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class="vector-toc-list"> </ul> </li> <li id="toc-Laws_as_consequences_of_mathematical_symmetries" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Laws_as_consequences_of_mathematical_symmetries"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Laws as consequences of mathematical symmetries</span> </div> </a> <ul id="toc-Laws_as_consequences_of_mathematical_symmetries-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Laws_of_physics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Laws_of_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Laws of physics</span> </div> </a> <button aria-controls="toc-Laws_of_physics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Laws of physics subsection</span> </button> <ul id="toc-Laws_of_physics-sublist" class="vector-toc-list"> <li id="toc-Conservation_laws" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Conservation_laws"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Conservation laws</span> </div> </a> <ul id="toc-Conservation_laws-sublist" class="vector-toc-list"> <li id="toc-Conservation_and_symmetry" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Conservation_and_symmetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Conservation and symmetry</span> </div> </a> <ul id="toc-Conservation_and_symmetry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Continuity_and_transfer" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Continuity_and_transfer"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2</span> <span>Continuity and transfer</span> </div> </a> <ul id="toc-Continuity_and_transfer-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Laws_of_classical_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Laws_of_classical_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Laws of classical mechanics</span> </div> </a> <ul id="toc-Laws_of_classical_mechanics-sublist" class="vector-toc-list"> <li id="toc-Principle_of_least_action" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Principle_of_least_action"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Principle of least action</span> </div> </a> <ul id="toc-Principle_of_least_action-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Laws_of_gravitation_and_relativity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Laws_of_gravitation_and_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Laws of gravitation and relativity</span> </div> </a> <ul id="toc-Laws_of_gravitation_and_relativity-sublist" class="vector-toc-list"> <li id="toc-Modern_laws" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Modern_laws"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.1</span> <span>Modern laws</span> </div> </a> <ul id="toc-Modern_laws-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Classical_laws" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Classical_laws"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.2</span> <span>Classical laws</span> </div> </a> <ul id="toc-Classical_laws-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Thermodynamics</span> </div> </a> <ul id="toc-Thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electromagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electromagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Electromagnetism</span> </div> </a> <ul id="toc-Electromagnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Photonics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Photonics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Photonics</span> </div> </a> <ul id="toc-Photonics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Laws_of_quantum_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Laws_of_quantum_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Laws of quantum mechanics</span> </div> </a> <ul id="toc-Laws_of_quantum_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radiation_laws" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radiation_laws"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Radiation laws</span> </div> </a> <ul id="toc-Radiation_laws-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Laws_of_chemistry" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Laws_of_chemistry"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Laws of chemistry</span> </div> </a> <ul id="toc-Laws_of_chemistry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Laws_of_biology" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Laws_of_biology"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Laws of biology</span> </div> </a> <button aria-controls="toc-Laws_of_biology-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Laws of biology subsection</span> </button> <ul id="toc-Laws_of_biology-sublist" class="vector-toc-list"> <li id="toc-Ecology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ecology"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Ecology</span> </div> </a> <ul id="toc-Ecology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Genetics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Genetics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Genetics</span> </div> </a> <ul id="toc-Genetics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Natural_selection" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Natural_selection"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Natural selection</span> </div> </a> <ul id="toc-Natural_selection-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Laws_of_Earth_sciences" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Laws_of_Earth_sciences"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Laws of Earth sciences</span> </div> </a> <button aria-controls="toc-Laws_of_Earth_sciences-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Laws of Earth sciences subsection</span> </button> <ul id="toc-Laws_of_Earth_sciences-sublist" class="vector-toc-list"> <li id="toc-Geography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geography"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Geography</span> </div> </a> <ul id="toc-Geography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geology"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Geology</span> </div> </a> <ul id="toc-Geology-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Other_fields" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Other_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Other fields</span> </div> </a> <ul id="toc-Other_fields-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Scientific law</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="Go to an article in another language. Available in 44 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-44" 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">44 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%B9%D9%84%D9%85%D9%8A" title="قانون علمي – Arabic" lang="ar" hreflang="ar" data-title="قانون علمي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AC%E0%A5%88%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8%E0%A4%BF%E0%A4%95_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="बैज्ञानिक नियम – Bhojpuri" lang="bh" hreflang="bh" data-title="बैज्ञानिक नियम" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Nau%C4%8Dni_zakon" title="Naučni zakon – Bosnian" lang="bs" hreflang="bs" data-title="Naučni zakon" data-language-autonym="Bosanski" data-language-local-name="Bosnian" 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/Llei_cient%C3%ADfica" title="Llei científica – Catalan" lang="ca" hreflang="ca" data-title="Llei científica" data-language-autonym="Català" data-language-local-name="Catalan" 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/V%C4%9Bdeck%C3%BD_z%C3%A1kon" title="Vědecký zákon – Czech" lang="cs" hreflang="cs" data-title="Vědecký zákon" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Mutemo_(ruzivo)" title="Mutemo (ruzivo) – Shona" lang="sn" hreflang="sn" data-title="Mutemo (ruzivo)" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Lov_(naturvidenskab)" title="Lov (naturvidenskab) – Danish" lang="da" hreflang="da" data-title="Lov (naturvidenskab)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Naturgesetz" title="Naturgesetz – German" lang="de" hreflang="de" data-title="Naturgesetz" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Loodusseadus" title="Loodusseadus – Estonian" lang="et" hreflang="et" data-title="Loodusseadus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A6%CF%85%CF%83%CE%B9%CE%BA%CF%8C%CF%82_%CE%BD%CF%8C%CE%BC%CE%BF%CF%82" title="Φυσικός νόμος – Greek" lang="el" hreflang="el" data-title="Φυσικός νόμος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ley_cient%C3%ADfica" title="Ley científica – Spanish" lang="es" hreflang="es" data-title="Ley científica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Scienca_le%C4%9Do" title="Scienca leĝo – Esperanto" lang="eo" hreflang="eo" data-title="Scienca leĝo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Lege_(zientzia)" title="Lege (zientzia) – Basque" lang="eu" hreflang="eu" data-title="Lege (zientzia)" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%82%D8%A7%D9%86%D9%88%D9%86_%D8%B9%D9%84%D9%85%DB%8C" title="قانون علمی – Persian" lang="fa" hreflang="fa" data-title="قانون علمی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Loi_scientifique" title="Loi scientifique – French" lang="fr" hreflang="fr" data-title="Loi scientifique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8_%E0%A4%95%E0%A5%87_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE" title="विज्ञान के नियम – Hindi" lang="hi" hreflang="hi" data-title="विज्ञान के नियम" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Lego_ciencala" title="Lego ciencala – Ido" lang="io" hreflang="io" data-title="Lego ciencala" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hukum_ilmiah" title="Hukum ilmiah – Indonesian" lang="id" hreflang="id" data-title="Hukum ilmiah" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Lege_scientific" title="Lege scientific – Interlingua" lang="ia" hreflang="ia" data-title="Lege scientific" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Lwa_(syans)" title="Lwa (syans) – Haitian Creole" lang="ht" hreflang="ht" data-title="Lwa (syans)" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D1%8B%D0%B9%D0%B7%D0%B0%D0%BC_(%D0%B8%D0%BB%D0%B8%D0%BC)" title="Мыйзам (илим) – Kyrgyz" lang="ky" hreflang="ky" data-title="Мыйзам (илим)" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Lex_scientifica" title="Lex scientifica – Latin" lang="la" hreflang="la" data-title="Lex scientifica" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Lege_siensal" title="Lege siensal – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Lege siensal" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Undang-undang_saintifik" title="Undang-undang saintifik – Malay" lang="ms" hreflang="ms" data-title="Undang-undang saintifik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wet_(wetenschap)" title="Wet (wetenschap) – Dutch" lang="nl" hreflang="nl" data-title="Wet (wetenschap)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Naturlov" title="Naturlov – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Naturlov" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A8%BF%E0%A8%97%E0%A8%BF%E0%A8%86%E0%A8%A8_%E0%A8%A6%E0%A9%87_%E0%A8%A8%E0%A8%BF%E0%A8%AF%E0%A8%AE" title="ਵਿਗਿਆਨ ਦੇ ਨਿਯਮ – Punjabi" lang="pa" hreflang="pa" data-title="ਵਿਗਿਆਨ ਦੇ ਨਿਯਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%D9%BE%D9%88%D9%87%DB%90_%D9%82%D8%A7%D9%86%D9%88%D9%86" title="د پوهې قانون – Pashto" lang="ps" hreflang="ps" data-title="د پوهې قانون" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Prawo_nauki" title="Prawo nauki – Polish" lang="pl" hreflang="pl" data-title="Prawo nauki" data-language-autonym="Polski" data-language-local-name="Polish" 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class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Statement based on repeated empirical observations that describes some natural phenomenon</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Laws of the universe" redirects here. For the anime film series, see <a href="/wiki/The_Laws_of_the_Universe" title="The Laws of the Universe"><i>The Laws of the Universe</i></a>.</div> <p><b>Scientific laws</b> or <b>laws of science</b> are statements, based on <a href="/wiki/Reproducibility" title="Reproducibility">repeated</a> <a href="/wiki/Experiment" title="Experiment">experiments</a> or <a href="/wiki/Observation" title="Observation">observations</a>, that describe or <a href="/wiki/Prediction" title="Prediction">predict</a> a range of <a href="/wiki/Natural_phenomena" class="mw-redirect" title="Natural phenomena">natural phenomena</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The term <i>law</i> has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of <a href="/wiki/Natural_science" title="Natural science">natural science</a> (<a href="/wiki/Physics" title="Physics">physics</a>, <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>, <a href="/wiki/Geoscience" class="mw-redirect" title="Geoscience">geoscience</a>, <a href="/wiki/Biology" title="Biology">biology</a>). Laws are developed from data and can be further developed through <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>; in all cases they are directly or indirectly based on <a href="/wiki/Empirical_evidence" title="Empirical evidence">empirical evidence</a>. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, scientific laws do not express absolute certainty, as <a href="/wiki/Law_(mathematics)" title="Law (mathematics)">mathematical laws</a> do. A scientific law may be contradicted, restricted, or extended by future observations. </p><p>A law can often be formulated as one or several statements or <a href="/wiki/Equation" title="Equation">equations</a>, so that it can predict the outcome of an experiment. Laws differ from <a href="/wiki/Hypotheses" class="mw-redirect" title="Hypotheses">hypotheses</a> and <a href="/wiki/Postulates" class="mw-redirect" title="Postulates">postulates</a>, which are proposed during the <a href="/wiki/Scientific_method" title="Scientific method">scientific process</a> before and during validation by experiment and observation. Hypotheses and postulates are not laws, since they have not been verified to the same degree, although they may lead to the formulation of laws. Laws are narrower in scope than <a href="/wiki/Scientific_theory" title="Scientific theory">scientific theories</a>, which may entail one or several laws.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Science distinguishes a law or theory from facts.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Calling a law a <a href="/wiki/Scientific_fact" class="mw-redirect" title="Scientific fact">fact</a> is <a href="/wiki/Ambiguous" class="mw-redirect" title="Ambiguous">ambiguous</a>, an <a href="/wiki/Overstatement" class="mw-redirect" title="Overstatement">overstatement</a>, or an <a href="/wiki/Equivocation" title="Equivocation">equivocation</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The nature of scientific laws has been much discussed in <a href="/wiki/Philosophy" title="Philosophy">philosophy</a>, but in essence scientific laws are simply empirical conclusions reached by the scientific method; they are intended to be neither laden with <a href="/wiki/Ontology" title="Ontology">ontological</a> commitments nor statements of logical <a href="https://en.wiktionary.org/wiki/absolute#Noun" class="extiw" title="wikt:absolute">absolutes</a>. </p><p><a href="/wiki/Social_science" title="Social science">Social sciences</a> such as <a href="/wiki/Economics" title="Economics">economics</a> have also attempted to formulate scientific laws, though these generally have much less predictive power. </p> <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A scientific law always applies to a <a href="/wiki/Physical_system" title="Physical system">physical system</a> under repeated conditions, and it implies that there is a causal relationship involving the elements of the system. <a href="/wiki/Scientific_fact" class="mw-redirect" title="Scientific fact">Factual</a> and well-confirmed statements like "Mercury is liquid at standard temperature and pressure" are considered too specific to qualify as scientific laws. A central problem in the <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>, going back to <a href="/wiki/David_Hume" title="David Hume">David Hume</a>, is that of distinguishing causal relationships (such as those implied by laws) from principles that arise due to <a href="/wiki/Constant_conjunction" title="Constant conjunction">constant conjunction</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Laws differ from <a href="/wiki/Scientific_theory" title="Scientific theory">scientific theories</a> in that they do not posit a mechanism or explanation of phenomena: they are merely distillations of the results of repeated observation. As such, the applicability of a law is limited to circumstances resembling those already observed, and the law may be found to be false when extrapolated. <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a> only applies to linear networks; <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a> only applies in weak gravitational fields; the early laws of <a href="/wiki/Aerodynamics" title="Aerodynamics">aerodynamics</a>, such as <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a>, do not apply in the case of <a href="/wiki/Compressible_flow" title="Compressible flow">compressible flow</a> such as occurs in <a href="/wiki/Transonic" title="Transonic">transonic</a> and <a href="/wiki/Supersonic" class="mw-redirect" title="Supersonic">supersonic</a> flight; <a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's law</a> only applies to <a href="/wiki/Strain_(physics)" class="mw-redirect" title="Strain (physics)">strain</a> below the <a href="/wiki/Elastic_limit" class="mw-redirect" title="Elastic limit">elastic limit</a>; <a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a> applies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the specified conditions where they apply. </p><p>Many laws take <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> forms, and thus can be stated as an equation; for example, the <a href="/wiki/Law_of_conservation_of_energy" class="mw-redirect" title="Law of conservation of energy">law of conservation of energy</a> can be written as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/736e2ba2135436d4654d56d498609b2eada4a5c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.972ex; height:2.176ex;" alt="{\displaystyle \Delta E=0}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is the total amount of energy in the universe. Similarly, the <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">first law of thermodynamics</a> can be written as <span class="mwe-math-element"><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 {d} U=\delta Q-\delta W\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>−</mo> <mi>δ</mi> <mi>W</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=\delta Q-\delta W\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad7835fa46e07e18557270acfb692ea2bf8cbcbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.772ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} U=\delta Q-\delta W\,}"></span>, and <a href="/wiki/Newton%27s_laws_of_motion#Newton's_second_law" title="Newton's laws of motion">Newton's second law</a> can be written as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle F={\frac {dp}{dt}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>p</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle F={\frac {dp}{dt}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d2d31ed16a182e7fede231453fba0af3b4d6b05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:8.009ex; height:4.009ex;" alt="{\displaystyle \textstyle F={\frac {dp}{dt}}.}"></span> While these scientific laws explain what our senses perceive, they are still empirical (acquired by observation or scientific experiment) and so are not like mathematical theorems which can be proved purely by mathematics. </p><p>Like theories and hypotheses, laws make predictions; specifically, they predict that new observations will conform to the given law. Laws can be <a href="/wiki/Falsifiability" title="Falsifiability">falsified</a> if they are found in contradiction with new data. </p><p>Some laws are only approximations of other more general laws, and are good approximations with a restricted domain of applicability. For example, <a href="/wiki/Newtonian_dynamics" title="Newtonian dynamics">Newtonian dynamics</a> (which is based on Galilean transformations) is the low-speed limit of special relativity (since the Galilean transformation is the low-speed approximation to the Lorentz transformation). Similarly, the <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newtonian gravitation law</a> is a low-mass approximation of general relativity, and <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a> is an approximation to quantum electrodynamics at large distances (compared to the range of weak interactions). In such cases it is common to use the simpler, approximate versions of the laws, instead of the more accurate general laws. </p><p>Laws are constantly being tested experimentally to increasing degrees of precision, which is one of the main goals of science. The fact that laws have never been observed to be violated does not preclude testing them at increased accuracy or in new kinds of conditions to confirm whether they continue to hold, or whether they break, and what can be discovered in the process. It is always possible for laws to be invalidated or proven to have limitations, by repeatable experimental evidence, should any be observed. Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations, to which other terms or factors must be added to cover previously unaccounted-for conditions, e.g. very large or very small scales of time or space, enormous speeds or masses, etc. Thus, rather than unchanging knowledge, physical laws are better viewed as a series of improving and more precise generalizations. </p> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=2" title="Edit section: Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Scientific laws are typically conclusions based on repeated scientific <a href="/wiki/Experiment" title="Experiment">experiments</a> and <a href="/wiki/Observations" class="mw-redirect" title="Observations">observations</a> over many years and which have become accepted universally within the <a href="/wiki/Scientific_community" title="Scientific community">scientific community</a>. A scientific law is "<a href="/wiki/Inferred" class="mw-redirect" title="Inferred">inferred</a> from particular facts, applicable to a defined group or class of <a href="/wiki/Phenomena" class="mw-redirect" title="Phenomena">phenomena</a>, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present".<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The production of a summary description of our environment in the form of such laws is a fundamental aim of <a href="/wiki/Science" title="Science">science</a>. </p><p>Several general properties of scientific laws, particularly when referring to laws in <a href="/wiki/Physics" title="Physics">physics</a>, have been identified. Scientific laws are: </p> <ul><li>True, at least within their regime of validity. By definition, there have never been repeatable contradicting observations.</li> <li>Universal. They appear to apply everywhere in the universe.<sup id="cite_ref-Davies_8-0" class="reference"><a href="#cite_note-Davies-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 82">: 82 </span></sup></li> <li>Simple. They are typically expressed in terms of a single mathematical equation.</li> <li>Absolute. Nothing in the universe appears to affect them.<sup id="cite_ref-Davies_8-1" class="reference"><a href="#cite_note-Davies-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 82">: 82 </span></sup></li> <li>Stable. Unchanged since first discovered (although they may have been shown to be approximations of more accurate laws),</li> <li>All-encompassing. Everything in the universe apparently must comply with them (according to observations).</li> <li>Generally <a href="/wiki/Conservation_law_(physics)" class="mw-redirect" title="Conservation law (physics)">conservative</a> of quantity.<sup id="cite_ref-Feynman_9-0" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 59">: 59 </span></sup></li> <li>Often expressions of existing homogeneities (<a href="/wiki/Symmetries" class="mw-redirect" title="Symmetries">symmetries</a>) of <a href="/wiki/Space" title="Space">space</a> and time.<sup id="cite_ref-Feynman_9-1" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>Typically theoretically reversible in time (if non-<a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum</a>), although <a href="/wiki/Arrow_of_time" title="Arrow of time">time itself is irreversible</a>.<sup id="cite_ref-Feynman_9-2" class="reference"><a href="#cite_note-Feynman-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>Broad. In physics, laws exclusively refer to the broad domain of matter, motion, energy, and force itself, rather than more specific <a href="/wiki/Physical_system" title="Physical system">systems</a> in the universe, such as <a href="/wiki/Physiology" title="Physiology">living systems</a>, e.g. the <a href="/wiki/Biomechanics" title="Biomechanics">mechanics</a> of the <a href="/wiki/Human_body" title="Human body">human body</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li></ul> <p>The term "scientific law" is traditionally associated with the <a href="/wiki/Natural_sciences" class="mw-redirect" title="Natural sciences">natural sciences</a>, though the <a href="/wiki/Social_sciences" class="mw-redirect" title="Social sciences">social sciences</a> also contain laws.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> For example, <a href="/wiki/Zipf%27s_law" title="Zipf's law">Zipf's law</a> is a law in the social sciences which is based on <a href="/wiki/Mathematical_statistics" title="Mathematical statistics">mathematical statistics</a>. In these cases, laws may describe general trends or expected behaviors rather than being absolutes. </p><p>In natural science, <a href="/wiki/Proof_of_impossibility" title="Proof of impossibility">impossibility assertions</a> come to be widely accepted as overwhelmingly probable rather than considered proved to the point of being unchallengeable. The basis for this strong acceptance is a combination of extensive evidence of something not occurring, combined with an underlying <a href="/wiki/Scientific_theory" title="Scientific theory">theory</a>, very successful in making predictions, whose assumptions lead logically to the conclusion that something is impossible. While an impossibility assertion in natural science can never be absolutely proved, it could be refuted by the observation of a single <a href="/wiki/Counterexample" title="Counterexample">counterexample</a>. Such a counterexample would require that the assumptions underlying the theory that implied the impossibility be re-examined. </p><p>Some examples of widely accepted impossibilities in <a href="/wiki/Physics" title="Physics">physics</a> are <a href="/wiki/Perpetual_motion_machines" class="mw-redirect" title="Perpetual motion machines">perpetual motion machines</a>, which violate the <a href="/wiki/Law_of_conservation_of_energy" class="mw-redirect" title="Law of conservation of energy">law of conservation of energy</a>, exceeding the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>, which violates the implications of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>, the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">uncertainty principle</a> of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, which asserts the impossibility of simultaneously knowing both the position and the momentum of a particle, and <a href="/wiki/Bell%27s_theorem" title="Bell's theorem">Bell's theorem</a>: no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. </p> <div class="mw-heading mw-heading2"><h2 id="Laws_as_consequences_of_mathematical_symmetries">Laws as consequences of mathematical symmetries</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=3" title="Edit section: Laws as consequences of mathematical symmetries"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Symmetry_(physics)" title="Symmetry (physics)">Symmetry (physics)</a></div> <p>Some laws reflect mathematical symmetries found in nature (e.g. the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a> reflects identity of electrons, conservation laws reflect <a href="/wiki/Homogeneity_(physics)" title="Homogeneity (physics)">homogeneity</a> of <a href="/wiki/Space" title="Space">space</a>, time, and <a href="/wiki/Lorentz_transformations" class="mw-redirect" title="Lorentz transformations">Lorentz transformations</a> reflect rotational symmetry of <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>). Many fundamental physical laws are mathematical consequences of various <a href="/wiki/Symmetries" class="mw-redirect" title="Symmetries">symmetries</a> of space, time, or other aspects of nature. Specifically, <a href="/wiki/Noether%27s_theorem" title="Noether's theorem">Noether's theorem</a> connects some conservation laws to certain symmetries. For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different from any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the <a href="/wiki/Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics">Dirac</a> and <a href="/wiki/Bose%E2%80%93Einstein_statistics" title="Bose–Einstein statistics">Bose</a> quantum statistics which in turn result in the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a> for <a href="/wiki/Fermion" title="Fermion">fermions</a> and in <a href="/wiki/Bose%E2%80%93Einstein_condensation" class="mw-redirect" title="Bose–Einstein condensation">Bose–Einstein condensation</a> for <a href="/wiki/Boson" title="Boson">bosons</a>. <a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a> uses <a href="/wiki/Rapidity" title="Rapidity">rapidity</a> to express motion according to the symmetries of <a href="/wiki/Hyperbolic_rotation" class="mw-redirect" title="Hyperbolic rotation">hyperbolic rotation</a>, a transformation mixing <a href="/wiki/Space" title="Space">space</a> and time. Symmetry between <a href="/wiki/Inertial" class="mw-redirect" title="Inertial">inertial</a> and gravitational <a href="/wiki/Mass" title="Mass">mass</a> results in <a href="/wiki/General_relativity" title="General relativity">general relativity</a>. </p><p>The <a href="/wiki/Inverse_square_law" class="mw-redirect" title="Inverse square law">inverse square law</a> of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of <a href="/wiki/Space" title="Space">space</a>. </p><p>One strategy in the search for the most fundamental laws of nature is to search for the most general mathematical symmetry group that can be applied to the fundamental interactions. </p> <div class="mw-heading mw-heading2"><h2 id="Laws_of_physics">Laws of physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=4" title="Edit section: Laws of physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Conservation_laws">Conservation laws</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=5" title="Edit section: Conservation laws"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Conservation_and_symmetry">Conservation and symmetry</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=6" title="Edit section: Conservation and symmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Symmetry_(physics)" title="Symmetry (physics)">Symmetry (physics)</a></div> <p><a href="/wiki/Conservation_laws" class="mw-redirect" title="Conservation laws">Conservation laws</a> are fundamental laws that follow from the homogeneity of space, time and <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a>, in other words <i>symmetry</i>. </p> <ul><li><b><a href="/wiki/Noether%27s_theorem" title="Noether's theorem">Noether's theorem</a>:</b> Any quantity with a continuously differentiable symmetry in the action has an associated conservation law.</li> <li><a href="/wiki/Conservation_of_mass" title="Conservation of mass">Conservation of mass</a> was the first law to be understood since most macroscopic physical processes involving masses, for example, collisions of massive particles or fluid flow, provide the apparent belief that mass is conserved. Mass conservation was observed to be true for all chemical reactions. In general, this is only approximative because with the advent of relativity and experiments in nuclear and particle physics: mass can be transformed into energy and vice versa, so mass is not always conserved but part of the more general conservation of <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">mass–energy</a>.</li> <li><b><a href="/wiki/Conservation_of_energy" title="Conservation of energy">Conservation of energy</a></b>, <b><a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">momentum</a></b> and <b><a href="/wiki/Conservation_of_angular_momentum" class="mw-redirect" title="Conservation of angular momentum">angular momentum</a></b> for isolated systems can be found to be <a href="/wiki/Time_translation_symmetry" class="mw-redirect" title="Time translation symmetry">symmetries in time</a>, translation, and rotation.</li> <li><b><a href="/wiki/Conservation_of_charge" class="mw-redirect" title="Conservation of charge">Conservation of charge</a></b> was also realized since charge has never been observed to be created or destroyed and only found to move from place to place.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Continuity_and_transfer">Continuity and transfer</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=7" title="Edit section: Continuity and transfer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Conservation laws can be expressed using the general <a href="/wiki/Continuity_equation" title="Continuity equation">continuity equation</a> (for a conserved quantity) can be written in differential form as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ρ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62bd69e75485a67884a35dce01812ea85b786743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.258ex; height:5.676ex;" alt="{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J} }"></span></dd></dl> <p>where <i>ρ</i> is some quantity per unit volume, <b>J</b> is the <a href="/wiki/Flux" title="Flux">flux</a> of that quantity (change in quantity per unit time per unit area). Intuitively, the <a href="/wiki/Divergence" title="Divergence">divergence</a> (denoted ∇⋅) of a <a href="/wiki/Vector_field" title="Vector field">vector field</a> is a measure of flux diverging radially outwards from a point, so the negative is the amount piling up at a point; hence the rate of change of density in a region of space must be the amount of flux leaving or collecting in some region (see the main article for details). In the table below, the fluxes flows for various physical quantities in transport, and their associated continuity equations, are collected for comparison. </p> <dl><dd><table class="wikitable" align="center"> <tbody><tr> <th scope="col" style="width:150px;">Physics, conserved quantity </th> <th scope="col" style="width:140px;">Conserved quantity <i>q</i> </th> <th scope="col" style="width:140px;">Volume density <i>ρ</i> (of <i>q</i>) </th> <th scope="col" style="width:140px;">Flux <b>J</b> (of <i>q</i>) </th> <th scope="col" style="width:10px;">Equation </th></tr> <tr> <td><a href="/wiki/Hydrodynamics" class="mw-redirect" title="Hydrodynamics">Hydrodynamics</a>, <a href="/wiki/Fluid" title="Fluid">fluids</a> <br /> </td> <td><i>m</i> = <a href="/wiki/Mass" title="Mass">mass</a> (kg) </td> <td><i>ρ</i> = volume <a href="/wiki/Mass_density" class="mw-redirect" title="Mass density">mass density</a> (kg m<sup>−3</sup>) </td> <td><i>ρ</i> <b>u</b>, where<br /> <p><b>u</b> = <a href="/wiki/Velocity_field" class="mw-redirect" title="Velocity field">velocity field</a> of fluid (m s<sup>−1</sup>) </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 {\frac {\partial \rho }{\partial t}}=-\nabla \cdot (\rho \mathbf {u} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ρ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot (\rho \mathbf {u} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b85d7e9a18ceeda6e566a6ef1c7c5d92d6a17063" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.374ex; height:5.676ex;" alt="{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot (\rho \mathbf {u} )}"></span> </td></tr> <tr> <td><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a>, <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> </td> <td><i>q</i> = electric charge (C) </td> <td><i>ρ</i> = volume electric <a href="/wiki/Charge_density" title="Charge density">charge density</a> (C m<sup>−3</sup>) </td> <td><b>J</b> = electric <a href="/wiki/Current_density" title="Current density">current density</a> (A m<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 {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ρ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62bd69e75485a67884a35dce01812ea85b786743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.258ex; height:5.676ex;" alt="{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {J} }"></span> </td></tr> <tr> <td><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a>, <a href="/wiki/Energy" title="Energy">energy</a> </td> <td><i>E</i> = energy (J) </td> <td><i>u</i> = volume <a href="/wiki/Energy_density" title="Energy density">energy density</a> (J m<sup>−3</sup>) </td> <td><b>q</b> = <a href="/wiki/Heat_flux" title="Heat flux">heat flux</a> (W m<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 {\frac {\partial u}{\partial t}}=-\nabla \cdot \mathbf {q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial u}{\partial t}}=-\nabla \cdot \mathbf {q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8e7ca9296b7d9d4f03dfe8bf12cb8c59245207f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.421ex; height:5.509ex;" alt="{\displaystyle {\frac {\partial u}{\partial t}}=-\nabla \cdot \mathbf {q} }"></span> </td></tr> <tr> <td><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a>, <a href="/wiki/Probability" title="Probability">probability</a> </td> <td>Ψ|<sup>2</sup>d<sup>3</sup><b>r</b> = <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> </td> <td>Ψ|<sup>2</sup> = <a href="/wiki/Probability_density_function" title="Probability density function">probability density function</a> (m<sup>−3</sup>),<br /> <p>Ψ = <a href="/wiki/Wavefunction" class="mw-redirect" title="Wavefunction">wavefunction</a> of quantum system </p> </td> <td><b>j</b> = <a href="/wiki/Probability_current" title="Probability current">probability current</a>/flux </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 {\partial |\Psi |^{2}}{\partial t}}=-\nabla \cdot \mathbf {j} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial |\Psi |^{2}}{\partial t}}=-\nabla \cdot \mathbf {j} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2148cfb789c22f501e008c3f34209937acdae551" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.648ex; height:6.176ex;" alt="{\displaystyle {\frac {\partial |\Psi |^{2}}{\partial t}}=-\nabla \cdot \mathbf {j} }"></span> </td></tr></tbody></table></dd></dl> <p>More general equations are the <a href="/wiki/Convection%E2%80%93diffusion_equation" title="Convection–diffusion equation">convection–diffusion equation</a> and <a href="/wiki/Boltzmann_transport_equation" class="mw-redirect" title="Boltzmann transport equation">Boltzmann transport equation</a>, which have their roots in the continuity equation. </p> <div class="mw-heading mw-heading3"><h3 id="Laws_of_classical_mechanics">Laws of classical mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=8" title="Edit section: Laws of classical mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Principle_of_least_action">Principle of least action</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=9" title="Edit section: Principle of least action"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Principle_of_least_action" class="mw-redirect" title="Principle of least action">Principle of least action</a></div> <p>Classical mechanics, including <a href="/wiki/Newton%27s_laws" class="mw-redirect" title="Newton's laws">Newton's laws</a>, <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrange's equations</a>, <a href="/wiki/Hamiltonian_mechanics" title="Hamiltonian mechanics">Hamilton's equations</a>, etc., can be derived from the following principle: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta {\mathcal {S}}=\delta \int _{t_{1}}^{t_{2}}L(\mathbf {q} ,\mathbf {\dot {q}} ,t)\,dt=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">S</mi> </mrow> </mrow> <mo>=</mo> <mi>δ</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msubsup> <mi>L</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold">q</mi> <mo mathvariant="bold">˙</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta {\mathcal {S}}=\delta \int _{t_{1}}^{t_{2}}L(\mathbf {q} ,\mathbf {\dot {q}} ,t)\,dt=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/912c4d51bb9176f72592229b06196f3ec836359f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:27.418ex; height:6.509ex;" alt="{\displaystyle \delta {\mathcal {S}}=\delta \int _{t_{1}}^{t_{2}}L(\mathbf {q} ,\mathbf {\dot {q}} ,t)\,dt=0}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">S</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2302a18e269dbecc43c57c0c2aced3bfae15278d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.492ex; height:2.176ex;" alt="{\displaystyle {\mathcal {S}}}"></span> is the <a href="/wiki/Action_(physics)" title="Action (physics)">action</a>; the integral of the <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L(\mathbf {q} ,\mathbf {\dot {q}} ,t)=T(\mathbf {\dot {q}} ,t)-V(\mathbf {q} ,\mathbf {\dot {q}} ,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold">q</mi> <mo mathvariant="bold">˙</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>T</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold">q</mi> <mo mathvariant="bold">˙</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold">q</mi> <mo mathvariant="bold">˙</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L(\mathbf {q} ,\mathbf {\dot {q}} ,t)=T(\mathbf {\dot {q}} ,t)-V(\mathbf {q} ,\mathbf {\dot {q}} ,t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc2919b08550e752cc365c1b81682916732b7314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.14ex; height:2.843ex;" alt="{\displaystyle L(\mathbf {q} ,\mathbf {\dot {q}} ,t)=T(\mathbf {\dot {q}} ,t)-V(\mathbf {q} ,\mathbf {\dot {q}} ,t)}"></span></dd></dl> <p>of the physical system between two times <i>t</i><sub>1</sub> and <i>t</i><sub>2</sub>. The kinetic energy of the system is <i>T</i> (a function of the rate of change of the <a href="/wiki/Configuration_space_(physics)" title="Configuration space (physics)">configuration</a> of the system), and <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a> is <i>V</i> (a function of the configuration and its rate of change). The configuration of a system which has <i>N</i> <a href="/wiki/Degrees_of_freedom_(mechanics)" title="Degrees of freedom (mechanics)">degrees of freedom</a> is defined by <a href="/wiki/Generalized_coordinates" title="Generalized coordinates">generalized coordinates</a> <b>q</b> = (<i>q</i><sub>1</sub>, <i>q</i><sub>2</sub>, ... <i>q<sub>N</sub></i>). </p><p>There are <a href="/wiki/Canonical_coordinates" title="Canonical coordinates">generalized momenta</a> conjugate to these coordinates, <b>p</b> = (<i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, ..., <i>p<sub>N</sub></i>), where: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>L</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff9f730bbf0559ea59e59eafb7b852875676c62d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:9.488ex; height:6.009ex;" alt="{\displaystyle p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}}"></span></dd></dl> <p>The action and Lagrangian both contain the dynamics of the system for all times. The term "path" simply refers to a curve traced out by the system in terms of the <a href="/wiki/Generalized_coordinates" title="Generalized coordinates">generalized coordinates</a> in the <a href="/wiki/Configuration_space_(physics)" title="Configuration space (physics)">configuration space</a>, i.e. the curve <b>q</b>(<i>t</i>), parameterized by time (see also <a href="/wiki/Parametric_equation" title="Parametric equation">parametric equation</a> for this concept). </p><p>The action is a <i><a href="/wiki/Functional_(mathematics)" title="Functional (mathematics)">functional</a></i> rather than a <i><a href="/wiki/Function_(mathematics)" title="Function (mathematics)">function</a></i>, since it depends on the Lagrangian, and the Lagrangian depends on the path <b>q</b>(<i>t</i>), so the action depends on the <i>entire</i> "shape" of the path for all times (in the time interval from <i>t</i><sub>1</sub> to <i>t</i><sub>2</sub>). Between two instants of time, there are infinitely many paths, but one for which the action is stationary (to the first order) is the true path. The stationary value for the <i>entire continuum</i> of Lagrangian values corresponding to some path, <i>not just one value</i> of the Lagrangian, is required (in other words it is <i>not</i> as simple as "differentiating a function and setting it to zero, then solving the equations to find the points of <a href="/wiki/Maxima_and_minima" class="mw-redirect" title="Maxima and minima">maxima and minima</a> etc", rather this idea is applied to the entire "shape" of the function, see <a href="/wiki/Calculus_of_variations" title="Calculus of variations">calculus of variations</a> for more details on this procedure).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Notice <i>L</i> is <i>not</i> the total energy <i>E</i> of the system due to the difference, rather than the sum: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=T+V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>T</mi> <mo>+</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=T+V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39f4206d30814f7457f644748fa37068ca219be4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.138ex; height:2.343ex;" alt="{\displaystyle E=T+V}"></span></dd></dl> <p>The following<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> general approaches to classical mechanics are summarized below in the order of establishment. They are equivalent formulations. Newton's is commonly used due to simplicity, but Hamilton's and Lagrange's equations are more general, and their range can extend into other branches of physics with suitable modifications. </p> <dl><dd><table class="wikitable" align="center"> <tbody><tr> <th scope="col" style="width:600px;" colspan="2"><b>Laws of motion</b> </th></tr> <tr> <td colspan="2"><b><a href="/wiki/Principle_of_least_action" class="mw-redirect" title="Principle of least action">Principle of least action</a>:</b> <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 {\mathcal {S}}=\int _{t_{1}}^{t_{2}}L\,\mathrm {d} t\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">S</mi> </mrow> </mrow> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msubsup> <mi>L</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {S}}=\int _{t_{1}}^{t_{2}}L\,\mathrm {d} t\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14557a506f8aebcfa92029d01e6d07e1409f5722" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-right: -0.387ex; width:13.589ex; height:6.509ex;" alt="{\displaystyle {\mathcal {S}}=\int _{t_{1}}^{t_{2}}L\,\mathrm {d} t\,\!}"></span> </p> </td></tr> <tr valign="top"> <td rowspan="2" scope="col" style="width:300px;"><b>The <a href="/wiki/Euler%E2%80%93Lagrange_equation" title="Euler–Lagrange equation">Euler–Lagrange equations</a> are:</b> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left({\frac {\partial L}{\partial {\dot {q}}_{i}}}\right)={\frac {\partial L}{\partial q_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>L</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>L</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left({\frac {\partial L}{\partial {\dot {q}}_{i}}}\right)={\frac {\partial L}{\partial q_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d4bdf20fb476096ff0032f276ce58c35b33058f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.197ex; height:6.176ex;" alt="{\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left({\frac {\partial L}{\partial {\dot {q}}_{i}}}\right)={\frac {\partial L}{\partial q_{i}}}}"></span></dd></dl> <p>Using the definition of generalized momentum, there is the symmetry: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}\quad {\dot {p}}_{i}={\frac {\partial L}{\partial {q}_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>L</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mspace width="1em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>L</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}\quad {\dot {p}}_{i}={\frac {\partial L}{\partial {q}_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b87186509d16602710d86cc41b2f0474b37c839" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:21.059ex; height:6.009ex;" alt="{\displaystyle p_{i}={\frac {\partial L}{\partial {\dot {q}}_{i}}}\quad {\dot {p}}_{i}={\frac {\partial L}{\partial {q}_{i}}}}"></span></dd></dl> </td> <td style="width:300px;"><b>Hamilton's equations</b> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dfrac {\partial \mathbf {p} }{\partial t}}=-{\dfrac {\partial H}{\partial \mathbf {q} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mstyle> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dfrac {\partial \mathbf {p} }{\partial t}}=-{\dfrac {\partial H}{\partial \mathbf {q} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e90ed8a1d1545a608eb1af27d7ac947906239fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.764ex; height:5.843ex;" alt="{\displaystyle {\dfrac {\partial \mathbf {p} }{\partial t}}=-{\dfrac {\partial H}{\partial \mathbf {q} }}}"></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 {\dfrac {\partial \mathbf {q} }{\partial t}}={\dfrac {\partial H}{\partial \mathbf {p} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dfrac {\partial \mathbf {q} }{\partial t}}={\dfrac {\partial H}{\partial \mathbf {p} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed2e10b3c587538be8db509bd296e0d2f733f530" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.886ex; height:5.843ex;" alt="{\displaystyle {\dfrac {\partial \mathbf {q} }{\partial t}}={\dfrac {\partial H}{\partial \mathbf {p} }}}"></span></dd></dl> <p>The Hamiltonian as a function of generalized coordinates and momenta has the general form: <br /> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H(\mathbf {q} ,\mathbf {p} ,t)=\mathbf {p} \cdot \mathbf {\dot {q}} -L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold">q</mi> <mo mathvariant="bold">˙</mo> </mover> </mrow> </mrow> <mo>−</mo> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(\mathbf {q} ,\mathbf {p} ,t)=\mathbf {p} \cdot \mathbf {\dot {q}} -L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7de8888318736bdc221b7274b89ced7260fb1b92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.783ex; height:2.843ex;" alt="{\displaystyle H(\mathbf {q} ,\mathbf {p} ,t)=\mathbf {p} \cdot \mathbf {\dot {q}} -L}"></span></dd></dl> </td></tr> <tr> <td><a href="/wiki/Hamilton%E2%80%93Jacobi_equation" title="Hamilton–Jacobi equation">Hamilton–Jacobi equation</a> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H\left(\mathbf {q} ,{\frac {\partial S}{\partial \mathbf {q} }},t\right)=-{\frac {\partial S}{\partial t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">q</mi> </mrow> </mrow> </mfrac> </mrow> <mo>,</mo> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H\left(\mathbf {q} ,{\frac {\partial S}{\partial \mathbf {q} }},t\right)=-{\frac {\partial S}{\partial t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0010b8a7dcc5d0f275957ad4d92c42a305b23fe8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.408ex; height:6.176ex;" alt="{\displaystyle H\left(\mathbf {q} ,{\frac {\partial S}{\partial \mathbf {q} }},t\right)=-{\frac {\partial S}{\partial t}}}"></span></dd></dl> </td></tr> <tr style="border-top: 3px solid;"> <td colspan="2" scope="col" style="width:600px;"><b>Newton's laws</b> <p><b><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a></b> </p><p>They are low-limit solutions to <a href="/wiki/Theory_of_relativity" title="Theory of relativity">relativity</a>. Alternative formulations of Newtonian mechanics are <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian</a> and <a href="/wiki/Hamiltonian_mechanics" title="Hamiltonian mechanics">Hamiltonian</a> mechanics. </p><p>The laws can be summarized by two equations (since the 1st is a special case of the 2nd, zero resultant acceleration): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},\quad \mathbf {F} _{ij}=-\mathbf {F} _{ji}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},\quad \mathbf {F} _{ij}=-\mathbf {F} _{ji}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eceab2ce64b0bf334c9b4465be12e6f1c9708c6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.978ex; height:5.509ex;" alt="{\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},\quad \mathbf {F} _{ij}=-\mathbf {F} _{ji}}"></span></dd></dl> <p>where <b>p</b> = momentum of body, <b>F</b><sub><i>ij</i></sub> = force <i>on</i> body <i>i</i> <i>by</i> body <i>j</i>, <b>F</b><sub><i>ji</i></sub> = force <i>on</i> body <i>j</i> <i>by</i> body <i>i</i>. </p><p>For a <a href="/wiki/Dynamical_system" title="Dynamical system">dynamical system</a> the two equations (effectively) combine into one: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {d} \mathbf {p} _{\mathrm {i} }}{\mathrm {d} t}}=\mathbf {F} _{\text{E}}+\sum _{\mathrm {i} \neq \mathrm {j} }\mathbf {F} _{\mathrm {ij} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>E</mtext> </mrow> </msub> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> </mrow> <mo>≠</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">j</mi> </mrow> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">j</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} \mathbf {p} _{\mathrm {i} }}{\mathrm {d} t}}=\mathbf {F} _{\text{E}}+\sum _{\mathrm {i} \neq \mathrm {j} }\mathbf {F} _{\mathrm {ij} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4555da921bb4824623be2ad817005f9020085663" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:19.894ex; height:7.176ex;" alt="{\displaystyle {\frac {\mathrm {d} \mathbf {p} _{\mathrm {i} }}{\mathrm {d} t}}=\mathbf {F} _{\text{E}}+\sum _{\mathrm {i} \neq \mathrm {j} }\mathbf {F} _{\mathrm {ij} }}"></span></dd></dl> <p>in which <b>F</b><sub>E</sub> = resultant external force (due to any agent not part of system). Body <i>i</i> does not exert a force on itself. </p> </td></tr></tbody></table></dd></dl> <p>From the above, any equation of motion in classical mechanics can be derived. </p><p><b>Corollaries in mechanics :</b> </p> <ul><li><a href="/wiki/Euler%27s_laws_of_motion" title="Euler's laws of motion">Euler's laws of motion</a></li> <li><a href="/wiki/Euler%27s_equations_(rigid_body_dynamics)" title="Euler's equations (rigid body dynamics)">Euler's equations (rigid body dynamics)</a></li></ul> <p><b>Corollaries in <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a> :</b><br /> </p><p>Equations describing fluid flow in various situations can be derived, using the above classical equations of motion and often conservation of mass, energy and momentum. Some elementary examples follow. </p> <ul><li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a></li> <li><a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a></li> <li><a href="/wiki/Poiseuille%27s_law" class="mw-redirect" title="Poiseuille's law">Poiseuille's law</a></li> <li><a href="/wiki/Stokes%27_law" title="Stokes' law">Stokes' law</a></li> <li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li> <li><a href="/wiki/Fax%C3%A9n%27s_law" title="Faxén's law">Faxén's law</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Laws_of_gravitation_and_relativity">Laws of gravitation and relativity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=10" title="Edit section: Laws of gravitation and relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some of the more famous laws of nature are found in <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>'s theories of (now) <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>, presented in his <i><a href="/wiki/Philosophiae_Naturalis_Principia_Mathematica" class="mw-redirect" title="Philosophiae Naturalis Principia Mathematica">Philosophiae Naturalis Principia Mathematica</a></i>, and in <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>'s <a href="/wiki/Theory_of_relativity" title="Theory of relativity">theory of relativity</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Modern_laws">Modern laws</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=11" title="Edit section: Modern laws"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a> :</b><br /> </p><p>The two postulates of special relativity are not "laws" in themselves, but assumptions of their nature in terms of <i>relative motion</i>. </p><p>They can be stated as "the laws of physics are the same in all <a href="/wiki/Inertial_frames" class="mw-redirect" title="Inertial frames">inertial frames</a>" and "the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> is constant and has the same value in all inertial frames". </p><p>The said postulates lead to the <a href="/wiki/Lorentz_transformations" class="mw-redirect" title="Lorentz transformations">Lorentz transformations</a> – the transformation law between two <a href="/wiki/Frame_of_reference" title="Frame of reference">frame of references</a> moving relative to each other. For any <a href="/wiki/4-vector" class="mw-redirect" title="4-vector">4-vector</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A'=\Lambda A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mo>′</mo> </msup> <mo>=</mo> <mi mathvariant="normal">Λ</mi> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A'=\Lambda A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79eb016669b54a5a20e61d42b64c0ae2cc579d3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.882ex; height:2.509ex;" alt="{\displaystyle A'=\Lambda A}"></span></dd></dl> <p>this replaces the <a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a> law from classical mechanics. The Lorentz transformations reduce to the Galilean transformations for low velocities much less than the speed of light <i>c</i>. </p><p>The magnitudes of 4-vectors are invariants – <i>not</i> "conserved", but the same for all inertial frames (i.e. every observer in an inertial frame will agree on the same value), in particular if <i>A</i> is the <a href="/wiki/Four-momentum" title="Four-momentum">four-momentum</a>, the magnitude can derive the famous invariant equation for mass–energy and momentum conservation (see <a href="/wiki/Invariant_mass" title="Invariant mass">invariant mass</a>): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E^{2}=(pc)^{2}+(mc^{2})^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}=(pc)^{2}+(mc^{2})^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/605c86001959e2c19055c26b7b9ad76132296728" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.792ex; height:3.176ex;" alt="{\displaystyle E^{2}=(pc)^{2}+(mc^{2})^{2}}"></span></dd></dl> <p>in which the (more famous) <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">mass–energy equivalence</a> <span class="nowrap"><i>E</i> = <i>mc</i><sup>2</sup></span> is a special case. </p><p><b><a href="/wiki/General_relativity" title="General relativity">General relativity</a> :</b><br /> </p><p>General relativity is governed by the <a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a>, which describe the curvature of space-time due to mass–energy equivalent to the gravitational field. Solving the equation for the geometry of space warped due to the mass distribution gives the <a href="/wiki/Metric_tensor" title="Metric tensor">metric tensor</a>. Using the geodesic equation, the motion of masses falling along the geodesics can be calculated. </p><p><b><a href="/wiki/Gravitoelectromagnetism" title="Gravitoelectromagnetism">Gravitoelectromagnetism</a> :</b><br /> </p><p>In a relatively flat spacetime due to weak gravitational fields, gravitational analogues of Maxwell's equations can be found; the <b>GEM equations</b>, to describe an analogous <i><a href="/wiki/Gravitoelectromagnetism" title="Gravitoelectromagnetism">gravitomagnetic field</a></i>. They are well established by the theory, and experimental tests form ongoing research.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><table class="wikitable" align="center"> <tbody><tr valign="top"> <td scope="col" style="width:300px;"><b><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a> (EFE):</b> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mu \nu }+\left(\Lambda -{\frac {R}{2}}\right)g_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Λ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>G</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mu \nu }+\left(\Lambda -{\frac {R}{2}}\right)g_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f3509063a74d76dcf464e0929b9e2e74f6fbeaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-right: -0.387ex; width:32.86ex; height:6.176ex;" alt="{\displaystyle R_{\mu \nu }+\left(\Lambda -{\frac {R}{2}}\right)g_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }\,\!}"></span></dd></dl> <p>where Λ = <a href="/wiki/Cosmological_constant" title="Cosmological constant">cosmological constant</a>, <i>R<sub>μν</sub></i> = <a href="/wiki/Ricci_curvature_tensor" class="mw-redirect" title="Ricci curvature tensor">Ricci curvature tensor</a>, <i>T<sub>μν</sub></i> = <a href="/wiki/Stress%E2%80%93energy_tensor" title="Stress–energy tensor">stress–energy tensor</a>, <i>g<sub>μν</sub></i> = <a href="/wiki/Metric_tensor" title="Metric tensor">metric tensor</a> </p> </td> <td scope="col" style="width:300px;"><b><a href="/wiki/Geodesic_equation" class="mw-redirect" title="Geodesic equation">Geodesic equation</a>:</b> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\rm {d}}^{2}x^{\lambda }}{{\rm {d}}t^{2}}}+\Gamma _{\mu \nu }^{\lambda }{\frac {{\rm {d}}x^{\mu }}{{\rm {d}}t}}{\frac {{\rm {d}}x^{\nu }}{{\rm {d}}t}}=0\ ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msup> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msubsup> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ν</mi> </mrow> </msup> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\rm {d}}^{2}x^{\lambda }}{{\rm {d}}t^{2}}}+\Gamma _{\mu \nu }^{\lambda }{\frac {{\rm {d}}x^{\mu }}{{\rm {d}}t}}{\frac {{\rm {d}}x^{\nu }}{{\rm {d}}t}}=0\ ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a86a34dc36baaeb68f17616a8e1cedcbd18d1e90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:26.823ex; height:6.009ex;" alt="{\displaystyle {\frac {{\rm {d}}^{2}x^{\lambda }}{{\rm {d}}t^{2}}}+\Gamma _{\mu \nu }^{\lambda }{\frac {{\rm {d}}x^{\mu }}{{\rm {d}}t}}{\frac {{\rm {d}}x^{\nu }}{{\rm {d}}t}}=0\ ,}"></span></dd></dl> <p>where Γ is a <a href="/wiki/Christoffel_symbol" class="mw-redirect" title="Christoffel symbol">Christoffel symbol</a> of the <a href="/wiki/Christoffel_symbols#Christoffel_symbols_of_the_second_kind_(symmetric_definition)" title="Christoffel symbols">second kind</a>, containing the metric. </p> </td></tr> <tr style="border-top: 3px solid;"> <td colspan="2"><b>GEM Equations</b> <p>If <b>g</b> the gravitational field and <b>H</b> the gravitomagnetic field, the solutions in these limits are: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \mathbf {g} =-4\pi G\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">g</mi> </mrow> <mo>=</mo> <mo>−</mo> <mn>4</mn> <mi>π</mi> <mi>G</mi> <mi>ρ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {g} =-4\pi G\rho \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28b3737e153baca269b4c733ba2970f59fa680d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:15.768ex; height:2.676ex;" alt="{\displaystyle \nabla \cdot \mathbf {g} =-4\pi G\rho \,\!}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \mathbf {H} =\mathbf {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">H</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {H} =\mathbf {0} \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a16e5bb52a2b70d58deaa23e29f224155e947d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:10.529ex; height:2.176ex;" alt="{\displaystyle \nabla \cdot \mathbf {H} =\mathbf {0} \,\!}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {g} =-{\frac {\partial \mathbf {H} }{\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">g</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">H</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 {g} =-{\frac {\partial \mathbf {H} }{\partial t}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3d2623319dfa2783f7e8ba81684f90d43b2d685" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:15.652ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {g} =-{\frac {\partial \mathbf {H} }{\partial t}}\,\!}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {H} ={\frac {4}{c^{2}}}\left(-4\pi G\mathbf {J} +{\frac {\partial \mathbf {g} }{\partial t}}\right)\,\!}"> <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">H</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>4</mn> <mi>π</mi> <mi>G</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">g</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {H} ={\frac {4}{c^{2}}}\left(-4\pi G\mathbf {J} +{\frac {\partial \mathbf {g} }{\partial t}}\right)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1b6d7876c85d34eef1351447903d5b4ae88743a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-right: -0.387ex; width:30.9ex; height:6.176ex;" alt="{\displaystyle \nabla \times \mathbf {H} ={\frac {4}{c^{2}}}\left(-4\pi G\mathbf {J} +{\frac {\partial \mathbf {g} }{\partial t}}\right)\,\!}"></span></dd></dl> <p>where <i>ρ</i> is the <a href="/wiki/Density" title="Density">mass density</a> and <b>J</b> is the mass current density or <a href="/wiki/Mass_flux" title="Mass flux">mass flux</a>. </p> </td></tr> <tr> <td colspan="2">In addition there is the <b>gravitomagnetic Lorentz force</b>: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =\gamma (\mathbf {v} )m\left(\mathbf {g} +\mathbf {v} \times \mathbf {H} \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mi>γ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">)</mo> <mi>m</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =\gamma (\mathbf {v} )m\left(\mathbf {g} +\mathbf {v} \times \mathbf {H} \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33fbb03d9f09d1685644238d7aaa6522a347d1eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.02ex; height:2.843ex;" alt="{\displaystyle \mathbf {F} =\gamma (\mathbf {v} )m\left(\mathbf {g} +\mathbf {v} \times \mathbf {H} \right)}"></span></dd></dl> <p>where <i>m</i> is the <a href="/wiki/Rest_mass" class="mw-redirect" title="Rest mass">rest mass</a> of the particlce and γ is the <a href="/wiki/Lorentz_factor" title="Lorentz factor">Lorentz factor</a>. </p> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Classical_laws">Classical laws</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=12" title="Edit section: Classical laws"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a> and <a href="/wiki/Newton%27s_law_of_gravitation" class="mw-redirect" title="Newton's law of gravitation">Newton's law of gravitation</a></div> <p>Kepler's laws, though originally discovered from planetary observations (also due to <a href="/wiki/Tycho_Brahe" title="Tycho Brahe">Tycho Brahe</a>), are true for any <i><a href="/wiki/Central_force" title="Central force">central forces</a></i>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><table class="wikitable" align="center"> <tbody><tr valign="top"> <td scope="col" style="width:300px;"><b><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a>:</b> <p>For two point masses: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} ={\frac {Gm_{1}m_{2}}{\left|\mathbf {r} \right|^{2}}}\mathbf {\hat {r}} \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <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> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold">r</mi> <mo mathvariant="bold" stretchy="false">^</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} ={\frac {Gm_{1}m_{2}}{\left|\mathbf {r} \right|^{2}}}\mathbf {\hat {r}} \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62d51ef66127320f23526e1fb5e75d3795aa3cd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:15.357ex; height:6.509ex;" alt="{\displaystyle \mathbf {F} ={\frac {Gm_{1}m_{2}}{\left|\mathbf {r} \right|^{2}}}\mathbf {\hat {r}} \,\!}"></span></dd></dl> <p>For a non uniform mass distribution of local mass density <i>ρ</i> (<b>r</b>) of body of Volume <i>V</i>, this becomes: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {g} =G\int _{V}{\frac {\mathbf {r} \rho \,\mathrm {d} {V}}{\left|\mathbf {r} \right|^{3}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <mo>=</mo> <mi>G</mi> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mi>ρ</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </mrow> <msup> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {g} =G\int _{V}{\frac {\mathbf {r} \rho \,\mathrm {d} {V}}{\left|\mathbf {r} \right|^{3}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5056c3846d05842ac75a59038461d113a4680654" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:16.819ex; height:6.509ex;" alt="{\displaystyle \mathbf {g} =G\int _{V}{\frac {\mathbf {r} \rho \,\mathrm {d} {V}}{\left|\mathbf {r} \right|^{3}}}\,\!}"></span></dd></dl> </td> <td scope="col" style="width:300px;"><b><a href="/wiki/Gauss%27s_law_for_gravity" title="Gauss's law for gravity">Gauss's law for gravity</a>:</b> <p>An equivalent statement to Newton's law is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \mathbf {g} =4\pi G\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">g</mi> </mrow> <mo>=</mo> <mn>4</mn> <mi>π</mi> <mi>G</mi> <mi>ρ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {g} =4\pi G\rho \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f74a91e5c781ff2f7fe4d92de4c097af2ae8bf56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:13.96ex; height:2.676ex;" alt="{\displaystyle \nabla \cdot \mathbf {g} =4\pi G\rho \,\!}"></span></dd></dl> </td></tr> <tr style="border-top: 3px solid;"> <td colspan="2" scope="col" style="width:600px;"><b>Kepler's 1st law:</b> Planets move in an ellipse, with the star at a focus <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {\ell }{1+e\cos \theta }}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ℓ</mi> <mrow> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {\ell }{1+e\cos \theta }}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2167e52e6e43a2231e650b81dca42c588e81821c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:15.432ex; height:5.676ex;" alt="{\displaystyle r={\frac {\ell }{1+e\cos \theta }}\,\!}"></span></dd></dl> <p>where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e={\sqrt {1-(b/a)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>a</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e={\sqrt {1-(b/a)^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3d4ef29008fbaa9842a886ef7441c592cc9d508" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:16.762ex; height:4.843ex;" alt="{\displaystyle e={\sqrt {1-(b/a)^{2}}}}"></span></dd></dl> <p>is the <a href="/wiki/Eccentricity_(mathematics)" title="Eccentricity (mathematics)">eccentricity</a> of the elliptic orbit, of semi-major axis <i>a</i> and semi-minor axis <i>b</i>, and <i>ℓ</i> is the semi-latus rectum. This equation in itself is nothing physically fundamental; simply the <a href="/wiki/Polar_coordinate_system" title="Polar coordinate system">polar equation</a> of an <a href="/wiki/Ellipse" title="Ellipse">ellipse</a> in which the pole (origin of polar coordinate system) is positioned at a focus of the ellipse, where the orbited star is. </p> </td></tr> <tr> <td colspan="2" style="width:600px;"><b>Kepler's 2nd law:</b> equal areas are swept out in equal times (area bounded by two radial distances and the orbital circumference): <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {d} A}{\mathrm {d} t}}={\frac {\left|\mathbf {L} \right|}{2m}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>A</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">L</mi> </mrow> <mo>|</mo> </mrow> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} A}{\mathrm {d} t}}={\frac {\left|\mathbf {L} \right|}{2m}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f855e372c357570b772a7c4e21bbf0633032e777" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.387ex; width:11.396ex; height:5.843ex;" alt="{\displaystyle {\frac {\mathrm {d} A}{\mathrm {d} t}}={\frac {\left|\mathbf {L} \right|}{2m}}\,\!}"></span></dd></dl> <p>where <b>L</b> is the orbital angular momentum of the particle (i.e. planet) of mass <i>m</i> about the focus of orbit, </p> </td></tr> <tr> <td colspan="2"><b>Kepler's 3rd law:</b> The square of the orbital time period <i>T</i> is proportional to the cube of the semi-major axis <i>a</i>: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T^{2}={\frac {4\pi ^{2}}{G\left(m+M\right)}}a^{3}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mrow> <mi>m</mi> <mo>+</mo> <mi>M</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{2}={\frac {4\pi ^{2}}{G\left(m+M\right)}}a^{3}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a91aa95cbed6d421982a37baf5cd07245f3cb83f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-right: -0.387ex; width:20.726ex; height:6.509ex;" alt="{\displaystyle T^{2}={\frac {4\pi ^{2}}{G\left(m+M\right)}}a^{3}\,\!}"></span></dd></dl> <p>where <i>M</i> is the mass of the central body (i.e. star). </p> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Thermodynamics">Thermodynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=13" title="Edit section: Thermodynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><table class="wikitable" align="center"> <tbody><tr> <th colspan="2"><b><a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">Laws of thermodynamics</a></b> </th></tr> <tr valign="top"> <td scope="col" style="width:150px;"><b><a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First law of thermodynamics</a>:</b> The change in internal energy d<i>U</i> in a closed system is accounted for entirely by the heat δ<i>Q</i> absorbed by the system and the work δ<i>W</i> done by the system: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=\delta Q-\delta W\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mo>−</mo> <mi>δ</mi> <mi>W</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=\delta Q-\delta W\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad7835fa46e07e18557270acfb692ea2bf8cbcbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.772ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} U=\delta Q-\delta W\,}"></span></dd></dl> <p><b><a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">Second law of thermodynamics</a>:</b> There are many statements of this law, perhaps the simplest is "the entropy of isolated systems never decreases", </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta S\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S\geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa331aee4875f49fa0f9bc35b807212533254270" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.696ex; height:2.343ex;" alt="{\displaystyle \Delta S\geq 0}"></span></dd></dl> <p>meaning reversible changes have zero entropy change, irreversible process are positive, and impossible process are negative. </p> </td> <td rowspan="2" style="width:150px;"><b><a href="/wiki/Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">Zeroth law of thermodynamics</a>:</b> If two systems are in <a href="/wiki/Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a> with a third system, then they are in thermal equilibrium with one another. <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{A}=T_{B}\,,T_{B}=T_{C}\Rightarrow T_{A}=T_{C}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>,</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">⇒</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{A}=T_{B}\,,T_{B}=T_{C}\Rightarrow T_{A}=T_{C}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f87b3ac4938b7522483919a2ee87014f6b1b1319" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:31.714ex; height:2.509ex;" alt="{\displaystyle T_{A}=T_{B}\,,T_{B}=T_{C}\Rightarrow T_{A}=T_{C}\,\!}"></span></dd></dl> <p><b><a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">Third law of thermodynamics</a>:</b> </p> <dl><dd>As the temperature <i>T</i> of a system approaches absolute zero, the entropy <i>S</i> approaches a minimum value <i>C</i>: as <i>T</i> → 0, <i>S</i> → <i>C</i>.</dd></dl> </td></tr> <tr> <td>For homogeneous systems the first and second law can be combined into the <b><a href="/wiki/Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">Fundamental thermodynamic relation</a></b>: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8eb3898c641672c61543d27149152c905e634977" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:32.558ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,\!}"></span></dd></dl> </td></tr> <tr style="border-top: 3px solid;"> <td colspan="2" style="width:500px;"><b><a href="/wiki/Onsager_reciprocal_relations" title="Onsager reciprocal relations">Onsager reciprocal relations</a>:</b> sometimes called the <i>fourth law of thermodynamics</i> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{u}=L_{uu}\,\nabla (1/T)-L_{ur}\,\nabla (m/T);}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> <mi>u</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi mathvariant="normal">∇</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> <mi>r</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi mathvariant="normal">∇</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo stretchy="false">)</mo> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{u}=L_{uu}\,\nabla (1/T)-L_{ur}\,\nabla (m/T);}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4766a7cf786d2cc2709583e862f6056bd757b5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.396ex; height:2.843ex;" alt="{\displaystyle \mathbf {J} _{u}=L_{uu}\,\nabla (1/T)-L_{ur}\,\nabla (m/T);}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J} _{r}=L_{ru}\,\nabla (1/T)-L_{rr}\,\nabla (m/T).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>u</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi mathvariant="normal">∇</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi mathvariant="normal">∇</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {J} _{r}=L_{ru}\,\nabla (1/T)-L_{rr}\,\nabla (m/T).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e8a93c9cf331d3bf9255d344b868d65aaa7f0d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.8ex; height:2.843ex;" alt="{\displaystyle \mathbf {J} _{r}=L_{ru}\,\nabla (1/T)-L_{rr}\,\nabla (m/T).}"></span></dd></dl> </td></tr></tbody></table></dd></dl> <ul><li><a href="/wiki/Newton%27s_law_of_cooling" title="Newton's law of cooling">Newton's law of cooling</a></li> <li><a href="/wiki/Conduction_(heat)" class="mw-redirect" title="Conduction (heat)">Fourier's law</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a>, combines a number of separately developed gas laws; <ul><li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Avogadro%27s_law" title="Avogadro's law">Avogadro's law</a>, into one</li></ul></li></ul> <dl><dd>now improved by other <a href="/wiki/Equations_of_state" class="mw-redirect" title="Equations of state">equations of state</a></dd></dl> <ul><li><a href="/wiki/Dalton%27s_law" title="Dalton's law">Dalton's law</a> (of partial pressures)</li> <li><a href="/wiki/Boltzmann_equation" title="Boltzmann equation">Boltzmann equation</a></li> <li><a href="/wiki/Carnot%27s_theorem_(thermodynamics)" title="Carnot's theorem (thermodynamics)">Carnot's theorem</a></li> <li><a href="/wiki/Kopp%27s_law" title="Kopp's law">Kopp's law</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Electromagnetism">Electromagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=14" title="Edit section: Electromagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a> give the time-evolution of the <a href="/wiki/Electric_field" title="Electric field">electric</a> and <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic</a> fields due to <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> and <a href="/wiki/Electric_current" title="Electric current">current</a> distributions. Given the fields, the <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a> law is the <a href="/wiki/Equation_of_motion" class="mw-redirect" title="Equation of motion">equation of motion</a> for charges in the fields. </p> <dl><dd><table class="wikitable" align="center"> <tbody><tr valign="top"> <td scope="col" style="width:300px;"><b><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></b> <p><b><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss's law</a> for electricity</b> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{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">E</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff0076e721a4b485bda8ff427f00e73c6efb6006" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.444ex; height:5.176ex;" alt="{\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}}"></span></dd></dl> <p><b><a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss's law for magnetism</a></b> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \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> </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/16ee950683349dacdd9e9c262ff6133812747edd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.777ex; height:2.176ex;" alt="{\displaystyle \nabla \cdot \mathbf {B} =0}"></span></dd></dl> <p><b><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law</a></b> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \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> </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/2eb118e22c941e34f5537dbbdcaa3d7ba23603e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.495ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}"></span></dd></dl> <p><b><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère's circuital law</a> (with Maxwell's correction)</b> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +{\frac {1}{c^{2}}}{\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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <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> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} }{\partial t}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf5a00ba724838d95f4d80e84236fd8cddf23b60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.842ex; height:5.676ex;" alt="{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +{\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} }{\partial t}}\ }"></span></dd></dl> </td> <td scope="col" style="width:300px;"><b><a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a> law:</b> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mi>q</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb96d860cadff3d60e8ffb90b067b7f2b453c8e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.797ex; height:2.843ex;" alt="{\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)}"></span></dd></dl> </td></tr> <tr style="border-top: 3px solid;"> <td colspan="2" scope="col" style="width:600px;"><b><a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a> (QED):</b> Maxwell's equations are generally true and consistent with relativity - but they do not predict some observed quantum phenomena (e.g. light propagation as <a href="/wiki/EM_wave" class="mw-redirect" title="EM wave">EM waves</a>, rather than <a href="/wiki/Photons" class="mw-redirect" title="Photons">photons</a>, see <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a> for details). They are modified in QED theory. </td></tr></tbody></table></dd></dl> <p>These equations can be modified to include <a href="/wiki/Magnetic_monopole" title="Magnetic monopole">magnetic monopoles</a>, and are consistent with our observations of monopoles either existing or not existing; if they do not exist, the generalized equations reduce to the ones above, if they do, the equations become fully symmetric in electric and magnetic charges and currents. Indeed, there is a duality transformation where electric and magnetic charges can be "rotated into one another", and still satisfy Maxwell's equations. </p><p><b>Pre-Maxwell laws :</b><br /> </p><p>These laws were found before the formulation of Maxwell's equations. They are not fundamental, since they can be derived from Maxwell's equations. Coulomb's law can be found from Gauss's law (electrostatic form) and the Biot–Savart law can be deduced from Ampere's law (magnetostatic form). Lenz's law and Faraday's law can be incorporated into the Maxwell–Faraday equation. Nonetheless, they are still very effective for simple calculations. </p> <ul><li><a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a></li> <li><a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a></li> <li><a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a></li></ul> <p><b>Other laws :</b> </p> <ul><li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff's laws</a></li> <li><a href="/wiki/Joule%27s_first_law" class="mw-redirect" title="Joule's first law">Joule's law</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Photonics">Photonics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=15" title="Edit section: Photonics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Classically, <a href="/wiki/Optics" title="Optics">optics</a> is based on a <a href="/wiki/Variational_principle" title="Variational principle">variational principle</a>: light travels from one point in space to another in the shortest time. </p> <ul><li><a href="/wiki/Fermat%27s_principle" title="Fermat's principle">Fermat's principle</a></li></ul> <p>In <a href="/wiki/Geometric_optics" class="mw-redirect" title="Geometric optics">geometric optics</a> laws are based on approximations in Euclidean geometry (such as the <a href="/wiki/Paraxial_approximation" title="Paraxial approximation">paraxial approximation</a>). </p> <ul><li><a href="/wiki/Law_of_reflection" class="mw-redirect" title="Law of reflection">Law of reflection</a></li> <li><a href="/wiki/Law_of_refraction" class="mw-redirect" title="Law of refraction">Law of refraction</a>, <a href="/wiki/Snell%27s_law" title="Snell's law">Snell's law</a></li></ul> <p>In <a href="/wiki/Physical_optics" title="Physical optics">physical optics</a>, laws are based on physical properties of materials. </p> <ul><li><a href="/wiki/Brewster%27s_law" class="mw-redirect" title="Brewster's law">Brewster's angle</a></li> <li><a href="/wiki/Malus%27s_law" class="mw-redirect" title="Malus's law">Malus's law</a></li> <li><a href="/wiki/Beer%E2%80%93Lambert_law" title="Beer–Lambert law">Beer–Lambert law</a></li></ul> <p>In actuality, optical properties of matter are significantly more complex and require quantum mechanics. </p> <div class="mw-heading mw-heading3"><h3 id="Laws_of_quantum_mechanics">Laws of quantum mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=16" title="Edit section: Laws of quantum mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum mechanics has its roots in <a href="/wiki/Postulates_of_quantum_mechanics" class="mw-redirect" title="Postulates of quantum mechanics">postulates</a>. This leads to results which are not usually called "laws", but hold the same status, in that all of quantum mechanics follows from them. These postulates can be summarized as follows: </p> <ul><li>The state of a physical system, be it a particle or a system of many particles, is described by a <a href="/wiki/Wavefunction" class="mw-redirect" title="Wavefunction">wavefunction</a>.</li> <li>Every physical quantity is described by an <a href="/wiki/Operators_(physics)" class="mw-redirect" title="Operators (physics)">operator</a> acting on the system; the measured quantity has a <a href="/wiki/Born_rule" title="Born rule">probabilistic nature</a>.</li> <li>The <a href="/wiki/Wavefunction" class="mw-redirect" title="Wavefunction">wavefunction</a> obeys the <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a>. Solving this wave equation predicts the time-evolution of the system's behavior, analogous to solving Newton's laws in classical mechanics.</li> <li>Two <a href="/wiki/Identical_particles" class="mw-redirect" title="Identical particles">identical particles</a>, such as two electrons, cannot be distinguished from one another by any means. Physical systems are classified by their symmetry properties.</li></ul> <p>These postulates in turn imply many other phenomena, e.g., <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">uncertainty principles</a> and the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a>. </p> <dl><dd><table class="wikitable" align="center"> <tbody><tr valign="top"> <td style="width:300px;"><b><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a>, <a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></b> <p><b><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> (general form):</b> Describes the time dependence of a quantum mechanical system. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {d}{dt}}\left|\psi \right\rangle ={\hat {H}}\left|\psi \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow> <mo>|</mo> <mi>ψ</mi> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {d}{dt}}\left|\psi \right\rangle ={\hat {H}}\left|\psi \right\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a6810a2cb4850d70726faa2e6ef5e8d26d9cd0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.066ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {d}{dt}}\left|\psi \right\rangle ={\hat {H}}\left|\psi \right\rangle }"></span></dd></dl> <p>The <a href="/wiki/Hamiltonian_quaternions" class="mw-redirect" title="Hamiltonian quaternions">Hamiltonian</a> (in quantum mechanics) <i>H</i> is a <a href="/wiki/Self-adjoint_operator" title="Self-adjoint operator">self-adjoint operator</a> acting on the state space, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle |\psi \rangle }"></span> (see <a href="/wiki/Dirac_notation" class="mw-redirect" title="Dirac notation">Dirac notation</a>) is the instantaneous <a href="/wiki/Quantum_state_vector" class="mw-redirect" title="Quantum state vector">quantum state vector</a> at time <i>t</i>, position <b>r</b>, <i>i</i> is the unit <a href="/wiki/Imaginary_number" title="Imaginary number">imaginary number</a>, <span class="nowrap"><i>ħ</i> = <i>h</i>/2π</span> is the <a href="/wiki/Reduced_Planck_constant" class="mw-redirect" title="Reduced Planck constant">reduced Planck constant</a>. </p> </td> <td rowspan="2" scope="col" style="width:300px;"><b><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></b> <p><b><a href="/wiki/Planck_constant" title="Planck constant">Planck–Einstein law</a>:</b> the <a href="/wiki/Energy" title="Energy">energy</a> of <a href="/wiki/Photon" title="Photon">photons</a> is proportional to the <a href="/wiki/Frequency" title="Frequency">frequency</a> of the light (the constant is the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a>, <i>h</i>). </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=h\nu =\hbar \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>ν</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=h\nu =\hbar \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d967b27858abe0ceb0b374fe181dcf18aa96bf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.296ex; height:2.176ex;" alt="{\displaystyle E=h\nu =\hbar \omega }"></span></dd></dl> <p><b><a href="/wiki/Matter_wave" title="Matter wave">De Broglie wavelength</a>:</b> this laid the foundations of wave–particle duality, and was the key concept in the <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a>, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {p} ={\frac {h}{\lambda }}\mathbf {\hat {k}} =\hbar \mathbf {k} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mi>λ</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold">k</mi> <mo mathvariant="bold" stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {p} ={\frac {h}{\lambda }}\mathbf {\hat {k}} =\hbar \mathbf {k} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e726b0c7afeff00f681a1516b7d2404a713e6698" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.002ex; height:5.509ex;" alt="{\displaystyle \mathbf {p} ={\frac {h}{\lambda }}\mathbf {\hat {k}} =\hbar \mathbf {k} }"></span></dd></dl> <p><b><a href="/wiki/Heisenberg_uncertainty_principle" class="mw-redirect" title="Heisenberg uncertainty principle">Heisenberg uncertainty principle</a>:</b> <a href="/wiki/Uncertainty" title="Uncertainty">Uncertainty</a> in position multiplied by uncertainty in <a href="/wiki/Momentum" title="Momentum">momentum</a> is at least half of the <a href="/wiki/Reduced_Planck_constant" class="mw-redirect" title="Reduced Planck constant">reduced Planck constant</a>, similarly for time and <a href="/wiki/Energy" title="Energy">energy</a>; </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta x\,\Delta p\geq {\frac {\hbar }{2}},\,\Delta E\,\Delta t\geq {\frac {\hbar }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">Δ</mi> <mi>p</mi> <mo>≥</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>≥</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x\,\Delta p\geq {\frac {\hbar }{2}},\,\Delta E\,\Delta t\geq {\frac {\hbar }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f683d056ec4ba9ee1401e69ac5eeb7c2e0d33d28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.535ex; height:5.343ex;" alt="{\displaystyle \Delta x\,\Delta p\geq {\frac {\hbar }{2}},\,\Delta E\,\Delta t\geq {\frac {\hbar }{2}}}"></span></dd></dl> <p>The uncertainty principle can be generalized to any pair of observables – see main article. </p> </td></tr> <tr> <td><b>Wave mechanics</b> <p><b><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a> (original form):</b> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi +V\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>ψ</mi> <mo>=</mo> <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>+</mo> <mi>V</mi> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi +V\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/221fd7ddff69c3c26354c6e111ab795de7af20ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.206ex; height:5.843ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi +V\psi }"></span></dd></dl> </td></tr> <tr style="border-top: 3px solid;"> <td colspan="2" style="width:600px;"><b><a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a>:</b> No two identical <a href="/wiki/Fermion" title="Fermion">fermions</a> can occupy the same quantum state (<a href="/wiki/Boson" title="Boson">bosons</a> can). Mathematically, if two particles are interchanged, fermionic wavefunctions are anti-symmetric, while bosonic wavefunctions are symmetric: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (\cdots \mathbf {r} _{i}\cdots \mathbf {r} _{j}\cdots )=(-1)^{2s}\psi (\cdots \mathbf {r} _{j}\cdots \mathbf {r} _{i}\cdots )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mo>⋯</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>⋯</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>⋯</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>s</mi> </mrow> </msup> <mi>ψ</mi> <mo stretchy="false">(</mo> <mo>⋯</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>⋯</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>⋯</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (\cdots \mathbf {r} _{i}\cdots \mathbf {r} _{j}\cdots )=(-1)^{2s}\psi (\cdots \mathbf {r} _{j}\cdots \mathbf {r} _{i}\cdots )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83f1db9c255b832a24646a3f50bf16d3a1389378" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:43.612ex; height:3.343ex;" alt="{\displaystyle \psi (\cdots \mathbf {r} _{i}\cdots \mathbf {r} _{j}\cdots )=(-1)^{2s}\psi (\cdots \mathbf {r} _{j}\cdots \mathbf {r} _{i}\cdots )}"></span></dd></dl> <p>where <b>r</b><sub><i>i</i></sub> is the position of particle <i>i</i>, and <i>s</i> is the <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> of the particle. There is no way to keep track of particles physically, labels are only used mathematically to prevent confusion. </p> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Radiation_laws">Radiation laws</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=17" title="Edit section: Radiation laws"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Applying electromagnetism, thermodynamics, and quantum mechanics, to atoms and molecules, some laws of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> and light are as follows. </p> <ul><li><a href="/wiki/Stefan%E2%80%93Boltzmann_law" title="Stefan–Boltzmann law">Stefan–Boltzmann law</a></li> <li><a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a> of black-body radiation</li> <li><a href="/wiki/Wien%27s_displacement_law" title="Wien's displacement law">Wien's displacement law</a></li> <li><a href="/wiki/Radioactive_decay_law" class="mw-redirect" title="Radioactive decay law">Radioactive decay law</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Laws_of_chemistry">Laws of chemistry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=18" title="Edit section: Laws of chemistry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chemical_law" title="Chemical law">Chemical law</a></div> <p><b>Chemical laws</b> are those laws of nature relevant to <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>. Historically, observations led to many empirical laws, though now it is known that chemistry has its foundations in <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>. </p><p><b><a href="/wiki/Quantitative_analysis_(chemistry)" title="Quantitative analysis (chemistry)">Quantitative analysis</a> :</b><br /> </p><p>The most fundamental concept in chemistry is the <a href="/wiki/Law_of_conservation_of_mass" class="mw-redirect" title="Law of conservation of mass">law of conservation of mass</a>, which states that there is no detectable change in the quantity of matter during an ordinary <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a>. Modern physics shows that it is actually <a href="/wiki/Energy" title="Energy">energy</a> that is conserved, and that <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">energy and mass are related</a>; a concept which becomes important in <a href="/wiki/Nuclear_chemistry" title="Nuclear chemistry">nuclear chemistry</a>. <a href="/wiki/Conservation_of_energy" title="Conservation of energy">Conservation of energy</a> leads to the important concepts of <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a>, <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, and <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">kinetics</a>. </p><p>Additional laws of chemistry elaborate on the law of conservation of mass. <a href="/wiki/Joseph_Proust" title="Joseph Proust">Joseph Proust</a>'s <a href="/wiki/Law_of_definite_composition" class="mw-redirect" title="Law of definite composition">law of definite composition</a> says that pure chemicals are composed of elements in a definite formulation; we now know that the structural arrangement of these elements is also important. </p><p><a href="/wiki/John_Dalton" title="John Dalton">Dalton</a>'s <a href="/wiki/Law_of_multiple_proportions" title="Law of multiple proportions">law of multiple proportions</a> says that these chemicals will present themselves in proportions that are small whole numbers; although in many systems (notably <a href="/wiki/Biomolecule" title="Biomolecule">biomacromolecules</a> and <a href="/wiki/Minerals" class="mw-redirect" title="Minerals">minerals</a>) the ratios tend to require large numbers, and are frequently represented as a fraction. </p><p>The law of definite composition and the law of multiple proportions are the first two of the three laws of <a href="/wiki/Stoichiometry" title="Stoichiometry">stoichiometry</a>, the proportions by which the chemical elements combine to form chemical compounds. The third law of stoichiometry is the <a href="/wiki/Law_of_reciprocal_proportions" title="Law of reciprocal proportions">law of reciprocal proportions</a>, which provides the basis for establishing <a href="/wiki/Equivalent_weight" title="Equivalent weight">equivalent weights</a> for each chemical element. Elemental equivalent weights can then be used to derive <a href="/wiki/Standard_atomic_weight" title="Standard atomic weight">atomic weights</a> for each element. </p><p>More modern laws of chemistry define the relationship between energy and its transformations. </p><p><b><a href="/wiki/Reaction_kinetics" class="mw-redirect" title="Reaction kinetics">Reaction kinetics</a> and <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">equilibria</a> :</b> </p> <ul><li>In equilibrium, molecules exist in mixture defined by the transformations possible on the timescale of the equilibrium, and are in a ratio defined by the intrinsic energy of the molecules—the lower the intrinsic energy, the more abundant the molecule. <a href="/wiki/Le_Chatelier%27s_principle" title="Le Chatelier's principle">Le Chatelier's principle</a> states that the system opposes changes in conditions from equilibrium states, i.e. there is an opposition to change the state of an equilibrium reaction.</li> <li>Transforming one structure to another requires the input of energy to cross an energy barrier; this can come from the intrinsic energy of the molecules themselves, or from an external source which will generally accelerate transformations. The higher the energy barrier, the slower the transformation occurs.</li> <li>There is a hypothetical intermediate, or <i>transition structure</i>, that corresponds to the structure at the top of the energy barrier. The <a href="/wiki/Hammond%27s_postulate" title="Hammond's postulate">Hammond–Leffler postulate</a> states that this structure looks most similar to the product or starting material which has intrinsic energy closest to that of the energy barrier. Stabilizing this hypothetical intermediate through chemical interaction is one way to achieve <a href="/wiki/Catalysis" title="Catalysis">catalysis</a>.</li> <li>All chemical processes are reversible (law of <a href="/wiki/Microscopic_reversibility" title="Microscopic reversibility">microscopic reversibility</a>) although some processes have such an energy bias, they are essentially irreversible.</li> <li>The reaction rate has the mathematical parameter known as the <a href="/wiki/Rate_constant" class="mw-redirect" title="Rate constant">rate constant</a>. The <a href="/wiki/Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a> gives the temperature and <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a> dependence of the rate constant, an empirical law.</li></ul> <p><b><a href="/wiki/Thermochemistry" title="Thermochemistry">Thermochemistry</a> :</b> </p> <ul><li><a href="/wiki/Dulong%E2%80%93Petit_law" title="Dulong–Petit law">Dulong–Petit law</a></li> <li><a href="/wiki/Gibbs%E2%80%93Helmholtz_equation" title="Gibbs–Helmholtz equation">Gibbs–Helmholtz equation</a></li> <li><a href="/wiki/Hess%27s_law" title="Hess's law">Hess's law</a></li></ul> <p><b>Gas laws :</b> </p> <ul><li><a href="/wiki/Raoult%27s_law" title="Raoult's law">Raoult's law</a></li> <li><a href="/wiki/Henry%27s_law" title="Henry's law">Henry's law</a></li></ul> <p><b>Chemical transport :</b> </p> <ul><li><a href="/wiki/Fick%27s_laws_of_diffusion" title="Fick's laws of diffusion">Fick's laws of diffusion</a></li> <li><a href="/wiki/Graham%27s_law" title="Graham's law">Graham's law</a></li> <li><a href="/wiki/Lamm_equation" title="Lamm equation">Lamm equation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Laws_of_biology">Laws of biology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=19" title="Edit section: Laws of biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Biological_rules" title="Biological rules">Biological rules</a></div> <div class="mw-heading mw-heading3"><h3 id="Ecology">Ecology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=20" title="Edit section: Ecology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Competitive_exclusion_principle" title="Competitive exclusion principle">Competitive exclusion principle</a> or Gause's law</li></ul> <div class="mw-heading mw-heading3"><h3 id="Genetics">Genetics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=21" title="Edit section: Genetics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Mendelian_laws" class="mw-redirect" title="Mendelian laws">Mendelian laws</a> (Dominance and Uniformity, segregation of genes, and Independent Assortment)</li> <li><a href="/wiki/Hardy%E2%80%93Weinberg_principle" title="Hardy–Weinberg principle">Hardy–Weinberg principle</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Natural_selection">Natural selection</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=22" title="Edit section: Natural selection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Whether or not <a href="/wiki/Natural_Selection" class="mw-redirect" title="Natural Selection">Natural Selection</a> is a “law of nature” is controversial among biologists.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Byerly1983_18-0" class="reference"><a href="#cite_note-Byerly1983-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Henry_Byerly" title="Henry Byerly">Henry Byerly</a>, an American philosopher known for his work on evolutionary theory, discussed the problem of interpreting a principle of natural selection as a law. He suggested a formulation of natural selection as a framework principle that can contribute to a better understanding of evolutionary theory.<sup id="cite_ref-Byerly1983_18-1" class="reference"><a href="#cite_note-Byerly1983-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> His approach was to express relative <a href="/wiki/Fitness_(biology)" title="Fitness (biology)">fitness</a>, the propensity of a <a href="/wiki/Genotype" title="Genotype">genotype</a> to increase in proportionate representation in a competitive environment, as a function of <a href="/wiki/Adaptation" title="Adaptation">adaptedness</a> (adaptive design) of the organism. </p> <div class="mw-heading mw-heading2"><h2 id="Laws_of_Earth_sciences">Laws of Earth sciences</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=23" title="Edit section: Laws of Earth sciences"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Geography">Geography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=24" title="Edit section: Geography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Arbia%27s_law_of_geography" title="Arbia's law of geography">Arbia's law of geography</a></li> <li><a href="/wiki/Tobler%27s_first_law_of_geography" title="Tobler's first law of geography">Tobler's first law of geography</a></li> <li><a href="/wiki/Tobler%27s_second_law_of_geography" title="Tobler's second law of geography">Tobler's second law of geography</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Geology">Geology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=25" title="Edit section: Geology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Archie%27s_law" title="Archie's law">Archie's law</a></li> <li><a href="/wiki/Buys_Ballot%27s_law" title="Buys Ballot's law">Buys Ballot's law</a></li> <li><a href="/wiki/Birch%27s_law" title="Birch's law">Birch's law</a></li> <li><a href="/wiki/Byerlee%27s_law" title="Byerlee's law">Byerlee's law</a></li> <li><a href="/wiki/Principle_of_original_horizontality" title="Principle of original horizontality">Principle of original horizontality</a></li> <li><a href="/wiki/Law_of_superposition" title="Law of superposition">Law of superposition</a></li> <li><a href="/wiki/Principle_of_lateral_continuity" title="Principle of lateral continuity">Principle of lateral continuity</a></li> <li><a href="/wiki/Principle_of_cross-cutting_relationships" class="mw-redirect" title="Principle of cross-cutting relationships">Principle of cross-cutting relationships</a></li> <li><a href="/wiki/Principle_of_faunal_succession" title="Principle of faunal succession">Principle of faunal succession</a></li> <li><a href="/wiki/Law_of_included_fragments" title="Law of included fragments">Principle of inclusions and components</a></li> <li><a href="/wiki/Walther%27s_law" class="mw-redirect" title="Walther's law">Walther's law</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Other_fields">Other fields</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=26" title="Edit section: Other fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> <a href="/wiki/Theorem" title="Theorem">theorems</a> and <a href="/wiki/Axiom" title="Axiom">axioms</a> are referred to as laws because they provide logical foundation to empirical laws. </p><p>Examples of other observed phenomena sometimes described as laws include the <a href="/wiki/Titius%E2%80%93Bode_law" title="Titius–Bode law">Titius–Bode law</a> of planetary positions, <a href="/wiki/Zipf%27s_law" title="Zipf's law">Zipf's law</a> of linguistics, and <a href="/wiki/Moore%27s_law" title="Moore's law">Moore's law</a> of technological growth. Many of these laws fall within the scope of <a href="/wiki/Uncomfortable_science" title="Uncomfortable science">uncomfortable science</a>. Other laws are pragmatic and observational, such as the <a href="/wiki/Law_of_unintended_consequences" class="mw-redirect" title="Law of unintended consequences">law of unintended consequences</a>. By analogy, principles in other fields of study are sometimes loosely referred to as "laws". These include <a href="/wiki/Occam%27s_razor" title="Occam's razor">Occam's razor</a> as a principle of philosophy and the <a href="/wiki/Pareto_principle" title="Pareto principle">Pareto principle</a> of economics. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=27" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The observation and detection of underlying regularities in nature date from <a href="/wiki/Prehistoric" class="mw-redirect" title="Prehistoric">prehistoric</a> times – the recognition of cause-and-effect relationships implicitly recognises the existence of laws of nature. The recognition of such regularities as independent scientific laws <i><a href="/wiki/Per_se_(phrase)" class="mw-redirect" title="Per se (phrase)">per se</a></i>, though, was limited by their entanglement in <a href="/wiki/Animism" title="Animism">animism</a>, and by the attribution of many effects that do not have readily obvious causes—such as physical phenomena—to the actions of <a href="/wiki/Deity" title="Deity">gods</a>, spirits, <a href="/wiki/Supernatural_being" class="mw-redirect" title="Supernatural being">supernatural beings</a>, etc. Observation and speculation about nature were intimately bound up with metaphysics and morality. </p><p> In Europe, systematic theorizing about nature (<i><a href="/wiki/Physis" title="Physis">physis</a></i>) began with the early <a href="/wiki/History_of_science_in_classical_antiquity" class="mw-redirect" title="History of science in classical antiquity">Greek philosophers and scientists</a> and continued into the <a href="/wiki/Hellenistic_period" title="Hellenistic period">Hellenistic</a> and <a href="/wiki/Roman_Empire" title="Roman Empire">Roman imperial</a> periods, during which times the intellectual influence of <a href="/wiki/Roman_law" title="Roman law">Roman law</a> increasingly became paramount.</p><blockquote><p>The formula "law of nature" first appears as "a live metaphor" favored by Latin poets <a href="/wiki/Lucretius" title="Lucretius">Lucretius</a>, <a href="/wiki/Virgil" title="Virgil">Virgil</a>, <a href="/wiki/Ovid" title="Ovid">Ovid</a>, <a href="/wiki/Marcus_Manilius" title="Marcus Manilius">Manilius</a>, in time gaining a firm theoretical presence in the prose treatises of <a href="/wiki/Seneca_the_Younger" title="Seneca the Younger">Seneca</a> and <a href="/wiki/Pliny_the_Elder" title="Pliny the Elder">Pliny</a>. Why this Roman origin? According to [historian and classicist Daryn] Lehoux's persuasive narrative,<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> the idea was made possible by the pivotal role of codified law and <a href="/wiki/Law_court" class="mw-redirect" title="Law court">forensic</a> argument in Roman life and culture.<br /><br /> For the Romans ... the place par excellence where ethics, law, nature, religion and politics overlap is the <a href="/wiki/Law_court" class="mw-redirect" title="Law court">law court</a>. When we read Seneca's <a href="/wiki/Naturales_quaestiones" title="Naturales quaestiones"><i>Natural Questions</i></a>, and watch again and again just how he applies standards of evidence, witness evaluation, argument and proof, we can recognize that we are reading one of the great Roman rhetoricians of the age, thoroughly immersed in forensic method. And not Seneca alone. Legal models of scientific judgment turn up all over the place, and for example prove equally integral to <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>'s approach to verification, where the mind is assigned the role of magistrate, the senses that of disclosure of evidence, and dialectical reason that of the law itself.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>The precise formulation of what are now recognized as modern and valid statements of the laws of nature dates from the 17th century in Europe, with the beginning of accurate experimentation and the development of advanced forms of mathematics. During this period, <a href="/wiki/Natural_philosophy" title="Natural philosophy">natural philosophers</a> such as <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> (1642–1727) were influenced by a <a href="/wiki/Religious" class="mw-redirect" title="Religious">religious</a> view – stemming from medieval concepts of <a href="/wiki/Divine_law" title="Divine law">divine law</a> – which held that God had instituted absolute, universal and immutable physical laws.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> In chapter 7 of <a href="/wiki/The_World_(Descartes)" class="mw-redirect" title="The World (Descartes)"><i>The World</i></a>, <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> (1596–1650) described "nature" as matter itself, unchanging as created by God, thus changes in parts "are to be attributed to nature. The rules according to which these changes take place I call the 'laws of nature'."<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> The modern <a href="/wiki/Scientific_method" title="Scientific method">scientific method</a> which took shape at this time (with <a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a> (1561–1626) and <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a> (1564–1642)) contributed to a trend of <a href="/wiki/Relationship_between_religion_and_science" title="Relationship between religion and science">separating science</a> from <a href="/wiki/Theology" title="Theology">theology</a>, with minimal speculation about <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a> and ethics. (<a href="/wiki/Natural_law" title="Natural law">Natural law</a> in the political sense, conceived as universal (i.e., divorced from sectarian religion and accidents of place), was also elaborated in this period by scholars such as <a href="/wiki/Grotius" class="mw-redirect" title="Grotius">Grotius</a> (1583–1645), <a href="/wiki/Spinoza" class="mw-redirect" title="Spinoza">Spinoza</a> (1632–1677), and <a href="/wiki/Hobbes" class="mw-redirect" title="Hobbes">Hobbes</a> (1588–1679).) </p><p>The distinction between <a href="/wiki/Natural_law" title="Natural law">natural law</a> in the political-legal sense and law of nature or physical law in the scientific sense is a modern one, both concepts being equally derived from <i><a href="/wiki/Physis" title="Physis">physis</a></i>, the Greek word (translated into Latin as <i>natura</i>) for <i>nature</i>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=28" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Empirical_research" title="Empirical research">Empirical research</a></li> <li><a href="/wiki/Empirical_statistical_laws" title="Empirical statistical laws">Empirical statistical laws</a></li> <li><a href="/wiki/Formula" title="Formula">Formula</a></li> <li><a href="/wiki/List_of_laws" title="List of laws">List of laws</a></li> <li><a href="/wiki/Law_(principle)" title="Law (principle)">Law (principle)</a></li> <li><a href="/wiki/Nomology" title="Nomology">Nomology</a></li> <li><a href="/wiki/Philosophy_of_science" title="Philosophy of science">Philosophy of science</a></li> <li><a href="/wiki/Physical_constant" title="Physical constant">Physical constant</a></li> <li><a href="/wiki/List_of_scientific_laws_named_after_people" title="List of scientific laws named after people">List of scientific laws named after people</a></li> <li><a href="/wiki/Theory" title="Theory">Theory</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=29" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFReference-OED-law_of_nature" class="citation encyclopaedia cs1"><span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oed.com/search/dictionary/?q=law+of+nature">"law of nature"</a></span>. <i><a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> (Online ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=law+of+nature&rft.btitle=Oxford+English+Dictionary&rft.edition=Online&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Fwww.oed.com%2Fsearch%2Fdictionary%2F%3Fq%3Dlaw%2Bof%2Bnature&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span> <span style="font-size:0.95em; font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliam_F._McComas2013" class="citation book cs1">William F. McComas (30 December 2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=aXzGBAAAQBAJ"><i>The Language of Science Education: An Expanded Glossary of Key Terms and Concepts in Science Teaching and Learning</i></a>. Springer Science & Business Media. p. 58. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-94-6209-497-0" title="Special:BookSources/978-94-6209-497-0"><bdi>978-94-6209-497-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Language+of+Science+Education%3A+An+Expanded+Glossary+of+Key+Terms+and+Concepts+in+Science+Teaching+and+Learning&rft.pages=58&rft.pub=Springer+Science+%26+Business+Media&rft.date=2013-12-30&rft.isbn=978-94-6209-497-0&rft.au=William+F.+McComas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DaXzGBAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://ncse.com/evolution/education/definitions-fact-theory-law-scientific-work">"Definitions from"</a>. the NCSE<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-03-18</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Definitions+from&rft.pub=the+NCSE&rft_id=http%3A%2F%2Fncse.com%2Fevolution%2Feducation%2Fdefinitions-fact-theory-law-scientific-work&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNational_Research_Council2008" class="citation book cs1">National Research Council (2008). <i>The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research</i>. Ebook ISBN 978-0-309-13417-0. Washington, DC: The National Academies Press. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.17226%2F12026">10.17226/12026</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-309-11249-9" title="Special:BookSources/978-0-309-11249-9"><bdi>978-0-309-11249-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Role+of+Theory+in+Advancing+21st-Century+Biology%3A+Catalyzing+Transformative+Research&rft.place=Washington%2C+DC&rft.pub=The+National+Academies+Press&rft.date=2008&rft_id=info%3Adoi%2F10.17226%2F12026&rft.isbn=978-0-309-11249-9&rft.au=National+Research+Council&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGould1981" class="citation journal cs1"><a href="/wiki/Stephen_Jay_Gould" title="Stephen Jay Gould">Gould, Stephen Jay</a> (1981-05-01). <a rel="nofollow" class="external text" href="http://www.inf.fu-berlin.de/lehre/pmo/eng/Gould-Fact&Theory.pdf">"Evolution as Fact and Theory"</a> <span class="cs1-format">(PDF)</span>. <i>Discover</i>. <b>2</b> (5): <span class="nowrap">34–</span>37.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Discover&rft.atitle=Evolution+as+Fact+and+Theory&rft.volume=2&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E34-%3C%2Fspan%3E37&rft.date=1981-05-01&rft.aulast=Gould&rft.aufirst=Stephen+Jay&rft_id=http%3A%2F%2Fwww.inf.fu-berlin.de%2Flehre%2Fpmo%2Feng%2FGould-Fact%26Theory.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHonderich1995" class="citation cs2">Honderich, Bike, ed. (1995), "Laws, natural or scientific", <a rel="nofollow" class="external text" href="https://archive.org/details/oxfordcompaniont00hond/page/474"><i>Oxford Companion to Philosophy</i></a>, Oxford: Oxford University Press, pp. <a rel="nofollow" class="external text" href="https://archive.org/details/oxfordcompaniont00hond/page/474">474–476</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-866132-0" title="Special:BookSources/0-19-866132-0"><bdi>0-19-866132-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Laws%2C+natural+or+scientific&rft.btitle=Oxford+Companion+to+Philosophy&rft.place=Oxford&rft.pages=474-476&rft.pub=Oxford+University+Press&rft.date=1995&rft.isbn=0-19-866132-0&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foxfordcompaniont00hond%2Fpage%2F474&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReference-OED-Law_of_nature" class="citation encyclopaedia cs1"><span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oed.com/search/dictionary/?q=Law+of+nature">"Law of nature"</a></span>. <i><a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> (Online ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Law+of+nature&rft.btitle=Oxford+English+Dictionary&rft.edition=Online&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Fwww.oed.com%2Fsearch%2Fdictionary%2F%3Fq%3DLaw%2Bof%2Bnature&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span> <span style="font-size:0.95em; font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span></span> </li> <li id="cite_note-Davies-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Davies_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Davies_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavies2005" class="citation book cs1">Davies, Paul (2005). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/mindof_dav_1992_00_1584"><i>The mind of God : the scientific basis for a rational world</i></a></span> (1st Simon & Schuster pbk. ed.). New York: Simon & Schuster. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-671-79718-8" title="Special:BookSources/978-0-671-79718-8"><bdi>978-0-671-79718-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+mind+of+God+%3A+the+scientific+basis+for+a+rational+world&rft.place=New+York&rft.edition=1st+Simon+%26+Schuster+pbk.&rft.pub=Simon+%26+Schuster&rft.date=2005&rft.isbn=978-0-671-79718-8&rft.aulast=Davies&rft.aufirst=Paul&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmindof_dav_1992_00_1584&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-Feynman-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Feynman_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Feynman_9-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Feynman_9-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynman1994" class="citation book cs1">Feynman, Richard (1994). <i>The character of physical law</i> (Modern Library ed.). New York: Modern Library. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-679-60127-2" title="Special:BookSources/978-0-679-60127-2"><bdi>978-0-679-60127-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+character+of+physical+law&rft.place=New+York&rft.edition=Modern+Library&rft.pub=Modern+Library&rft.date=1994&rft.isbn=978-0-679-60127-2&rft.aulast=Feynman&rft.aufirst=Richard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrisch2014" class="citation journal cs1">Frisch, Mathias (May 2014). <a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS1062798713000768">"Laws in Physics | European Review | Cambridge Core"</a>. <i>European Review</i>. <b>22</b> (S1): <span class="nowrap">S33 –</span> <span class="nowrap">S49</span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS1062798713000768">10.1017/S1062798713000768</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122262641">122262641</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Review&rft.atitle=Laws+in+Physics+%7C+European+Review+%7C+Cambridge+Core&rft.volume=22&rft.issue=S1&rft.pages=%3Cspan+class%3D%22nowrap%22%3ES33+-%3C%2Fspan%3E+%3Cspan+class%3D%22nowrap%22%3ES49%3C%2Fspan%3E&rft.date=2014-05&rft_id=info%3Adoi%2F10.1017%2FS1062798713000768&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122262641%23id-name%3DS2CID&rft.aulast=Frisch&rft.aufirst=Mathias&rft_id=https%3A%2F%2Fdoi.org%2F10.1017%252FS1062798713000768&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEhrenberg1993" class="citation journal cs1"><a href="/wiki/Andrew_S._C._Ehrenberg" title="Andrew S. C. Ehrenberg">Ehrenberg, Andrew</a> (1993). <a rel="nofollow" class="external text" href="http://www.nature.com/nature/journal/v365/n6445/pdf/365385a0.pdf">"Even the social sciences have laws"</a> <span class="cs1-format">(PDF)</span>. <i>Nature</i>. <b>365</b> (6445). Springer Science and Business Media LLC: 385. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F365385a0">10.1038/365385a0</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0028-0836">0028-0836</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Even+the+social+sciences+have+laws&rft.volume=365&rft.issue=6445&rft.pages=385&rft.date=1993&rft_id=info%3Adoi%2F10.1038%2F365385a0&rft.issn=0028-0836&rft.aulast=Ehrenberg&rft.aufirst=Andrew&rft_id=http%3A%2F%2Fwww.nature.com%2Fnature%2Fjournal%2Fv365%2Fn6445%2Fpdf%2F365385a0.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynmanLeightonSands1963" class="citation book cs1">Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew Linzee (1963). <i>The Feynman Lectures on Physics</i>. Reading/Mass.: Addison Wesley Longman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-02117-X" title="Special:BookSources/0-201-02117-X"><bdi>0-201-02117-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Feynman+Lectures+on+Physics&rft.place=Reading%2FMass.&rft.pub=Addison+Wesley+Longman&rft.date=1963&rft.isbn=0-201-02117-X&rft.aulast=Feynman&rft.aufirst=Richard+Phillips&rft.au=Leighton%2C+Robert+B.&rft.au=Sands%2C+Matthew+Linzee&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLernerTrigg1991" class="citation book cs1"><a href="/wiki/Rita_G._Lerner" title="Rita G. Lerner">Lerner, Rita G.</a>; Trigg, George L. (1991). <i>Encyclopedia of Physics</i>. New York Weinheim Cambridge Basel: VCH Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-89573-752-3" title="Special:BookSources/0-89573-752-3"><bdi>0-89573-752-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Encyclopedia+of+Physics&rft.place=New+York+Weinheim+Cambridge+Basel&rft.pub=VCH+Publishers&rft.date=1991&rft.isbn=0-89573-752-3&rft.aulast=Lerner&rft.aufirst=Rita+G.&rft.au=Trigg%2C+George+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKibble1973" class="citation book cs1">Kibble, T. W. B. (1973). <i>Classical Mechanics</i>. London; New York: McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-084018-0" title="Special:BookSources/0-07-084018-0"><bdi>0-07-084018-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Mechanics&rft.place=London%3B+New+York&rft.pub=McGraw+Hill&rft.date=1973&rft.isbn=0-07-084018-0&rft.aulast=Kibble&rft.aufirst=T.+W.+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCiufoliniWheeler1995" class="citation book cs1">Ciufolini, Ignazio; Wheeler, John Archibald (1995-08-13). <i>Gravitation and Inertia</i>. Princeton Physics. Princeton, N.J: Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-03323-4" title="Special:BookSources/0-691-03323-4"><bdi>0-691-03323-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gravitation+and+Inertia&rft.place=Princeton%2C+N.J&rft.series=Princeton+Physics&rft.pub=Princeton+University+Press&rft.date=1995-08-13&rft.isbn=0-691-03323-4&rft.aulast=Ciufolini&rft.aufirst=Ignazio&rft.au=Wheeler%2C+John+Archibald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKibble1973" class="citation book cs1">Kibble, T. W. B. (1973). <i>Classical Mechanics</i>. European Physics. London; New York: McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-084018-0" title="Special:BookSources/0-07-084018-0"><bdi>0-07-084018-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Mechanics&rft.place=London%3B+New+York&rft.series=European+Physics&rft.pub=McGraw+Hill&rft.date=1973&rft.isbn=0-07-084018-0&rft.aulast=Kibble&rft.aufirst=T.+W.+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Reed ES: The lawfulness of natural selection. Am Nat. 1981; 118(1): 61–71.</span> </li> <li id="cite_note-Byerly1983-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-Byerly1983_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Byerly1983_18-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Byerly HC: Natural selection as a law: Principles and processes. Am Nat. 1983; 121(5): 739–745.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">in Daryn Lehoux, <i>What Did the Romans Know? An Inquiry into Science and Worldmaking</i> (Chicago: University of Chicago Press, 2012), reviewed by David Sedley, "When Nature Got its Laws", <i>Times Literary Supplement</i> (12 October 2012).</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">Sedley, "When Nature Got Its Laws", <i>Times Literary Supplement</i> (12 October 2012).</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavies2007" class="citation news cs1">Davies, Paul (2007-11-24). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2007/11/24/opinion/24davies.html">"Taking Science on Faith"</a>. <i>The New York Times</i>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0362-4331">0362-4331</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-10-07</span></span>. <q>Isaac Newton first got the idea of absolute, universal, perfect, immutable laws from the Christian doctrine that God created the world and ordered it in a rational way.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Taking+Science+on+Faith&rft.date=2007-11-24&rft.issn=0362-4331&rft.aulast=Davies&rft.aufirst=Paul&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2007%2F11%2F24%2Fopinion%2F24davies.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarrison2012" class="citation web cs1">Harrison, Peter (8 May 2012). <a rel="nofollow" class="external text" href="http://www.abc.net.au/religion/articles/2012/05/08/3498202.htm">"Christianity and the rise of western science"</a>. <i>ABC</i>. <q>Individuals such as Galileo, Johannes Kepler, Rene Descartes and Isaac Newton were convinced that mathematical truths were not the products of human minds, but of the divine mind. God was the source of mathematical relations that were evident in the new laws of the universe.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ABC&rft.atitle=Christianity+and+the+rise+of+western+science&rft.date=2012-05-08&rft.aulast=Harrison&rft.aufirst=Peter&rft_id=http%3A%2F%2Fwww.abc.net.au%2Freligion%2Farticles%2F2012%2F05%2F08%2F3498202.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://bertie.ccsu.edu/naturesci/Cosmology/Cosmo5Newton.html">"Cosmological Revolution V: Descartes and Newton"</a>. <i>bertie.ccsu.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-11-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=bertie.ccsu.edu&rft.atitle=Cosmological+Revolution+V%3A+Descartes+and+Newton&rft_id=http%3A%2F%2Fbertie.ccsu.edu%2Fnaturesci%2FCosmology%2FCosmo5Newton.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"> Some modern philosophers, e.g. <a href="/wiki/Norman_Swartz" title="Norman Swartz">Norman Swartz</a>, use "physical law" to mean the laws of nature as they truly are and not as they are inferred by scientists. See Norman Swartz, <i>The Concept of Physical Law</i> (New York: Cambridge University Press), 1985. Second edition available online <a rel="nofollow" class="external autonumber" href="https://www.sfu.ca/philosophy/physical-law/">[1]</a>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=30" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarrow1992" class="citation book cs1"><a href="/wiki/John_D._Barrow" title="John D. Barrow">Barrow, John D.</a> (1992). <i>Theories of Everything: The Quest for Ultimate Explanations</i>. Ballantine Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-449-90738-4" title="Special:BookSources/0-449-90738-4"><bdi>0-449-90738-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theories+of+Everything%3A+The+Quest+for+Ultimate+Explanations&rft.pub=Ballantine+Books&rft.date=1992&rft.isbn=0-449-90738-4&rft.aulast=Barrow&rft.aufirst=John+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDilworth2007" class="citation book cs1">Dilworth, Craig (2007). "Appendix IV. On the nature of scientific laws and theories". <i>Scientific progress : a study concerning the nature of the relation between successive scientific theories</i> (4th ed.). Dordrecht: Springer Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-6353-4" title="Special:BookSources/978-1-4020-6353-4"><bdi>978-1-4020-6353-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Appendix+IV.+On+the+nature+of+scientific+laws+and+theories&rft.btitle=Scientific+progress+%3A+a+study+concerning+the+nature+of+the+relation+between+successive+scientific+theories&rft.place=Dordrecht&rft.edition=4th&rft.pub=Springer+Verlag&rft.date=2007&rft.isbn=978-1-4020-6353-4&rft.aulast=Dilworth&rft.aufirst=Craig&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li> <li><a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a> (1620). <i><a href="/wiki/Novum_Organum" title="Novum Organum">Novum Organum</a></i>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHanzel1999" class="citation book cs1">Hanzel, Igor (1999). <i>The concept of scientific law in the philosophy of science and epistemology : a study of theoretical reason</i>. Dordrecht [u.a.]: Kluwer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-5852-7" title="Special:BookSources/978-0-7923-5852-7"><bdi>978-0-7923-5852-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+concept+of+scientific+law+in+the+philosophy+of+science+and+epistemology+%3A+a+study+of+theoretical+reason&rft.place=Dordrecht+%5Bu.a.%5D&rft.pub=Kluwer&rft.date=1999&rft.isbn=978-0-7923-5852-7&rft.aulast=Hanzel&rft.aufirst=Igor&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLehoux2012" class="citation book cs1">Lehoux, Daryn (2012-02-28). <i>What Did the Romans Know? An Inquiry into Science and Worldmaking</i>. Chicago, Ill.: University of Chicago Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-47114-3" title="Special:BookSources/978-0-226-47114-3"><bdi>978-0-226-47114-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=What+Did+the+Romans+Know%3F+An+Inquiry+into+Science+and+Worldmaking&rft.place=Chicago%2C+Ill.&rft.pub=University+of+Chicago+Press&rft.date=2012-02-28&rft.isbn=978-0-226-47114-3&rft.aulast=Lehoux&rft.aufirst=Daryn&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNagel1984" class="citation book cs1">Nagel, Ernest (1984). "5. Experimental laws and theories". <i>The structure of science problems in the logic of scientific explanation</i> (2nd ed.). Indianapolis: Hackett. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-915144-71-6" title="Special:BookSources/978-0-915144-71-6"><bdi>978-0-915144-71-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=5.+Experimental+laws+and+theories&rft.btitle=The+structure+of+science+problems+in+the+logic+of+scientific+explanation&rft.place=Indianapolis&rft.edition=2nd&rft.pub=Hackett&rft.date=1984&rft.isbn=978-0-915144-71-6&rft.aulast=Nagel&rft.aufirst=Ernest&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._Penrose2007" class="citation book cs1">R. Penrose (2007). <a href="/wiki/The_Road_to_Reality" title="The Road to Reality"><i>The Road to Reality</i></a>. Vintage books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-679-77631-4" title="Special:BookSources/978-0-679-77631-4"><bdi>978-0-679-77631-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Road+to+Reality&rft.pub=Vintage+books&rft.date=2007&rft.isbn=978-0-679-77631-4&rft.au=R.+Penrose&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSwartz2009" class="citation encyclopaedia cs1">Swartz, Norman (20 February 2009). <a rel="nofollow" class="external text" href="http://www.iep.utm.edu/lawofnat/">"Laws of Nature"</a>. <i>Internet encyclopedia of philosophy</i><span class="reference-accessdate">. Retrieved <span class="nowrap">7 May</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Laws+of+Nature&rft.btitle=Internet+encyclopedia+of+philosophy&rft.date=2009-02-20&rft.aulast=Swartz&rft.aufirst=Norman&rft_id=http%3A%2F%2Fwww.iep.utm.edu%2Flawofnat%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_law&action=edit&section=31" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Scientific_laws" class="extiw" title="commons:Category:Scientific laws">Scientific laws</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.xs4all.nl/~johanw/contents.html">Physics Formulary</a>, a useful book in different formats containing many or the physical laws and formulae.</li> <li><a rel="nofollow" class="external text" href="http://www.eformulae.com/">Eformulae.com</a>, website containing most of the formulae in different disciplines.</li> <li><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a>: <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/laws-of-nature/">"Laws of Nature"</a> by John W. Carroll.</li> <li>Baaquie, Belal E. <a rel="nofollow" class="external text" href="http://www.srikant.org/core/phy11sep.html">"Laws of Physics : A Primer"</a>. Core Curriculum, <a href="/wiki/National_University_of_Singapore" title="National University of Singapore">National University of Singapore</a>.</li> <li>Francis, Erik Max. <a rel="nofollow" class="external text" href="http://www.alcyone.com/max/physics/laws/">"The laws list".</a>. <a rel="nofollow" class="external text" href="http://www.alcyone.com/max/physics/">Physics</a>. Alcyone Systems</li> <li>Pazameta, Zoran. <a rel="nofollow" class="external text" href="http://www.csicop.org/si/show/laws_of_nature_a_skeptics_guide">"The laws of nature".</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140226190326/http://www.csicop.org/si/show/laws_of_nature_a_skeptics_guide">Archived</a> 2014-02-26 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <a href="/wiki/CSICOP" class="mw-redirect" title="CSICOP">Committee for the scientific investigation of Claims of the Paranormal</a>.</li> <li><a href="/wiki/The_Internet_Encyclopedia_of_Philosophy" class="mw-redirect" title="The Internet Encyclopedia of Philosophy">The Internet Encyclopedia of Philosophy</a>. <a rel="nofollow" class="external text" href="http://www.utm.edu/research/iep/l/lawofnat.htm">"Laws of Nature"</a> – By <a href="/wiki/Norman_Swartz" title="Norman Swartz">Norman Swartz</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMark_BuchananFrank_CloseNancy_CartwrightMelvyn_Bragg_(host)2000" class="citation episode cs1">Mark Buchanan; Frank Close; Nancy Cartwright; Melvyn Bragg (host) (Oct 19, 2000). <a rel="nofollow" class="external text" href="https://www.bbc.co.uk/programmes/p00546x5">"Laws of Nature"</a>. <a href="/wiki/In_Our_Time_(radio_series)" title="In Our Time (radio series)"><i>In Our Time</i></a>. BBC Radio 4.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=In+Our+Time&rft.date=2000-10-19&rft.au=Mark+Buchanan&rft.au=Frank+Close&rft.au=Nancy+Cartwright&rft.au=Melvyn+Bragg+%28host%29&rft_id=http%3A%2F%2Fwww.bbc.co.uk%2Fprogrammes%2Fp00546x5&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+law" class="Z3988"></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.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 dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol 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independent</a></li></ul></li> <li><a href="/wiki/Index_of_philosophy_of_science_articles" title="Index of philosophy of science articles">more...</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coherentism" title="Coherentism">Coherentism</a></li> <li><a href="/wiki/Confirmation_holism" title="Confirmation holism">Confirmation holism</a></li> <li><a href="/wiki/Constructive_empiricism" title="Constructive empiricism">Constructive empiricism</a></li> <li><a href="/wiki/Constructive_realism" title="Constructive realism">Constructive realism</a></li> <li><a href="/wiki/Constructivist_epistemology" class="mw-redirect" title="Constructivist epistemology">Constructivist epistemology</a></li> <li><a href="/wiki/Contextualism" title="Contextualism">Contextualism</a></li> <li><a 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href="/wiki/Naturalism_(philosophy)" title="Naturalism (philosophy)">Naturalism</a></li> <li><a href="/wiki/Physicalism" title="Physicalism">Physicalism</a></li> <li><a href="/wiki/Positivism" title="Positivism">Positivism</a> / <a href="/wiki/Reductionism" title="Reductionism">Reductionism</a> / <a href="/wiki/Determinism" title="Determinism">Determinism</a></li> <li><a href="/wiki/Pragmatism" title="Pragmatism">Pragmatism</a></li> <li><a href="/wiki/Rationalism" title="Rationalism">Rationalism</a> / <a href="/wiki/Empiricism" title="Empiricism">Empiricism</a></li> <li><a href="/wiki/Received_view_of_theories" title="Received view of theories">Received view</a> / <a href="/wiki/Semantic_view_of_theories" title="Semantic view of theories">Semantic view of theories</a></li> <li><a href="/wiki/Scientific_essentialism" title="Scientific essentialism">Scientific essentialism</a></li> <li><a href="/wiki/Scientific_formalism" title="Scientific formalism">Scientific formalism</a></li> <li><a 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title="Philosophy of psychology">Psychology</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Criticism_of_science" title="Criticism of science">Criticism of science</a></li> <li><a href="/wiki/Descriptive_research" title="Descriptive research">Descriptive science</a></li> <li><a href="/wiki/Epistemology" title="Epistemology">Epistemology</a></li> <li><a href="/wiki/Exact_sciences" title="Exact sciences">Exact sciences</a></li> <li><a href="/wiki/Faith_and_rationality" title="Faith and rationality">Faith and rationality</a></li> <li><a href="/wiki/Hard_and_soft_science" title="Hard and soft science">Hard and soft science</a></li> <li><a href="/wiki/History_and_philosophy_of_science" title="History and philosophy of science">History and philosophy of science</a></li> <li><a href="/wiki/Non-science" title="Non-science">Non-science</a> <ul><li><a href="/wiki/Pseudoscience" title="Pseudoscience">Pseudoscience</a></li></ul></li> <li><a href="/wiki/Normative_science" title="Normative science">Normative science</a></li> <li><a href="/wiki/Protoscience" title="Protoscience">Protoscience</a></li> <li><a href="/wiki/Questionable_cause" title="Questionable cause">Questionable cause</a></li> <li><a href="/wiki/Relationship_between_religion_and_science" title="Relationship between religion and science">Relationship between religion and science</a></li> <li><a href="/wiki/Rhetoric_of_science" title="Rhetoric of science">Rhetoric of science</a></li> <li><a href="/wiki/Science_studies" title="Science studies">Science studies</a></li> <li><a href="/wiki/Sociology_of_scientific_ignorance" title="Sociology of scientific ignorance">Sociology of scientific ignorance</a></li> <li><a href="/wiki/Sociology_of_scientific_knowledge" title="Sociology of scientific knowledge">Sociology of scientific knowledge</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_philosophers_of_science" title="List of philosophers of science">Philosophers of science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Precursors10" scope="row" class="navbox-group" style="width:7.5em">Precursors</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Roger_Bacon" title="Roger Bacon">Roger Bacon</a></li> <li><a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></li> <li><a href="/wiki/David_Hume" title="David Hume">David Hume</a></li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Auguste_Comte" title="Auguste Comte">Auguste Comte</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Pierre Duhem</a></li> <li><a href="/wiki/Rudolf_Steiner" title="Rudolf Steiner">Rudolf Steiner</a></li> <li><a href="/wiki/Karl_Pearson" title="Karl Pearson">Karl Pearson</a></li> <li><a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a></li> <li><a href="/wiki/Wilhelm_Windelband" title="Wilhelm Windelband">Wilhelm Windelband</a></li> <li><a href="/wiki/Alfred_North_Whitehead" title="Alfred North Whitehead">Alfred North Whitehead</a></li> <li><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a></li> <li><a href="/wiki/Otto_Neurath" title="Otto Neurath">Otto Neurath</a></li> <li><a href="/wiki/C._D._Broad" title="C. D. Broad">C. D. Broad</a></li> <li><a href="/wiki/Michael_Polanyi" title="Michael Polanyi">Michael Polanyi</a></li> <li><a href="/wiki/Hans_Reichenbach" title="Hans Reichenbach">Hans Reichenbach</a></li> <li><a href="/wiki/Rudolf_Carnap" title="Rudolf Carnap">Rudolf Carnap</a></li> <li><a href="/wiki/Karl_Popper" title="Karl Popper">Karl Popper</a></li> <li><a href="/wiki/Carl_Gustav_Hempel" title="Carl Gustav Hempel">Carl Gustav Hempel</a></li> <li><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">W. V. O. Quine</a></li> <li><a href="/wiki/Thomas_Kuhn" title="Thomas Kuhn">Thomas Kuhn</a></li> <li><a href="/wiki/Imre_Lakatos" title="Imre Lakatos">Imre Lakatos</a></li> <li><a href="/wiki/Paul_Feyerabend" title="Paul Feyerabend">Paul Feyerabend</a></li> <li><a href="/wiki/Ian_Hacking" title="Ian Hacking">Ian Hacking</a></li> <li><a href="/wiki/Bas_van_Fraassen" title="Bas van Fraassen">Bas van Fraassen</a></li> <li><a href="/wiki/Larry_Laudan" title="Larry Laudan">Larry Laudan</a></li></ul></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <li><a href="/wiki/Category:Philosophy_of_science" title="Category:Philosophy of science">Category</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span> </span><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_kalzium.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/28px-Nuvola_apps_kalzium.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/42px-Nuvola_apps_kalzium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/56px-Nuvola_apps_kalzium.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Science" title="Portal:Science">Science portal</a></li> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Scientific_law&oldid=1273754950#Laws_of_physics">https://en.wikipedia.org/w/index.php?title=Scientific_law&oldid=1273754950#Laws_of_physics</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Causality" title="Category:Causality">Causality</a></li><li><a href="/wiki/Category:Empirical_laws" title="Category:Empirical laws">Empirical laws</a></li><li><a href="/wiki/Category:Metaphysics_of_science" title="Category:Metaphysics of science">Metaphysics of science</a></li><li><a href="/wiki/Category:Philosophy_of_science" title="Category:Philosophy of science">Philosophy of science</a></li><li><a href="/wiki/Category:Principles" title="Category:Principles">Principles</a></li><li><a href="/wiki/Category:Science-related_lists" title="Category:Science-related lists">Science-related lists</a></li><li><a href="/wiki/Category:Scientific_laws" title="Category:Scientific laws">Scientific laws</a></li><li><a href="/wiki/Category:Scientific_method" title="Category:Scientific method">Scientific method</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 3 February 2025, at 21:39<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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