezentacija</a></li> <li><a rel="nofollow" class="external text" href="http://www.einstein-online.info/en/elementary/index.html">Einstein Online - uvod u teoriju relativnosti, Max Planck institut</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100201234156/http://www.einstein-online.info/en/elementary/index.html">Arhivirana inačica izvorne stranice</a> od 1. veljače 2010. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>)</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20040206110957/http://www.geocities.com/autotheist/Bondi/intro.htm">Bondi K-Calculus - jednostavan uvod u posebnu teoriju relativnosti</a></li> <li><a rel="nofollow" class="external text" href="http://cosmo.nyu.edu/hogg/sr/">Bilješke o posebnoj teoriji relativnosti</a></li> <li><a rel="nofollow" class="external text" href="http://www.anu.edu.au/Physics/Savage/RTR/">Relativnost pravog vremena</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130508021027/http://www.anu.edu.au/Physics/Savage/RTR/">Arhivirana inačica izvorne stranice</a> od 8. svibnja 2013. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>)</li> <li><a rel="nofollow" class="external text" href="http://www.spacetimetravel.org">Skup vizualizacija učinaka relativnosti</a></li></ul> <p><br /> </p>    </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="">Dobavljeno iz "<a dir="ltr" href="https://hr.wikipedia.org/w/index.php?title=Posebna_teorija_relativnosti&oldid=6537866">https://hr.wikipedia.org/w/index.php?title=Posebna_teorija_relativnosti&oldid=6537866</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorije</a>: <ul><li><a href="/wiki/Kategorija:Izabrani_%C4%8Dlanci" title="Kategorija:Izabrani članci">Izabrani članci</a></li><li><a href="/wiki/Kategorija:Relativnost" title="Kategorija:Relativnost">Relativnost</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"> Ova stranica posljednji je put uređivana 30. studenoga 2022. u 08:03.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencijom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.hr">Creative Commons: Imenuj autora/Dijeli pod istim uvjetima</a>; mogu se primjenjivati i dodatni uvjeti. 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