普朗克單位制 - 维基百科，自由的百科全书

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href="#基本普朗克單位"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>基本普朗克單位</span> </div> </a> <ul id="toc-基本普朗克單位-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-衍生普朗克單位" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#衍生普朗克單位"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>衍生普朗克單位</span> </div> </a> <ul id="toc-衍生普朗克單位-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-簡化物理方程式" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#簡化物理方程式"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>簡化物理方程式</span> </div> </a> <ul id="toc-簡化物理方程式-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參閱" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參閱"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>參閱</span> </div> </a> <ul id="toc-參閱-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考文獻" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考文獻"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>參考文獻</span> </div> </a> <button aria-controls="toc-參考文獻-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>开关參考文獻子章节</span> </button> <ul id="toc-參考文獻-sublist" class="vector-toc-list"> <li id="toc-引用" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#引用"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>引用</span> </div> </a> <ul id="toc-引用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-来源" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#来源"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>来源</span> </div> </a> <ul id="toc-来源-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-外部連結" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部連結"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>外部連結</span> </div> </a> <ul id="toc-外部連結-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="目录" 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="开关目录" > <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">开关目录</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">普朗克單位制</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="前往另一种语言写成的文章。48种语言可用" > <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-48" 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">48种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%88%D8%AD%D8%AF%D8%A7%D8%AA_%D8%A8%D9%84%D8%A7%D9%86%D9%83" title="وحدات بلانك – 阿拉伯语" lang="ar" hreflang="ar" data-title="وحدات بلانك" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Unidaes_de_Planck" title="Unidaes de Planck – 阿斯图里亚斯语" lang="ast" hreflang="ast" data-title="Unidaes de Planck" data-language-autonym="Asturianu" data-language-local-name="阿斯图里亚斯语" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%B0%D1%9E%D1%81%D0%BA%D1%96%D1%8F_%D0%B0%D0%B4%D0%B7%D1%96%D0%BD%D0%BA%D1%96" title="Планкаўскія адзінкі – 白俄罗斯语" lang="be" hreflang="be" data-title="Планкаўскія адзінкі" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D0%B8_%D0%BD%D0%B0_%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA" title="Единици на Планк – 保加利亚语" lang="bg" hreflang="bg" data-title="Единици на Планк" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Prirodne_jedinice" title="Prirodne jedinice – 波斯尼亚语" lang="bs" hreflang="bs" data-title="Prirodne jedinice" data-language-autonym="Bosanski" data-language-local-name="波斯尼亚语" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Unitats_de_Planck" title="Unitats de Planck – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Unitats de Planck" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Planckovy_jednotky" title="Planckovy jednotky – 捷克语" lang="cs" hreflang="cs" data-title="Planckovy jednotky" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Planck-enheder" title="Planck-enheder – 丹麦语" lang="da" hreflang="da" data-title="Planck-enheder" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Planck-Einheiten" title="Planck-Einheiten – 德语" lang="de" hreflang="de" data-title="Planck-Einheiten" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%BF%CE%BD%CE%AC%CE%B4%CE%B5%CF%82_%CE%A0%CE%BB%CE%B1%CE%BD%CE%BA" title="Μονάδες Πλανκ – 希腊语" lang="el" hreflang="el" data-title="Μονάδες Πλανκ" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" 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/Planck_units" title="Planck units – 英语" lang="en" hreflang="en" data-title="Planck units" data-language-autonym="English" data-language-local-name="英语" 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/Unuoj_de_Planck" title="Unuoj de Planck – 世界语" lang="eo" hreflang="eo" data-title="Unuoj de Planck" data-language-autonym="Esperanto" data-language-local-name="世界语" 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/Unidades_de_Planck" title="Unidades de Planck – 西班牙语" lang="es" hreflang="es" data-title="Unidades de Planck" data-language-autonym="Español" data-language-local-name="西班牙语" 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/Plancki_%C3%BChikud" title="Plancki ühikud – 爱沙尼亚语" lang="et" hreflang="et" data-title="Plancki ühikud" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" 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/Plancken_unitateak" title="Plancken unitateak – 巴斯克语" lang="eu" hreflang="eu" data-title="Plancken unitateak" data-language-autonym="Euskara" data-language-local-name="巴斯克语" 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/%DB%8C%DA%A9%D8%A7%D9%87%D8%A7%DB%8C_%D9%BE%D9%84%D8%A7%D9%86%DA%A9" title="یکاهای پلانک – 波斯语" lang="fa" hreflang="fa" data-title="یکاهای پلانک" data-language-autonym="فارسی" data-language-local-name="波斯语" 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/Planckin_yksik%C3%B6t" title="Planckin yksiköt – 芬兰语" lang="fi" hreflang="fi" data-title="Planckin yksiköt" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_d%27unit%C3%A9s_de_Planck" title="Système d'unités de Planck – 法语" lang="fr" hreflang="fr" data-title="Système d'unités de Planck" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%99%D7%97%D7%99%D7%93%D7%95%D7%AA_%D7%A4%D7%9C%D7%90%D7%A0%D7%A7" title="יחידות פלאנק – 希伯来语" lang="he" hreflang="he" data-title="יחידות פלאנק" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Planck-egys%C3%A9gek" title="Planck-egységek – 匈牙利语" lang="hu" hreflang="hu" data-title="Planck-egységek" data-language-autonym="Magyar" data-language-local-name="匈牙利语" 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%8A%D5%AC%D5%A1%D5%B6%D5%AF%D5%AB_%D5%B4%D5%AB%D5%A1%D5%BE%D5%B8%D6%80%D5%B6%D5%A5%D6%80" title="Պլանկի միավորներ – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Պլանկի միավորներ" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Satuan_Planck" title="Satuan Planck – 印度尼西亚语" lang="id" hreflang="id" data-title="Satuan Planck" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Unit%C3%A0_di_misura_di_Planck" title="Unità di misura di Planck – 意大利语" lang="it" hreflang="it" data-title="Unità di misura di Planck" data-language-autonym="Italiano" data-language-local-name="意大利语" 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/%E3%83%97%E3%83%A9%E3%83%B3%E3%82%AF%E5%8D%98%E4%BD%8D%E7%B3%BB" title="プランク単位系 – 日语" lang="ja" hreflang="ja" data-title="プランク単位系" data-language-autonym="日本語" data-language-local-name="日语" 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%9E%E1%83%9A%E1%83%90%E1%83%9C%E1%83%99%E1%83%98%E1%83%A1_%E1%83%94%E1%83%A0%E1%83%97%E1%83%94%E1%83%A3%E1%83%9A%E1%83%94%E1%83%91%E1%83%98" title="პლანკის ერთეულები – 格鲁吉亚语" lang="ka" hreflang="ka" data-title="პლანკის ერთეულები" data-language-autonym="ქართული" data-language-local-name="格鲁吉亚语" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%8C%EB%9E%91%ED%81%AC_%EB%8B%A8%EC%9C%84%EA%B3%84" title="플랑크 단위계 – 韩语" lang="ko" hreflang="ko" data-title="플랑크 단위계" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Unitates_Planckianae" title="Unitates Planckianae – 拉丁语" lang="la" hreflang="la" data-title="Unitates Planckianae" data-language-autonym="Latina" data-language-local-name="拉丁语" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%B8%D0%B9%D0%BD_%D0%BD%D1%8D%D0%B3%D0%B6" title="Планкийн нэгж – 蒙古语" lang="mn" hreflang="mn" data-title="Планкийн нэгж" data-language-autonym="Монгол" data-language-local-name="蒙古语" 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%AA%E0%A5%8D%E0%A4%B2%E0%A4%BE%E0%A4%82%E0%A4%95_%E0%A4%8F%E0%A4%95%E0%A4%95%E0%A5%87" title="प्लांक एकके – 马拉地语" lang="mr" hreflang="mr" data-title="प्लांक एकके" data-language-autonym="मराठी" data-language-local-name="马拉地语" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Planck-eenheden" title="Planck-eenheden – 荷兰语" lang="nl" hreflang="nl" data-title="Planck-eenheden" data-language-autonym="Nederlands" data-language-local-name="荷兰语" 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/Planck-einingar" title="Planck-einingar – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Planck-einingar" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A8%B2%E0%A9%88%E0%A8%82%E0%A8%95_%E0%A8%AF%E0%A9%82%E0%A8%A8%E0%A8%BF%E0%A8%9F%E0%A8%BE%E0%A8%82" title="ਪਲੈਂਕ ਯੂਨਿਟਾਂ – 旁遮普语" lang="pa" hreflang="pa" data-title="ਪਲੈਂਕ ਯੂਨਿਟਾਂ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="旁遮普语" 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/Jednostki_Plancka" title="Jednostki Plancka – 波兰语" lang="pl" hreflang="pl" data-title="Jednostki Plancka" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Unidades_de_Planck" title="Unidades de Planck – 葡萄牙语" lang="pt" hreflang="pt" data-title="Unidades de Planck" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D0%B5_%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D1%8B" title="Планковские единицы – 俄语" lang="ru" hreflang="ru" data-title="Планковские единицы" data-language-autonym="Русский" data-language-local-name="俄语" 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/Unitati_di_misura_di_Planck" title="Unitati di misura di Planck – 西西里语" lang="scn" hreflang="scn" data-title="Unitati di misura di Planck" data-language-autonym="Sicilianu" data-language-local-name="西西里语" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prirodne_jedinice" title="Prirodne jedinice – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Prirodne jedinice" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Planck_units" title="Planck units – Simple English" lang="en-simple" hreflang="en-simple" data-title="Planck units" 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 mw-list-item"><a href="https://sk.wikipedia.org/wiki/Planckove_jednotky" title="Planckove jednotky – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Planckove jednotky" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" 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/Planckov_sistem_enot" title="Planckov sistem enot – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Planckov sistem enot" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%BD%D0%B5_%D1%98%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D0%B5" title="Природне јединице – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Природне јединице" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Planckenheter" title="Planckenheter – 瑞典语" lang="sv" hreflang="sv" data-title="Planckenheter" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Planck_birimleri" title="Planck birimleri – 土耳其语" lang="tr" hreflang="tr" data-title="Planck birimleri" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Plank_ber%C3%A4mlekl%C3%A4re" title="Plank berämlekläre – 鞑靼语" lang="tt" hreflang="tt" data-title="Plank berämlekläre" data-language-autonym="Татарча / tatarça" data-language-local-name="鞑靼语" 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%9F%D0%BB%D0%B0%D0%BD%D0%BA%D1%96%D0%B2%D1%81%D1%8C%D0%BA%D1%96_%D0%BE%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D1%96" title="Планківські одиниці – 乌克兰语" lang="uk" hreflang="uk" data-title="Планківські одиниці" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tabiiy_birliklar_tizimi" title="Tabiiy birliklar tizimi – 乌兹别克语" lang="uz" hreflang="uz" data-title="Tabiiy birliklar tizimi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="乌兹别克语" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_th%E1%BB%91ng_%C4%91o_l%C6%B0%E1%BB%9Dng_Planck" title="Hệ thống đo lường Planck – 越南语" lang="vi" hreflang="vi" data-title="Hệ thống đo lường Planck" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D" title="普朗克單位 – 吴语" lang="wuu" hreflang="wuu" data-title="普朗克單位" data-language-autonym="吴语" data-language-local-name="吴语" class="interlanguage-link-target"><span>吴语</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/Q468999#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</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="命名空间"> <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/%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="vector-tab-noicon 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class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-noteTA-5ff6fd68" class="mw-indicator"><div class="mw-parser-output"><span class="skin-invert" typeof="mw:File"><span title="本页使用了标题或全文手工转换"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></span></span></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</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="zh" dir="ltr"><div id="noteTA-5ff6fd68" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Physics"></div></div></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Max_planck.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Max_planck.jpg/200px-Max_planck.jpg" decoding="async" width="200" height="297" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/d/d7/Max_planck.jpg 1.5x" data-file-width="236" data-file-height="351" /></a><figcaption>馬克斯·普朗克</figcaption></figure> <p><b>普朗克單位制</b>是一種<a href="/wiki/%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D" class="mw-redirect" title="計量單位">計量單位</a>制度，由德國物理學家<a href="/wiki/%E9%A6%AC%E5%85%8B%E6%96%AF%C2%B7%E6%99%AE%E6%9C%97%E5%85%8B" class="mw-redirect" title="馬克斯·普朗克">馬克斯·普朗克</a>最先提出，因此命名為普朗克單位制。這種單位制是<a href="/wiki/%E8%87%AA%E7%84%B6%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="自然單位制">自然單位制</a>的一個實例，將某些基礎物理常數的值定為1，這些基礎物理常數是： </p> <ul><li>真空<a href="/wiki/%E5%85%89%E9%80%9F" title="光速">光速</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></li> <li><a href="/wiki/%E8%90%AC%E6%9C%89%E5%BC%95%E5%8A%9B%E5%B8%B8%E6%95%B8" class="mw-redirect" title="萬有引力常數">萬有引力常數</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 G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> <ul><li>普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a>將<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 4\pi G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4\pi G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3825cacab6911a8850ce596ccb20ec38c355bfc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.321ex; height:2.176ex;" alt="{\displaystyle 4\pi G}"></span>定為1，普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a>將<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span>定為1</li></ul></li> <li><a href="/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%E5%B8%B8%E6%95%B8" class="mw-redirect" title="狄拉克常數">狄拉克常數</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 \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }"></span></li> <li><a href="/wiki/%E7%9C%9F%E7%A9%BA%E7%94%B5%E5%AE%B9%E7%8E%87" title="真空电容率">真空電容率</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 \epsilon _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2cae6289b0fe626d1f9472a3416ac73e87bc5a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.998ex; height:2.009ex;" alt="{\displaystyle \epsilon _{0}}"></span> <ul><li>普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a>將<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 \epsilon _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2cae6289b0fe626d1f9472a3416ac73e87bc5a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.998ex; height:2.009ex;" alt="{\displaystyle \epsilon _{0}}"></span>定為1，普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a>將<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 4\pi \epsilon _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4\pi \epsilon _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7880bb558126aa4f4743737d2c425acb7b5179e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.493ex; height:2.509ex;" alt="{\displaystyle 4\pi \epsilon _{0}}"></span>定為1</li></ul></li> <li><a href="/wiki/%E6%B3%A2%E8%8C%B2%E6%9B%BC%E5%B8%B8%E6%95%B8" title="波茲曼常數">波茲曼常數</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 k_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70f38f7b73e53fd7b5d9ca64bec3a1438cc0eade" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.691ex; height:2.509ex;" alt="{\displaystyle k_{B}}"></span></li></ul> <p>上述每一個常數都至少出現於一個基本物理理論：<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </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/a26f20ddaaf267143f0e92c1648a49fbe5687e6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,\!}"></span>在<a href="/wiki/%E7%8B%B9%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" class="mw-redirect" title="狹義相對論">狹義相對論</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 G\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5360c2263beb7cabb600946e9d8d2f34f6eb17e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.214ex; height:2.176ex;" alt="{\displaystyle G\,\!}"></span>在<a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a>與<a href="/wiki/%E7%89%9B%E9%A0%93" class="mw-redirect" title="牛頓">牛頓</a>的<a href="/wiki/%E8%90%AC%E6%9C%89%E5%BC%95%E5%8A%9B%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="萬有引力定律">萬有引力定律</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 \hbar \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/174e8deb8ef7e3b864dbd370e987398aa1e3e4fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.694ex; height:2.176ex;" alt="{\displaystyle \hbar \,\!}"></span>在<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" class="mw-redirect" title="量子力學">量子力學</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 \epsilon _{0}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/320886200372fe77d6fea272c34564def3d8cca9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.385ex; height:2.009ex;" alt="{\displaystyle \epsilon _{0}\,\!}"></span>在<a href="/wiki/%E9%9D%9C%E9%9B%BB%E5%AD%B8" title="靜電學">靜電學</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 k_{B}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e1fbc4b2e5680bf7b1625249a55537129737706" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.078ex; height:2.509ex;" alt="{\displaystyle k_{B}\,\!}"></span>在<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%B8" class="mw-redirect" title="統計力學">統計力學</a>與<a href="/wiki/%E7%86%B1%E5%8A%9B%E5%AD%B8" class="mw-redirect" title="熱力學">熱力學</a>。实际上，以上的五个常数在許多物理定律的代數表達式中多次出现，因此引入普朗克單位制可以将這些代數表達式简化，普朗克單位制也因此成为了理論物理學一個非常有用的工具。在統一理論方面的研究，特別如<a href="/wiki/%E9%87%8F%E5%AD%90%E9%87%8D%E5%8A%9B" class="mw-redirect" title="量子重力">量子重力學</a>中，普朗克單位制能夠給研究者一點大概的提示。 </p><p>普朗克單位制是一種獨特的自然單位制，因為普朗克單位制不是以任何<a href="/w/index.php?title=%E5%8E%9F%E5%99%A8&action=edit&redlink=1" class="new" title="原器（页面不存在）">原器</a>、<a href="/wiki/%E4%BA%BA%E9%AB%94" class="mw-redirect" title="人體">人體</a>的性質（例如：<a href="/wiki/%E5%8F%91%E5%85%89%E5%BC%BA%E5%BA%A6" title="发光强度">發光強度</a>（<a href="/wiki/%E7%87%AD%E5%85%89" class="mw-redirect" title="燭光">燭光</a>）、<a href="/wiki/%E5%85%89%E9%80%9A%E9%87%8F" title="光通量">光通量</a>（<a href="/wiki/%E6%B5%81%E6%98%8E" title="流明">流明</a>）、<a href="/wiki/%E7%AD%89%E6%95%88%E5%8A%91%E9%87%8F" title="等效劑量">等效劑量</a>（<a href="/wiki/%E8%A5%BF%E5%BC%97" title="西弗">西弗</a>））、<a href="/wiki/%E5%9C%B0%E7%90%83" title="地球">地球</a>或<a href="/wiki/%E5%AE%87%E5%AE%99" title="宇宙">宇宙</a>的性質（例如：<a href="/wiki/%E6%A8%99%E6%BA%96%E9%87%8D%E5%8A%9B" title="標準重力">標準重力</a>、<a href="/wiki/%E6%A8%99%E6%BA%96%E5%A4%A7%E6%B0%A3%E5%A3%93" class="mw-redirect" title="標準大氣壓">標準大氣壓</a>、<a href="/wiki/%E5%93%88%E4%BC%AF%E5%B8%B8%E6%95%B8" class="mw-redirect" title="哈伯常數">哈伯常數</a>）、特定<a href="/wiki/%E7%89%A9%E8%B3%AA" class="mw-redirect" title="物質">物質</a>的性質（例如：<a href="/wiki/%E6%B0%B4" title="水">水</a>的<a href="/wiki/%E7%86%94%E9%BB%9E" class="mw-redirect" title="熔點">熔點</a>、<a href="/wiki/%E6%B0%B4" title="水">水</a>的<a href="/wiki/%E5%AF%86%E5%BA%A6" title="密度">密度</a>、<a href="/wiki/%E6%B0%B4" title="水">水</a>的<a href="/wiki/%E6%AF%94%E7%86%B1" class="mw-redirect" title="比熱">比熱</a>）、或甚至<a href="/wiki/%E5%9F%BA%E6%9C%AC%E7%B2%92%E5%AD%90" title="基本粒子">基本粒子</a>的性質（例如：<a href="/wiki/%E5%9F%BA%E6%9C%AC%E9%9B%BB%E8%8D%B7" class="mw-redirect" title="基本電荷">基本電荷</a>、<a href="/wiki/%E9%9B%BB%E5%AD%90%E8%B3%AA%E9%87%8F" title="電子質量">電子質量</a>、<a href="/wiki/%E8%B3%AA%E5%AD%90%E8%B3%AA%E9%87%8F" class="mw-redirect" title="質子質量">質子質量</a>）來定義的。普朗克單位制只以<a href="/wiki/%E8%87%AA%E7%94%B1%E7%A9%BA%E9%96%93" title="自由空間">自由空間</a>的性質（例如：<a href="/wiki/%E7%9C%9F%E7%A9%BA%E5%85%89%E9%80%9F" class="mw-redirect" title="真空光速">真空光速</a>、<a href="/wiki/%E8%87%AA%E7%94%B1%E7%A9%BA%E9%96%93%E9%98%BB%E6%8A%97" title="自由空間阻抗">自由空間阻抗</a>、<a href="/wiki/%E6%B3%A2%E8%8C%B2%E6%9B%BC%E5%B8%B8%E6%95%B8" title="波茲曼常數">波茲曼常數</a>）來定義及作為歸一化對象。 </p><p>有些學者認為普朗克單位制比其它自然單位制更為自然。例如，有些其它自然單位制使用<a href="/wiki/%E9%9B%BB%E5%AD%90%E8%B3%AA%E9%87%8F" title="電子質量">電子質量</a>為基本單位。但是<a href="/wiki/%E9%9B%BB%E5%AD%90" class="mw-redirect" title="電子">電子</a>只是許多種已知具有質量的基本粒子之一。這些粒子的質量都不一樣。在基礎物理學裏，並沒有任何絕對因素，促使選擇電子質量為基本單位，而不選擇其它粒子質量。 </p><p><a href="/wiki/%E7%89%A9%E8%B4%A8%E7%9A%84%E9%87%8F" title="物质的量">物質的量</a>（<a href="/wiki/%E8%8E%AB%E8%80%B3" class="mw-redirect" title="莫耳">莫耳</a>）的自然單位就用「個」（一個就是1）就可以了，不必用到「莫耳」，而<a href="/wiki/%E5%8F%91%E5%85%89%E5%BC%BA%E5%BA%A6" title="发光强度">發光強度</a>（<a href="/wiki/%E7%87%AD%E5%85%89" class="mw-redirect" title="燭光">燭光</a>）的自然單位就用「<a href="/wiki/%E7%93%A6%E7%89%B9" title="瓦特">瓦特</a>/<a href="/wiki/%E7%AB%8B%E5%BC%B3" class="mw-redirect" title="立弳">立弳</a>」就可以了，因為這兩者的比值僅為<a href="/wiki/%E7%99%BC%E5%85%89%E6%95%88%E7%8E%87" class="mw-redirect" title="發光效率">發光效率</a>，而發光效率是沒有單位因次的，就跟<a href="/wiki/%E8%A7%92%E5%BA%A6" class="mw-redirect" title="角度">角度</a>（<a href="/wiki/%E5%BC%B3" class="mw-redirect" title="弳">弳</a>）以及<a href="/wiki/%E7%B2%BE%E7%B4%B0%E7%B5%90%E6%A7%8B%E5%B8%B8%E6%95%B8" class="mw-redirect" title="精細結構常數">精細結構常數</a>一樣，另外電荷的部分，雖然SI制的基本單位是<a href="/wiki/%E9%9B%BB%E6%B5%81" class="mw-redirect" title="電流">電流</a>而非<a href="/wiki/%E9%9B%BB%E8%8D%B7" title="電荷">電荷</a>，但是實際上，電荷才是更基本的單位（就好比<a href="/wiki/%E9%87%8D%E5%8A%9B%E7%B1%B3%E5%88%B6" title="重力米制">重力米制</a>的基本單位是<a href="/wiki/%E5%8A%9B" title="力">力</a>而非<a href="/wiki/%E8%B3%AA%E9%87%8F" class="mw-redirect" title="質量">質量</a>，但是實際上，質量才是更基本的單位）。 </p><p>（或者你也可以這樣說：普朗克單位制也將<a href="/wiki/%E4%BA%9E%E4%BD%9B%E5%8A%A0%E5%8E%A5%E5%B8%B8%E6%95%B8" class="mw-redirect" title="亞佛加厥常數">亞佛加厥常數</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 N_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fa9233ef6a6a2c0576dbf65490ddb8307fde494" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.331ex; height:2.509ex;" alt="{\displaystyle N_{A}}"></span>定為1，從而用「個」（一個就是1）作為<a href="/wiki/%E7%89%A9%E8%B4%A8%E7%9A%84%E9%87%8F" title="物质的量">物質的量</a>的單位（對應<a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>的<a href="/wiki/%E8%8E%AB%E8%80%B3" class="mw-redirect" title="莫耳">莫耳</a>），並且普朗克單位制不考慮<a href="/wiki/%E5%8F%91%E5%85%89%E5%BC%BA%E5%BA%A6" title="发光强度">發光強度</a>（對應<a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>的<a href="/wiki/%E7%87%AD%E5%85%89" class="mw-redirect" title="燭光">燭光</a>），僅以<a href="/wiki/%E8%BE%90%E5%B0%84%E5%BC%BA%E5%BA%A6" title="辐射强度">輻射強度</a>（對應<a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>的「<a href="/wiki/%E7%93%A6%E7%89%B9" title="瓦特">瓦特</a>每<a href="/wiki/%E7%AB%8B%E5%BC%B3" class="mw-redirect" title="立弳">立弳</a>」來表示，就好比普朗克單位制不考慮<a href="/wiki/%E7%AD%89%E6%95%88%E5%8A%91%E9%87%8F" title="等效劑量">等效劑量</a>（對應<a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>的<a href="/wiki/%E8%A5%BF%E5%BC%97" title="西弗">西弗</a>），僅以<a href="/wiki/%E8%BC%BB%E5%B0%84%E5%8A%91%E9%87%8F" title="輻射劑量">輻射劑量</a>（對應<a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>的<a href="/wiki/%E6%88%88%E9%9B%B7" class="mw-redirect" title="戈雷">戈雷</a>）來表示，在普朗克單位制中，<a href="/wiki/%E7%99%BC%E5%85%89%E6%95%88%E7%8E%87" class="mw-redirect" title="發光效率">發光效率</a>屬於無因次量，就跟<a href="/wiki/%E5%BC%A7%E5%BA%A6" title="弧度">弧度</a>和<a href="/wiki/%E7%AB%8B%E5%BC%B3" class="mw-redirect" title="立弳">立弳</a>一樣） </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="基本普朗克單位"><span id=".E5.9F.BA.E6.9C.AC.E6.99.AE.E6.9C.97.E5.85.8B.E5.96.AE.E4.BD.8D"></span>基本普朗克單位</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=1" title="编辑章节：基本普朗克單位"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>每一個單位制都有一組基本單位。（在<a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>裏，<a href="/wiki/%E9%95%B7%E5%BA%A6" class="mw-redirect" title="長度">長度</a>的基本單位是<a href="/wiki/%E5%85%AC%E5%B0%BA" class="mw-redirect" title="公尺">公尺</a>，<a href="/wiki/%E6%99%82%E9%96%93" class="mw-redirect" title="時間">時間</a>的基本單位是<a href="/wiki/%E7%A7%92" title="秒">秒</a>，等等）在普朗克單位制裏，長度的基本單位是<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%95%B7%E5%BA%A6" title="普朗克長度">普朗克長度</a>，時間的基本單位是<a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E6%99%82%E9%96%93" title="普朗克時間">普朗克時間</a>，等等。這些單位都是由表1的五個基礎物理常數衍生的。表2展示出這些基本普朗克單位。 </p> <table class="wikitable" style="margin: 1em auto 1em auto; background-color: #ffffff"> <caption><b>表1：基礎物理常數</b> </caption> <tbody><tr> <th>常數 </th> <th>符號 </th> <th>因次 </th> <th>國際單位等值與不確定度<sup id="cite_ref-CODATA_1-0" class="reference"><a href="#cite_note-CODATA-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <td>真空<a href="/wiki/%E5%85%89%E9%80%9F" title="光速">光速</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </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/a26f20ddaaf267143f0e92c1648a49fbe5687e6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,\!}"></span> </td> <td>LT<sup>−1</sup> </td> <td><span class="nowrap">299 792 458 <a href="/wiki/%E5%85%AC%E5%B0%BA" class="mw-redirect" title="公尺">m</a> s<sup>−1</sup> </span> </td></tr> <tr> <td><a href="/wiki/%E8%90%AC%E6%9C%89%E5%BC%95%E5%8A%9B%E5%B8%B8%E6%95%B8" class="mw-redirect" title="萬有引力常數">萬有引力常數</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5360c2263beb7cabb600946e9d8d2f34f6eb17e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.214ex; height:2.176ex;" alt="{\displaystyle G\,\!}"></span> </td> <td>L<sup>3</sup>M<sup>−1</sup>T<sup>−2</sup> </td> <td><span class="nowrap">6.674 30(15)×10<sup>−11</sup> m<sup>3</sup> <a href="/wiki/%E5%85%AC%E6%96%A4" class="mw-redirect" title="公斤">kg</a><sup>−1</sup> s<sup>−2</sup></span> </td></tr> <tr> <td><a href="/wiki/%E7%BA%A6%E5%8C%96%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B0" class="mw-redirect" title="约化普朗克常数">約化普朗克常數</a> </td> <td><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 \hbar \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/174e8deb8ef7e3b864dbd370e987398aa1e3e4fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.694ex; height:2.176ex;" alt="{\displaystyle \hbar \,\!}"></span> </td> <td>L<sup>2</sup>MT<sup>−1</sup> </td> <td><span class="nowrap">1.054 571 817…×10<sup>−34</sup> <a href="/wiki/%E7%84%A6%E8%80%B3" title="焦耳">J</a> s</span> </td></tr> <tr> <td><a href="/wiki/%E7%9C%9F%E7%A9%BA%E7%94%B5%E5%AE%B9%E7%8E%87" title="真空电容率">真空電容率</a> </td> <td><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 \epsilon _{0}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/320886200372fe77d6fea272c34564def3d8cca9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.385ex; height:2.009ex;" alt="{\displaystyle \epsilon _{0}\,\!}"></span> </td> <td>L<sup>−3</sup>M<sup>−1</sup>T<sup>2</sup>Q<sup>2</sup> </td> <td><span class="nowrap">8.854 187 8128(13)×10<sup>−12</sup> <a href="/wiki/%E6%B3%95%E6%8B%89" title="法拉">F</a>/m</span> </td></tr> <tr> <td><a href="/wiki/%E6%B3%A2%E8%8C%B2%E6%9B%BC%E5%B8%B8%E6%95%B8" title="波茲曼常數">波茲曼常數</a> </td> <td><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 k_{B}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e1fbc4b2e5680bf7b1625249a55537129737706" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.078ex; height:2.509ex;" alt="{\displaystyle k_{B}\,\!}"></span> </td> <td>L<sup>2</sup>MT<sup>−2</sup>Θ<sup>−1</sup> </td> <td><span class="nowrap">1.380 649×10<sup>−23</sup> J <a href="/wiki/%E7%B5%95%E5%B0%8D%E6%BA%AB%E5%BA%A6" class="mw-redirect" title="絕對溫度">K</a><sup>−1</sup></span> </td></tr></tbody></table> <p>字鍵：<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 \mathrm {L} \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {L} \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16b3825720f13de25b2d022f7c647f4c9f1252c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.84ex; height:2.176ex;" alt="{\displaystyle \mathrm {L} \,\!}"></span> = <a href="/wiki/%E9%95%B7%E5%BA%A6" class="mw-redirect" title="長度">長度</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 \mathrm {T} \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {T} \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56dbcc5e593a30ec4c4623619703f3fd4c3ec2ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.065ex; height:2.176ex;" alt="{\displaystyle \mathrm {T} \,\!}"></span> = <a href="/wiki/%E6%99%82%E9%96%93" class="mw-redirect" title="時間">時間</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 \mathrm {M} \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {M} \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/935a9963e925e3e7fb51f5427daaff190b3f5e05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.518ex; height:2.176ex;" alt="{\displaystyle \mathrm {M} \,\!}"></span> = <a href="/wiki/%E8%B3%AA%E9%87%8F" class="mw-redirect" title="質量">質量</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 \mathrm {Q} \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Q</mi> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Q} \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa20acb4a4e5f9f40ea21910c29d69b99b7ec653" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.195ex; height:2.509ex;" alt="{\displaystyle \mathrm {Q} \,\!}"></span> = <a href="/wiki/%E9%9B%BB%E8%8D%B7" title="電荷">電荷</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 \Theta \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Θ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Theta \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f642027f8865ad6d85aaae2241490440cb9f87f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.195ex; height:2.176ex;" alt="{\displaystyle \Theta \,\!}"></span> = <a href="/wiki/%E6%BA%AB%E5%BA%A6" class="mw-redirect" title="溫度">溫度</a>。因為定義的關係，光速、約化普朗克常數與波茲曼常數的數值是精確值，不存在誤差（在2019年以前，約化普朗克常數與波茲曼常數的數值還不是精確值，反倒真空電容率的數值是精確值，只有光速從1983年以來一直都是精確值，見<a href="/wiki/2019%E5%B9%B4%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6%E5%9F%BA%E6%9C%AC%E5%96%AE%E4%BD%8D%E9%87%8D%E6%96%B0%E5%AE%9A%E7%BE%A9" title="2019年國際單位制基本單位重新定義">2019年國際單位制基本單位重新定義</a>）。 </p> <table class="wikitable" style="margin: 1em auto 1em auto; background-color: #ffffff"> <caption><b>表2：基本普朗克單位</b> </caption> <tbody><tr> <th rowspan="2">單位名稱 </th> <th rowspan="2">因次 </th> <th colspan="2">表達式 </th> <th colspan="2"><a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>等值 </th></tr> <tr> <th>普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a> </th> <th>普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a> </th> <th>普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a> </th> <th>普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a> </th></tr> <tr style="text-align:left;"> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%95%B7%E5%BA%A6" title="普朗克長度">普朗克長度</a> </td> <td><a href="/wiki/%E9%95%B7%E5%BA%A6" class="mw-redirect" title="長度">長度</a> (L) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{\text{P}}={\sqrt {\frac {4\pi \hbar G}{c^{3}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{\text{P}}={\sqrt {\frac {4\pi \hbar G}{c^{3}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5606dd2c8b83566ab5fd5f37bbd34b72556be4de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.931ex; height:6.343ex;" alt="{\displaystyle l_{\text{P}}={\sqrt {\frac {4\pi \hbar G}{c^{3}}}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{\text{P}}={\sqrt {\frac {\hbar G}{c^{3}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{\text{P}}={\sqrt {\frac {\hbar G}{c^{3}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9d60a28c192c5ad0e6e972ebc6432f9e370206e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.436ex; height:6.343ex;" alt="{\displaystyle l_{\text{P}}={\sqrt {\frac {\hbar G}{c^{3}}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6965572938000000000♠</span>5.729<span style="margin-left:.25em;">38</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−35</sup></span> <a href="/wiki/%E5%85%AC%E5%B0%BA" class="mw-redirect" title="公尺">m</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6965161623000000000♠</span>1.616<span style="margin-left:.25em;">23</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−35</sup></span> <a href="/wiki/%E5%85%AC%E5%B0%BA" class="mw-redirect" title="公尺">m</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E8%B3%AA%E9%87%8F" title="普朗克質量">普朗克質量</a> </td> <td><a href="/wiki/%E8%B3%AA%E9%87%8F" class="mw-redirect" title="質量">質量</a> (M) </td> <td><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_{\text{P}}={\sqrt {\frac {\hbar c}{4\pi G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <mi>c</mi> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\text{P}}={\sqrt {\frac {\hbar c}{4\pi G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1a5cef14e3a6c30a0b49c6e452d2d1fd0038bbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.971ex; height:6.176ex;" alt="{\displaystyle m_{\text{P}}={\sqrt {\frac {\hbar c}{4\pi G}}}}"></span> </td> <td><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_{\text{P}}={\sqrt {\frac {\hbar c}{G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <mi>c</mi> </mrow> <mi>G</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\text{P}}={\sqrt {\frac {\hbar c}{G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6afc1bf2ad649a02f26ceb8ab6db924e0258e20f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.964ex; height:6.176ex;" alt="{\displaystyle m_{\text{P}}={\sqrt {\frac {\hbar c}{G}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6991613971000000000♠</span>6.139<span style="margin-left:.25em;">71</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−9</sup></span> <a href="/wiki/%E5%85%AC%E6%96%A4" class="mw-redirect" title="公斤">kg</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6992217647000000000♠</span>2.176<span style="margin-left:.25em;">47</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−8</sup></span> <a href="/wiki/%E5%85%AC%E6%96%A4" class="mw-redirect" title="公斤">kg</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E6%99%82%E9%96%93" title="普朗克時間">普朗克時間</a> </td> <td><a href="/wiki/%E6%99%82%E9%96%93" class="mw-redirect" title="時間">時間</a> (T) </td> <td><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_{\text{P}}={\sqrt {\frac {4\pi \hbar G}{c^{5}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{\text{P}}={\sqrt {\frac {4\pi \hbar G}{c^{5}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba9d5e0318ca54b763bbc6b0418d8048f518fdfc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.077ex; height:6.343ex;" alt="{\displaystyle t_{\text{P}}={\sqrt {\frac {4\pi \hbar G}{c^{5}}}}}"></span> </td> <td><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_{\text{P}}={\sqrt {\frac {\hbar G}{c^{5}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{\text{P}}={\sqrt {\frac {\hbar G}{c^{5}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5126bc97b6a14509d7c1ea4b1e18513553fe10d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.583ex; height:6.343ex;" alt="{\displaystyle t_{\text{P}}={\sqrt {\frac {\hbar G}{c^{5}}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6957191112000000000♠</span>1.911<span style="margin-left:.25em;">12</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−43</sup></span> <a href="/wiki/%E7%A7%92" title="秒">s</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6956539115999999999♠</span>5.391<span style="margin-left:.25em;">16</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−44</sup></span> <a href="/wiki/%E7%A7%92" title="秒">s</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%9B%BB%E8%8D%B7" title="普朗克電荷">普朗克電荷</a> </td> <td><a href="/wiki/%E9%9B%BB%E8%8D%B7" title="電荷">電荷</a> (Q) </td> <td><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 q_{\text{P}}={\sqrt {\hbar c\epsilon _{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi class="MJX-variant">ℏ</mi> <mi>c</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{\text{P}}={\sqrt {\hbar c\epsilon _{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/127af3e73484f9637b756d8434fb3af0643b4a85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:12.122ex; height:3.509ex;" alt="{\displaystyle q_{\text{P}}={\sqrt {\hbar c\epsilon _{0}}}}"></span> </td> <td><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 q_{\text{P}}={\sqrt {4\pi \hbar c\epsilon _{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>4</mn> <mi>π</mi> <mi class="MJX-variant">ℏ</mi> <mi>c</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{\text{P}}={\sqrt {4\pi \hbar c\epsilon _{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3461fb5096b96cfc3fd0f86c109956417b195225" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:14.617ex; height:3.509ex;" alt="{\displaystyle q_{\text{P}}={\sqrt {4\pi \hbar c\epsilon _{0}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6981529081999999999♠</span>5.290<span style="margin-left:.25em;">82</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−19</sup></span> <a href="/wiki/%E5%BA%AB%E4%BE%96" class="mw-redirect" title="庫侖">C</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6982187555000000000♠</span>1.875<span style="margin-left:.25em;">55</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−18</sup></span> <a href="/wiki/%E5%BA%AB%E4%BE%96" class="mw-redirect" title="庫侖">C</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E6%BA%AB%E5%BA%A6" title="普朗克溫度">普朗克溫度</a> </td> <td><a href="/wiki/%E6%BA%AB%E5%BA%A6" class="mw-redirect" title="溫度">溫度</a> (Θ) </td> <td><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_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{4\pi G{k_{\text{B}}}^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{4\pi G{k_{\text{B}}}^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96b303754b11f73dd9472a4ec9ee47546086d65b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:16.95ex; height:7.676ex;" alt="{\displaystyle T_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{4\pi G{k_{\text{B}}}^{2}}}}}"></span> </td> <td><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_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{G{k_{\text{B}}}^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mi>G</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{G{k_{\text{B}}}^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c6293d9b3b7be7df65da87c725a5d6badd25932" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:14.455ex; height:7.676ex;" alt="{\displaystyle T_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{G{k_{\text{B}}}^{2}}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7031399674000000000♠</span>3.996<span style="margin-left:.25em;">74</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>31</sup></span> <a href="/wiki/%E5%85%8B%E8%80%B3%E6%96%87" class="mw-redirect" title="克耳文">K</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7032141681000000000♠</span>1.416<span style="margin-left:.25em;">81</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>32</sup></span> <a href="/wiki/%E5%85%8B%E8%80%B3%E6%96%87" class="mw-redirect" title="克耳文">K</a> </td></tr></tbody></table> <p>使用普朗克單位後，表1的五個基礎物理常數的數值都約化為1，因此表2的普朗克長度，普朗克質量，普朗克時間，普朗克電荷，與普朗克溫度這些計量也都約化為1。這可以無因次地表達為 </p><p>（普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a>）因為<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=4\pi G=\hbar =\epsilon _{0}=k_{B}=1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mn>4</mn> <mi>π</mi> <mi>G</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=4\pi G=\hbar =\epsilon _{0}=k_{B}=1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7801cf0da983081aab6165f9476773685d9521f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:28.366ex; height:2.509ex;" alt="{\displaystyle c=4\pi G=\hbar =\epsilon _{0}=k_{B}=1\,\!}"></span>，所以<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{\text{P}}=m_{\text{P}}=t_{\text{P}}=q_{\text{P}}=T_{\text{P}}=1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{\text{P}}=m_{\text{P}}=t_{\text{P}}=q_{\text{P}}=T_{\text{P}}=1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d2c05fd4389240cb7ffd737769256a67c4bb85e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:29.767ex; height:2.509ex;" alt="{\displaystyle l_{\text{P}}=m_{\text{P}}=t_{\text{P}}=q_{\text{P}}=T_{\text{P}}=1\,\!}"></span>。 </p><p>（普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a>）因為<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=G=\hbar ={\frac {1}{4\pi \epsilon _{0}}}=k_{B}=1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mi>G</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=G=\hbar ={\frac {1}{4\pi \epsilon _{0}}}=k_{B}=1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e492fc38cf5966a3eaa18430e396e9c25dc5cbde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:29.202ex; height:5.676ex;" alt="{\displaystyle c=G=\hbar ={\frac {1}{4\pi \epsilon _{0}}}=k_{B}=1\,\!}"></span>，所以<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{\text{P}}=m_{\text{P}}=t_{\text{P}}=q_{\text{P}}=T_{\text{P}}=1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{\text{P}}=m_{\text{P}}=t_{\text{P}}=q_{\text{P}}=T_{\text{P}}=1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d2c05fd4389240cb7ffd737769256a67c4bb85e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:29.767ex; height:2.509ex;" alt="{\displaystyle l_{\text{P}}=m_{\text{P}}=t_{\text{P}}=q_{\text{P}}=T_{\text{P}}=1\,\!}"></span>。 </p> <div class="mw-heading mw-heading2"><h2 id="衍生普朗克單位"><span id=".E8.A1.8D.E7.94.9F.E6.99.AE.E6.9C.97.E5.85.8B.E5.96.AE.E4.BD.8D"></span>衍生普朗克單位</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=2" title="编辑章节：衍生普朗克單位"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在任何單位系統裏，許多物理量的單位是由基本單位衍生的。表3展示了一些在理論物理研究裏常見的衍生普朗克單位。實際上，大多數普朗克單位不是太大，就是太小，並不適合於實驗或任何實際用途。 </p> <table class="wikitable" style="margin: 1em auto 1em auto; background-color: #ffffff"> <caption><b>表3：衍生普朗克單位</b> </caption> <tbody><tr> <th rowspan="2">單位名稱 </th> <th rowspan="2">因次 </th> <th colspan="2">表達式 </th> <th colspan="2"><a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>等值 </th></tr> <tr> <th>普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a> </th> <th>普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a> </th> <th>普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a> </th> <th>普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a> </th></tr> <tr align="left"> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%9D%A2%E7%A9%8D" class="mw-redirect" title="普朗克面積">普朗克面積</a> </td> <td><a href="/wiki/%E9%9D%A2%E7%A9%8D" class="mw-redirect" title="面積">面積</a>（L<sup>2</sup>） </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\text{P}}=l_{\text{P}}^{2}={\frac {4\pi \hbar G}{c^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msubsup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\text{P}}=l_{\text{P}}^{2}={\frac {4\pi \hbar G}{c^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a10efbe783913350927416aae06ce48baf36a58d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.8ex; height:5.676ex;" alt="{\displaystyle A_{\text{P}}=l_{\text{P}}^{2}={\frac {4\pi \hbar G}{c^{3}}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\text{P}}=l_{\text{P}}^{2}={\frac {\hbar G}{c^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msubsup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\text{P}}=l_{\text{P}}^{2}={\frac {\hbar G}{c^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc26a5cc95198923795188c017a476f4c3e39829" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.306ex; height:5.676ex;" alt="{\displaystyle A_{\text{P}}=l_{\text{P}}^{2}={\frac {\hbar G}{c^{3}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6931328258000000000♠</span>3.282<span style="margin-left:.25em;">58</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−69</sup></span> <a href="/wiki/%E5%B9%B3%E6%96%B9%E5%85%AC%E5%B0%BA" class="mw-redirect" title="平方公尺">m<sup>2</sup></a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">6930261220000000000♠</span>2.612<span style="margin-left:.25em;">20</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−70</sup></span> <a href="/wiki/%E5%B9%B3%E6%96%B9%E5%85%AC%E5%B0%BA" class="mw-redirect" title="平方公尺">m<sup>2</sup></a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%8B%95%E9%87%8F" title="普朗克動量">普朗克動量</a> </td> <td><a href="/wiki/%E5%8B%95%E9%87%8F" class="mw-redirect" title="動量">動量</a>（LMT<sup>−1</sup>） </td> <td><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_{\text{P}}=m_{\text{P}}v_{\text{P}}={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{4\pi G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{\text{P}}=m_{\text{P}}v_{\text{P}}={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{4\pi G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e08e0838a9803759ad46a409a12b81928695ce4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-left: -0.089ex; width:28.139ex; height:7.676ex;" alt="{\displaystyle p_{\text{P}}=m_{\text{P}}v_{\text{P}}={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{4\pi G}}}}"></span> </td> <td><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_{\text{P}}=m_{\text{P}}v_{\text{P}}={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mi>G</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{\text{P}}=m_{\text{P}}v_{\text{P}}={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b038a6089e7c8697aa64c9db4079953b18f8161f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-left: -0.089ex; width:27.185ex; height:7.676ex;" alt="{\displaystyle p_{\text{P}}=m_{\text{P}}v_{\text{P}}={\frac {\hbar }{l_{\text{P}}}}={\sqrt {\frac {\hbar c^{3}}{G}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7000184064000000000♠</span>1.840<span style="margin-left:.25em;">64</span></span> <a href="/w/index.php?title=%E7%89%9B%E9%A0%93-%E7%A7%92&action=edit&redlink=1" class="new" title="牛頓-秒（页面不存在）">N⋅s</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7000652489000000000♠</span>6.524<span style="margin-left:.25em;">89</span></span> <a href="/w/index.php?title=%E7%89%9B%E9%A0%93-%E7%A7%92&action=edit&redlink=1" class="new" title="牛頓-秒（页面不存在）">N⋅s</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E8%83%BD%E9%87%8F" title="普朗克能量">普朗克能量</a> </td> <td><a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能量</a>（L<sup>2</sup>MT<sup>−2</sup>） </td> <td><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_{\text{P}}=m_{\text{P}}v_{\text{P}}^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{4\pi G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{P}}=m_{\text{P}}v_{\text{P}}^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{4\pi G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/444aa92637d05cb14baf95d913afaba5b80dc1bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:28.741ex; height:7.676ex;" alt="{\displaystyle E_{\text{P}}=m_{\text{P}}v_{\text{P}}^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{4\pi G}}}}"></span> </td> <td><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_{\text{P}}=m_{\text{P}}v_{\text{P}}^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> <mi>G</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{P}}=m_{\text{P}}v_{\text{P}}^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cb89f039ebf7a372ef06f760ed1575d7471f697" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:27.788ex; height:7.676ex;" alt="{\displaystyle E_{\text{P}}=m_{\text{P}}v_{\text{P}}^{2}={\frac {\hbar }{t_{\text{P}}}}={\sqrt {\frac {\hbar c^{5}}{G}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7008551809000000000♠</span>5.518<span style="margin-left:.25em;">09</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>8</sup></span> <a href="/wiki/%E7%84%A6%E8%80%B3" title="焦耳">J</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7009195611000000000♠</span>1.956<span style="margin-left:.25em;">11</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>9</sup></span> <a href="/wiki/%E7%84%A6%E8%80%B3" title="焦耳">J</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%8A%9B" title="普朗克力">普朗克力</a> </td> <td><a href="/wiki/%E5%8A%9B" title="力">力</a>（LMT<sup>−2</sup>） </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\text{P}}=m_{\text{P}}a_{\text{P}}={\frac {p_{\text{P}}}{t_{\text{P}}}}={\frac {c^{4}}{4\pi G}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\text{P}}=m_{\text{P}}a_{\text{P}}={\frac {p_{\text{P}}}{t_{\text{P}}}}={\frac {c^{4}}{4\pi G}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e560e510d2d7b784d378caf051d3f40b5bc37b9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:26.629ex; height:6.009ex;" alt="{\displaystyle F_{\text{P}}=m_{\text{P}}a_{\text{P}}={\frac {p_{\text{P}}}{t_{\text{P}}}}={\frac {c^{4}}{4\pi G}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\text{P}}=m_{\text{P}}a_{\text{P}}={\frac {p_{\text{P}}}{t_{\text{P}}}}={\frac {c^{4}}{G}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>G</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\text{P}}=m_{\text{P}}a_{\text{P}}={\frac {p_{\text{P}}}{t_{\text{P}}}}={\frac {c^{4}}{G}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de6dc690944cedaa947a34d7dbd1585d10e77711" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:24.369ex; height:6.009ex;" alt="{\displaystyle F_{\text{P}}=m_{\text{P}}a_{\text{P}}={\frac {p_{\text{P}}}{t_{\text{P}}}}={\frac {c^{4}}{G}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7042963122000000000♠</span>9.631<span style="margin-left:.25em;">22</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>42</sup></span> <a href="/wiki/%E7%89%9B%E9%A0%93" class="mw-redirect" title="牛頓">N</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7044121029000000000♠</span>1.210<span style="margin-left:.25em;">29</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>44</sup></span> <a href="/wiki/%E7%89%9B%E9%A0%93" class="mw-redirect" title="牛頓">N</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%8A%9F%E7%8E%87" title="普朗克功率">普朗克功率</a> </td> <td><a href="/wiki/%E5%8A%9F%E7%8E%87" title="功率">功率</a>（L<sup>2</sup>MT<sup>−3</sup>） </td> <td><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_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{4\pi G}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msubsup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{4\pi G}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d5f365ff06dbbfed4a3d2b1ee1762ed4f3d4f0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:24.227ex; height:6.843ex;" alt="{\displaystyle P_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{4\pi G}}}"></span> </td> <td><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_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{G}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msubsup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>G</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{G}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bc5e93c71477a106e87c0c6d897c8aae9d34dd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.966ex; height:6.843ex;" alt="{\displaystyle P_{\text{P}}={\frac {E_{\text{P}}}{t_{\text{P}}}}={\frac {\hbar }{t_{\text{P}}^{2}}}={\frac {c^{5}}{G}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7051288737000000000♠</span>2.887<span style="margin-left:.25em;">37</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>51</sup></span> <a href="/wiki/%E7%93%A6%E7%89%B9" title="瓦特">W</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7052362837000000000♠</span>3.628<span style="margin-left:.25em;">37</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>52</sup></span> <a href="/wiki/%E7%93%A6%E7%89%B9" title="瓦特">W</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%AF%86%E5%BA%A6" title="普朗克密度">普朗克密度</a> </td> <td><a href="/wiki/%E5%AF%86%E5%BA%A6" title="密度">密度</a>（L<sup>−3</sup>M） </td> <td><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_{\text{P}}={\frac {m_{\text{P}}}{V_{\text{P}}}}={\frac {\hbar t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{16\pi ^{2}\hbar G^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mrow> <msubsup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mn>16</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi class="MJX-variant">ℏ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{\text{P}}={\frac {m_{\text{P}}}{V_{\text{P}}}}={\frac {\hbar t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{16\pi ^{2}\hbar G^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103e7d2913a6657b3b0a0a6196bcf184acca4e25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:30.154ex; height:6.843ex;" alt="{\displaystyle d_{\text{P}}={\frac {m_{\text{P}}}{V_{\text{P}}}}={\frac {\hbar t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{16\pi ^{2}\hbar G^{2}}}}"></span> </td> <td><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_{\text{P}}={\frac {m_{\text{P}}}{V_{\text{P}}}}={\frac {\hbar t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{\hbar G^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi class="MJX-variant">ℏ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mrow> <msubsup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{\text{P}}={\frac {m_{\text{P}}}{V_{\text{P}}}}={\frac {\hbar t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{\hbar G^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c32a756d153d38f5e70ab484b621c061f6d5be54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.441ex; height:6.843ex;" alt="{\displaystyle d_{\text{P}}={\frac {m_{\text{P}}}{V_{\text{P}}}}={\frac {\hbar t_{\text{P}}}{l_{\text{P}}^{5}}}={\frac {c^{5}}{\hbar G^{2}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7094326456000000000♠</span>3.264<span style="margin-left:.25em;">56</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>94</sup></span> <a href="/w/index.php?title=%E5%85%AC%E6%96%A4/%E7%AB%8B%E6%96%B9%E5%85%AC%E5%B0%BA&action=edit&redlink=1" class="new" title="公斤/立方公尺（页面不存在）">kg/m<sup>3</sup></a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7096515518000000000♠</span>5.155<span style="margin-left:.25em;">18</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>96</sup></span> <a href="/w/index.php?title=%E5%85%AC%E6%96%A4/%E7%AB%8B%E6%96%B9%E5%85%AC%E5%B0%BA&action=edit&redlink=1" class="new" title="公斤/立方公尺（页面不存在）">kg/m<sup>3</sup></a> </td></tr> <tr> <td><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E8%A7%92%E9%A0%BB%E7%8E%87&action=edit&redlink=1" class="new" title="普朗克角頻率（页面不存在）">普朗克角頻率</a> </td> <td><a href="/wiki/%E8%A7%92%E9%A0%BB%E7%8E%87" class="mw-redirect" title="角頻率">角頻率</a>（T<sup>−1</sup>） </td> <td><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 \omega _{\text{P}}={\frac {\theta _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{4\pi \hbar G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{\text{P}}={\frac {\theta _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{4\pi \hbar G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5d6b1d5f33be841e917241d154b4b53af6a4e75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.06ex; height:7.676ex;" alt="{\displaystyle \omega _{\text{P}}={\frac {\theta _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{4\pi \hbar G}}}}"></span> </td> <td><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 \omega _{\text{P}}={\frac {\theta _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{\hbar G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mi class="MJX-variant">ℏ</mi> <mi>G</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{\text{P}}={\frac {\theta _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{\hbar G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b8abbfe1af4dc8f52b6b29cd1433602efc0f13d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.565ex; height:7.676ex;" alt="{\displaystyle \omega _{\text{P}}={\frac {\theta _{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{5}}{\hbar G}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7042523254000000000♠</span>5.232<span style="margin-left:.25em;">54</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>42</sup></span> <a href="/w/index.php?title=%E5%BC%A7%E5%BA%A6/%E7%A7%92&action=edit&redlink=1" class="new" title="弧度/秒（页面不存在）">rad/s</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7043185488999999999♠</span>1.854<span style="margin-left:.25em;">89</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>43</sup></span> <a href="/w/index.php?title=%E5%BC%A7%E5%BA%A6/%E7%A7%92&action=edit&redlink=1" class="new" title="弧度/秒（页面不存在）">rad/s</a> </td></tr> <tr> <td><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%A3%93%E5%8A%9B&action=edit&redlink=1" class="new" title="普朗克壓力（页面不存在）">普朗克壓力</a> </td> <td><a href="/wiki/%E5%A3%93%E5%8A%9B" class="mw-redirect" title="壓力">壓力</a>（L<sup>−1</sup>MT<sup>−2</sup>） </td> <td><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 \Pi _{\text{P}}={\frac {F_{\text{P}}}{A_{\text{P}}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{16\pi ^{2}\hbar G^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Π</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mrow> <msubsup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <mn>16</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi class="MJX-variant">ℏ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pi _{\text{P}}={\frac {F_{\text{P}}}{A_{\text{P}}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{16\pi ^{2}\hbar G^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc1b110fbe0f95bbcb0b069f84d6bf02ed972f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.13ex; height:6.843ex;" alt="{\displaystyle \Pi _{\text{P}}={\frac {F_{\text{P}}}{A_{\text{P}}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{16\pi ^{2}\hbar G^{2}}}}"></span> </td> <td><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 \Pi _{\text{P}}={\frac {F_{\text{P}}}{A_{\text{P}}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{\hbar G^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Π</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mrow> <msubsup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <mi class="MJX-variant">ℏ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pi _{\text{P}}={\frac {F_{\text{P}}}{A_{\text{P}}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{\hbar G^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c592aab0beef28038855f6cfbce87c18a2c61fd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:26.416ex; height:6.843ex;" alt="{\displaystyle \Pi _{\text{P}}={\frac {F_{\text{P}}}{A_{\text{P}}}}={\frac {\hbar }{l_{\text{P}}^{3}t_{\text{P}}}}={\frac {c^{7}}{\hbar G^{2}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7111293404000000000♠</span>2.934<span style="margin-left:.25em;">04</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>111</sup></span> <a href="/wiki/%E5%B8%95%E6%96%AF%E5%8D%A1" title="帕斯卡">Pa</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7113463325000000000♠</span>4.633<span style="margin-left:.25em;">25</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>113</sup></span> <a href="/wiki/%E5%B8%95%E6%96%AF%E5%8D%A1" title="帕斯卡">Pa</a> </td></tr> <tr> <td><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E9%9B%BB%E6%B5%81&action=edit&redlink=1" class="new" title="普朗克電流（页面不存在）">普朗克電流</a> </td> <td><a href="/wiki/%E9%9B%BB%E6%B5%81" class="mw-redirect" title="電流">電流</a>（T<sup>−1</sup>Q） </td> <td><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_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{6}\epsilon _{0}}{4\pi G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{6}\epsilon _{0}}{4\pi G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5faabe1918614a6b2343c20778ee8e11b971caa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.057ex; height:7.676ex;" alt="{\displaystyle i_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {c^{6}\epsilon _{0}}{4\pi G}}}}"></span> </td> <td><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_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {4\pi c^{6}\epsilon _{0}}{G}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mi>G</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {4\pi c^{6}\epsilon _{0}}{G}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb8197f24e56fd79807317f2c48bb6b5c4a37da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.289ex; height:7.676ex;" alt="{\displaystyle i_{\text{P}}={\frac {q_{\text{P}}}{t_{\text{P}}}}={\sqrt {\frac {4\pi c^{6}\epsilon _{0}}{G}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7024276844000000000♠</span>2.768<span style="margin-left:.25em;">44</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>24</sup></span> <a href="/wiki/%E5%AE%89%E5%9F%B9" title="安培">A</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7025347893000000000♠</span>3.478<span style="margin-left:.25em;">93</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>25</sup></span> <a href="/wiki/%E5%AE%89%E5%9F%B9" title="安培">A</a> </td></tr> <tr> <td><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E9%9B%BB%E5%A3%93&action=edit&redlink=1" class="new" title="普朗克電壓（页面不存在）">普朗克電壓</a> </td> <td><a href="/wiki/%E9%9B%BB%E5%A3%93" title="電壓">電壓</a>（L<sup>2</sup>MT<sup>−2</sup>Q<sup>−1</sup>） </td> <td colspan="2"><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_{\text{P}}={\frac {E_{\text{P}}}{q_{\text{P}}}}={\frac {P_{\text{P}}}{i_{\text{P}}}}={\sqrt {\frac {c^{4}}{4\pi G\epsilon _{0}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π</mi> <mi>G</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\text{P}}={\frac {E_{\text{P}}}{q_{\text{P}}}}={\frac {P_{\text{P}}}{i_{\text{P}}}}={\sqrt {\frac {c^{4}}{4\pi G\epsilon _{0}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/597eb68f91523bc7b5560df4bac1d055caafa07a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:29.297ex; height:7.676ex;" alt="{\displaystyle U_{\text{P}}={\frac {E_{\text{P}}}{q_{\text{P}}}}={\frac {P_{\text{P}}}{i_{\text{P}}}}={\sqrt {\frac {c^{4}}{4\pi G\epsilon _{0}}}}}"></span> </td> <td colspan="2"><span class="nowrap"><span style="display:none" class="sortkey">7027104296000000000♠</span>1.042<span style="margin-left:.25em;">96</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>27</sup></span> <a href="/wiki/%E4%BC%8F%E7%89%B9" title="伏特">V</a> </td></tr> <tr> <td><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%98%BB%E6%8A%97" class="mw-redirect" title="普朗克阻抗">普朗克阻抗</a> </td> <td><a href="/wiki/%E9%98%BB%E6%8A%97" title="阻抗">阻抗</a>（L<sup>2</sup>MT<sup>−1</sup>Q<sup>−2</sup>） </td> <td><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_{\text{P}}={\frac {U_{\text{P}}}{i_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{c\epsilon _{0}}}=c\mu _{0}={\sqrt {\frac {\mu _{0}}{\epsilon _{0}}}}=Z_{0}={\frac {1}{Y_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>c</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>c</mi> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </msqrt> </mrow> <mo>=</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{\text{P}}={\frac {U_{\text{P}}}{i_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{c\epsilon _{0}}}=c\mu _{0}={\sqrt {\frac {\mu _{0}}{\epsilon _{0}}}}=Z_{0}={\frac {1}{Y_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ff7d9fe1905637f3aaefed97983f3b456bf7049" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:50.431ex; height:6.509ex;" alt="{\displaystyle Z_{\text{P}}={\frac {U_{\text{P}}}{i_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{c\epsilon _{0}}}=c\mu _{0}={\sqrt {\frac {\mu _{0}}{\epsilon _{0}}}}=Z_{0}={\frac {1}{Y_{0}}}}"></span> </td> <td><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_{\text{P}}={\frac {U_{\text{P}}}{i_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{4\pi c\epsilon _{0}}}={\frac {c\mu _{0}}{4\pi }}={\sqrt {\frac {\mu _{0}}{16\pi ^{2}\epsilon _{0}}}}={\frac {Z_{0}}{4\pi }}={\frac {1}{4\pi Y_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <msubsup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>P</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <mi>c</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>16</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>4</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{\text{P}}={\frac {U_{\text{P}}}{i_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{4\pi c\epsilon _{0}}}={\frac {c\mu _{0}}{4\pi }}={\sqrt {\frac {\mu _{0}}{16\pi ^{2}\epsilon _{0}}}}={\frac {Z_{0}}{4\pi }}={\frac {1}{4\pi Y_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcc2b8c7ed9d705752e433d21b4c3c0f46869b8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:61.348ex; height:6.509ex;" alt="{\displaystyle Z_{\text{P}}={\frac {U_{\text{P}}}{i_{\text{P}}}}={\frac {\hbar }{q_{\text{P}}^{2}}}={\frac {1}{4\pi c\epsilon _{0}}}={\frac {c\mu _{0}}{4\pi }}={\sqrt {\frac {\mu _{0}}{16\pi ^{2}\epsilon _{0}}}}={\frac {Z_{0}}{4\pi }}={\frac {1}{4\pi Y_{0}}}}"></span> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7002376730000000000♠</span>376.730</span> <a href="/wiki/%E6%AD%90%E5%A7%86" title="歐姆">Ω</a> </td> <td><span class="nowrap"><span style="display:none" class="sortkey">7001299792000000000♠</span>29.9792</span> <a href="/wiki/%E6%AD%90%E5%A7%86" title="歐姆">Ω</a> </td></tr></tbody></table> <p>註：<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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfcd49ab63d30163ac54e60a8e24ff9ccd7bcd44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.642ex; height:2.509ex;" alt="{\displaystyle Z_{0}}"></span>為<a href="/wiki/%E8%87%AA%E7%94%B1%E7%A9%BA%E9%96%93%E9%98%BB%E6%8A%97" title="自由空間阻抗">自由空間阻抗</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 Y_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4305e31e20568c004e0e4c8540bbfe2730a42cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.405ex; height:2.509ex;" alt="{\displaystyle Y_{0}}"></span>為<a href="/w/index.php?title=%E8%87%AA%E7%94%B1%E7%A9%BA%E9%96%93%E5%B0%8E%E7%B4%8D&action=edit&redlink=1" class="new" title="自由空間導納（页面不存在）">自由空間導納</a>。 </p> <div class="mw-heading mw-heading2"><h2 id="簡化物理方程式"><span id=".E7.B0.A1.E5.8C.96.E7.89.A9.E7.90.86.E6.96.B9.E7.A8.8B.E5.BC.8F"></span>簡化物理方程式</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=3" title="编辑章节：簡化物理方程式"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>嚴格地說，不同因次的物理量，雖然它們的數值可能相等，仍舊不能用在相等式的兩邊。但是，在理論物理學裏，為了簡化運算，我們可以把這顧慮放在一邊。簡化的過程稱為<b>無因次化</b>。表4展示出普朗克單位怎樣通过無因次化使許多物理方程式變得更簡單。 </p> <table class="wikitable" style="margin: 1em auto 1em auto; background-color: #ffffff"> <caption><b>表4：物理方程式與其無因次形式</b> </caption> <tbody><tr> <th> </th> <th>通常形式（<a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a>形式） </th> <th>普朗克<a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a>形式 </th> <th>普朗克<a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a>形式 </th></tr> <tr align="left"> <td><b><a href="/wiki/%E8%90%AC%E6%9C%89%E5%BC%95%E5%8A%9B%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="萬有引力定律">萬有引力定律</a></b> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=-G{\frac {m_{1}m_{2}}{r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mo>−</mo> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=-G{\frac {m_{1}m_{2}}{r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3cd66eabc86dd17973459ec8bc975ef849e502b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:15.887ex; height:5.009ex;" alt="{\displaystyle F=-G{\frac {m_{1}m_{2}}{r^{2}}}\,\!}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=-{\frac {m_{1}m_{2}}{4\pi r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=-{\frac {m_{1}m_{2}}{4\pi r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af9b7156c3c2372e1f2cb5fa56be22b2dfcf2cf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:14.06ex; height:5.009ex;" alt="{\displaystyle F=-{\frac {m_{1}m_{2}}{4\pi r^{2}}}\,\!}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=-{\frac {m_{1}m_{2}}{r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=-{\frac {m_{1}m_{2}}{r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30636d1eb4cc4355e51195ce32b0aa46a7d4d5ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:14.06ex; height:5.009ex;" alt="{\displaystyle F=-{\frac {m_{1}m_{2}}{r^{2}}}\,\!}"></span> </td></tr> <tr> <td><b><a href="/wiki/%E8%96%9B%E4%B8%81%E6%A0%BC%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="薛丁格方程式">薛丁格方程式</a></b> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi (\mathbf {r} ,\,t)+V(\mathbf {r} ,\,t)\psi (\mathbf {r} ,\,t)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi (\mathbf {r} ,\,t)+V(\mathbf {r} ,\,t)\psi (\mathbf {r} ,\,t)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2b85230bcd40ee1d1beab821918a51bc0a4495" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:32.394ex; height:5.676ex;" alt="{\displaystyle -{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi (\mathbf {r} ,\,t)+V(\mathbf {r} ,\,t)\psi (\mathbf {r} ,\,t)\,\!}"></span><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =i\hbar {\frac {\partial \psi }{\partial t}}(\mathbf {r} ,\,t)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ψ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =i\hbar {\frac {\partial \psi }{\partial t}}(\mathbf {r} ,\,t)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed42ca526275828f0e1364a0b04d4dfbb384325d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:13.789ex; height:5.676ex;" alt="{\displaystyle =i\hbar {\frac {\partial \psi }{\partial t}}(\mathbf {r} ,\,t)\,\!}"></span> </td> <td colspan="2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {1}{2m}}\nabla ^{2}\psi (\mathbf {r} ,\,t)+V(\mathbf {r} ,\,t)\psi (\mathbf {r} ,\,t)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mi>ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {1}{2m}}\nabla ^{2}\psi (\mathbf {r} ,\,t)+V(\mathbf {r} ,\,t)\psi (\mathbf {r} ,\,t)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcf2c159337386bc0a3877fd605ca4398cdc382e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:32.394ex; height:5.176ex;" alt="{\displaystyle -{\frac {1}{2m}}\nabla ^{2}\psi (\mathbf {r} ,\,t)+V(\mathbf {r} ,\,t)\psi (\mathbf {r} ,\,t)\,\!}"></span><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =i{\frac {\partial \psi }{\partial t}}(\mathbf {r} ,\,t)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ψ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =i{\frac {\partial \psi }{\partial t}}(\mathbf {r} ,\,t)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b2b69f23820c0b765000a9cad983a5ddab00fe5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:12.482ex; height:5.676ex;" alt="{\displaystyle =i{\frac {\partial \psi }{\partial t}}(\mathbf {r} ,\,t)\,\!}"></span> </td></tr> <tr> <td><b><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%97%9C%E4%BF%82%E5%BC%8F" class="mw-redirect" title="普朗克關係式">普朗克關係式</a></b> </td> <td><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=\hbar \omega }\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mi>ω</mi> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E=\hbar \omega }\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef3828458aebd76c65cbae66b8bbd9354cf5c3c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:8.594ex; height:2.176ex;" alt="{\displaystyle {E=\hbar \omega }\ \,\!}"></span> </td> <td colspan="2"><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=\omega }\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mo>=</mo> <mi>ω</mi> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E=\omega }\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7aacae2d40cb07d26e7775ed7f914c4a1890d029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:7.288ex; height:2.176ex;" alt="{\displaystyle {E=\omega }\ \,\!}"></span> </td></tr> <tr> <td><b><a href="/wiki/%E7%8B%B9%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" class="mw-redirect" title="狹義相對論">狹義相對論</a>的<a href="/wiki/%E8%B3%AA%E8%83%BD%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="質能方程式">質能方程式</a></b> </td> <td><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=mc^{2}}\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mo>=</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E=mc^{2}}\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35cd8b509863a7bb63030a23a75d1d319b32c2cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:9.943ex; height:2.676ex;" alt="{\displaystyle {E=mc^{2}}\ \,\!}"></span> </td> <td colspan="2"><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}\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mo>=</mo> <mi>m</mi> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E=m}\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef5a3aa96caa81fcfaf5affe78e7171d1dc3d1bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:7.882ex; height:2.176ex;" alt="{\displaystyle {E=m}\ \,\!}"></span> </td></tr> <tr> <td><b><a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a>的<a href="/wiki/%E6%84%9B%E5%9B%A0%E6%96%AF%E5%9D%A6%E5%A0%B4%E6%96%B9%E7%A8%8B%E5%BC%8F" class="mw-redirect" title="愛因斯坦場方程式">愛因斯坦場方程式</a></b> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {G_{\mu \nu }=8\pi {G \over c^{4}}T_{\mu \nu }}\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mn>8</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>G</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {G_{\mu \nu }=8\pi {G \over c^{4}}T_{\mu \nu }}\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89b9803cd463dbf9407e8b37487bb565180b15e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:16.831ex; height:5.676ex;" alt="{\displaystyle {G_{\mu \nu }=8\pi {G \over c^{4}}T_{\mu \nu }}\ \,\!}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {G_{\mu \nu }=2T_{\mu \nu }}\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {G_{\mu \nu }=2T_{\mu \nu }}\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b0a5f2a8c452406cf0a06ab5b2176958af05bef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:12.602ex; height:2.843ex;" alt="{\displaystyle {G_{\mu \nu }=2T_{\mu \nu }}\ \,\!}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {G_{\mu \nu }=8\pi T_{\mu \nu }}\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mn>8</mn> <mi>π</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {G_{\mu \nu }=8\pi T_{\mu \nu }}\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e635cd9f621d2a5c968d48e93161afab807141e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:13.934ex; height:2.843ex;" alt="{\displaystyle {G_{\mu \nu }=8\pi T_{\mu \nu }}\ \,\!}"></span> </td></tr> <tr> <td><b>一個粒子的每個<a href="/wiki/%E8%87%AA%E7%94%B1%E5%BA%A6" class="mw-disambig" title="自由度">自由度</a>的<a href="/wiki/%E7%83%AD%E8%83%BD" title="热能">熱能</a></b> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E={\frac {1}{2}}k_{B}T}\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E={\frac {1}{2}}k_{B}T}\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08be64d0f095c9b5d471f93c6a3905497e0ac3dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:12.168ex; height:5.176ex;" alt="{\displaystyle {E={\frac {1}{2}}k_{B}T}\ \,\!}"></span> </td> <td colspan="2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E={\frac {1}{2}}T}\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>T</mi> </mrow> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E={\frac {1}{2}}T}\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baa0e0faef2153e7f6bcc1f093b5d95d694156ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:9.477ex; height:5.176ex;" alt="{\displaystyle {E={\frac {1}{2}}T}\ \,\!}"></span> </td></tr> <tr> <td><b><a href="/wiki/%E5%BA%AB%E4%BE%96%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="庫侖定律">庫侖定律</a></b> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cab6a30d841280f838d98bdb06b815f4bd467b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:15.574ex; height:5.676ex;" alt="{\displaystyle F={\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}\,\!}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\frac {q_{1}q_{2}}{4\pi r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\frac {q_{1}q_{2}}{4\pi r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ca4700c530362724c24fd709bcaf08cebb0e94b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:10.66ex; height:5.176ex;" alt="{\displaystyle F={\frac {q_{1}q_{2}}{4\pi r^{2}}}\,\!}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\frac {q_{1}q_{2}}{r^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\frac {q_{1}q_{2}}{r^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0454c2be3a405b6858911f6876530aa950cd60b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:10.245ex; height:5.176ex;" alt="{\displaystyle F={\frac {q_{1}q_{2}}{r^{2}}}\,\!}"></span> </td></tr> <tr> <td><b><a href="/wiki/%E9%BA%A5%E5%85%8B%E6%96%AF%E9%9F%8B%E6%96%B9%E7%A8%8B%E7%B5%84" class="mw-redirect" title="麥克斯韋方程組">麦克斯韦方程組</a></b> </td> <td><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 \nabla \cdot \mathbf {E} ={\frac {1}{\epsilon _{0}}}\rho \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mi>ρ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {E} ={\frac {1}{\epsilon _{0}}}\rho \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2a30b85f7565611e806233533962c0f36894a90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:12.894ex; height:5.509ex;" alt="{\displaystyle \nabla \cdot \mathbf {E} ={\frac {1}{\epsilon _{0}}}\rho \,\!}"></span> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd6518db364124ce80896ca0f33b8320a10faf50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:10.745ex; height:2.176ex;" alt="{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}"></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f64f9bdcfbd6514b0a1dbdb2789e2f373393d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:15.882ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}"></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>+</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61ac1191950e751441e32deb6819921c9645eaaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:25.206ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\,\!}"></span> </p> </td> <td><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 \nabla \cdot \mathbf {E} =\rho \ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mi>ρ</mi> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {E} =\rho \ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44e30f06b92d4f64749e505155fea2cf32c0ebb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:10.64ex; height:2.676ex;" alt="{\displaystyle \nabla \cdot \mathbf {E} =\rho \ \,\!}"></span> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd6518db364124ce80896ca0f33b8320a10faf50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:10.745ex; height:2.176ex;" alt="{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}"></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f64f9bdcfbd6514b0a1dbdb2789e2f373393d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:15.882ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}"></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {B} =\mathbf {J} +{\frac {\partial \mathbf {E} }{\partial t}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {B} =\mathbf {J} +{\frac {\partial \mathbf {E} }{\partial t}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4ff6a9e16730f62bb7c0dfecfc074ef03014f71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:18.295ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {B} =\mathbf {J} +{\frac {\partial \mathbf {E} }{\partial t}}\,\!}"></span> </p> </td> <td><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 \nabla \cdot \mathbf {E} =4\pi \rho \ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mn>4</mn> <mi>π</mi> <mi>ρ</mi> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {E} =4\pi \rho \ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26f0b1f48aacf2a0a313efc95d4ad26a7c39fc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:13.135ex; height:2.676ex;" alt="{\displaystyle \nabla \cdot \mathbf {E} =4\pi \rho \ \,\!}"></span> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd6518db364124ce80896ca0f33b8320a10faf50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:10.745ex; height:2.176ex;" alt="{\displaystyle \nabla \cdot \mathbf {B} =0\ \,\!}"></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f64f9bdcfbd6514b0a1dbdb2789e2f373393d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:15.882ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}"></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {B} =4\pi \mathbf {J} +{\frac {\partial \mathbf {E} }{\partial t}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mn>4</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {B} =4\pi \mathbf {J} +{\frac {\partial \mathbf {E} }{\partial t}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1428a7df47d89a4b3de0b6039c43fae55c9ee96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:20.79ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {B} =4\pi \mathbf {J} +{\frac {\partial \mathbf {E} }{\partial t}}\,\!}"></span> </p> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="參閱"><span id=".E5.8F.83.E9.96.B1"></span>參閱</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=4" title="编辑章节：參閱"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E5%9B%A0%E6%AC%A1%E5%88%86%E6%9E%90" title="因次分析">因次分析</a></li> <li><a href="/wiki/%E7%89%A9%E7%90%86%E5%B8%B8%E6%95%B8" title="物理常數">物理常數</a></li> <li><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%B0%BA%E5%AF%B8&action=edit&redlink=1" class="new" title="普朗克尺寸（页面不存在）">普朗克尺寸</a></li> <li><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E7%B2%92%E5%AD%90" title="普朗克粒子">普朗克粒子</a></li> <li><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E7%B4%80%E5%85%83&action=edit&redlink=1" class="new" title="普朗克紀元（页面不存在）">普朗克紀元</a></li> <li><a href="/wiki/%E5%8B%9E%E4%BE%96%E8%8C%B2-%E9%BB%91%E7%B6%AD%E5%A1%9E%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="勞侖茲-黑維塞單位制">勞侖茲-黑維塞單位制</a></li> <li><a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a></li> <li><a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6" class="mw-redirect" title="國際單位制">國際單位制</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="參考文獻"><span id=".E5.8F.83.E8.80.83.E6.96.87.E7.8D.BB"></span>參考文獻</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=5" title="编辑章节：參考文獻"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="引用"><span id=".E5.BC.95.E7.94.A8"></span>引用</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=6" title="编辑章节：引用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-CODATA-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-CODATA_1-0">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://physics.nist.gov/cuu/Constants/index.html">NIST 的基礎物理常數</a>. <span class="reference-accessdate"> [<span class="nowrap">2008-09-12</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20010813140947/http://physics.nist.gov/cuu/Constants/index.html">存档</a>于2001-08-13）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&rft.btitle=NIST+%E7%9A%84%E5%9F%BA%E7%A4%8E%E7%89%A9%E7%90%86%E5%B8%B8%E6%95%B8&rft.genre=unknown&rft_id=http%3A%2F%2Fphysics.nist.gov%2Fcuu%2FConstants%2Findex.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="来源"><span id=".E6.9D.A5.E6.BA.90"></span>来源</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=7" title="编辑章节：来源"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r80540462">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .refbegin-100{font-size:100%}</style><div class="refbegin" style=""> <ul><li><cite class="citation book">Barrow, John D. <a rel="nofollow" class="external text" href="https://archive.org/details/constantsofnatur0000barr">The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe</a>. New York: Pantheon Books. 2002. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0375422218" title="Special:网络书源/0375422218"><span title="国际标准书号">ISBN</span> 0375422218</a>.（這是本簡單易解的書）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&rft.aufirst=John+D.&rft.aulast=Barrow&rft.btitle=The+Constants+of+Nature%3B+From+Alpha+to+Omega+-+The+Numbers+that+Encode+the+Deepest+Secrets+of+the+Universe&rft.date=2002&rft.genre=book&rft.isbn=0375422218&rft.place=New+York&rft.pub=Pantheon+Books&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fconstantsofnatur0000barr&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFDuff2002" class="citation">Duff, Michael, <a rel="nofollow" class="external text" href="http://arxiv.org/abs/hep-th/0208093">Comment on time-variation of fundamental constants</a>, ArΧiv e-prints, 2002 <span class="reference-accessdate"> [<span class="nowrap">2008-09-11</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20170207084555/https://arxiv.org/abs/hep-th/0208093">存档</a>于2017-02-07）.（這篇文章評論基礎物理常數可能隨時間而改變）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&rft.atitle=Comment+on+time-variation+of+fundamental+constants&rft.aufirst=Michael&rft.aulast=Duff&rft.date=2002&rft.genre=article&rft.jtitle=Ar%CE%A7iv+e-prints&rft_id=http%3A%2F%2Farxiv.org%2Fabs%2Fhep-th%2F0208093&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFDuffOkunVeneziano2002" class="citation">Duff, Michael; Okun, L. B.; Veneziano, Gabriele, <a rel="nofollow" class="external text" href="http://arxiv.org/abs/physics/0110060">Trialogue on the number of fundamental constants</a>, Journal of High Energy Physics, 2002, <b>3</b>: 023 <span class="reference-accessdate"> [<span class="nowrap">2008-09-11</span>]</span>, <a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1126-6708%2F2002%2F03%2F023"><span title="數位物件識別號">doi:10.1088/1126-6708/2002/03/023</span></a>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20150415033331/http://arxiv.org/abs/physics/0110060">存档</a>于2015-04-15）（關於到底有幾個最基礎的物理常數的對話）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&rft.atitle=Trialogue+on+the+number+of+fundamental+constants&rft.au=Okun%2C+L.+B.&rft.au=Veneziano%2C+Gabriele&rft.aufirst=Michael&rft.aulast=Duff&rft.date=2002&rft.genre=article&rft.jtitle=Journal+of+High+Energy+Physics&rft.pages=023&rft.volume=3&rft_id=http%3A%2F%2Farxiv.org%2Fabs%2Fphysics%2F0110060&rft_id=info%3Adoi%2F10.1088%2F1126-6708%2F2002%2F03%2F023&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFPlanck1899" class="citation"><a href="/wiki/%E9%A6%AC%E5%85%8B%E6%96%AF%C2%B7%E6%99%AE%E6%9C%97%E5%85%8B" class="mw-redirect" title="馬克斯·普朗克">Planck, Max</a>, <a rel="nofollow" class="external text" href="http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=10-sitz/1899-1&seite:int=454">Über irreversible Strahlungsvorgänge</a>, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, 1899, <b>5</b>: 440–480 <span class="reference-accessdate"> [<span class="nowrap">2008-09-11</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20090403115109/http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=10-sitz%2F1899-1&seite%3Aint=454">存档</a>于2009-04-03）.（除了普朗克電荷與普朗克常數以外，普朗克單位最先出現於這篇文章裡面。）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&rft.atitle=%C3%9Cber+irreversible+Strahlungsvorg%C3%A4nge&rft.aufirst=Max&rft.aulast=Planck&rft.date=1899&rft.genre=article&rft.jtitle=Sitzungsberichte+der+K%C3%B6niglich+Preu%C3%9Fischen+Akademie+der+Wissenschaften+zu+Berlin&rft.pages=440-480&rft.volume=5&rft_id=http%3A%2F%2Fbibliothek.bbaw.de%2Fbibliothek-digital%2Fdigitalequellen%2Fschriften%2Fanzeige%2Findex_html%3Fband%3D10-sitz%2F1899-1%26seite%3Aint%3D454&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book"><a href="/wiki/%E7%BE%85%E5%82%91%C2%B7%E6%BD%98%E6%B4%9B%E6%96%AF" title="羅傑·潘洛斯">Penrose, Roger</a>. Section 31.1. <a rel="nofollow" class="external text" href="https://archive.org/details/roadtorealitycom00penr_0">The Road to Reality</a>. New York: Alfred A. Knopf. 2005. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0679454438" title="Special:网络书源/0679454438"><span title="国际标准书号">ISBN</span> 0679454438</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&rft.atitle=Section+31.1&rft.aufirst=Roger&rft.aulast=Penrose&rft.btitle=The+Road+to+Reality&rft.date=2005&rft.genre=bookitem&rft.isbn=0679454438&rft.place=New+York&rft.pub=Alfred+A.+Knopf&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Froadtorealitycom00penr_0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="外部連結"><span id=".E5.A4.96.E9.83.A8.E9.80.A3.E7.B5.90"></span>外部連結</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D%E5%88%B6&action=edit&section=8" title="编辑章节：外部連結"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://physics.nist.gov/cuu/Constants/index.html">NIST 的基本物理常數數值列表，包括普朗克單位。</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20010813140947/http://physics.nist.gov/cuu/Constants/index.html">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li></ul> <div style="clear: both; height: 1em"></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl 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a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:110%;margin:0 8em}.mw-parser-output .navbar-ct-mini{font-size:110%;margin:0 5em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D" title="Template:普朗克單位"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D" title="Template talk:普朗克單位"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E6%99%AE%E6%9C%97%E5%85%8B%E5%96%AE%E4%BD%8D" title="Special:编辑页面/Template:普朗克單位"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="普朗克單位制" style="font-size:110%;margin:0 5em"><a class="mw-selflink selflink">普朗克單位制</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">基本單位</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E6%99%82%E9%96%93" title="普朗克時間">普朗克時間</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%95%B7%E5%BA%A6" title="普朗克長度">普朗克長度</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E8%B3%AA%E9%87%8F" title="普朗克質量">普朗克質量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%9B%BB%E8%8D%B7" title="普朗克電荷">普朗克電荷</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E6%BA%AB%E5%BA%A6" title="普朗克溫度">普朗克溫度</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B0" title="普朗克常数">普朗克常数</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">衍生單位</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E8%83%BD%E9%87%8F" title="普朗克能量">普朗克能量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%8A%9B" title="普朗克力">普朗克力</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%8B%95%E9%87%8F" title="普朗克動量">普朗克動量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%8A%9F%E7%8E%87" title="普朗克功率">普朗克功率</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%AF%86%E5%BA%A6" title="普朗克密度">普朗克密度</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E8%A7%92%E9%A0%BB%E7%8E%87&action=edit&redlink=1" class="new" title="普朗克角頻率（页面不存在）">普朗克角頻率</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E5%A3%93%E5%8A%9B&action=edit&redlink=1" class="new" title="普朗克壓力（页面不存在）">普朗克壓力</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E9%9B%BB%E6%B5%81&action=edit&redlink=1" class="new" title="普朗克電流（页面不存在）">普朗克電流</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%E6%99%AE%E6%9C%97%E5%85%8B%E9%9B%BB%E5%A3%93&action=edit&redlink=1" class="new" title="普朗克電壓（页面不存在）">普朗克電壓</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E9%98%BB%E6%8A%97" class="mw-redirect" title="普朗克阻抗">普朗克阻抗</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox" aria-labelledby="-&#123;zh-cn:计量制度;_zh-hant:度量衡制度;&#125;-" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E8%AE%A1%E9%87%8F%E5%88%B6%E5%BA%A6" title="Template:计量制度"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E8%AE%A1%E9%87%8F%E5%88%B6%E5%BA%A6" title="Template talk:计量制度"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E8%AE%A1%E9%87%8F%E5%88%B6%E5%BA%A6" title="Special:编辑页面/Template:计量制度"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="-&#123;zh-cn:计量制度;_zh-hant:度量衡制度;&#125;-" style="font-size:110%;margin:0 5em"><a href="/wiki/%E8%AE%A1%E9%87%8F%E5%8D%95%E4%BD%8D%E5%88%B6" title="计量单位制">度量衡制度</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%85%AC%E5%88%B6" title="公制">米制</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%9B%BD%E9%99%85%E5%8D%95%E4%BD%8D%E5%88%B6" title="国际单位制">国际单位制</a> · <span class="nowrap"><a href="/wiki/%E7%B1%B3-%E5%8D%83%E5%85%8B-%E7%A7%92%E5%88%B6" title="米-千克-秒制">米-千克-秒制</a> ·</span> <span class="nowrap"><a href="/wiki/%E5%8E%98%E7%B1%B3-%E5%85%8B-%E7%A7%92%E5%88%B6" title="厘米-克-秒制">厘米-克-秒制</a> ·</span> <span class="nowrap"><a href="/wiki/%E7%B1%B3-%E5%90%A8-%E7%A7%92%E5%88%B6" title="米-吨-秒制">米-吨-秒制</a> ·</span> <span class="nowrap"><a href="/wiki/%E9%87%8D%E5%8A%9B%E7%B1%B3%E5%88%B6" title="重力米制">重力米制</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%87%AA%E7%84%B6%E5%8D%95%E4%BD%8D%E5%88%B6" title="自然单位制">自然单位制</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%AB%98%E6%96%AF%E5%96%AE%E4%BD%8D%E5%88%B6" title="高斯單位制">高斯單位制</a> · <span class="nowrap"><a href="/wiki/%E5%B9%BE%E4%BD%95%E5%8C%96%E5%96%AE%E4%BD%8D%E5%88%B6" title="幾何化單位制">幾何化單位制</a> ·</span> <span class="nowrap"><a class="mw-selflink selflink">普朗克單位制</a> ·</span> <span class="nowrap"><a href="/wiki/%E5%8F%B2%E6%9D%B1%E7%B4%8D%E5%96%AE%E4%BD%8D%E5%88%B6" title="史東納單位制">史東納單位制</a> ·</span> <span class="nowrap"><a href="/wiki/%E6%B4%9B%E4%BC%A6%E5%85%B9-%E4%BA%A5%E7%BB%B4%E8%B5%9B%E5%8D%95%E4%BD%8D%E5%88%B6" title="洛伦兹-亥维赛单位制">洛伦兹-亥维赛单位制</a> ·</span> <span class="nowrap"><a href="/wiki/%E5%8E%9F%E5%AD%90%E5%8D%95%E4%BD%8D%E5%88%B6" title="原子单位制">原子單位制</a> ·</span> <span class="nowrap"><a href="/wiki/%E8%87%AA%E7%84%B6%E5%8D%95%E4%BD%8D%E5%88%B6#量子色動力學單位制" title="自然单位制">量子色動力學單位制</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">常規單位</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%A4%A9%E6%96%87%E5%AD%B8%E5%96%AE%E4%BD%8D" class="mw-redirect" title="天文學單位">天文學單位</a> · <span class="nowrap"><span class="ilh-all" data-orig-title="電學常規單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Conventional electrical unit"><span class="ilh-page"><a href="/w/index.php?title=%E9%9B%BB%E5%AD%B8%E5%B8%B8%E8%A6%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="電學常規單位（页面不存在）">電學常規單位</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Conventional_electrical_unit" class="extiw" title="en:Conventional electrical unit"><span lang="en" dir="auto">Conventional electrical unit</span></a></span>）</span></span> ·</span> <span class="nowrap"><a href="/wiki/%E5%9B%BD%E9%99%85%E5%AE%9E%E7%94%A8%E6%B8%A9%E6%A0%87" title="国际实用温标">国际实用温标</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">日常單位</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E4%B8%AD%E5%9C%8B%E5%BA%A6%E9%87%8F%E8%A1%A1" title="中國度量衡">中國傳統</a> · <span class="nowrap"><a href="/wiki/%E5%B8%B8%E8%A1%A1" title="常衡">常衡</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="藥劑師度量衡" data-lang-code="en" data-lang-name="英语" data-foreign-title="Apothecaries' system"><span class="ilh-page"><a href="/w/index.php?title=%E8%97%A5%E5%8A%91%E5%B8%AB%E5%BA%A6%E9%87%8F%E8%A1%A1&action=edit&redlink=1" class="new" title="藥劑師度量衡（页面不存在）">藥劑師</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Apothecaries%27_system" class="extiw" title="en:Apothecaries' system"><span lang="en" dir="auto">Apothecaries' system</span></a></span>）</span></span> ·</span> <span class="nowrap"><a href="/wiki/%E8%8B%B1%E5%88%B6%E5%8D%95%E4%BD%8D" title="英制单位">英制</a> ·</span> <span class="nowrap"><a href="/wiki/%E7%BC%85%E7%94%B8%E8%AE%A1%E9%87%8F%E5%8D%95%E4%BD%8D" title="缅甸计量单位">緬甸</a> ·</span> <span class="nowrap"><a href="/wiki/%E5%B8%82%E5%88%B6" title="市制">市制</a>、<a href="/wiki/%E7%87%9F%E9%80%A0%E5%B0%BA%E5%BA%AB%E5%B9%B3%E5%88%B6" title="營造尺庫平制">營造尺庫平制</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="康沃爾計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Old Cornish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%BA%B7%E6%B2%83%E7%88%BE%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="康沃爾計量單位（页面不存在）">康沃爾</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Old_Cornish_units_of_measurement" class="extiw" title="en:Old Cornish units of measurement"><span lang="en" dir="auto">Old Cornish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="丹麥計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Danish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E4%B8%B9%E9%BA%A5%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="丹麥計量單位（页面不存在）">丹麥</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Danish_units_of_measurement" class="extiw" title="en:Danish units of measurement"><span lang="en" dir="auto">Danish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="荷蘭計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Dutch units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E8%8D%B7%E8%98%AD%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="荷蘭計量單位（页面不存在）">荷蘭</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Dutch_units_of_measurement" class="extiw" title="en:Dutch units of measurement"><span lang="en" dir="auto">Dutch units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="英格蘭計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="English units"><span class="ilh-page"><a href="/w/index.php?title=%E8%8B%B1%E6%A0%BC%E8%98%AD%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="英格蘭計量單位（页面不存在）">英格蘭</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/English_units" class="extiw" title="en:English units"><span lang="en" dir="auto">English units</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="芬蘭計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Finnish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E8%8A%AC%E8%98%AD%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="芬蘭計量單位（页面不存在）">芬蘭</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Finnish_units_of_measurement" class="extiw" title="en:Finnish units of measurement"><span lang="en" dir="auto">Finnish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="法國計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="French units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E6%B3%95%E5%9C%8B%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="法國計量單位（页面不存在）">法國</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/French_units_of_measurement" class="extiw" title="en:French units of measurement"><span lang="en" dir="auto">French units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="德國計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="German units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%BE%B7%E5%9C%8B%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="德國計量單位（页面不存在）">德國</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/German_units_of_measurement" class="extiw" title="en:German units of measurement"><span lang="en" dir="auto">German units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="印度計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Hindu units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%8D%B0%E5%BA%A6%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="印度計量單位（页面不存在）">印度</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Hindu_units_of_measurement" class="extiw" title="en:Hindu units of measurement"><span lang="en" dir="auto">Hindu units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><a href="/wiki/%E9%A6%99%E6%B8%AF%E5%BA%A6%E9%87%8F%E8%A1%A1%E5%88%B6%E5%BA%A6" title="香港度量衡制度">香港</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="愛爾蘭計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Old Irish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E6%84%9B%E7%88%BE%E8%98%AD%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="愛爾蘭計量單位（页面不存在）">愛爾蘭</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Old_Irish_units_of_measurement" class="extiw" title="en:Old Irish units of measurement"><span lang="en" dir="auto">Old Irish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><a href="/wiki/%E6%97%A5%E6%9C%AC%E5%BA%A6%E9%87%8F%E8%A1%A1" class="mw-redirect" title="日本度量衡">日本</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="馬耳他計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Maltese units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E9%A6%AC%E8%80%B3%E4%BB%96%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="馬耳他計量單位（页面不存在）">馬耳他</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Maltese_units_of_measurement" class="extiw" title="en:Maltese units of measurement"><span lang="en" dir="auto">Maltese units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="挪威計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Norwegian units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E6%8C%AA%E5%A8%81%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="挪威計量單位（页面不存在）">挪威</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Norwegian_units_of_measurement" class="extiw" title="en:Norwegian units of measurement"><span lang="en" dir="auto">Norwegian units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="勃固計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Pegu Weights and Measures"><span class="ilh-page"><a href="/w/index.php?title=%E5%8B%83%E5%9B%BA%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="勃固計量單位（页面不存在）">勃固</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Pegu_Weights_and_Measures" class="extiw" title="en:Pegu Weights and Measures"><span lang="en" dir="auto">Pegu Weights and Measures</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="波蘭計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Obsolete Polish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E6%B3%A2%E8%98%AD%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="波蘭計量單位（页面不存在）">波蘭</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Obsolete_Polish_units_of_measurement" class="extiw" title="en:Obsolete Polish units of measurement"><span lang="en" dir="auto">Obsolete Polish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="葡萄牙計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Portuguese customary units"><span class="ilh-page"><a href="/w/index.php?title=%E8%91%A1%E8%90%84%E7%89%99%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="葡萄牙計量單位（页面不存在）">葡萄牙</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Portuguese_customary_units" class="extiw" title="en:Portuguese customary units"><span lang="en" dir="auto">Portuguese customary units</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="羅馬尼亞計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Romanian units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E7%BE%85%E9%A6%AC%E5%B0%BC%E4%BA%9E%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="羅馬尼亞計量單位（页面不存在）">羅馬尼亞</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Romanian_units_of_measurement" class="extiw" title="en:Romanian units of measurement"><span lang="en" dir="auto">Romanian units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="俄羅斯計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Obsolete Russian units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E4%BF%84%E7%BE%85%E6%96%AF%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="俄羅斯計量單位（页面不存在）">俄羅斯</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Obsolete_Russian_units_of_measurement" class="extiw" title="en:Obsolete Russian units of measurement"><span lang="en" dir="auto">Obsolete Russian units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="蘇格蘭計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Obsolete Scottish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E8%98%87%E6%A0%BC%E8%98%AD%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="蘇格蘭計量單位（页面不存在）">蘇格蘭</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Obsolete_Scottish_units_of_measurement" class="extiw" title="en:Obsolete Scottish units of measurement"><span lang="en" dir="auto">Obsolete Scottish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="西班牙計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Spanish customary units"><span class="ilh-page"><a href="/w/index.php?title=%E8%A5%BF%E7%8F%AD%E7%89%99%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="西班牙計量單位（页面不存在）">西班牙</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Spanish_customary_units" class="extiw" title="en:Spanish customary units"><span lang="en" dir="auto">Spanish customary units</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="瑞典計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Swedish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E7%91%9E%E5%85%B8%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="瑞典計量單位（页面不存在）">瑞典</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Swedish_units_of_measurement" class="extiw" title="en:Swedish units of measurement"><span lang="en" dir="auto">Swedish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><a href="/wiki/%E5%8F%B0%E5%88%B6" title="台制">台灣</a> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="韃靼計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Obsolete Tatar units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E9%9F%83%E9%9D%BC%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="韃靼計量單位（页面不存在）">韃靼</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Obsolete_Tatar_units_of_measurement" class="extiw" title="en:Obsolete Tatar units of measurement"><span lang="en" dir="auto">Obsolete Tatar units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="奧斯曼計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Traditional Turkish units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%A5%A7%E6%96%AF%E6%9B%BC%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="奧斯曼計量單位（页面不存在）">奧斯曼</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Traditional_Turkish_units_of_measurement" class="extiw" title="en:Traditional Turkish units of measurement"><span lang="en" dir="auto">Traditional Turkish units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><a href="/wiki/%E9%87%91%E8%A1%A1%E5%88%B6" title="金衡制">金衡制</a> ·</span> <span class="nowrap"><a href="/wiki/%E7%BE%8E%E5%88%B6%E5%8D%95%E4%BD%8D" title="美制单位">美制</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">古單位制</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><span class="ilh-all" data-orig-title="古希臘計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ancient Greek weights and measures"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E5%B8%8C%E8%87%98%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="古希臘計量單位（页面不存在）">古希臘</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ancient_Greek_weights_and_measures" class="extiw" title="en:Ancient Greek weights and measures"><span lang="en" dir="auto">Ancient Greek weights and measures</span></a></span>）</span></span> · <span class="nowrap"><span class="ilh-all" data-orig-title="古羅馬計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ancient Roman weights and measures"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E7%BE%85%E9%A6%AC%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="古羅馬計量單位（页面不存在）">古羅馬</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ancient_Roman_weights_and_measures" class="extiw" title="en:Ancient Roman weights and measures"><span lang="en" dir="auto">Ancient Roman weights and measures</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="古埃及計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ancient Egyptian weights and measures"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E5%9F%83%E5%8F%8A%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="古埃及計量單位（页面不存在）">古埃及</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ancient_Egyptian_weights_and_measures" class="extiw" title="en:Ancient Egyptian weights and measures"><span lang="en" dir="auto">Ancient Egyptian weights and measures</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="古希伯來計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Biblical and Talmudic units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E5%B8%8C%E4%BC%AF%E4%BE%86%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="古希伯來計量單位（页面不存在）">古希伯來</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Biblical_and_Talmudic_units_of_measurement" class="extiw" title="en:Biblical and Talmudic units of measurement"><span lang="en" dir="auto">Biblical and Talmudic units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="古阿拉伯計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ancient Arabic units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E9%98%BF%E6%8B%89%E4%BC%AF%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="古阿拉伯計量單位（页面不存在）">古阿拉伯</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ancient_Arabic_units_of_measurement" class="extiw" title="en:Ancient Arabic units of measurement"><span lang="en" dir="auto">Ancient Arabic units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="古美索不達米亞計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ancient Mesopotamian units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E7%BE%8E%E7%B4%A2%E4%B8%8D%E9%81%94%E7%B1%B3%E4%BA%9E%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="古美索不達米亞計量單位（页面不存在）">古美索不達米亞</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ancient_Mesopotamian_units_of_measurement" class="extiw" title="en:Ancient Mesopotamian units of measurement"><span lang="en" dir="auto">Ancient Mesopotamian units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="古波斯計量單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Persian units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E6%B3%A2%E6%96%AF%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="古波斯計量單位（页面不存在）">古波斯</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Persian_units_of_measurement" class="extiw" title="en:Persian units of measurement"><span lang="en" dir="auto">Persian units of measurement</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="印度單位制歷史" data-lang-code="en" data-lang-name="英语" data-foreign-title="History of measurement systems in India"><span class="ilh-page"><a href="/w/index.php?title=%E5%8D%B0%E5%BA%A6%E5%96%AE%E4%BD%8D%E5%88%B6%E6%AD%B7%E5%8F%B2&action=edit&redlink=1" class="new" title="印度單位制歷史（页面不存在）">印度單位制歷史</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/History_of_measurement_systems_in_India" class="extiw" title="en:History of measurement systems in India"><span lang="en" dir="auto">History of measurement systems in India</span></a></span>）</span></span> ·</span> <span class="nowrap"><a href="/wiki/%E4%BC%A0%E7%BB%9F%E6%B3%95%E5%9B%BD%E8%AE%A1%E9%87%8F%E5%8D%95%E4%BD%8D" title="传统法国计量单位">古法国</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">其他單位</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><span class="ilh-all" data-orig-title="非常規計量單位列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="List of unusual units of measurement"><span class="ilh-page"><a href="/w/index.php?title=%E9%9D%9E%E5%B8%B8%E8%A6%8F%E8%A8%88%E9%87%8F%E5%96%AE%E4%BD%8D%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="非常規計量單位列表（页面不存在）">非常規</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/List_of_unusual_units_of_measurement" class="extiw" title="en:List of unusual units of measurement"><span lang="en" dir="auto">List of unusual units of measurement</span></a></span>）</span></span> · <span class="nowrap"><span class="ilh-all" data-orig-title="法國常用單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mesures usuelles"><span class="ilh-page"><a href="/w/index.php?title=%E6%B3%95%E5%9C%8B%E5%B8%B8%E7%94%A8%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="法國常用單位（页面不存在）">法國常用單位</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mesures_usuelles" class="extiw" title="en:Mesures usuelles"><span lang="en" dir="auto">Mesures usuelles</span></a></span>）</span></span> ·</span> <span class="nowrap"><span class="ilh-all" data-orig-title="N體單位" data-lang-code="en" data-lang-name="英语" data-foreign-title="N-body units"><span class="ilh-page"><a href="/w/index.php?title=N%E9%AB%94%E5%96%AE%E4%BD%8D&action=edit&redlink=1" class="new" title="N體單位（页面不存在）">N體單位</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/N-body_units" class="extiw" title="en:N-body units"><span lang="en" dir="auto">N-body units</span></a></span>）</span></span></span></div></td></tr></tbody></table></div>    </div><noscript><img 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普朗克單位制 - 维基百科，自由的百科全书