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</a> </li> <li id="page-actions-edit" class="page-actions-menu__list-item"> <a role="button" id="ca-edit" href="/w/index.php?title=Photon&action=edit" data-event-name="menu.edit" data-mw="interface" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet edit-page menu__item--page-actions-edit"> Edit </a> </li> </ul> </nav>  <div id="mw-content-subtitle"></div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"><script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><section class="mf-section-0" id="mf-section-0"> <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">This article is about the elementary particle or quantum of light. For other uses, see <a href="/wiki/Photon_(disambiguation)" class="mw-disambig" title="Photon (disambiguation)">Photon (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style>A photon (from <a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a> <a href="https://en.wiktionary.org/wiki/%CF%86%E1%BF%B6%CF%82#Ancient_Greek" class="extiw" title="wikt:φῶς">φῶς</a>, <a href="https://en.wiktionary.org/wiki/%CF%86%CF%89%CF%84%CF%8C%CF%82#Ancient_Greek" class="extiw" title="wikt:φωτός">φωτός</a> (phôs, phōtós) 'light') is an <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particle</a> that is a <a href="/wiki/Quantum" title="Quantum">quantum</a> of the <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a>, including <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> such as <a href="/wiki/Light" title="Light">light</a> and <a href="/wiki/Radio_wave" title="Radio wave">radio waves</a>, and the <a href="/wiki/Force_carrier" title="Force carrier">force carrier</a> for the <a href="/wiki/Electromagnetic_force" class="mw-redirect" title="Electromagnetic force">electromagnetic force</a>. Photons are <a href="/wiki/Massless_particle" title="Massless particle">massless particles</a> that always move at the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> measured in vacuum. The photon belongs to the class of <a href="/wiki/Boson" title="Boson">boson</a> particles. <table class="infobox"><caption class="infobox-title">Photon</caption><tbody><tr><th scope="row" class="infobox-label"><a href="/wiki/Particle#Composition" title="Particle">Composition</a></th><td class="infobox-data"><a href="/wiki/Elementary_particle" title="Elementary particle">Elementary particle</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Particle_statistics" title="Particle statistics">Statistics</a></th><td class="infobox-data"><a href="/wiki/Bosonic" class="mw-redirect" title="Bosonic">Bosonic</a></td></tr><tr><th scope="row" class="infobox-label">Family</th><td class="infobox-data"><a href="/wiki/Gauge_boson" title="Gauge boson">Gauge boson</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Fundamental_interaction" title="Fundamental interaction">Interactions</a></th><td class="infobox-data"><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetic</a>, <a href="/wiki/Weak_interaction" title="Weak interaction">weak</a> (and <a href="/wiki/Gravity" title="Gravity">gravity</a>)</td></tr><tr><th scope="row" class="infobox-label">Symbol</th><td class="infobox-data"> γ</td></tr><tr><th scope="row" class="infobox-label">Theorized</th><td class="infobox-data"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> (1905) The name "photon" is generally attributed to <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a> (1926)</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Invariant_mass" title="Invariant mass">Mass</a></th><td class="infobox-data">0 (theoretical value) < 1×10−18 <a href="/wiki/Electronvolt#Mass" title="Electronvolt">eV/c2</a> (experimental limit)<a href="#cite_note-Particle_table_2009-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Mean_lifetime" class="mw-redirect" title="Mean lifetime">Mean lifetime</a></th><td class="infobox-data">Stable<a href="#cite_note-Particle_table_2009-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Electric_charge" title="Electric charge">Electric charge</a></th><td class="infobox-data">0 < 1×10−35 <a href="/wiki/Elementary_charge" title="Elementary charge">e</a><a href="#cite_note-Particle_table_2009-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Color_charge" title="Color charge">Color charge</a></th><td class="infobox-data">No</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Spin_(physics)" title="Spin (physics)">Spin</a></th><td class="infobox-data">1 <a href="/wiki/Reduced_Planck_constant" class="mw-redirect" title="Reduced Planck constant">ħ</a></td></tr><tr><th scope="row" class="infobox-label">Spin states</th><td class="infobox-data">+1 ħ, −1 ħ</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Parity_(physics)" title="Parity (physics)">Parity</a></th><td class="infobox-data">−1<a href="#cite_note-Particle_table_2009-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/C-parity" class="mw-redirect" title="C-parity">C parity</a></th><td class="infobox-data">−1<a href="#cite_note-Particle_table_2009-1">[1]</a></td></tr><tr><th scope="row" class="infobox-label">Condensed</th><td class="infobox-data"><a href="/wiki/Weak_isospin" title="Weak isospin">I</a>(<a href="/wiki/Total_angular_momentum" class="mw-redirect" title="Total angular momentum">J</a><a href="/wiki/Parity_(physics)" title="Parity (physics)">P</a> <a href="/wiki/C_parity" title="C parity">C</a>)=0,1(1−−)<a href="#cite_note-Particle_table_2009-1">[1]</a></td></tr></tbody></table> As with other elementary particles, photons are best explained by <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> and exhibit <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">wave–particle duality</a>, their behavior featuring properties of both <a href="/wiki/Wave" title="Wave">waves</a> and <a href="/wiki/Particle" title="Particle">particles</a>.<a href="#cite_note-2">[2]</a> The modern photon concept originated during the first two decades of the 20th century with the work of <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, who built upon the research of <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>. While Planck was trying to explain how <a href="/wiki/Matter" title="Matter">matter</a> and electromagnetic radiation could be in <a href="/wiki/Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a> with one another, he proposed that the energy stored within a <a href="/wiki/Material" title="Material">material</a> object should be regarded as composed of an <a href="/wiki/Integer" title="Integer">integer</a> number of discrete, equal-sized parts. To explain the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>, Einstein introduced the idea that light itself is made of discrete units of energy. In 1926, <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a> popularized the term photon for these energy units.<a href="#cite_note-www.aps.org-3">[3]</a><a href="#cite_note-4">[4]</a><a href="#cite_note-kragh-5">[5]</a> Subsequently, many other experiments validated Einstein's approach.<a href="#cite_note-compton-lecture-6">[6]</a><a href="#cite_note-7">[7]</a><a href="#cite_note-8">[8]</a> In the <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a> of <a href="/wiki/Particle_physics" title="Particle physics">particle physics</a>, photons and other elementary particles are described as a necessary consequence of physical laws having a certain <a href="/wiki/Symmetry_(physics)" title="Symmetry (physics)">symmetry</a> at every point in <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. The intrinsic properties of particles, such as <a href="/wiki/Electric_charge" title="Electric charge">charge</a>, <a href="/wiki/Invariant_mass" title="Invariant mass">mass</a>, and <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a>, are determined by <a href="/wiki/Gauge_symmetry" class="mw-redirect" title="Gauge symmetry">gauge symmetry</a>. The photon concept has led to momentous advances in experimental and theoretical physics, including <a href="/wiki/Laser" title="Laser">lasers</a>, <a href="/wiki/Bose%E2%80%93Einstein_condensation" class="mw-redirect" title="Bose–Einstein condensation">Bose–Einstein condensation</a>, <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, and the <a href="/wiki/Probability_amplitude" title="Probability amplitude">probabilistic interpretation</a> of quantum mechanics. It has been applied to <a href="/wiki/Photochemistry" title="Photochemistry">photochemistry</a>, <a href="/wiki/Two-photon_excitation_microscopy" title="Two-photon excitation microscopy">high-resolution microscopy</a>, and <a href="/wiki/Fluorescence_resonance_energy_transfer" class="mw-redirect" title="Fluorescence resonance energy transfer">measurements of molecular distances</a>. Moreover, photons have been studied as elements of <a href="/wiki/Quantum_computer" class="mw-redirect" title="Quantum computer">quantum computers</a>, and for applications in <a href="/wiki/Optical_imaging" class="mw-redirect" title="Optical imaging">optical imaging</a> and <a href="/wiki/Optical_communication" title="Optical communication">optical communication</a> such as <a href="/wiki/Quantum_cryptography" title="Quantum cryptography">quantum cryptography</a>. <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><label class="toctogglelabel" for="toctogglecheckbox"></label></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Nomenclature">1 Nomenclature</a></li> <li class="toclevel-1 tocsection-2"><a href="#Physical_properties">2 Physical properties</a> <ul> <li class="toclevel-2 tocsection-3"><a href="#Relativistic_energy_and_momentum">2.1 Relativistic energy and momentum</a></li> <li class="toclevel-2 tocsection-4"><a href="#Polarization_and_spin_angular_momentum">2.2 Polarization and spin angular momentum</a></li> <li class="toclevel-2 tocsection-5"><a href="#Antiparticle_annihilation">2.3 Antiparticle annihilation</a></li> <li class="toclevel-2 tocsection-6"><a href="#Experimental_checks_on_photon_mass">2.4 Experimental checks on photon mass</a></li> </ul> </li> <li class="toclevel-1 tocsection-7"><a href="#Historical_development">3 Historical development</a></li> <li class="toclevel-1 tocsection-8"><a href="#Wave%E2%80%93particle_duality_and_uncertainty_principles">4 Wave–particle duality and uncertainty principles</a></li> <li class="toclevel-1 tocsection-9"><a href="#Bose%E2%80%93Einstein_model_of_a_photon_gas">5 Bose–Einstein model of a photon gas</a></li> <li class="toclevel-1 tocsection-10"><a href="#Stimulated_and_spontaneous_emission">6 Stimulated and spontaneous emission</a></li> <li class="toclevel-1 tocsection-11"><a href="#Quantum_field_theory">7 Quantum field theory</a> <ul> <li class="toclevel-2 tocsection-12"><a href="#Quantization_of_the_electromagnetic_field">7.1 Quantization of the electromagnetic field</a></li> <li class="toclevel-2 tocsection-13"><a href="#As_a_gauge_boson">7.2 As a gauge boson</a></li> <li class="toclevel-2 tocsection-14"><a href="#Hadronic_properties">7.3 Hadronic properties</a></li> <li class="toclevel-2 tocsection-15"><a href="#Contributions_to_the_mass_of_a_system">7.4 Contributions to the mass of a system</a></li> </ul> </li> <li class="toclevel-1 tocsection-16"><a href="#In_matter">8 In matter</a></li> <li class="toclevel-1 tocsection-17"><a href="#Technological_applications">9 Technological applications</a></li> <li class="toclevel-1 tocsection-18"><a href="#Quantum_optics_and_computation">10 Quantum optics and computation</a></li> <li class="toclevel-1 tocsection-19"><a href="#See_also">11 See also</a></li> <li class="toclevel-1 tocsection-20"><a href="#Notes">12 Notes</a></li> <li class="toclevel-1 tocsection-21"><a href="#References">13 References</a></li> <li class="toclevel-1 tocsection-22"><a href="#Further_reading">14 Further reading</a></li> <li class="toclevel-1 tocsection-23"><a href="#External_links">15 External links</a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><h2 id="Nomenclature">Nomenclature</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=1" title="Edit section: Nomenclature" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Photoelectric_effect_in_a_solid_-_diagram.svg" class="mw-file-description"><noscript><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/220px-Photoelectric_effect_in_a_solid_-_diagram.svg.png" decoding="async" width="220" height="220" class="mw-file-element" data-file-width="364" data-file-height="364"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 220px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/220px-Photoelectric_effect_in_a_solid_-_diagram.svg.png" data-alt="" data-width="220" data-height="220" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/330px-Photoelectric_effect_in_a_solid_-_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Photoelectric_effect_in_a_solid_-_diagram.svg/440px-Photoelectric_effect_in_a_solid_-_diagram.svg.png 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Photoelectric_effect" title="Photoelectric effect">Photoelectric effect</a>: the emission of electrons from a metal plate caused by light quanta – photons</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg/660px-1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg" decoding="async" width="660" height="609" class="mw-file-element" data-file-width="2603" data-file-height="2403"></noscript><span class="lazy-image-placeholder" style="width: 660px;height: 609px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg/660px-1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg" data-width="660" data-height="609" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg/990px-1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg/1320px-1926_Gilbert_N._Lewis_letter_which_brought_the_word_%22photon%22_into_common_usage.jpg 2x" data-class="mw-file-element"> </a><figcaption>1926 <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a> letter which brought the word "photon" into common usage</figcaption></figure> The word <a href="/wiki/Quantum" title="Quantum">quanta</a> (singular quantum, Latin for <a href="https://en.wiktionary.org/wiki/quantum" class="extiw" title="wikt:quantum">how much</a>) was used before 1900 to mean particles or amounts of different <a href="/wiki/Quantity" title="Quantity">quantities</a>, including <a href="/wiki/Electron" title="Electron">electricity</a>. In 1900, the German physicist <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> was studying <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a>, and he suggested that the experimental observations, specifically at <a href="/wiki/Ultraviolet_catastrophe" title="Ultraviolet catastrophe">shorter wavelengths</a>, would be explained if the energy stored within a molecule was a "discrete quantity composed of an integral number of finite equal parts", which he called "energy elements".<a href="#cite_note-9">[9]</a> In 1905, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> published a paper in which he proposed that many light-related phenomena—including black-body radiation and the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>—would be better explained by modelling electromagnetic waves as consisting of spatially localized, discrete energy quanta.<a href="#cite_note-Einstein1905-10">[10]</a> He called these a light quantum (German: ein Lichtquant).<a href="#cite_note-11">[a]</a> The name photon derives from the <a href="/wiki/Greek_language" title="Greek language">Greek word</a> for light, φῶς (transliterated phôs). <a href="/wiki/Arthur_Compton" title="Arthur Compton">Arthur Compton</a> used photon in 1928, referring to <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a>, who coined the term in a letter to <a href="/wiki/Nature_(journal)" title="Nature (journal)">Nature</a> on 18 December 1926.<a href="#cite_note-www.aps.org-3">[3]</a><a href="#cite_note-12">[11]</a> The same name was used earlier but was never widely adopted before Lewis: in 1916 by the American physicist and psychologist <a href="/wiki/Leonard_T._Troland" title="Leonard T. Troland">Leonard T. Troland</a>, in 1921 by the Irish physicist <a href="/wiki/John_Joly" title="John Joly">John Joly</a>, in 1924 by the French physiologist René Wurmser (1890–1993), and in 1926 by the French physicist Frithiof Wolfers (1891–1971).<a href="#cite_note-kragh-5">[5]</a> The name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolfers's and Lewis's theories were contradicted by many experiments and never accepted, the new name was adopted by most physicists very soon after Compton used it.<a href="#cite_note-kragh-5">[5]</a><a href="#cite_note-14">[b]</a> In physics, a photon is usually denoted by the symbol <a href="/wiki/Gamma" title="Gamma">γ</a> (the <a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek letter</a> <a href="/wiki/Gamma" title="Gamma">gamma</a>). This symbol for the photon probably derives from <a href="/wiki/Gamma_ray" title="Gamma ray">gamma rays</a>, which were discovered in 1900 by <a href="/wiki/Paul_Ulrich_Villard" title="Paul Ulrich Villard">Paul Villard</a>,<a href="#cite_note-15">[13]</a><a href="#cite_note-16">[14]</a> named by <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> in 1903, and shown to be a form of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> in 1914 by Rutherford and <a href="/wiki/Edward_Andrade" title="Edward Andrade">Edward Andrade</a>.<a href="#cite_note-17">[15]</a> In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a> and <a href="/wiki/Optical_engineering" title="Optical engineering">optical engineering</a>, photons are usually symbolized by hν, which is the <a href="/wiki/Photon_energy" title="Photon energy">photon energy</a>, where h is the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a> and the <a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek letter</a> ν (<a href="/wiki/Nu_(letter)" title="Nu (letter)">nu</a>) is the photon's <a href="/wiki/Frequency" title="Frequency">frequency</a>.<a href="#cite_note-Liddle2015-18">[16]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><h2 id="Physical_properties">Physical properties</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=2" title="Edit section: Physical properties" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> The photon has no <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a>,<a href="#cite_note-19">[17]</a><a href="#cite_note-chargeless-20">[18]</a> is generally considered to have zero <a href="/wiki/Rest_mass" class="mw-redirect" title="Rest mass">rest mass</a><a href="#cite_note-21">[19]</a> and is a <a href="/wiki/Stable_particle" class="mw-redirect" title="Stable particle">stable particle</a>. The experimental upper limit on the photon mass<a href="#cite_note-22">[20]</a><a href="#cite_note-23">[21]</a> is very small, on the order of 10−50 kg; its lifetime would be more than 1018 years.<a href="#cite_note-24">[22]</a> For comparison the <a href="/wiki/Age_of_the_universe" title="Age of the universe">age of the universe</a> is about 1.38×1010 years. In a vacuum, a photon has two possible <a href="/wiki/Photon_polarization" title="Photon polarization">polarization</a> states.<a href="#cite_note-Schwartz2014-25">[23]</a> The photon is the <a href="/wiki/Gauge_boson" title="Gauge boson">gauge boson</a> for <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>,<a href="#cite_note-26">[24]</a>: 29–30 and therefore all other quantum numbers of the photon (such as <a href="/wiki/Lepton_number" title="Lepton number">lepton number</a>, <a href="/wiki/Baryon_number" title="Baryon number">baryon number</a>, and <a href="/wiki/Flavor_(particle_physics)#Flavour_quantum_numbers" class="mw-redirect" title="Flavor (particle physics)">flavour quantum numbers</a>) are zero.<a href="#cite_note-27">[25]</a> Also, the photon obeys <a href="/wiki/Bose%E2%80%93Einstein_statistics" title="Bose–Einstein statistics">Bose–Einstein statistics</a>, and not <a href="/wiki/Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics">Fermi–Dirac statistics</a>. That is, they do not obey the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a><a href="#cite_note-Halliday-28">[26]</a>: 1221 and more than one can occupy the same bound quantum state. Photons are emitted in many natural processes. For example, when a charge is <a href="/wiki/Acceleration" title="Acceleration">accelerated</a> it emits <a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">synchrotron radiation</a>. During a <a href="/wiki/Molecule" title="Molecule">molecular</a>, <a href="/wiki/Atom" title="Atom">atomic</a> or <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">nuclear</a> transition to a lower <a href="/wiki/Energy_level" title="Energy level">energy level</a>, photons of various energy will be emitted, ranging from <a href="/wiki/Radio_wave" title="Radio wave">radio waves</a> to <a href="/wiki/Gamma_ray" title="Gamma ray">gamma rays</a>. Photons can also be emitted when a particle and its corresponding <a href="/wiki/Antiparticle" title="Antiparticle">antiparticle</a> are <a href="/wiki/Annihilation" title="Annihilation">annihilated</a> (for example, <a href="/wiki/Electron%E2%80%93positron_annihilation" title="Electron–positron annihilation">electron–positron annihilation</a>).<a href="#cite_note-Halliday-28">[26]</a>: 572, 1114, 1172 <div class="mw-heading mw-heading3"><h3 id="Relativistic_energy_and_momentum">Relativistic energy and momentum</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=3" title="Edit section: Relativistic energy and momentum" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Photon_energy" title="Photon energy">Photon energy</a> and <a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Light_cone_colour.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Light_cone_colour.svg/220px-Light_cone_colour.svg.png" decoding="async" width="220" height="340" class="mw-file-element" data-file-width="333" data-file-height="515"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 340px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Light_cone_colour.svg/220px-Light_cone_colour.svg.png" data-width="220" data-height="340" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Light_cone_colour.svg/330px-Light_cone_colour.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Light_cone_colour.svg/440px-Light_cone_colour.svg.png 2x" data-class="mw-file-element"> </a><figcaption>The cone shows possible values of wave 4-vector of a photon. The "time" axis gives the angular frequency (<a href="/wiki/Radians_per_second" class="mw-redirect" title="Radians per second">rad⋅s−1</a>) and the "space" axis represents the angular wavenumber (rad⋅m−1). Green and indigo represent left and right polarization.</figcaption></figure> In empty space, the photon moves at c (the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>) and its <a href="/wiki/Energy" title="Energy">energy</a> and <a href="/wiki/Momentum" title="Momentum">momentum</a> are related by E = pc, where p is the <a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitude</a> of the momentum vector p. This derives from the following relativistic relation, with m = 0:<a href="#cite_note-29">[27]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E^{2}=p^{2}c^{2}+m^{2}c^{4}~.}"> <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> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}=p^{2}c^{2}+m^{2}c^{4}~.}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1c3c77e3e91403a14be4b0afd8a5f7ffea5bef4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.455ex; height:3.009ex;" alt="{\displaystyle E^{2}=p^{2}c^{2}+m^{2}c^{4}~.}"></noscript><span class="lazy-image-placeholder" style="width: 19.455ex;height: 3.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1c3c77e3e91403a14be4b0afd8a5f7ffea5bef4" data-alt="{\displaystyle E^{2}=p^{2}c^{2}+m^{2}c^{4}~.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> The energy and momentum of a photon depend only on its <a href="/wiki/Frequency" title="Frequency">frequency</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></noscript><span class="lazy-image-placeholder" style="width: 1.232ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" data-alt="{\displaystyle \nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> ) or inversely, its <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> (λ): <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\hbar \,\omega =h\nu ={\frac {\,h\,c\,}{\lambda }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mspace width="thinmathspace"></mspace> <mi>ω</mi> <mo>=</mo> <mi>h</mi> <mi>ν</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mspace width="thinmathspace"></mspace> <mi>h</mi> <mspace width="thinmathspace"></mspace> <mi>c</mi> <mspace width="thinmathspace"></mspace> </mrow> <mi>λ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\hbar \,\omega =h\nu ={\frac {\,h\,c\,}{\lambda }}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c8f257fcca9e4b916d7e08f89f02e4ce3bb5d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.125ex; height:5.509ex;" alt="{\displaystyle E=\hbar \,\omega =h\nu ={\frac {\,h\,c\,}{\lambda }}}"></noscript><span class="lazy-image-placeholder" style="width: 21.125ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c8f257fcca9e4b916d7e08f89f02e4ce3bb5d7a" data-alt="{\displaystyle E=\hbar \,\omega =h\nu ={\frac {\,h\,c\,}{\lambda }}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd> <dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {p}}=\hbar {\boldsymbol {k}}~,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}=\hbar {\boldsymbol {k}}~,}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a0b5a5515b290455e05eff6fa0977ee65892d7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.052ex; width:8.486ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {p}}=\hbar {\boldsymbol {k}}~,}"></noscript><span class="lazy-image-placeholder" style="width: 8.486ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a0b5a5515b290455e05eff6fa0977ee65892d7c" data-alt="{\displaystyle {\boldsymbol {p}}=\hbar {\boldsymbol {k}}~,}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> where k is the <a href="/wiki/Wave_vector" title="Wave vector">wave vector</a>, where <ul><li> k ≡ |k| = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>⁠ 2π /λ⁠ is the <a href="/wiki/Wave_number" class="mw-redirect" title="Wave number">wave number</a>, and</li> <li> ω ≡ 2 πν is the <a href="/wiki/Angular_frequency" title="Angular frequency">angular frequency</a>, and</li> <li> ħ ≡ <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠h/ 2π ⁠ is the <a href="/wiki/Reduced_Planck_constant" class="mw-redirect" title="Reduced Planck constant">reduced Planck constant</a>.<a href="#cite_note-30">[28]</a></li></ul> Since <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04cff366782c9fb192fc63992ef75ad59ee77695" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.052ex; width:1.449ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {p}}}"></noscript><span class="lazy-image-placeholder" style="width: 1.449ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04cff366782c9fb192fc63992ef75ad59ee77695" data-alt="{\displaystyle {\boldsymbol {p}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  points in the direction of the photon's propagation, the magnitude of its momentum is <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p\equiv \left|{\boldsymbol {p}}\right|=\hbar k={\frac {\,h\nu \,}{c}}={\frac {\,h\,}{\lambda }}~.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>≡</mo> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mi class="MJX-variant">ℏ</mi> <mi>k</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mspace width="thinmathspace"></mspace> <mi>h</mi> <mi>ν</mi> <mspace width="thinmathspace"></mspace> </mrow> <mi>c</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mspace width="thinmathspace"></mspace> <mi>h</mi> <mspace width="thinmathspace"></mspace> </mrow> <mi>λ</mi> </mfrac> </mrow> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\equiv \left|{\boldsymbol {p}}\right|=\hbar k={\frac {\,h\nu \,}{c}}={\frac {\,h\,}{\lambda }}~.}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97aa5a30d0e477fe757b910973031b685d3e26d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.089ex; width:27.219ex; height:5.509ex;" alt="{\displaystyle p\equiv \left|{\boldsymbol {p}}\right|=\hbar k={\frac {\,h\nu \,}{c}}={\frac {\,h\,}{\lambda }}~.}"></noscript><span class="lazy-image-placeholder" style="width: 27.219ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97aa5a30d0e477fe757b910973031b685d3e26d4" data-alt="{\displaystyle p\equiv \left|{\boldsymbol {p}}\right|=\hbar k={\frac {\,h\nu \,}{c}}={\frac {\,h\,}{\lambda }}~.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> <div class="mw-heading mw-heading3"><h3 id="Polarization_and_spin_angular_momentum">Polarization and spin angular momentum</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=4" title="Edit section: Polarization and spin angular momentum" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </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/Photon_polarization" title="Photon polarization">Photon polarization</a> and <a href="/wiki/Spin_angular_momentum_of_light" title="Spin angular momentum of light">Spin angular momentum of light</a></div> The photon also carries <a href="/wiki/Spin_angular_momentum_of_light" title="Spin angular momentum of light">spin angular momentum</a>, which is related to <a href="/wiki/Photon_polarization" title="Photon polarization">photon polarization</a>. (Beams of light also exhibit properties described as <a href="/wiki/Orbital_angular_momentum_of_light" title="Orbital angular momentum of light">orbital angular momentum of light</a>). The angular momentum of the photon has two possible values, either +ħ or −ħ. These two possible values correspond to the two possible pure states of <a href="/wiki/Circular_polarization" title="Circular polarization">circular polarization</a>. Collections of photons in a light beam may have mixtures of these two values; a linearly polarized light beam will act as if it were composed of equal numbers of the two possible angular momenta.<a href="#cite_note-Hecht-31">[29]</a>: 325 The spin angular momentum of light does not depend on its frequency, and was experimentally verified by <a href="/wiki/C._V._Raman" title="C. V. Raman">C. V. Raman</a> and S. Bhagavantam in 1931.<a href="#cite_note-spin-32">[30]</a> <div class="mw-heading mw-heading3"><h3 id="Antiparticle_annihilation">Antiparticle annihilation</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=5" title="Edit section: Antiparticle annihilation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </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/Annihilation" title="Annihilation">Annihilation</a> and <a href="/wiki/Electron-positron_annihilation" class="mw-redirect" title="Electron-positron annihilation">Electron-positron annihilation</a></div> The collision of a particle with its antiparticle can create photons. In free space at least two photons must be created since, in the <a href="/wiki/Center_of_momentum_frame" class="mw-redirect" title="Center of momentum frame">center of momentum frame</a>, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (determined by the photon's frequency or wavelength, which cannot be zero). Hence, <a href="/wiki/Momentum" title="Momentum">conservation of momentum</a> (or equivalently, <a href="/wiki/Translational_invariance" class="mw-redirect" title="Translational invariance">translational invariance</a>) requires that at least two photons are created, with zero net momentum.<a href="#cite_note-33">[c]</a><a href="#cite_note-Griffiths2008-34">[31]</a>: 64–65 The energy of the two photons, or, equivalently, their frequency, may be determined from <a href="/wiki/Conservation_law_(physics)" class="mw-redirect" title="Conservation law (physics)">conservation of four-momentum</a>. Seen another way, the photon can be considered as <a href="/wiki/Truly_neutral_particle" title="Truly neutral particle">its own antiparticle</a> (thus an "antiphoton" is simply a normal photon with opposite momentum, equal polarization, and 180° out of phase). The reverse process, <a href="/wiki/Pair_production" title="Pair production">pair production</a>, is the dominant mechanism by which high-energy photons such as <a href="/wiki/Gamma_ray" title="Gamma ray">gamma rays</a> lose energy while passing through matter.<a href="#cite_note-35">[32]</a> That process is the reverse of "annihilation to one photon" allowed in the electric field of an atomic nucleus. The classical formulae for the energy and momentum of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> can be re-expressed in terms of photon events. For example, the <a href="/wiki/Radiation_pressure" title="Radiation pressure">pressure of electromagnetic radiation</a> on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in <a href="/wiki/Momentum" title="Momentum">momentum</a> per unit time.<a href="#cite_note-36">[33]</a> <div class="mw-heading mw-heading3"><h3 id="Experimental_checks_on_photon_mass">Experimental checks on photon mass</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=6" title="Edit section: Experimental checks on photon mass" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Current commonly accepted physical theories imply or assume the photon to be strictly massless. If photons were not purely massless, their speeds would vary with frequency, with lower-energy (redder) photons moving slightly slower than higher-energy photons. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the <a href="/wiki/Upper_bound" class="mw-redirect" title="Upper bound">upper bound</a> on speed that any object could theoretically attain in spacetime.<a href="#cite_note-37">[34]</a> Thus, it would still be the speed of spacetime ripples (<a href="/wiki/Gravitational_waves" class="mw-redirect" title="Gravitational waves">gravitational waves</a> and <a href="/wiki/Graviton" title="Graviton">gravitons</a>), but it would not be the speed of photons. If a photon did have non-zero mass, there would be other effects as well. <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a> would be modified and the <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a> would have an extra physical <a href="/wiki/Degree_of_freedom" class="mw-redirect" title="Degree of freedom">degree of freedom</a>. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb's law is not exactly valid, then that would allow the presence of an <a href="/wiki/Electric_field" title="Electric field">electric field</a> to exist within a hollow conductor when it is subjected to an external electric field. This provides a means for precision <a href="/wiki/Tests_of_electromagnetism" class="mw-redirect" title="Tests of electromagnetism">tests of Coulomb's law</a>.<a href="#cite_note-38">[35]</a> A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2.<a href="#cite_note-39">[36]</a> Sharper upper limits on the mass of light have been obtained in experiments designed to detect effects caused by the galactic <a href="/wiki/Magnetic_vector_potential" title="Magnetic vector potential">vector potential</a>. Although the galactic vector potential is large because the galactic <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> exists on great length scales, only the magnetic field would be observable if the photon is massless. In the case that the photon has mass, the mass term <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/2⁠m2AμAμ would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m < 3×10−27 eV/c2.<a href="#cite_note-40">[37]</a> The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.<a href="#cite_note-41">[38]</a> Such methods were used to obtain the sharper upper limit of 1.07×10−27 eV/c2 (the equivalent of 10−36 <a href="/wiki/Dalton_(unit)" title="Dalton (unit)">daltons</a>) given by the <a href="/wiki/Particle_Data_Group" title="Particle Data Group">Particle Data Group</a>.<a href="#cite_note-amsler-42">[39]</a> These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model-dependent.<a href="#cite_note-43">[40]</a> If the photon mass is generated via the <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a> then the upper limit of m ≲ 10−14 eV/c2 from the test of Coulomb's law is valid. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><h2 id="Historical_development">Historical development</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=7" title="Edit section: Historical development" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Light" title="Light">Light</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Young_Diffraction.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Young_Diffraction.png/220px-Young_Diffraction.png" decoding="async" width="220" height="98" class="mw-file-element" data-file-width="1988" data-file-height="882"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 98px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Young_Diffraction.png/220px-Young_Diffraction.png" data-width="220" data-height="98" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Young_Diffraction.png/330px-Young_Diffraction.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Young_Diffraction.png/440px-Young_Diffraction.png 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a>'s <a href="/wiki/Double-slit_experiment" title="Double-slit experiment">double-slit experiment</a> in 1801 showed that light can act as a <a href="/wiki/Wave" title="Wave">wave</a>, helping to invalidate early <a href="/wiki/Elementary_particle" title="Elementary particle">particle</a> theories of light.<a href="#cite_note-Halliday-28">[26]</a>: 964 </figcaption></figure> In most theories up to the eighteenth century, light was pictured as being made of particles. Since <a href="/wiki/Subatomic_particle" title="Subatomic particle">particle</a> models cannot easily account for the <a href="/wiki/Refraction" title="Refraction">refraction</a>, <a href="/wiki/Diffraction" title="Diffraction">diffraction</a> and <a href="/wiki/Birefringence" title="Birefringence">birefringence</a> of light, wave theories of light were proposed by <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> (1637),<a href="#cite_note-44">[41]</a> <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a> (1665),<a href="#cite_note-45">[42]</a> and <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> (1678);<a href="#cite_note-46">[43]</a> however, particle models remained dominant, chiefly due to the influence of <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>.<a href="#cite_note-Newton1730-47">[44]</a> In the early 19th century, <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> and <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">August Fresnel</a> clearly demonstrated the <a href="/wiki/Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">interference</a> and diffraction of light, and by 1850 wave models were generally accepted.<a href="#cite_note-48">[45]</a> <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a>'s 1865 <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">prediction</a><a href="#cite_note-maxwell-49">[46]</a> that light was an electromagnetic wave – which was confirmed experimentally in 1888 by <a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Heinrich Hertz</a>'s detection of <a href="/wiki/Radio" title="Radio">radio waves</a><a href="#cite_note-hertz-50">[47]</a> – seemed to be the final blow to particle models of light. <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Light-wave.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Light-wave.svg/280px-Light-wave.svg.png" decoding="async" width="280" height="147" class="mw-file-element" data-file-width="554" data-file-height="290"></noscript><span class="lazy-image-placeholder" style="width: 280px;height: 147px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Light-wave.svg/280px-Light-wave.svg.png" data-width="280" data-height="147" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Light-wave.svg/420px-Light-wave.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Light-wave.svg/560px-Light-wave.svg.png 2x" data-class="mw-file-element"> </a><figcaption>In 1900, <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell's</a> <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">theoretical model of light</a> as oscillating <a href="/wiki/Electric_field" title="Electric field">electric</a> and <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic fields</a> seemed complete. However, several observations could not be explained by any wave model of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>, leading to the idea that light-energy was packaged into quanta described by E = hν. Later experiments showed that these light-quanta also carry momentum and, thus, can be considered <a href="/wiki/Elementary_particle" title="Elementary particle">particles</a>: The photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.</figcaption></figure> The <a href="/wiki/Electromagnetic_wave_equation" title="Electromagnetic wave equation">Maxwell wave theory</a>, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its <a href="/wiki/Intensity_(physics)" title="Intensity (physics)">intensity</a>, not on its <a href="/wiki/Frequency" title="Frequency">frequency</a>; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, <a href="/wiki/Photochemistry" title="Photochemistry">some chemical reactions</a> are provoked only by light of frequency higher than a certain threshold; light of frequency lower than the threshold, no matter how intense, does not initiate the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>); the energy of the ejected electron is related only to the light's frequency, not to its intensity.<a href="#cite_note-51">[48]</a><a href="#cite_note-53">[d]</a> At the same time, investigations of <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a> carried out over four decades (1860–1900) by various researchers<a href="#cite_note-Wien1911-54">[50]</a> culminated in <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>'s <a href="/wiki/Planck_constant" title="Planck constant">hypothesis</a><a href="#cite_note-Planck1901-55">[51]</a><a href="#cite_note-Planck1918-56">[52]</a> that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E = hν . As shown by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>,<a href="#cite_note-Einstein1905-10">[10]</a><a href="#cite_note-Einstein1909-57">[53]</a> some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>; for this explanation of the photoelectric effect, Einstein received the 1921 <a href="/wiki/Nobel_Prize" title="Nobel Prize">Nobel Prize</a> in physics.<a href="#cite_note-58">[54]</a> Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself.<a href="#cite_note-Einstein1905-10">[10]</a> Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over space.<a href="#cite_note-Einstein1905-10">[10]</a> In 1909<a href="#cite_note-Einstein1909-57">[53]</a> and 1916,<a href="#cite_note-Einstein1916b-59">[55]</a> Einstein showed that, if <a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a> regarding black-body radiation is accepted, the energy quanta must also carry <a href="/wiki/Momentum" title="Momentum">momentum</a> p = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠ h / λ ⁠ , making them full-fledged particles. This photon momentum was observed experimentally by <a href="/wiki/Arthur_Compton" title="Arthur Compton">Arthur Compton</a>,<a href="#cite_note-Compton1923-60">[56]</a> for which he received the Nobel Prize in 1927. The pivotal question then, was how to unify Maxwell's wave theory of light with its experimentally observed particle nature. The answer to this question occupied Albert Einstein for the rest of his life,<a href="#cite_note-Pais1982-61">[57]</a> and was solved in <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> and its successor, the <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a>. (See <a href="#Quantum_field_theory">§ Quantum field theory</a> and <a href="#As_a_gauge_boson">§ As a gauge boson</a>, below.) <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bohr_atom_model.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Bohr_atom_model.svg/220px-Bohr_atom_model.svg.png" decoding="async" width="220" height="192" class="mw-file-element" data-file-width="310" data-file-height="270"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 192px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Bohr_atom_model.svg/220px-Bohr_atom_model.svg.png" data-width="220" data-height="192" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Bohr_atom_model.svg/330px-Bohr_atom_model.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Bohr_atom_model.svg/440px-Bohr_atom_model.svg.png 2x" data-class="mw-file-element"> </a><figcaption>Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behaviour by quantizing only matter, as in the <a href="/wiki/Bohr_model" title="Bohr model">Bohr model</a> of the <a href="/wiki/Hydrogen_atom" title="Hydrogen atom">hydrogen atom</a> (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>.</figcaption></figure> Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in <a href="/wiki/Robert_Millikan" class="mw-redirect" title="Robert Millikan">Robert Millikan</a>'s Nobel lecture.<a href="#cite_note-Millikan1923-62">[58]</a> However, before Compton's experiment<a href="#cite_note-Compton1923-60">[56]</a> showed that photons carried momentum proportional to their <a href="/wiki/Wave_number" class="mw-redirect" title="Wave number">wave number</a> (1922),[<a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources">full citation needed</a>] most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of <a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wien</a>,<a href="#cite_note-Wien1911-54">[50]</a> Planck<a href="#cite_note-Planck1918-56">[52]</a> and Millikan.)<a href="#cite_note-Millikan1923-62">[58]</a> Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbed or emitted radiation. Attitudes changed over time. In part, the change can be traced to experiments such as those revealing <a href="/wiki/Compton_scattering" title="Compton scattering">Compton scattering</a>, where it was much more difficult not to ascribe quantization to light itself to explain the observed results.<a href="#cite_note-63">[59]</a> Even after Compton's experiment, <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>, <a href="/wiki/Hendrik_Anthony_Kramers" class="mw-redirect" title="Hendrik Anthony Kramers">Hendrik Kramers</a> and <a href="/wiki/John_C._Slater" title="John C. Slater">John Slater</a> made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called <a href="/wiki/BKS_theory" title="BKS theory">BKS theory</a>.<a href="#cite_note-Bohr1924-64">[60]</a> An important feature of the BKS theory is how it treated the <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a> and the <a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">conservation of momentum</a>. In the BKS theory, energy and momentum are only conserved on the average across many interactions between matter and radiation. However, refined Compton experiments showed that the conservation laws hold for individual interactions.<a href="#cite_note-65">[61]</a> Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible".<a href="#cite_note-Pais1982-61">[57]</a> Nevertheless, the failures of the BKS model inspired <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Werner Heisenberg</a> in his development of <a href="/wiki/Matrix_mechanics" title="Matrix mechanics">matrix mechanics</a>.<a href="#cite_note-Heisenberg1932-66">[62]</a> A few physicists persisted<a href="#cite_note-Mandel1976-67">[63]</a> in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>. Although the evidence from chemical and physical experiments for the existence of photons was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, and a sufficiently complete theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photon-correlation experiments.<a href="#cite_note-70">[e]</a> Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><h2 id="Wave–particle_duality_and_uncertainty_principles">Wave–particle duality and uncertainty principles</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=8" title="Edit section: Wave–particle duality and uncertainty principles" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> Photons obey the laws of quantum mechanics, and so their behavior has both wave-like and particle-like aspects. When a photon is detected by a measuring instrument, it is registered as a single, particulate unit. However, the probability of detecting a photon is calculated by equations that describe waves. This combination of aspects is known as <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">wave–particle duality</a>. For example, the <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> for the location at which a photon might be detected displays clearly wave-like phenomena such as <a href="/wiki/Diffraction" title="Diffraction">diffraction</a> and <a href="/wiki/Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">interference</a>. A single photon passing through a <a href="/wiki/Double-slit_experiment" title="Double-slit experiment">double slit</a> has its energy received at a point on the screen with a probability distribution given by its interference pattern determined by <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's wave equations</a>.<a href="#cite_note-Taylor1909-71">[66]</a> However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; a photon's Maxwell waves will diffract, but photon energy does not spread out as it propagates, nor does this energy divide when it encounters a <a href="/wiki/Beam_splitter" title="Beam splitter">beam splitter</a>.<a href="#cite_note-Saleh-72">[67]</a> Rather, the received photon acts like a <a href="/wiki/Point-like_particle" class="mw-redirect" title="Point-like particle">point-like particle</a> since it is absorbed or emitted as a whole by arbitrarily small systems, including systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like <a href="/wiki/Electron" title="Electron">electron</a>. While many introductory texts treat photons using the mathematical techniques of non-relativistic quantum mechanics, this is in some ways an awkward oversimplification, as photons are by nature intrinsically relativistic. Because photons have zero <a href="/wiki/Rest_mass" class="mw-redirect" title="Rest mass">rest mass</a>, no <a href="/wiki/Wave_function" title="Wave function">wave function</a> defined for a photon can have all the properties familiar from wave functions in non-relativistic quantum mechanics.<a href="#cite_note-77">[f]</a> In order to avoid these difficulties, physicists employ the second-quantized theory of photons described below, <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a>, in which photons are quantized excitations of electromagnetic modes.<a href="#cite_note-scully1997-78">[72]</a> Another difficulty is finding the proper analogue for the <a href="/wiki/Uncertainty_principle" title="Uncertainty principle">uncertainty principle</a>, an idea frequently attributed to Heisenberg, who introduced the concept in analyzing a <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a> involving <a href="/wiki/Heisenberg%27s_microscope" title="Heisenberg's microscope">an electron and a high-energy photon</a>. However, Heisenberg did not give precise mathematical definitions of what the "uncertainty" in these measurements meant. The precise mathematical statement of the position–momentum uncertainty principle is due to <a href="/wiki/Earle_Hesse_Kennard" title="Earle Hesse Kennard">Kennard</a>, <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli</a>, and <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a>.<a href="#cite_note-79">[73]</a><a href="#cite_note-80">[74]</a> The uncertainty principle applies to situations where an experimenter has a choice of measuring either one of two "canonically conjugate" quantities, like the position and the momentum of a particle. According to the uncertainty principle, no matter how the particle is prepared, it is not possible to make a precise prediction for both of the two alternative measurements: if the outcome of the position measurement is made more certain, the outcome of the momentum measurement becomes less so, and vice versa.<a href="#cite_note-L&L-81">[75]</a> A <a href="/wiki/Coherent_state" title="Coherent state">coherent state</a> minimizes the overall uncertainty as far as quantum mechanics allows.<a href="#cite_note-scully1997-78">[72]</a> <a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a> makes use of coherent states for modes of the electromagnetic field. There is a tradeoff, reminiscent of the position–momentum uncertainty relation, between measurements of an electromagnetic wave's amplitude and its phase.<a href="#cite_note-scully1997-78">[72]</a> This is sometimes informally expressed in terms of the uncertainty in the number of photons present in the electromagnetic wave, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta N}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2fca110bac4b3427ef640cdf356ae92a7432214" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.999ex; height:2.176ex;" alt="{\displaystyle \Delta N}"></noscript><span class="lazy-image-placeholder" style="width: 3.999ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2fca110bac4b3427ef640cdf356ae92a7432214" data-alt="{\displaystyle \Delta N}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , and the uncertainty in the phase of the wave, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \phi }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/125968846e9883e0b0ddef5f1d70f53023ec74b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.321ex; height:2.509ex;" alt="{\displaystyle \Delta \phi }"></noscript><span class="lazy-image-placeholder" style="width: 3.321ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/125968846e9883e0b0ddef5f1d70f53023ec74b0" data-alt="{\displaystyle \Delta \phi }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . However, this cannot be an uncertainty relation of the Kennard–Pauli–Weyl type, since unlike position and momentum, the phase <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></noscript><span class="lazy-image-placeholder" style="width: 1.385ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" data-alt="{\displaystyle \phi }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  cannot be represented by a <a href="/wiki/Hermitian_operator" class="mw-redirect" title="Hermitian operator">Hermitian operator</a>.<a href="#cite_note-82">[76]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><h2 id="Bose–Einstein_model_of_a_photon_gas">Bose–Einstein model of a photon gas</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=9" title="Edit section: Bose–Einstein model of a photon gas" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Bose_gas" title="Bose gas">Bose gas</a>, <a href="/wiki/Bose%E2%80%93Einstein_statistics" title="Bose–Einstein statistics">Bose–Einstein statistics</a>, <a href="/wiki/Spin-statistics_theorem" class="mw-redirect" title="Spin-statistics theorem">Spin-statistics theorem</a>, <a href="/wiki/Gas_in_a_box" title="Gas in a box">Gas in a box</a>, and <a href="/wiki/Photon_gas" title="Photon gas">Photon gas</a></div> In 1924, <a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Satyendra Nath Bose</a> derived <a href="/wiki/Planck%27s_law_of_black-body_radiation" class="mw-redirect" title="Planck's law of black-body radiation">Planck's law of black-body radiation</a> without using any electromagnetism, but rather by using a modification of coarse-grained counting of <a href="/wiki/Phase_space" title="Phase space">phase space</a>.<a href="#cite_note-Bose1924-83">[77]</a> Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction",<a href="#cite_note-Einstein1924-84">[78]</a><a href="#cite_note-Einstein1925-85">[79]</a> now understood as the requirement for a <a href="/wiki/Identical_particles" class="mw-redirect" title="Identical particles">symmetric quantum mechanical state</a>. This work led to the concept of <a href="/wiki/Coherent_state" title="Coherent state">coherent states</a> and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (bosons) and predicted that they would condense into their lowest <a href="/wiki/Quantum_state" title="Quantum state">quantum state</a> at low enough temperatures; this <a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensation</a> was observed experimentally in 1995.<a href="#cite_note-86">[80]</a> It was later used by <a href="/wiki/Lene_Hau" title="Lene Hau">Lene Hau</a> to slow, and then completely stop, light in 1999<a href="#cite_note-87">[81]</a> and 2001.<a href="#cite_note-88">[82]</a> The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to <a href="/wiki/Fermion" title="Fermion">fermions</a> with half-integer spin). By the <a href="/wiki/Spin-statistics_theorem" class="mw-redirect" title="Spin-statistics theorem">spin-statistics theorem</a>, all bosons obey Bose–Einstein statistics (whereas all fermions obey <a href="/wiki/Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics">Fermi–Dirac statistics</a>).<a href="#cite_note-89">[83]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"><h2 id="Stimulated_and_spontaneous_emission">Stimulated and spontaneous emission</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=10" title="Edit section: Stimulated and spontaneous emission" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-6 collapsible-block" id="mf-section-6"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Stimulated_emission" title="Stimulated emission">Stimulated emission</a> and <a href="/wiki/Laser" title="Laser">Laser</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Stimulatedemission.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Stimulatedemission.png/390px-Stimulatedemission.png" decoding="async" width="390" height="171" class="mw-file-element" data-file-width="640" data-file-height="281"></noscript><span class="lazy-image-placeholder" style="width: 390px;height: 171px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Stimulatedemission.png/390px-Stimulatedemission.png" data-width="390" data-height="171" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Stimulatedemission.png/585px-Stimulatedemission.png 1.5x, //upload.wikimedia.org/wikipedia/commons/8/8a/Stimulatedemission.png 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Stimulated_emission" title="Stimulated emission">Stimulated emission</a> (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the <a href="/wiki/Laser" title="Laser">laser</a>. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.</figcaption></figure> In 1916, Albert Einstein showed that Planck's radiation law could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a link between the rates at which atoms emit and absorb photons. The condition follows from the assumption that functions of the emission and absorption of radiation by the atoms are independent of each other, and that thermal equilibrium is made by way of the radiation's interaction with the atoms. Consider a cavity in <a href="/wiki/Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a> with all parts of itself and filled with <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> and that the atoms can emit and absorb that radiation. Thermal equilibrium requires that the energy density <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho (\nu )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho (\nu )}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/771818acdb33bf67ca39d6f197a871dae92752b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.243ex; height:2.843ex;" alt="{\displaystyle \rho (\nu )}"></noscript><span class="lazy-image-placeholder" style="width: 4.243ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/771818acdb33bf67ca39d6f197a871dae92752b3" data-alt="{\displaystyle \rho (\nu )}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  of photons with frequency <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></noscript><span class="lazy-image-placeholder" style="width: 1.232ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" data-alt="{\displaystyle \nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  (which is proportional to their <a href="/wiki/Number_density" title="Number density">number density</a>) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate at which they are absorbed.<a href="#cite_note-Einstein1916a-90">[84]</a> Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{ji}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ji}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07aa016887d6fd7c4d7f5041899cb34d8ba1154e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle R_{ji}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07aa016887d6fd7c4d7f5041899cb34d8ba1154e" data-alt="{\displaystyle R_{ji}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  for a system to absorb a photon of frequency <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></noscript><span class="lazy-image-placeholder" style="width: 1.232ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" data-alt="{\displaystyle \nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and transition from a lower energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{j}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.625ex; height:2.843ex;" alt="{\displaystyle E_{j}}"></noscript><span class="lazy-image-placeholder" style="width: 2.625ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" data-alt="{\displaystyle E_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  to a higher energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.515ex; height:2.509ex;" alt="{\displaystyle E_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.515ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c" data-alt="{\displaystyle E_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is proportional to the number <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{j}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e42efe207e17a74b4c17b1aa0cced7a84501bec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.776ex; height:2.843ex;" alt="{\displaystyle N_{j}}"></noscript><span class="lazy-image-placeholder" style="width: 2.776ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e42efe207e17a74b4c17b1aa0cced7a84501bec9" data-alt="{\displaystyle N_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  of atoms with energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{j}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.625ex; height:2.843ex;" alt="{\displaystyle E_{j}}"></noscript><span class="lazy-image-placeholder" style="width: 2.625ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" data-alt="{\displaystyle E_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and to the energy density <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho (\nu )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho (\nu )}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/771818acdb33bf67ca39d6f197a871dae92752b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.243ex; height:2.843ex;" alt="{\displaystyle \rho (\nu )}"></noscript><span class="lazy-image-placeholder" style="width: 4.243ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/771818acdb33bf67ca39d6f197a871dae92752b3" data-alt="{\displaystyle \rho (\nu )}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  of ambient photons of that frequency, <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{ji}=N_{j}B_{ji}\rho (\nu )\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi>ν</mi> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ji}=N_{j}B_{ji}\rho (\nu )\!}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c77cd3b1d4802a0110925a4cfe934b76a66a45b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.166ex; width:16.379ex; height:3.009ex;" alt="{\displaystyle R_{ji}=N_{j}B_{ji}\rho (\nu )\!}"></noscript><span class="lazy-image-placeholder" style="width: 16.379ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c77cd3b1d4802a0110925a4cfe934b76a66a45b" data-alt="{\displaystyle R_{ji}=N_{j}B_{ji}\rho (\nu )\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ji}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ji}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baf9e62f616a2934a55bccd69e744f38035d8b93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle B_{ji}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baf9e62f616a2934a55bccd69e744f38035d8b93" data-alt="{\displaystyle B_{ji}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the <a href="/wiki/Rate_constant" class="mw-redirect" title="Rate constant">rate constant</a> for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, or the emission of a photon initiated by the interaction of the atom with a passing photon and the return of the atom to the lower-energy state. Following Einstein's approach, the corresponding rate <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50382df1fd3bebf0baf22e2eab56a7a471d6621a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle R_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50382df1fd3bebf0baf22e2eab56a7a471d6621a" data-alt="{\displaystyle R_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  for the emission of photons of frequency <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></noscript><span class="lazy-image-placeholder" style="width: 1.232ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" data-alt="{\displaystyle \nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and transition from a higher energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.515ex; height:2.509ex;" alt="{\displaystyle E_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.515ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c" data-alt="{\displaystyle E_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  to a lower energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{j}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.625ex; height:2.843ex;" alt="{\displaystyle E_{j}}"></noscript><span class="lazy-image-placeholder" style="width: 2.625ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" data-alt="{\displaystyle E_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{ij}=N_{i}A_{ij}+N_{i}B_{ij}\rho (\nu )\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mi>ρ</mi> <mo stretchy="false">(</mo> <mi>ν</mi> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ij}=N_{i}A_{ij}+N_{i}B_{ij}\rho (\nu )\!}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3715c7cb37eb0865f07655b7b0318c8308279369" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.166ex; width:24.996ex; height:3.009ex;" alt="{\displaystyle R_{ij}=N_{i}A_{ij}+N_{i}B_{ij}\rho (\nu )\!}"></noscript><span class="lazy-image-placeholder" style="width: 24.996ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3715c7cb37eb0865f07655b7b0318c8308279369" data-alt="{\displaystyle R_{ij}=N_{i}A_{ij}+N_{i}B_{ij}\rho (\nu )\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.22ex; height:2.843ex;" alt="{\displaystyle A_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.22ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" data-alt="{\displaystyle A_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the rate constant for <a href="/wiki/Spontaneous_emission" title="Spontaneous emission">emitting a photon spontaneously</a>, and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle B_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" data-alt="{\displaystyle B_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the rate constant for emissions in response to ambient photons (<a href="/wiki/Stimulated_emission" title="Stimulated emission">induced or stimulated emission</a>). In thermodynamic equilibrium, the number of atoms in state <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and those in state <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></noscript><span class="lazy-image-placeholder" style="width: 0.985ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" data-alt="{\displaystyle j}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  must, on average, be constant; hence, the rates <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{ji}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ji}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07aa016887d6fd7c4d7f5041899cb34d8ba1154e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle R_{ji}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07aa016887d6fd7c4d7f5041899cb34d8ba1154e" data-alt="{\displaystyle R_{ji}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50382df1fd3bebf0baf22e2eab56a7a471d6621a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle R_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50382df1fd3bebf0baf22e2eab56a7a471d6621a" data-alt="{\displaystyle R_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  must be equal. Also, by arguments analogous to the derivation of <a href="/wiki/Boltzmann_statistics" class="mw-redirect" title="Boltzmann statistics">Boltzmann statistics</a>, the ratio of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fef58cebf23adff9199f17325aefb5515fdca99d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.666ex; height:2.509ex;" alt="{\displaystyle N_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.666ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fef58cebf23adff9199f17325aefb5515fdca99d" data-alt="{\displaystyle N_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{j}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e42efe207e17a74b4c17b1aa0cced7a84501bec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.776ex; height:2.843ex;" alt="{\displaystyle N_{j}}"></noscript><span class="lazy-image-placeholder" style="width: 2.776ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e42efe207e17a74b4c17b1aa0cced7a84501bec9" data-alt="{\displaystyle N_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mi>exp</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dffee654ba7c336692545142574aa3990632752b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:25.672ex; height:3.009ex;" alt="{\displaystyle g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},}"></noscript><span class="lazy-image-placeholder" style="width: 25.672ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dffee654ba7c336692545142574aa3990632752b" data-alt="{\displaystyle g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ce36142a0a1c6660e82bdf3ef3f1551317efe0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.909ex; height:2.009ex;" alt="{\displaystyle g_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 1.909ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ce36142a0a1c6660e82bdf3ef3f1551317efe0c" data-alt="{\displaystyle g_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{j}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc0c1f707e4786c1121db1ba0a608fe85a94e2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.019ex; height:2.343ex;" alt="{\displaystyle g_{j}}"></noscript><span class="lazy-image-placeholder" style="width: 2.019ex;height: 2.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc0c1f707e4786c1121db1ba0a608fe85a94e2d" data-alt="{\displaystyle g_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  are the <a href="/wiki/Degenerate_energy_level" class="mw-redirect" title="Degenerate energy level">degeneracy</a> of the state <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and that of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></noscript><span class="lazy-image-placeholder" style="width: 0.985ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" data-alt="{\displaystyle j}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , respectively, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.515ex; height:2.509ex;" alt="{\displaystyle E_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.515ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba9f6e3041b052cf13a0ede4ecf35fb4c9cd16c" data-alt="{\displaystyle E_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{j}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.625ex; height:2.843ex;" alt="{\displaystyle E_{j}}"></noscript><span class="lazy-image-placeholder" style="width: 2.625ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01babf2293d37d9ff73b61202cfc3a3933eaf19" data-alt="{\displaystyle E_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  their energies, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></noscript><span class="lazy-image-placeholder" style="width: 1.211ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" data-alt="{\displaystyle k}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  the <a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></noscript><span class="lazy-image-placeholder" style="width: 1.636ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" data-alt="{\displaystyle T}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  the system's <a href="/wiki/Temperature" title="Temperature">temperature</a>. From this, it is readily derived that <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{i}B_{ij}=g_{j}B_{ji}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{i}B_{ij}=g_{j}B_{ji}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b05f1a0bd93673e8867ac6c3728a2fd60108f6bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.508ex; height:2.843ex;" alt="{\displaystyle g_{i}B_{ij}=g_{j}B_{ji}}"></noscript><span class="lazy-image-placeholder" style="width: 13.508ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b05f1a0bd93673e8867ac6c3728a2fd60108f6bc" data-alt="{\displaystyle g_{i}B_{ij}=g_{j}B_{ji}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{ij}={\frac {8\pi h\nu ^{3}}{c^{3}}}B_{ij}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>h</mi> <msup> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{ij}={\frac {8\pi h\nu ^{3}}{c^{3}}}B_{ij}.}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9cc46d6112932e77fcb8f37f57214992420d544" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.188ex; height:6.009ex;" alt="{\displaystyle A_{ij}={\frac {8\pi h\nu ^{3}}{c^{3}}}B_{ij}.}"></noscript><span class="lazy-image-placeholder" style="width: 17.188ex;height: 6.009ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9cc46d6112932e77fcb8f37f57214992420d544" data-alt="{\displaystyle A_{ij}={\frac {8\pi h\nu ^{3}}{c^{3}}}B_{ij}.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> The <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.22ex; height:2.843ex;" alt="{\displaystyle A_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.22ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" data-alt="{\displaystyle A_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle B_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" data-alt="{\displaystyle B_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  are collectively known as the Einstein coefficients.<a href="#cite_note-91">[85]</a> Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.22ex; height:2.843ex;" alt="{\displaystyle A_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.22ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" data-alt="{\displaystyle A_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ji}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ji}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baf9e62f616a2934a55bccd69e744f38035d8b93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle B_{ji}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baf9e62f616a2934a55bccd69e744f38035d8b93" data-alt="{\displaystyle B_{ji}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle B_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" data-alt="{\displaystyle B_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".<a href="#cite_note-92">[86]</a> Not long thereafter, in 1926, <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> derived the <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle B_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" data-alt="{\displaystyle B_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  rate constants by using a semiclassical approach,<a href="#cite_note-Dirac1926-93">[87]</a> and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory.<a href="#cite_note-Dirac1927a-94">[88]</a><a href="#cite_note-Dirac1927b-95">[89]</a> Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>;<a href="#cite_note-Heisenberg1929-96">[90]</a><a href="#cite_note-Heisenberg1930-97">[91]</a><a href="#cite_note-Fermi1932-98">[92]</a> earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field. Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> in his treatment of <a href="/wiki/Birefringence" title="Birefringence">birefringence</a> and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which of the two paths a single photon would take.<a href="#cite_note-Newton1730-47">[44]</a> Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation<a href="#cite_note-Pais1982-61">[57]</a> from quantum mechanics. Ironically, <a href="/wiki/Max_Born" title="Max Born">Max Born</a>'s <a href="/wiki/Probability_amplitude" title="Probability amplitude">probabilistic interpretation</a> of the <a href="/wiki/Wave_function" title="Wave function">wave function</a><a href="#cite_note-Born1926a-99">[93]</a><a href="#cite_note-Born1926b-100">[94]</a> was inspired by Einstein's later work searching for a more complete theory.<a href="#cite_note-ghost_field-101">[95]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"><h2 id="Quantum_field_theory">Quantum field theory</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=11" title="Edit section: Quantum field theory" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-7 collapsible-block" id="mf-section-7"> <div class="mw-heading mw-heading3"><h3 id="Quantization_of_the_electromagnetic_field">Quantization of the electromagnetic field</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=12" title="Edit section: Quantization of the electromagnetic field" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </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/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:VisibleEmrWavelengths.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/VisibleEmrWavelengths.svg/260px-VisibleEmrWavelengths.svg.png" decoding="async" width="260" height="238" class="mw-file-element" data-file-width="480" data-file-height="440"></noscript><span class="lazy-image-placeholder" style="width: 260px;height: 238px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/VisibleEmrWavelengths.svg/260px-VisibleEmrWavelengths.svg.png" data-width="260" data-height="238" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/VisibleEmrWavelengths.svg/390px-VisibleEmrWavelengths.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/VisibleEmrWavelengths.svg/520px-VisibleEmrWavelengths.svg.png 2x" data-class="mw-file-element"> </a><figcaption>Different electromagnetic modes (such as those depicted here) can be treated as independent <a href="/wiki/Quantum_harmonic_oscillator" title="Quantum harmonic oscillator">simple harmonic oscillators</a>. A photon corresponds to a unit of energy E = hν in its electromagnetic mode.</figcaption></figure> In 1910, <a href="/wiki/Peter_Debye" title="Peter Debye">Peter Debye</a> derived <a href="/wiki/Planck%27s_law_of_black-body_radiation" class="mw-redirect" title="Planck's law of black-body radiation">Planck's law of black-body radiation</a> from a relatively simple assumption.<a href="#cite_note-Debye1910-102">[96]</a> He decomposed the electromagnetic field in a cavity into its <a href="/wiki/Fourier_series" title="Fourier series">Fourier modes</a>, and assumed that the energy in any mode was an integer multiple of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc23768f43b26085f80e1882a94b31d24abd653" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.571ex; height:2.176ex;" alt="{\displaystyle h\nu }"></noscript><span class="lazy-image-placeholder" style="width: 2.571ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc23768f43b26085f80e1882a94b31d24abd653" data-alt="{\displaystyle h\nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></noscript><span class="lazy-image-placeholder" style="width: 1.232ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" data-alt="{\displaystyle \nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the frequency of the electromagnetic mode. Planck's law of black-body radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of black-body radiation, which were derived by Einstein in 1909.<a href="#cite_note-Einstein1909-57">[53]</a> In 1925, <a href="/wiki/Max_Born" title="Max Born">Born</a>, <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg</a> and <a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Jordan</a> reinterpreted Debye's concept in a key way.<a href="#cite_note-Born1925-103">[97]</a> As may be shown classically, the <a href="/wiki/Fourier_series" title="Fourier series">Fourier modes</a> of the <a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">electromagnetic field</a>—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled <a href="/wiki/Simple_harmonic_oscillator" class="mw-redirect" title="Simple harmonic oscillator">simple harmonic oscillators</a>. Treated quantum mechanically, the energy levels of such oscillators are known to be <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=nh\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>n</mi> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=nh\nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5a53b66a9439e07293b61135c915a7b19c33096" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.84ex; height:2.176ex;" alt="{\displaystyle E=nh\nu }"></noscript><span class="lazy-image-placeholder" style="width: 8.84ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5a53b66a9439e07293b61135c915a7b19c33096" data-alt="{\displaystyle E=nh\nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></noscript><span class="lazy-image-placeholder" style="width: 1.232ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" data-alt="{\displaystyle \nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=nh\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>n</mi> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=nh\nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5a53b66a9439e07293b61135c915a7b19c33096" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.84ex; height:2.176ex;" alt="{\displaystyle E=nh\nu }"></noscript><span class="lazy-image-placeholder" style="width: 8.84ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5a53b66a9439e07293b61135c915a7b19c33096" data-alt="{\displaystyle E=nh\nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  as a state with <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></noscript><span class="lazy-image-placeholder" style="width: 1.395ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" data-alt="{\displaystyle n}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  photons, each of energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc23768f43b26085f80e1882a94b31d24abd653" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.571ex; height:2.176ex;" alt="{\displaystyle h\nu }"></noscript><span class="lazy-image-placeholder" style="width: 2.571ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc23768f43b26085f80e1882a94b31d24abd653" data-alt="{\displaystyle h\nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . This approach gives the correct energy fluctuation formula. <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Electron-scattering.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Electron-scattering.svg/220px-Electron-scattering.svg.png" decoding="async" width="220" height="190" class="mw-file-element" data-file-width="976" data-file-height="841"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 190px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Electron-scattering.svg/220px-Electron-scattering.svg.png" data-width="220" data-height="190" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Electron-scattering.svg/330px-Electron-scattering.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Electron-scattering.svg/440px-Electron-scattering.svg.png 2x" data-class="mw-file-element"> </a><figcaption><a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagram</a> of two electrons interacting by exchange of a virtual photon.</figcaption></figure> <a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a> took this one step further.<a href="#cite_note-Dirac1927a-94">[88]</a><a href="#cite_note-Dirac1927b-95">[89]</a> He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.22ex; height:2.843ex;" alt="{\displaystyle A_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.22ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8272b28f5aae6dbb8d6f829d58bab353b21bde20" data-alt="{\displaystyle A_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{ij}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.241ex; height:2.843ex;" alt="{\displaystyle B_{ij}}"></noscript><span class="lazy-image-placeholder" style="width: 3.241ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57c134504644caba8b83f479c9f27dbfa990b79a" data-alt="{\displaystyle B_{ij}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  coefficients from first principles, and showed that the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived <a href="/wiki/Planck%27s_law_of_black-body_radiation" class="mw-redirect" title="Planck's law of black-body radiation">Planck's law of black-body radiation</a> by assuming B–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics. Dirac's second-order <a href="/wiki/Perturbation_theory_(quantum_mechanics)" title="Perturbation theory (quantum mechanics)">perturbation theory</a> can involve <a href="/wiki/Virtual_particle" title="Virtual particle">virtual photons</a>, transient intermediate states of the electromagnetic field; the static <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">electric</a> and <a href="/wiki/Magnetism" title="Magnetism">magnetic</a> interactions are mediated by such virtual photons. In such <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theories</a>, the <a href="/wiki/Probability_amplitude" title="Probability amplitude">probability amplitude</a> of observable events is calculated by summing over all possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=pc}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>p</mi> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=pc}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5498982f39427c7573448da10de26a7b3209e47a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.05ex; height:2.509ex;" alt="{\displaystyle E=pc}"></noscript><span class="lazy-image-placeholder" style="width: 7.05ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5498982f39427c7573448da10de26a7b3209e47a" data-alt="{\displaystyle E=pc}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , and may have extra <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a> states; depending on the <a href="/wiki/Gauge_fixing" title="Gauge fixing">gauge</a> used, virtual photons may have three or four polarization states, instead of the two states of real photons. Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events.<a href="#cite_note-104">[98]</a> Indeed, such second-order and higher-order perturbation calculations can give apparently <a href="/wiki/Infinity" title="Infinity">infinite</a> contributions to the sum. Such unphysical results are corrected for using the technique of <a href="/wiki/Renormalization" title="Renormalization">renormalization</a>.<a href="#cite_note-105">[99]</a> Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual <a href="/wiki/Electron" title="Electron">electron</a>–<a href="/wiki/Positron" title="Positron">positron</a> <a href="/wiki/Pair_production" title="Pair production">pairs</a>.<a href="#cite_note-106">[100]</a> Such photon–photon scattering (see <a href="/wiki/Two-photon_physics" title="Two-photon physics">two-photon physics</a>), as well as electron–photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, the <a href="/wiki/International_Linear_Collider" title="International Linear Collider">International Linear Collider</a>.<a href="#cite_note-107">[101]</a> In <a href="/wiki/Modern_physics" title="Modern physics">modern physics</a> notation, the <a href="/wiki/Quantum_state" title="Quantum state">quantum state</a> of the electromagnetic field is written as a <a href="/wiki/Fock_state" title="Fock state">Fock state</a>, a <a href="/wiki/Tensor_product" title="Tensor product">tensor product</a> of the states for each electromagnetic mode <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |n_{k_{0}}\rangle \otimes |n_{k_{1}}\rangle \otimes \dots \otimes |n_{k_{n}}\rangle \dots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo>⊗</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo>⊗</mo> <mo>⋯</mo> <mo>⊗</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |n_{k_{0}}\rangle \otimes |n_{k_{1}}\rangle \otimes \dots \otimes |n_{k_{n}}\rangle \dots }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf1d8ffa71f6f78681ad32f6ff5870627b1cd79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.088ex; height:3.009ex;" alt="{\displaystyle |n_{k_{0}}\rangle \otimes |n_{k_{1}}\rangle \otimes \dots \otimes |n_{k_{n}}\rangle \dots }"></noscript><span class="lazy-image-placeholder" style="width: 29.088ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf1d8ffa71f6f78681ad32f6ff5870627b1cd79" data-alt="{\displaystyle |n_{k_{0}}\rangle \otimes |n_{k_{1}}\rangle \otimes \dots \otimes |n_{k_{n}}\rangle \dots }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |n_{k_{i}}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |n_{k_{i}}\rangle }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/261582c861f317f3e8cd9e33c36c8d10e0d62a49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.66ex; height:3.009ex;" alt="{\displaystyle |n_{k_{i}}\rangle }"></noscript><span class="lazy-image-placeholder" style="width: 4.66ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/261582c861f317f3e8cd9e33c36c8d10e0d62a49" data-alt="{\displaystyle |n_{k_{i}}\rangle }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  represents the state in which <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,n_{k_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,n_{k_{i}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6945fb83c5b12e2c726c9a26195feb2207b0d1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.495ex; height:2.343ex;" alt="{\displaystyle \,n_{k_{i}}}"></noscript><span class="lazy-image-placeholder" style="width: 3.495ex;height: 2.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6945fb83c5b12e2c726c9a26195feb2207b0d1d" data-alt="{\displaystyle \,n_{k_{i}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  photons are in the mode <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f29138ed3ad54ffce527daccadc49c520459b0b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.011ex; height:2.509ex;" alt="{\displaystyle k_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.011ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f29138ed3ad54ffce527daccadc49c520459b0b0" data-alt="{\displaystyle k_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . In this notation, the creation of a new photon in mode <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f29138ed3ad54ffce527daccadc49c520459b0b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.011ex; height:2.509ex;" alt="{\displaystyle k_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.011ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f29138ed3ad54ffce527daccadc49c520459b0b0" data-alt="{\displaystyle k_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  (e.g., emitted from an atomic transition) is written as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |n_{k_{i}}\rangle \rightarrow |n_{k_{i}}+1\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo fence="false" stretchy="false">⟩</mo> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |n_{k_{i}}\rangle \rightarrow |n_{k_{i}}+1\rangle }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98ad7c2b75079bb41e6e1719263ff9fc799e8161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.937ex; height:3.009ex;" alt="{\displaystyle |n_{k_{i}}\rangle \rightarrow |n_{k_{i}}+1\rangle }"></noscript><span class="lazy-image-placeholder" style="width: 16.937ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98ad7c2b75079bb41e6e1719263ff9fc799e8161" data-alt="{\displaystyle |n_{k_{i}}\rangle \rightarrow |n_{k_{i}}+1\rangle }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics. <div class="mw-heading mw-heading3"><h3 id="As_a_gauge_boson">As a gauge boson</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=13" title="Edit section: As a gauge boson" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </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/Gauge_theory" title="Gauge theory">Gauge theory</a></div> The electromagnetic field can be understood as a <a href="/wiki/Gauge_field" class="mw-redirect" title="Gauge field">gauge field</a>, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>.<a href="#cite_note-Ryder-108">[102]</a> For the <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a>, this gauge symmetry is the <a href="/wiki/Abelian_group" title="Abelian group">Abelian</a> <a href="/wiki/Unitary_group" title="Unitary group">U(1) symmetry</a> of <a href="/wiki/Complex_number" title="Complex number">complex numbers</a> of absolute value 1, which reflects the ability to vary the <a href="/wiki/Complex_geometry" title="Complex geometry">phase</a> of a complex field without affecting <a href="/wiki/Observable" title="Observable">observables</a> or <a href="/wiki/Real_number" title="Real number">real valued functions</a> made from it, such as the <a href="/wiki/Energy" title="Energy">energy</a> or the <a href="/wiki/Lagrangian_(field_theory)" title="Lagrangian (field theory)">Lagrangian</a>. The quanta of an <a href="/wiki/Gauge_theory" title="Gauge theory">Abelian gauge field</a> must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> and integer spin. The particular form of the <a href="/wiki/Electromagnetic_interaction" class="mw-redirect" title="Electromagnetic interaction">electromagnetic interaction</a> specifies that the photon must have <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> ±1; thus, its <a href="/wiki/Helicity_(particle_physics)" title="Helicity (particle physics)">helicity</a> must be <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pm \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>±</mo> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pm \hbar }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c578ae2b02e515c92a2981d6db0ffb5943e3357" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.115ex; height:2.176ex;" alt="{\displaystyle \pm \hbar }"></noscript><span class="lazy-image-placeholder" style="width: 3.115ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c578ae2b02e515c92a2981d6db0ffb5943e3357" data-alt="{\displaystyle \pm \hbar }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . These two spin components correspond to the classical concepts of <a href="/wiki/Circular_polarization" title="Circular polarization">right-handed and left-handed circularly polarized</a> light. However, the transient <a href="/wiki/Virtual_photon" title="Virtual photon">virtual photons</a> of <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> may also adopt unphysical polarization states.<a href="#cite_note-Ryder-108">[102]</a> In the prevailing <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a> of physics, the photon is one of four gauge bosons in the <a href="/wiki/Electroweak_interaction" title="Electroweak interaction">electroweak interaction</a>; the <a href="/wiki/W_and_Z_bosons" title="W and Z bosons">other three</a> are denoted W+, W− and Z0 and are responsible for the <a href="/wiki/Weak_interaction" title="Weak interaction">weak interaction</a>. Unlike the photon, these gauge bosons have <a href="/wiki/Invariant_mass" title="Invariant mass">mass</a>, owing to a <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">mechanism</a> that breaks their <a href="/wiki/Special_unitary_group" title="Special unitary group">SU(2) gauge symmetry</a>. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by <a href="/wiki/Sheldon_Glashow" title="Sheldon Glashow">Sheldon Glashow</a>, <a href="/wiki/Abdus_Salam" title="Abdus Salam">Abdus Salam</a> and <a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Steven Weinberg</a>, for which they were awarded the 1979 <a href="/wiki/Nobel_Prize" title="Nobel Prize">Nobel Prize</a> in physics.<a href="#cite_note-Glashow-109">[103]</a><a href="#cite_note-Salam-110">[104]</a><a href="#cite_note-Weinberg-111">[105]</a> Physicists continue to hypothesize <a href="/wiki/Grand_unification_theory" class="mw-redirect" title="Grand unification theory">grand unified theories</a> that connect these four gauge bosons with the eight <a href="/wiki/Gluon" title="Gluon">gluon</a> gauge bosons of <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">quantum chromodynamics</a>; however, key predictions of these theories, such as <a href="/wiki/Proton_decay" title="Proton decay">proton decay</a>, have not been observed experimentally.<a href="#cite_note-112">[106]</a> <div class="mw-heading mw-heading3"><h3 id="Hadronic_properties">Hadronic properties</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=14" title="Edit section: Hadronic properties" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </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/Photon_structure_function" title="Photon structure function">Photon structure function</a></div> Measurements of the interaction between energetic photons and <a href="/wiki/Hadron" title="Hadron">hadrons</a> show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons<a href="#cite_note-113">[107]</a> in spite of the fact that the electrical charge structures of protons and neutrons are substantially different. A theory called <a href="/wiki/Vector_Meson_Dominance" class="mw-redirect" title="Vector Meson Dominance">Vector Meson Dominance</a> (VMD) was developed to explain this effect. According to VMD, the photon is a superposition of the pure electromagnetic photon, which interacts only with electric charges, and vector mesons, which mediate the residual <a href="/wiki/Nuclear_force" title="Nuclear force">nuclear force</a>.<a href="#cite_note-114">[108]</a> However, if experimentally probed at very short distances, the intrinsic structure of the photon appears to have as components a charge-neutral flux of quarks and gluons, quasi-free according to asymptotic freedom in <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">QCD</a>. That flux is described by the <a href="/wiki/Photon_Structure_Function" class="mw-redirect" title="Photon Structure Function">photon structure function</a>.<a href="#cite_note-115">[109]</a><a href="#cite_note-116">[110]</a> A review by <a href="#CITEREFNisius2000">Nisius (2000)</a> presented a comprehensive comparison of data with theoretical predictions.<a href="#cite_note-117">[111]</a> <div class="mw-heading mw-heading3"><h3 id="Contributions_to_the_mass_of_a_system">Contributions to the mass of a system</h3> <a role="button" href="/w/index.php?title=Photon&action=edit&section=15" title="Edit section: Contributions to the mass of a system" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Mass in special relativity</a> and <a href="/wiki/Mass_in_general_relativity" title="Mass in general relativity">Mass in general relativity</a></div> The energy of a system that emits a photon is decreased by the energy <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><noscript><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}"></noscript><span class="lazy-image-placeholder" style="width: 1.776ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" data-alt="{\displaystyle E}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}/{c^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}/{c^{2}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61f55812ff776dde9279b91f06e7993ddff94932" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.999ex; height:3.176ex;" alt="{\displaystyle {E}/{c^{2}}}"></noscript><span class="lazy-image-placeholder" style="width: 4.999ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61f55812ff776dde9279b91f06e7993ddff94932" data-alt="{\displaystyle {E}/{c^{2}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}/{c^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}/{c^{2}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61f55812ff776dde9279b91f06e7993ddff94932" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.999ex; height:3.176ex;" alt="{\displaystyle {E}/{c^{2}}}"></noscript><span class="lazy-image-placeholder" style="width: 4.999ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61f55812ff776dde9279b91f06e7993ddff94932" data-alt="{\displaystyle {E}/{c^{2}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).<a href="#cite_note-118">[112]</a> This concept is applied in key predictions of <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> (QED, see above). In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as <a href="/wiki/Renormalization" title="Renormalization">renormalization</a>. Such "<a href="/wiki/Radiative_correction" class="mw-redirect" title="Radiative correction">radiative corrections</a>" contribute to a number of predictions of QED, such as the <a href="/wiki/Anomalous_magnetic_dipole_moment" title="Anomalous magnetic dipole moment">magnetic dipole moment</a> of <a href="/wiki/Lepton" title="Lepton">leptons</a>, the <a href="/wiki/Lamb_shift" title="Lamb shift">Lamb shift</a>, and the <a href="/wiki/Hyperfine_structure" title="Hyperfine structure">hyperfine structure</a> of bound lepton pairs, such as <a href="/wiki/Muonium" title="Muonium">muonium</a> and <a href="/wiki/Positronium" title="Positronium">positronium</a>.<a href="#cite_note-119">[113]</a> Since photons contribute to the <a href="/wiki/Stress%E2%80%93energy_tensor" title="Stress–energy tensor">stress–energy tensor</a>, they exert a <a href="/wiki/Gravity" title="Gravity">gravitational attraction</a> on other objects, according to the theory of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>, as in <a href="/wiki/Gravitational_lens" title="Gravitational lens">gravitational lensing</a>, and <a href="/wiki/Gravitational_redshift" title="Gravitational redshift">their frequencies may be lowered</a> by moving to a higher <a href="/wiki/Potential_energy" title="Potential energy">gravitational potential</a>, as in the <a href="/wiki/Pound%E2%80%93Rebka_experiment" title="Pound–Rebka experiment">Pound–Rebka experiment</a>. However, these effects are not specific to photons; exactly the same effects would be predicted for classical <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic waves</a>.<a href="#cite_note-120">[114]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"><h2 id="In_matter">In matter</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=16" title="Edit section: In matter" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-8 collapsible-block" id="mf-section-8"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Refractive_index" title="Refractive index">Refractive index</a>, <a href="/wiki/Group_velocity" title="Group velocity">Group velocity</a>, and <a href="/wiki/Photochemistry" title="Photochemistry">Photochemistry</a></div> Light that travels through transparent matter does so at a lower speed than c, the speed of light in vacuum. The factor by which the speed is decreased is called the <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> of the material. In a classical wave picture, the slowing can be explained by the light inducing <a href="/wiki/Electric_polarization" class="mw-redirect" title="Electric polarization">electric polarization</a> in the matter, the polarized matter radiating new light, and that new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitations of the matter to produce <a href="/wiki/Quasi-particle" class="mw-redirect" title="Quasi-particle">quasi-particles</a> known as <a href="/wiki/Polariton" title="Polariton">polaritons</a>. Polaritons have a nonzero <a href="/wiki/Effective_mass_(solid-state_physics)" title="Effective mass (solid-state physics)">effective mass</a>, which means that they cannot travel at c. Light of different frequencies may travel through matter at <a href="/wiki/Variable_speed_of_light" title="Variable speed of light">different speeds</a>; this is called <a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">dispersion</a> (not to be confused with scattering). In some cases, it can result in <a href="/wiki/Slow_light" title="Slow light">extremely slow speeds of light</a> in matter. The effects of photon interactions with other quasi-particles may be observed directly in <a href="/wiki/Raman_scattering" title="Raman scattering">Raman scattering</a> and <a href="/wiki/Brillouin_scattering" title="Brillouin scattering">Brillouin scattering</a>.<a href="#cite_note-121">[115]</a> Photons can be scattered by matter. For example, photons engage in so many collisions on the way from the <a href="/wiki/Solar_core" title="Solar core">core of the Sun</a> that <a href="/wiki/Radiant_energy" title="Radiant energy">radiant energy</a> can take about a million years to reach the surface;<a href="#cite_note-122">[116]</a> however, once in open space, a photon takes only 8.3 minutes to reach Earth.<a href="#cite_note-123">[117]</a> Photons can also be <a href="/wiki/Absorption_(electromagnetic_radiation)" title="Absorption (electromagnetic radiation)">absorbed</a> by nuclei, atoms or molecules, provoking transitions between their <a href="/wiki/Energy_level" title="Energy level">energy levels</a>. A classic example is the molecular transition of <a href="/wiki/Retinal" title="Retinal">retinal</a> (C20H28O), which is responsible for <a href="/wiki/Visual_perception" title="Visual perception">vision</a>, as discovered in 1958 by Nobel laureate <a href="/wiki/Biochemist" title="Biochemist">biochemist</a> <a href="/wiki/George_Wald" title="George Wald">George Wald</a> and co-workers. The absorption provokes a <a href="/wiki/Cis%E2%80%93trans" class="mw-redirect" title="Cis–trans">cis–trans</a> <a href="/wiki/Isomerization" title="Isomerization">isomerization</a> that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the <a href="/wiki/Photodissociation" title="Photodissociation">photodissociation</a> of <a href="/wiki/Chlorine" title="Chlorine">chlorine</a>; this is the subject of <a href="/wiki/Photochemistry" title="Photochemistry">photochemistry</a>.<a href="#cite_note-124">[118]</a><a href="#cite_note-125">[119]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(9)"><h2 id="Technological_applications">Technological applications</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=17" title="Edit section: Technological applications" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-9 collapsible-block" id="mf-section-9"> Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an important application and is discussed above under <a href="/wiki/Stimulated_emission" title="Stimulated emission">stimulated emission</a>. Individual photons can be detected by several methods. The classic <a href="/wiki/Photomultiplier" title="Photomultiplier">photomultiplier</a> tube exploits the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>: a photon of sufficient energy strikes a metal plate and knocks free an electron, initiating an ever-amplifying avalanche of electrons. <a href="/wiki/Semiconductor" title="Semiconductor">Semiconductor</a> <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">charge-coupled device</a> chips use a similar effect: an incident photon generates a charge on a microscopic <a href="/wiki/Capacitor" title="Capacitor">capacitor</a> that can be detected. Other detectors such as <a href="/wiki/Geiger_counter" title="Geiger counter">Geiger counters</a> use the ability of photons to <a href="/wiki/Ionize" class="mw-redirect" title="Ionize">ionize</a> gas molecules contained in the device, causing a detectable change of <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">conductivity</a> of the gas.<a href="#cite_note-126">[120]</a> Planck's energy formula <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=h\nu }</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c0386dc6d9530519404f95570fcc8548ed2326" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.445ex; height:2.176ex;" alt="{\displaystyle E=h\nu }"></noscript><span class="lazy-image-placeholder" style="width: 7.445ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c0386dc6d9530519404f95570fcc8548ed2326" data-alt="{\displaystyle E=h\nu }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to determine the frequency of the light emitted from a given photon emission. For example, the <a href="/wiki/Emission_spectrum" title="Emission spectrum">emission spectrum</a> of a <a href="/wiki/Gas-discharge_lamp" title="Gas-discharge lamp">gas-discharge lamp</a> can be altered by filling it with (mixtures of) gases with different electronic <a href="/wiki/Energy_level" title="Energy level">energy level</a> configurations.<a href="#cite_note-127">[121]</a> Under some conditions, an energy transition can be excited by "two" photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the spectrum where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see <a href="/wiki/Two-photon_excitation_microscopy" title="Two-photon excitation microscopy">two-photon excitation microscopy</a>). Moreover, these photons cause less damage to the sample, since they are of lower energy.<a href="#cite_note-128">[122]</a> In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of <a href="/wiki/Fluorescence_resonance_energy_transfer" class="mw-redirect" title="Fluorescence resonance energy transfer">fluorescence resonance energy transfer</a>, a technique that is used in <a href="/wiki/Molecular_biology" title="Molecular biology">molecular biology</a> to study the interaction of suitable <a href="/wiki/Protein" title="Protein">proteins</a>.<a href="#cite_note-129">[123]</a> Several different kinds of <a href="/wiki/Hardware_random_number_generator" title="Hardware random number generator">hardware random number generators</a> involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a <a href="/wiki/Beam-splitter" class="mw-redirect" title="Beam-splitter">beam-splitter</a>. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is "0" or "1".<a href="#cite_note-130">[124]</a><a href="#cite_note-131">[125]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(10)"><h2 id="Quantum_optics_and_computation">Quantum optics and computation</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=18" title="Edit section: Quantum optics and computation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-10 collapsible-block" id="mf-section-10"> Much research has been devoted to applications of photons in the field of <a href="/wiki/Quantum_optics" title="Quantum optics">quantum optics</a>. Photons seem well-suited to be elements of an extremely fast <a href="/wiki/Quantum_computer" class="mw-redirect" title="Quantum computer">quantum computer</a>, and the <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">quantum entanglement</a> of photons is a focus of research. <a href="/wiki/Nonlinear_optics" title="Nonlinear optics">Nonlinear optical processes</a> are another active research area, with topics such as <a href="/wiki/Two-photon_absorption" title="Two-photon absorption">two-photon absorption</a>, <a href="/wiki/Self-phase_modulation" title="Self-phase modulation">self-phase modulation</a>, <a href="/wiki/Modulational_instability" title="Modulational instability">modulational instability</a> and <a href="/wiki/Optical_parametric_oscillator" title="Optical parametric oscillator">optical parametric oscillators</a>. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of <a href="/wiki/Spontaneous_parametric_down_conversion" class="mw-redirect" title="Spontaneous parametric down conversion">spontaneous parametric down conversion</a> is often used to produce single-photon states. Finally, photons are essential in some aspects of <a href="/wiki/Optical_communication" title="Optical communication">optical communication</a>, especially for <a href="/wiki/Quantum_cryptography" title="Quantum cryptography">quantum cryptography</a>.<a href="#cite_note-132">[126]</a> <a href="/wiki/Two-photon_physics" title="Two-photon physics">Two-photon physics</a> studies interactions between photons, which are rare. In 2018, Massachusetts Institute of Technology researchers announced the discovery of bound photon triplets, which may involve <a href="/wiki/Polariton" title="Polariton">polaritons</a>.<a href="#cite_note-NW-20180216-133">[127]</a><a href="#cite_note-SCI-20180216-134">[128]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(11)"><h2 id="See_also">See also</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=19" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-11 collapsible-block" id="mf-section-11"> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><noscript><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/25px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" data-file-width="530" data-file-height="600"></noscript><span class="lazy-image-placeholder" style="width: 25px;height: 28px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/25px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" data-alt="icon" data-width="25" data-height="28" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/37px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/49px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-class="mw-file-element"> </a><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></li></ul> <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: 15em;"> <ul><li><a href="/wiki/Advanced_Photon_Source" title="Advanced Photon Source">Advanced Photon Source</a> at Argonne National Laboratory</li> <li><a href="/wiki/Ballistic_photon" title="Ballistic photon">Ballistic photon</a></li> <li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac equation</a></li> <li><a href="/wiki/Doppler_effect" title="Doppler effect">Doppler effect</a></li> <li><a href="/wiki/EPR_paradox" class="mw-redirect" title="EPR paradox">EPR paradox</a></li> <li><a href="/wiki/High_energy_X-ray_imaging_technology" title="High energy X-ray imaging technology">High energy X-ray imaging technology</a></li> <li><a href="/wiki/Luminiferous_aether" title="Luminiferous aether">Luminiferous aether</a></li> <li><a href="/wiki/Medipix" title="Medipix">Medipix</a></li> <li><a href="/wiki/Phonon" title="Phonon">Phonon</a></li> <li><a href="/wiki/Photography" title="Photography">Photography</a></li> <li><a href="/wiki/Photon_counting" title="Photon counting">Photon counting</a></li> <li><a href="/wiki/Photon_epoch" title="Photon epoch">Photon epoch</a></li> <li><a href="/wiki/Photonic_molecule" title="Photonic molecule">Photonic molecule</a></li> <li><a href="/wiki/Photonics" title="Photonics">Photonics</a></li> <li><a href="/wiki/Single-photon_source" title="Single-photon source">Single-photon source</a></li> <li><a href="/wiki/Static_forces_and_virtual-particle_exchange" title="Static forces and virtual-particle exchange">Static forces and virtual-particle exchange</a></li> <li><a href="/wiki/Variable_speed_of_light" title="Variable speed of light">Variable speed of light</a></li></ul></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(12)"><h2 id="Notes">Notes</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=20" title="Edit section: Notes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-12 collapsible-block" id="mf-section-12"> <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 reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-11"><a href="#cite_ref-11">^</a> Although the 1967 <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html">Elsevier translation</a> of Planck's Nobel Lecture interprets Planck's Lichtquant as "photon", the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein <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="CITEREFPlanck1922" class="citation book cs1">Planck, Max (1922). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=4UC4AAAAIAAJ">"via Google Books"</a>. <a rel="nofollow" class="external text" href="https://archive.org/details/origindevelopmen00planrich">The Origin and Development of the Quantum Theory</a>. Clarendon Press – via Internet Archive (archive.org, 2007-03-01).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=via+Google+Books&rft.btitle=The+Origin+and+Development+of+the+Quantum+Theory&rft.pub=Clarendon+Press&rft.date=1922&rft.aulast=Planck&rft.aufirst=Max&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D4UC4AAAAIAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> uses "light-quantum". No evidence is known that Planck himself had used the term "photon" as of 1926 (<a rel="nofollow" class="external text" href="http://www.nobeliefs.com/photon.htm">see also</a>). </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <a href="/wiki/Isaac_Asimov" title="Isaac Asimov">Asimov</a><a href="#cite_note-Asimov-1971-1983-13">[12]</a> credits <a href="/wiki/Arthur_Compton" title="Arthur Compton">Arthur Compton</a> with defining quanta of energy as photons in 1923.<a href="#cite_note-Asimov-1971-1983-13">[12]</a> </li> <li id="cite_note-33"><a href="#cite_ref-33">^</a> However, it is possible if the system interacts with a third particle or field for the annihilation to produce one photon, since the third particle or field can absorb momentum equal and opposite to the single photon, providing dynamic balance. An example is when a positron annihilates with a bound atomic electron; in that case, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry. </li> <li id="cite_note-53"><a href="#cite_ref-53">^</a> The phrase "no matter how intense" refers to intensities below approximately 1013 W/cm2 at which point <a href="/wiki/Perturbation_theory" title="Perturbation theory">perturbation theory</a> begins to break down. In contrast, in the intense regime, which for visible light is above approximately 1014 W/cm2, the classical wave description correctly predicts the energy acquired by electrons, called <a href="/wiki/Ponderomotive_energy" title="Ponderomotive energy">ponderomotive energy</a>.<a href="#cite_note-52">[49]</a> By comparison, sunlight is only about 0.1 W/cm2. </li> <li id="cite_note-70"><a href="#cite_ref-70">^</a> These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the <a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">quantum measurement process</a>. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical <a href="/wiki/Cauchy%E2%80%93Schwarz_inequality" title="Cauchy–Schwarz inequality">Cauchy–Schwarz inequality</a>. In 1977, Kimble et al. demonstrated an analogous anti-bunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photon-anticorrelation experiment of Grangier, Roger, & Aspect (1986);<a href="#cite_note-68">[64]</a> This work is reviewed and simplified further in Thorn, Neel, et al. (2004).<a href="#cite_note-69">[65]</a> </li> <li id="cite_note-77"><a href="#cite_ref-77">^</a> The issue was first formulated by Theodore Duddell Newton and <a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Eugene Wigner</a>.<a href="#cite_note-73">[68]</a><a href="#cite_note-74">[69]</a><a href="#cite_note-75">[70]</a> The challenges arise from the fundamental nature of the <a href="/wiki/Lorentz_group" title="Lorentz group">Lorentz group</a>, which describes the symmetries of <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> in special relativity. Unlike the generators of <a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformations</a>, the generators of <a href="/wiki/Lorentz_boost" class="mw-redirect" title="Lorentz boost">Lorentz boosts</a> do not commute, and so simultaneously assigning low uncertainties to all coordinates of a relativistic particle's position becomes problematic.<a href="#cite_note-76">[71]</a> </li> </ol></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(13)"><h2 id="References">References</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=21" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-13 collapsible-block" id="mf-section-13"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 25em;"> <ol class="references"> <li id="cite_note-Particle_table_2009-1">^ <a href="#cite_ref-Particle_table_2009_1-0">a</a> <a href="#cite_ref-Particle_table_2009_1-1">b</a> <a href="#cite_ref-Particle_table_2009_1-2">c</a> <a href="#cite_ref-Particle_table_2009_1-3">d</a> <a href="#cite_ref-Particle_table_2009_1-4">e</a> <a href="#cite_ref-Particle_table_2009_1-5">f</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAmsler2008" class="citation journal cs1">Amsler, C.; et al. (<a href="/wiki/Particle_Data_Group" title="Particle Data Group">Particle Data Group</a>) (2008). <a rel="nofollow" class="external text" href="http://pdg.lbl.gov/2009/tables/rpp2009-sum-gauge-higgs-bosons.pdf">"Review of Particle Physics: Gauge and Higgs bosons"</a> (PDF). <a href="/wiki/Physics_Letters_B" class="mw-redirect" title="Physics Letters B">Physics Letters B</a>. 667 (1): 1. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008PhLB..667....1A">2008PhLB..667....1A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physletb.2008.07.018">10.1016/j.physletb.2008.07.018</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1854%2FLU-685594">1854/LU-685594</a>. <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:227119789">227119789</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20181225235527/http://pdg.lbl.gov/2009/tables/rpp2009-sum-gauge-higgs-bosons.pdf%0A">Archived</a> from the original on 2018-12-25. 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(1965) [12 Dec 1927]. <a rel="nofollow" class="external text" href="https://www.nobelprize.org/uploads/2018/06/compton-lecture.pdf">"X-rays as a branch of optics"</a> (PDF). From Nobel Lectures, Physics 1922–1941. Amsterdam: Elsevier Publishing Company. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240512231537/https://www.nobelprize.org/uploads/2018/06/compton-lecture.pdf">Archived</a> (PDF) from the original on 12 May 2024. 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(1977). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/6051/1/KIMprl77.pdf">"Photon Anti-bunching in Resonance Fluorescence"</a> (PDF). <a href="/wiki/Physical_Review_Letters" title="Physical Review Letters">Physical Review Letters</a>. 39 (11): 691–695. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1977PhRvL..39..691K">1977PhRvL..39..691K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.39.691">10.1103/PhysRevLett.39.691</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201125123348/https://authors.library.caltech.edu/6051/1/KIMprl77.pdf">Archived</a> (PDF) from the original on 2020-11-25. Retrieved 2019-01-03.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Photon+Anti-bunching+in+Resonance+Fluorescence&rft.volume=39&rft.issue=11&rft.pages=691-695&rft.date=1977&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.39.691&rft_id=info%3Abibcode%2F1977PhRvL..39..691K&rft.aulast=Kimble&rft.aufirst=H.J.&rft.au=Dagenais%2C+M.&rft.au=Mandel%2C+L.&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F6051%2F1%2FKIMprl77.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-8"><a href="#cite_ref-8">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrangierRogerAspect1986" class="citation journal cs1">Grangier, P.; Roger, G.; Aspect, A. (1986). "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences". <a href="/wiki/EPL_(journal)" title="EPL (journal)">Europhysics Letters</a>. 1 (4): 173–179. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1986EL......1..173G">1986EL......1..173G</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.4356">10.1.1.178.4356</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1209%2F0295-5075%2F1%2F4%2F004">10.1209/0295-5075/1/4/004</a>. <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:250837011">250837011</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Europhysics+Letters&rft.atitle=Experimental+Evidence+for+a+Photon+Anticorrelation+Effect+on+a+Beam+Splitter%3A+A+New+Light+on+Single-Photon+Interferences&rft.volume=1&rft.issue=4&rft.pages=173-179&rft.date=1986&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.178.4356%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250837011%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1209%2F0295-5075%2F1%2F4%2F004&rft_id=info%3Abibcode%2F1986EL......1..173G&rft.aulast=Grangier&rft.aufirst=P.&rft.au=Roger%2C+G.&rft.au=Aspect%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKragh2000" class="citation journal cs1"><a href="/wiki/Helge_Kragh" title="Helge Kragh">Kragh, Helge</a> (2000-12-01). 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Retrieved 2010-08-25. <q>According to this picture, the energy of a light wave emitted from a point source is not spread continuously over ever larger volumes, but consists of a finite number of energy quanta that are spatially localized at points of space, move without dividing and are absorbed or generated only as a whole.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=%C3%9Cber+einen+die+Erzeugung+und+Verwandlung+des+Lichtes+betreffenden+heuristischen+Gesichtspunkt&rft.volume=17&rft.issue=6&rft.pages=132-148&rft.date=1905&rft_id=info%3Adoi%2F10.1002%2Fandp.19053220607&rft_id=info%3Abibcode%2F1905AnP...322..132E&rft.aulast=Einstein&rft.aufirst=Albert&rft_id=http%3A%2F%2Fwww.physik.uni-augsburg.de%2Fannalen%2Fhistory%2Feinstein-papers%2F1905_17_132-148.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> An <a href="https://en.wikisource.org/wiki/Translation:On_a_Heuristic_Point_of_View_about_the_Creation_and_Conversion_of_Light" class="extiw" title="wikisource:Translation:On a Heuristic Point of View about the Creation and Conversion of Light">English translation</a> is available from <a href="/wiki/Wikisource" title="Wikisource">Wikisource</a>. </li> <li id="cite_note-12"><a href="#cite_ref-12">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLewis1926" class="citation journal cs1"><a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Lewis, Gilbert N.</a> (18 December 1926). "The conservation of photons". Nature. 118 (2981): 874–875. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926Natur.118..874L">1926Natur.118..874L</a>. <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%2F118874a0">10.1038/118874a0</a>. <a href="/wiki/EISSN_(identifier)" class="mw-redirect" title="EISSN (identifier)">eISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1476-4687">1476-4687</a>. <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:4110026">4110026</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=The+conservation+of+photons&rft.volume=118&rft.issue=2981&rft.pages=874-875&rft.date=1926-12-18&rft_id=info%3Adoi%2F10.1038%2F118874a0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4110026%23id-name%3DS2CID&rft.eissn=1476-4687&rft_id=info%3Abibcode%2F1926Natur.118..874L&rft.aulast=Lewis&rft.aufirst=Gilbert+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> see also <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation conference cs1 cs1-prop-location-test cs1-prop-foreign-lang-source">"Discordances entre l'expérience et la théorie électromagnétique du rayonnement". Written at Bruxelles, Belgium. Electrons et photons: Rapports et discussions du cinquième Conseil de Physique tenu à Bruxelles du 24 au 29 octobre 1927 sous les auspices de l'Institut International de Physique Solvay. Cinquième Conseil de Physique (in French). l'Institut International de Physique Solvay (host institution). Paris, France: Gauthier-Villars et Cie (published 1928). 24–29 October 1927. pp. 55–85.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Discordances+entre+l%27exp%C3%A9rience+et+la+th%C3%A9orie+%C3%A9lectromagn%C3%A9tique+du+rayonnement&rft.btitle=Electrons+et+photons%3A+Rapports+et+discussions+du+cinqui%C3%A8me+Conseil+de+Physique+tenu+%C3%A0+Bruxelles+du+24+au+29+octobre+1927+sous+les+auspices+de+l%27Institut+International+de+Physique+Solvay&rft.place=Paris%2C+France&rft.pages=55-85&rft.pub=Gauthier-Villars+et+Cie&rft.date=1927-10-24%2F1927-10-29&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"><code class="cs1-code">{{<a href="/wiki/Template:Cite_conference" title="Template:Cite conference">cite conference</a>}}</code>: CS1 maint: others (<a href="/wiki/Category:CS1_maint:_others" title="Category:CS1 maint: others">link</a>) </li> <li id="cite_note-Asimov-1971-1983-13">^ <a href="#cite_ref-Asimov-1971-1983_13-0">a</a> <a href="#cite_ref-Asimov-1971-1983_13-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAsimov1983" class="citation book cs1"><a href="/wiki/Isaac_Asimov" title="Isaac Asimov">Asimov, Isaac</a> (1983). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-SkMngEACAAJ">The Neutrino: Ghost particle of the atom</a>. Garden City, NY: Avon Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-380-00483-6" title="Special:BookSources/978-0-380-00483-6"><bdi>978-0-380-00483-6</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+Neutrino%3A+Ghost+particle+of+the+atom&rft.place=Garden+City%2C+NY&rft.pub=Avon+Books&rft.date=1983&rft.isbn=978-0-380-00483-6&rft.aulast=Asimov&rft.aufirst=Isaac&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-SkMngEACAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAsimov1971" class="citation book cs1"><a href="/wiki/Isaac_Asimov" title="Isaac Asimov">Asimov, Isaac</a> (1971). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Eo5xpO83YpoC">The Universe: From flat Earth to quasar</a>. New York: <a href="/wiki/Walker_(publisher)" class="mw-redirect" title="Walker (publisher)">Walker</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8027-0316-3" title="Special:BookSources/978-0-8027-0316-3"><bdi>978-0-8027-0316-3</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/66022515">66022515</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Universe%3A+From+flat+Earth+to+quasar&rft.place=New+York&rft.pub=Walker&rft.date=1971&rft_id=info%3Alccn%2F66022515&rft.isbn=978-0-8027-0316-3&rft.aulast=Asimov&rft.aufirst=Isaac&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DEo5xpO83YpoC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-15"><a href="#cite_ref-15">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVillard1900" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Paul_Ulrich_Villard" title="Paul Ulrich Villard">Villard, Paul Ulrich</a> (1900). 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Physical Review Letters. 111 (2): 021801. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1304.2821">1304.2821</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PhRvL.111b1801H">2013PhRvL.111b1801H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.111.021801">10.1103/PhysRevLett.111.021801</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/0031-9007">0031-9007</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23889385">23889385</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240513012534/https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.021801">Archived</a> from the original on 2024-05-13. Retrieved 2024-02-01.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=How+Stable+is+the+Photon%3F&rft.volume=111&rft.issue=2&rft.pages=021801&rft.date=2013-07-11&rft_id=info%3Abibcode%2F2013PhRvL.111b1801H&rft_id=info%3Aarxiv%2F1304.2821&rft_id=info%3Apmid%2F23889385&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.111.021801&rft.issn=0031-9007&rft.aulast=Heeck&rft.aufirst=Julian&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FPhysRevLett.111.021801&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Schwartz2014-25"><a href="#cite_ref-Schwartz2014_25-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartz2014" class="citation book cs1">Schwartz, Matthew D. (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HbdEAgAAQBAJ&pg=PA66">Quantum Field Theory and the Standard Model</a>. Cambridge University Press. p. 66. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-03473-0" title="Special:BookSources/978-1-107-03473-0"><bdi>978-1-107-03473-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Field+Theory+and+the+Standard+Model&rft.pages=66&rft.pub=Cambridge+University+Press&rft.date=2014&rft.isbn=978-1-107-03473-0&rft.aulast=Schwartz&rft.aufirst=Matthew+D.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHbdEAgAAQBAJ%26pg%3DPA66&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-26"><a href="#cite_ref-26">^</a> "Role as gauge boson and polarization" §5.1 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAitchisonHey1993" class="citation book cs1">Aitchison, I.J.R.; Hey, A.J.G. (1993). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZJ-ZY8NW9TIC">Gauge Theories in Particle Physics</a>. <a href="/wiki/IOP_Publishing" title="IOP Publishing">IOP Publishing</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-85274-328-7" title="Special:BookSources/978-0-85274-328-7"><bdi>978-0-85274-328-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230117203733/https://books.google.com/books?id=ZJ-ZY8NW9TIC">Archived</a> from the original on 2023-01-17. Retrieved 2016-10-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gauge+Theories+in+Particle+Physics&rft.pub=IOP+Publishing&rft.date=1993&rft.isbn=978-0-85274-328-7&rft.aulast=Aitchison&rft.aufirst=I.J.R.&rft.au=Hey%2C+A.J.G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZJ-ZY8NW9TIC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-27"><a href="#cite_ref-27">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAmsler2008" class="citation journal cs1">Amsler, C.; et al. (2008). <a rel="nofollow" class="external text" href="http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf">"Review of Particle Physics"</a> (PDF). <a href="/wiki/Physics_Letters_B" class="mw-redirect" title="Physics Letters B">Physics Letters B</a>. 667 (1–5): 31. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008PhLB..667....1A">2008PhLB..667....1A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physletb.2008.07.018">10.1016/j.physletb.2008.07.018</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1854%2FLU-685594">1854/LU-685594</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10020536">10020536</a>. <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:227119789">227119789</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200601115825/http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf">Archived</a> (PDF) from the original on 2020-06-01. Retrieved 2017-10-26.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Review+of+Particle+Physics&rft.volume=667&rft.issue=1%E2%80%935&rft.pages=31&rft.date=2008&rft_id=info%3Ahdl%2F1854%2FLU-685594&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A227119789%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2008PhLB..667....1A&rft_id=info%3Apmid%2F10020536&rft_id=info%3Adoi%2F10.1016%2Fj.physletb.2008.07.018&rft.aulast=Amsler&rft.aufirst=C.&rft_id=http%3A%2F%2Fscipp.ucsc.edu%2F%257Ehaber%2Fpubs%2FReview_of_Particle_Physics_2014.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Halliday-28">^ <a href="#cite_ref-Halliday_28-0">a</a> <a href="#cite_ref-Halliday_28-1">b</a> <a href="#cite_ref-Halliday_28-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHallidayResnickWalker2005" class="citation book cs1">Halliday, David; Resnick, Robert; Walker, Jerl (2005). <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_0471216437">Fundamental of Physics</a> (7th ed.). John Wiley and Sons, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-23231-5" title="Special:BookSources/978-0-471-23231-5"><bdi>978-0-471-23231-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamental+of+Physics&rft.edition=7th&rft.pub=John+Wiley+and+Sons%2C+Inc.&rft.date=2005&rft.isbn=978-0-471-23231-5&rft.aulast=Halliday&rft.aufirst=David&rft.au=Resnick%2C+Robert&rft.au=Walker%2C+Jerl&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_0471216437&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-29"><a href="#cite_ref-29">^</a> See <a href="#CITEREFAlonsoFinn1968">Alonso & Finn 1968</a>, Section 1.6. </li> <li id="cite_note-30"><a href="#cite_ref-30">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoper" class="citation web cs1">Soper, Davison E. <a rel="nofollow" class="external text" href="http://pages.uoregon.edu/soper/Light/photons.html">"Electromagnetic radiation is made of photons"</a>. Institute of Theoretical Science. <a href="/wiki/University_of_Oregon" title="University of Oregon">University of Oregon</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230408082934/https://pages.uoregon.edu/soper/Light/photons.html">Archived</a> from the original on 2023-04-08. Retrieved 2024-03-21.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Electromagnetic+radiation+is+made+of+photons&rft.pub=University+of+Oregon&rft.aulast=Soper&rft.aufirst=Davison+E.&rft_id=http%3A%2F%2Fpages.uoregon.edu%2Fsoper%2FLight%2Fphotons.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Hecht-31"><a href="#cite_ref-Hecht_31-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHecht1998" class="citation book cs1">Hecht, Eugene (1998). Optics (3rd ed.). Reading, Massachusetts; Harlow: Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-83887-9" title="Special:BookSources/978-0-201-83887-9"><bdi>978-0-201-83887-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics&rft.place=Reading%2C+Massachusetts%3B+Harlow&rft.edition=3rd&rft.pub=Addison-Wesley&rft.date=1998&rft.isbn=978-0-201-83887-9&rft.aulast=Hecht&rft.aufirst=Eugene&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-spin-32"><a href="#cite_ref-spin_32-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRamanBhagavantam1931" class="citation journal cs1"><a href="/wiki/C._V._Raman" title="C. V. Raman">Raman, C. V.</a>; Bhagavantam, S. (1931). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160603235132/http://dspace.rri.res.in/bitstream/2289/2123/1/1931%20IJP%20V6%20p353.pdf">"Experimental proof of the spin of the photon"</a> (PDF). Indian Journal of Physics. 6 (3244): 353. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1932Natur.129...22R">1932Natur.129...22R</a>. <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%2F129022a0">10.1038/129022a0</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10821%2F664">10821/664</a>. <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:4064852">4064852</a>. Archived from <a rel="nofollow" class="external text" href="http://dspace.rri.res.in/bitstream/2289/2123/1/1931%20IJP%20V6%20p353.pdf">the original</a> (PDF) on 2016-06-03. Retrieved 2008-12-28.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Indian+Journal+of+Physics&rft.atitle=Experimental+proof+of+the+spin+of+the+photon&rft.volume=6&rft.issue=3244&rft.pages=353&rft.date=1931&rft_id=info%3Ahdl%2F10821%2F664&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4064852%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F129022a0&rft_id=info%3Abibcode%2F1932Natur.129...22R&rft.aulast=Raman&rft.aufirst=C.+V.&rft.au=Bhagavantam%2C+S.&rft_id=http%3A%2F%2Fdspace.rri.res.in%2Fbitstream%2F2289%2F2123%2F1%2F1931%2520IJP%2520V6%2520p353.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Griffiths2008-34"><a href="#cite_ref-Griffiths2008_34-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGriffiths2008" class="citation book cs1">Griffiths, David J. (2008). Introduction to Elementary Particles (2nd revised ed.). WILEY-VCH. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-40601-2" title="Special:BookSources/978-3-527-40601-2"><bdi>978-3-527-40601-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Elementary+Particles&rft.edition=2nd+revised&rft.pub=WILEY-VCH&rft.date=2008&rft.isbn=978-3-527-40601-2&rft.aulast=Griffiths&rft.aufirst=David+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-35"><a href="#cite_ref-35">^</a> <a href="#CITEREFAlonsoFinn1968">Alonso & Finn 1968</a>, Section 9.3. </li> <li id="cite_note-36"><a href="#cite_ref-36">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBornBlin-StoyleRadcliffe1989" class="citation book cs1">Born, Max; Blin-Stoyle, Roger John; Radcliffe, J. M. (1989). "Appendix XXXII". <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NmM-KujxMtoC">Atomic Physics</a>. Courier Corporation. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-65984-8" title="Special:BookSources/978-0-486-65984-8"><bdi>978-0-486-65984-8</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+XXXII&rft.btitle=Atomic+Physics&rft.pub=Courier+Corporation&rft.date=1989&rft.isbn=978-0-486-65984-8&rft.aulast=Born&rft.aufirst=Max&rft.au=Blin-Stoyle%2C+Roger+John&rft.au=Radcliffe%2C+J.+M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNmM-KujxMtoC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-37"><a href="#cite_ref-37">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMermin,_David1984" class="citation journal cs1">Mermin, David (February 1984). "Relativity without light". American Journal of Physics. 52 (2): 119–124. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1984AmJPh..52..119M">1984AmJPh..52..119M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.13917">10.1119/1.13917</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Relativity+without+light&rft.volume=52&rft.issue=2&rft.pages=119-124&rft.date=1984-02&rft_id=info%3Adoi%2F10.1119%2F1.13917&rft_id=info%3Abibcode%2F1984AmJPh..52..119M&rft.au=Mermin%2C+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-38"><a href="#cite_ref-38">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlimptonLawton1936" class="citation journal cs1">Plimpton, S.; Lawton, W. (1936). "A Very Accurate Test of Coulomb's Law of Force Between Charges". Physical Review. 50 (11): 1066. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1936PhRv...50.1066P">1936PhRv...50.1066P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.50.1066">10.1103/PhysRev.50.1066</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=A+Very+Accurate+Test+of+Coulomb%27s+Law+of+Force+Between+Charges&rft.volume=50&rft.issue=11&rft.pages=1066&rft.date=1936&rft_id=info%3Adoi%2F10.1103%2FPhysRev.50.1066&rft_id=info%3Abibcode%2F1936PhRv...50.1066P&rft.aulast=Plimpton&rft.aufirst=S.&rft.au=Lawton%2C+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-39"><a href="#cite_ref-39">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliamsFallerHill1971" class="citation journal cs1">Williams, E.; Faller, J.; Hill, H. (1971). "New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass". Physical Review Letters. 26 (12): 721. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1971PhRvL..26..721W">1971PhRvL..26..721W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.26.721">10.1103/PhysRevLett.26.721</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=New+Experimental+Test+of+Coulomb%27s+Law%3A+A+Laboratory+Upper+Limit+on+the+Photon+Rest+Mass&rft.volume=26&rft.issue=12&rft.pages=721&rft.date=1971&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.26.721&rft_id=info%3Abibcode%2F1971PhRvL..26..721W&rft.aulast=Williams&rft.aufirst=E.&rft.au=Faller%2C+J.&rft.au=Hill%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-40"><a href="#cite_ref-40">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChibisov1976" class="citation journal cs1">Chibisov, G. V. (1976). "Astrophysical upper limits on the photon rest mass". Soviet Physics Uspekhi. 19 (7): 624. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1976SvPhU..19..624C">1976SvPhU..19..624C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1070%2FPU1976v019n07ABEH005277">10.1070/PU1976v019n07ABEH005277</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Soviet+Physics+Uspekhi&rft.atitle=Astrophysical+upper+limits+on+the+photon+rest+mass&rft.volume=19&rft.issue=7&rft.pages=624&rft.date=1976&rft_id=info%3Adoi%2F10.1070%2FPU1976v019n07ABEH005277&rft_id=info%3Abibcode%2F1976SvPhU..19..624C&rft.aulast=Chibisov&rft.aufirst=G.+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-41"><a href="#cite_ref-41">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLakes1998" class="citation journal cs1">Lakes, Roderic (1998). "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential". Physical Review Letters. 80 (9): 1826. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998PhRvL..80.1826L">1998PhRvL..80.1826L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.80.1826">10.1103/PhysRevLett.80.1826</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Experimental+Limits+on+the+Photon+Mass+and+Cosmic+Magnetic+Vector+Potential&rft.volume=80&rft.issue=9&rft.pages=1826&rft.date=1998&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.80.1826&rft_id=info%3Abibcode%2F1998PhRvL..80.1826L&rft.aulast=Lakes&rft.aufirst=Roderic&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-amsler-42"><a href="#cite_ref-amsler_42-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAmslerDoserAntonelliAsner2008" class="citation journal cs1">Amsler, C; Doser, M; Antonelli, M; Asner, D; Babu, K; Baer, H; Band, H; Barnett, R; et al. (2008). <a rel="nofollow" class="external text" href="http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf">"Review of Particle Physics⁎"</a> (PDF). <a href="/wiki/Physics_Letters_B" class="mw-redirect" title="Physics Letters B">Physics Letters B</a>. 667 (1–5): 1. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008PhLB..667....1A">2008PhLB..667....1A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.physletb.2008.07.018">10.1016/j.physletb.2008.07.018</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1854%2FLU-685594">1854/LU-685594</a>. <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:227119789">227119789</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200601115825/http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf">Archived</a> (PDF) from the original on 2020-06-01. Retrieved 2017-10-26.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Review+of+Particle+Physics%E2%81%8E&rft.volume=667&rft.issue=1%E2%80%935&rft.pages=1&rft.date=2008&rft_id=info%3Ahdl%2F1854%2FLU-685594&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A227119789%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.physletb.2008.07.018&rft_id=info%3Abibcode%2F2008PhLB..667....1A&rft.aulast=Amsler&rft.aufirst=C&rft.au=Doser%2C+M&rft.au=Antonelli%2C+M&rft.au=Asner%2C+D&rft.au=Babu%2C+K&rft.au=Baer%2C+H&rft.au=Band%2C+H&rft.au=Barnett%2C+R&rft.au=Bergren%2C+E&rft_id=http%3A%2F%2Fscipp.ucsc.edu%2F%257Ehaber%2Fpubs%2FReview_of_Particle_Physics_2014.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> <a rel="nofollow" class="external text" href="http://pdg.lbl.gov/2009/tables/contents_tables.html">Summary Table</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100109093036/http://pdg.lbl.gov/2009/tables/contents_tables.html">Archived</a> 2010-01-09 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> </li> <li id="cite_note-43"><a href="#cite_ref-43">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdelbergerDvaliGruzinov2007" class="citation journal cs1">Adelberger, Eric; Dvali, Gia; Gruzinov, Andrei (2007). "Photon-Mass Bound Destroyed by Vortices". Physical Review Letters. 98 (1): 010402. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-ph/0306245">hep-ph/0306245</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007PhRvL..98a0402A">2007PhRvL..98a0402A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.98.010402">10.1103/PhysRevLett.98.010402</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17358459">17358459</a>. <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:31249827">31249827</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Photon-Mass+Bound+Destroyed+by+Vortices&rft.volume=98&rft.issue=1&rft.pages=010402&rft.date=2007&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A31249827%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2007PhRvL..98a0402A&rft_id=info%3Aarxiv%2Fhep-ph%2F0306245&rft_id=info%3Apmid%2F17358459&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.98.010402&rft.aulast=Adelberger&rft.aufirst=Eric&rft.au=Dvali%2C+Gia&rft.au=Gruzinov%2C+Andrei&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-44"><a href="#cite_ref-44">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDescartes1637" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes, René</a> (1637). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=difXAAAAMAAJ">Discours de la méthode (Discourse on Method)</a> (in French). Imprimerie de Ian Maire. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-268-00870-3" title="Special:BookSources/978-0-268-00870-3"><bdi>978-0-268-00870-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discours+de+la+m%C3%A9thode+%28Discourse+on+Method%29&rft.pub=Imprimerie+de+Ian+Maire&rft.date=1637&rft.isbn=978-0-268-00870-3&rft.aulast=Descartes&rft.aufirst=Ren%C3%A9&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DdifXAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-45"><a href="#cite_ref-45">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHooke1667" class="citation book cs1"><a href="/wiki/Robert_Hooke" title="Robert Hooke">Hooke, Robert</a> (1667). <a rel="nofollow" class="external text" href="http://digital.library.wisc.edu/1711.dl/HistSciTech.HookeMicro">Micrographia: or some physiological descriptions of minute bodies made by magnifying glasses with observations and inquiries thereupon ...</a> London, UK: <a href="/wiki/Royal_Society_of_London" class="mw-redirect" title="Royal Society of London">Royal Society of London</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-49564-4" title="Special:BookSources/978-0-486-49564-4"><bdi>978-0-486-49564-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081202101129/http://digital.library.wisc.edu/1711.dl/HistSciTech.HookeMicro">Archived</a> from the original on 2008-12-02. Retrieved 2006-09-26.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Micrographia%3A+or+some+physiological+descriptions+of+minute+bodies+made+by+magnifying+glasses+with+observations+and+inquiries+thereupon+...&rft.place=London%2C+UK&rft.pub=Royal+Society+of+London&rft.date=1667&rft.isbn=978-0-486-49564-4&rft.aulast=Hooke&rft.aufirst=Robert&rft_id=http%3A%2F%2Fdigital.library.wisc.edu%2F1711.dl%2FHistSciTech.HookeMicro&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-46"><a href="#cite_ref-46">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuygens1678" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens, Christiaan</a> (1678). <a href="/wiki/Trait%C3%A9_de_la_lumi%C3%A8re" class="mw-redirect" title="Traité de la lumière">Traité de la lumière</a> (in French).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Trait%C3%A9+de+la+lumi%C3%A8re&rft.date=1678&rft.aulast=Huygens&rft.aufirst=Christiaan&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988">. An <a href="https://www.gutenberg.org/ebooks/14725" class="extiw" title="gutenberg:14725">English translation</a> is available from <a href="/wiki/Project_Gutenberg" title="Project Gutenberg">Project Gutenberg</a> </li> <li id="cite_note-Newton1730-47">^ <a href="#cite_ref-Newton1730_47-0">a</a> <a href="#cite_ref-Newton1730_47-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1952" class="citation book cs1"><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton, Isaac</a> (1952) [1730]. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=bSiTKcLf07UC">Opticks</a> (4th ed.). Dover, New York: Dover Publications. Book II, Part III, Propositions XII–XX; Queries 25–29. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-60205-9" title="Special:BookSources/978-0-486-60205-9"><bdi>978-0-486-60205-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Opticks&rft.place=Dover%2C+New+York&rft.pages=Book+II%2C+Part+III%2C+Propositions+XII-XX%3B+Queries+25-29&rft.edition=4th&rft.pub=Dover+Publications&rft.date=1952&rft.isbn=978-0-486-60205-9&rft.aulast=Newton&rft.aufirst=Isaac&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DbSiTKcLf07UC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-48"><a href="#cite_ref-48">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBuchwald1989" class="citation journal cs1">Buchwald, J. Z. (1989). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=EbDw1lV_MKsC">"The Rise of the Wave Theory of Light: Optical theory and experiment in the early nineteenth century"</a>. Physics Today. 43 (4). University of Chicago Press: 78–80. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1990PhT....43d..78B">1990PhT....43d..78B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.2810533">10.1063/1.2810533</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-07886-1" title="Special:BookSources/978-0-226-07886-1"><bdi>978-0-226-07886-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/18069573">18069573</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=The+Rise+of+the+Wave+Theory+of+Light%3A+Optical+theory+and+experiment+in+the+early+nineteenth+century&rft.volume=43&rft.issue=4&rft.pages=78-80&rft.date=1989&rft_id=info%3Aoclcnum%2F18069573&rft_id=info%3Adoi%2F10.1063%2F1.2810533&rft_id=info%3Abibcode%2F1990PhT....43d..78B&rft.isbn=978-0-226-07886-1&rft.aulast=Buchwald&rft.aufirst=J.+Z.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DEbDw1lV_MKsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-maxwell-49"><a href="#cite_ref-maxwell_49-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaxwell1865" class="citation journal cs1"><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell, James Clerk</a> (1865). <a href="/wiki/A_dynamical_theory_of_the_electromagnetic_field" class="mw-redirect" title="A dynamical theory of the electromagnetic field">"A Dynamical Theory of the Electromagnetic Field"</a>. <a href="/wiki/Philosophical_Transactions_of_the_Royal_Society" title="Philosophical Transactions of the Royal Society">Philosophical Transactions of the Royal Society</a>. 155: 459–512. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1865RSPT..155..459M">1865RSPT..155..459M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1865.0008">10.1098/rstl.1865.0008</a>. <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:186207827">186207827</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society&rft.atitle=A+Dynamical+Theory+of+the+Electromagnetic+Field&rft.volume=155&rft.pages=459-512&rft.date=1865&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A186207827%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1098%2Frstl.1865.0008&rft_id=info%3Abibcode%2F1865RSPT..155..459M&rft.aulast=Maxwell&rft.aufirst=James+Clerk&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> This article followed a presentation by Maxwell on 8 December 1864 to the Royal Society. </li> <li id="cite_note-hertz-50"><a href="#cite_ref-hertz_50-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHertz1888" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz, Heinrich</a> (1888). "Über Strahlen elektrischer Kraft". Sitzungsberichte der Preussischen Akademie der Wissenschaften (in German). 1888. Berlin, Deutschland: 1297–1307.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Sitzungsberichte+der+Preussischen+Akademie+der+Wissenschaften&rft.atitle=%C3%9Cber+Strahlen+elektrischer+Kraft&rft.volume=1888&rft.pages=1297-1307&rft.date=1888&rft.aulast=Hertz&rft.aufirst=Heinrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-51"><a href="#cite_ref-51">^</a> "Frequency-dependence of luminiscence" pp. 276ff., §1.4 "photoelectric effect" in <a href="#CITEREFAlonsoFinn1968">Alonso & Finn 1968</a>. </li> <li id="cite_note-52"><a href="#cite_ref-52">^</a> See also: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBorehamHoraBolton1996" class="citation journal cs1">Boreham, Bruce W.; Hora, Heinrich; Bolton, Paul R. (1996). "Photon density and the correspondence principle of electromagnetic interaction". AIP Conference Proceedings. 369: 1234–1243. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996AIPC..369.1234B">1996AIPC..369.1234B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.50410">10.1063/1.50410</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=AIP+Conference+Proceedings&rft.atitle=Photon+density+and+the+correspondence+principle+of+electromagnetic+interaction&rft.volume=369&rft.pages=1234-1243&rft.date=1996&rft_id=info%3Adoi%2F10.1063%2F1.50410&rft_id=info%3Abibcode%2F1996AIPC..369.1234B&rft.aulast=Boreham&rft.aufirst=Bruce+W.&rft.au=Hora%2C+Heinrich&rft.au=Bolton%2C+Paul+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Wien1911-54">^ <a href="#cite_ref-Wien1911_54-0">a</a> <a href="#cite_ref-Wien1911_54-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWien1911" class="citation web cs1"><a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wien, W.</a> (1911). <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1911/wien-lecture.html">"Wilhelm Wien Nobel Lecture"</a>. nobelprize.org. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110715190243/http://nobelprize.org/nobel_prizes/physics/laureates/1911/wien-lecture.html">Archived</a> from the original on 2011-07-15. Retrieved 2006-08-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=nobelprize.org&rft.atitle=Wilhelm+Wien+Nobel+Lecture&rft.date=1911&rft.aulast=Wien&rft.aufirst=W.&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1911%2Fwien-lecture.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Planck1901-55"><a href="#cite_ref-Planck1901_55-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlanck1901" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Max_Planck" title="Max Planck">Planck, Max</a> (1901). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19013090310">"Über das Gesetz der Energieverteilung im Normalspectrum"</a>. <a href="/wiki/Annalen_der_Physik" title="Annalen der Physik">Annalen der Physik</a> (in German). 4 (3): 553–563. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1901AnP...309..553P">1901AnP...309..553P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19013090310">10.1002/andp.19013090310</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=%C3%9Cber+das+Gesetz+der+Energieverteilung+im+Normalspectrum&rft.volume=4&rft.issue=3&rft.pages=553-563&rft.date=1901&rft_id=info%3Adoi%2F10.1002%2Fandp.19013090310&rft_id=info%3Abibcode%2F1901AnP...309..553P&rft.aulast=Planck&rft.aufirst=Max&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fandp.19013090310&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html">English translation</a> </li> <li id="cite_note-Planck1918-56">^ <a href="#cite_ref-Planck1918_56-0">a</a> <a href="#cite_ref-Planck1918_56-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlanck1920" class="citation web cs1"><a href="/wiki/Max_Planck" title="Max Planck">Planck, Max</a> (1920). <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html">"Max Planck's Nobel Lecture"</a>. nobelprize.org. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110715190331/http://nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html">Archived</a> from the original on 2011-07-15. Retrieved 2006-08-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Max+Planck%27s+Nobel+Lecture&rft.pub=nobelprize.org&rft.date=1920&rft.aulast=Planck&rft.aufirst=Max&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1918%2Fplanck-lecture.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Einstein1909-57">^ <a href="#cite_ref-Einstein1909_57-0">a</a> <a href="#cite_ref-Einstein1909_57-1">b</a> <a href="#cite_ref-Einstein1909_57-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1909" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, Albert</a> (1909). <a rel="nofollow" class="external text" href="http://www.ekkehard-friebe.de/EINSTEIN-1909-P.pdf">"Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung"</a> (PDF). <a href="/wiki/Physikalische_Zeitschrift" title="Physikalische Zeitschrift">Physikalische Zeitschrift</a> (in German). 10: 817–825. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110607135402/http://www.ekkehard-friebe.de/EINSTEIN-1909-P.pdf">Archived</a> (PDF) from the original on 2011-06-07. Retrieved 2010-08-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physikalische+Zeitschrift&rft.atitle=%C3%9Cber+die+Entwicklung+unserer+Anschauungen+%C3%BCber+das+Wesen+und+die+Konstitution+der+Strahlung&rft.volume=10&rft.pages=817-825&rft.date=1909&rft.aulast=Einstein&rft.aufirst=Albert&rft_id=http%3A%2F%2Fwww.ekkehard-friebe.de%2FEINSTEIN-1909-P.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> An <a href="https://en.wikisource.org/wiki/Translation:The_Development_of_Our_Views_on_the_Composition_and_Essence_of_Radiation" class="extiw" title="wikisource:Translation:The Development of Our Views on the Composition and Essence of Radiation">English translation</a> is available from <a href="/wiki/Wikisource" title="Wikisource">Wikisource</a>. </li> <li id="cite_note-58"><a href="#cite_ref-58">^</a> Presentation speech by <a href="/wiki/Svante_Arrhenius" title="Svante Arrhenius">Svante Arrhenius</a> for the 1921 Nobel Prize in Physics, December 10, 1922. <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1921/press.html">Online text</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110904232203/http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/press.html">Archived</a> 2011-09-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> from [nobelprize.org], The Nobel Foundation 2008. Access date 2008-12-05. </li> <li id="cite_note-Einstein1916b-59"><a href="#cite_ref-Einstein1916b_59-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1916" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, Albert</a> (1916). "Zur Quantentheorie der Strahlung". Mitteilungen der Physikalischen Gesellschaft zu Zürich (in German). 16: 47.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mitteilungen+der+Physikalischen+Gesellschaft+zu+Z%C3%BCrich&rft.atitle=Zur+Quantentheorie+der+Strahlung&rft.volume=16&rft.pages=47&rft.date=1916&rft.aulast=Einstein&rft.aufirst=Albert&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> Also Physikalische Zeitschrift (in German), 18, 121–128 (1917). </li> <li id="cite_note-Compton1923-60">^ <a href="#cite_ref-Compton1923_60-0">a</a> <a href="#cite_ref-Compton1923_60-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCompton1923" class="citation journal cs1"><a href="/wiki/Arthur_Compton" title="Arthur Compton">Compton, Arthur</a> (1923). <a rel="nofollow" class="external text" href="https://history.aip.org/history/exhibits/gap/Compton/Compton.html#compton1">"A quantum theory of the scattering of X-rays by light elements"</a>. <a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a>. 21 (5): 483–502. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1923PhRv...21..483C">1923PhRv...21..483C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.21.483">10.1103/PhysRev.21.483</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180129004433/https://history.aip.org/history/exhibits/gap/Compton/Compton.html#compton1">Archived</a> from the original on 2018-01-29. Retrieved 2020-11-08.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=A+quantum+theory+of+the+scattering+of+X-rays+by+light+elements&rft.volume=21&rft.issue=5&rft.pages=483-502&rft.date=1923&rft_id=info%3Adoi%2F10.1103%2FPhysRev.21.483&rft_id=info%3Abibcode%2F1923PhRv...21..483C&rft.aulast=Compton&rft.aufirst=Arthur&rft_id=https%3A%2F%2Fhistory.aip.org%2Fhistory%2Fexhibits%2Fgap%2FCompton%2FCompton.html%23compton1&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Pais1982-61">^ <a href="#cite_ref-Pais1982_61-0">a</a> <a href="#cite_ref-Pais1982_61-1">b</a> <a href="#cite_ref-Pais1982_61-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPais1982" class="citation book cs1"><a href="/wiki/Abraham_Pais" title="Abraham Pais">Pais, A.</a> (1982). <a rel="nofollow" class="external text" href="https://archive.org/details/subtleislordscie00pais">Subtle is the Lord: The science and the life of Albert Einstein</a>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853907-0" title="Special:BookSources/978-0-19-853907-0"><bdi>978-0-19-853907-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Subtle+is+the+Lord%3A+The+science+and+the+life+of+Albert+Einstein&rft.pub=Oxford+University+Press&rft.date=1982&rft.isbn=978-0-19-853907-0&rft.aulast=Pais&rft.aufirst=A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsubtleislordscie00pais&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Millikan1923-62">^ <a href="#cite_ref-Millikan1923_62-0">a</a> <a href="#cite_ref-Millikan1923_62-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMillikan1924" class="citation web cs1"><a href="/wiki/Robert_Millikan" class="mw-redirect" title="Robert Millikan">Millikan, Robert A.</a> (1924). <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1923/millikan-lecture.html">"Robert A. Millikan's Nobel Lecture"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110715190254/http://nobelprize.org/nobel_prizes/physics/laureates/1923/millikan-lecture.html">Archived</a> from the original on 2011-07-15. Retrieved 2006-08-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Robert+A.+Millikan%27s+Nobel+Lecture&rft.date=1924&rft.aulast=Millikan&rft.aufirst=Robert+A.&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1923%2Fmillikan-lecture.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-63"><a href="#cite_ref-63">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHendry1980" class="citation journal cs1">Hendry, J. (1980). "The development of attitudes to the wave–particle duality of light and quantum theory, 1900–1920". <a href="/wiki/Annals_of_Science" title="Annals of Science">Annals of Science</a>. 37 (1): 59–79. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00033798000200121">10.1080/00033798000200121</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Science&rft.atitle=The+development+of+attitudes+to+the+wave%E2%80%93particle+duality+of+light+and+quantum+theory%2C+1900%E2%80%931920&rft.volume=37&rft.issue=1&rft.pages=59-79&rft.date=1980&rft_id=info%3Adoi%2F10.1080%2F00033798000200121&rft.aulast=Hendry&rft.aufirst=J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Bohr1924-64"><a href="#cite_ref-Bohr1924_64-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBohrKramersSlater1924" class="citation journal cs1"><a href="/wiki/Niels_Bohr" title="Niels Bohr">Bohr, Niels</a>; <a href="/wiki/Hendrik_Anthony_Kramers" class="mw-redirect" title="Hendrik Anthony Kramers">Kramers, Hendrik Anthony</a>; <a href="/wiki/John_C._Slater" title="John C. Slater">Slater, John C.</a> (1924). "The Quantum Theory of Radiation". <a href="/wiki/Philosophical_Magazine" title="Philosophical Magazine">Philosophical Magazine</a>. 47 (281): 785–802. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F14786442408565262">10.1080/14786442408565262</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=The+Quantum+Theory+of+Radiation&rft.volume=47&rft.issue=281&rft.pages=785-802&rft.date=1924&rft_id=info%3Adoi%2F10.1080%2F14786442408565262&rft.aulast=Bohr&rft.aufirst=Niels&rft.au=Kramers%2C+Hendrik+Anthony&rft.au=Slater%2C+John+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> Also <a href="/wiki/European_Physical_Journal" title="European Physical Journal">Zeitschrift für Physik</a> (in German), 24, p. 69 (1924). </li> <li id="cite_note-65"><a href="#cite_ref-65">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoward2004" class="citation journal cs1">Howard, Don (December 2004). "Who Invented the "Copenhagen Interpretation"? A Study in Mythology". <a href="/wiki/Philosophy_of_Science_(journal)" title="Philosophy of Science (journal)">Philosophy of Science</a>. 71 (5): 669–682. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F425941">10.1086/425941</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/0031-8248">0031-8248</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/10.1086/425941">10.1086/425941</a>. <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:9454552">9454552</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophy+of+Science&rft.atitle=Who+Invented+the+%22Copenhagen+Interpretation%22%3F+A+Study+in+Mythology&rft.volume=71&rft.issue=5&rft.pages=669-682&rft.date=2004-12&rft.issn=0031-8248&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9454552%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F10.1086%2F425941%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1086%2F425941&rft.aulast=Howard&rft.aufirst=Don&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Heisenberg1932-66"><a href="#cite_ref-Heisenberg1932_66-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeisenberg1933" class="citation web cs1"><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg, Werner</a> (1933). <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1932/heisenberg-lecture.html">"Heisenberg Nobel lecture"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110719053050/http://nobelprize.org/nobel_prizes/physics/laureates/1932/heisenberg-lecture.html">Archived</a> from the original on 2011-07-19. Retrieved 2006-09-11.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Heisenberg+Nobel+lecture&rft.date=1933&rft.aulast=Heisenberg&rft.aufirst=Werner&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1932%2Fheisenberg-lecture.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Mandel1976-67"><a href="#cite_ref-Mandel1976_67-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandel1976" class="citation book cs1"><a href="/wiki/Leonard_Mandel" title="Leonard Mandel">Mandel, Leonard</a> (1976). Wolf, E. (ed.). II the Case for and Against Semiclassical Radiation Theory. <a href="/wiki/Progress_in_Optics" title="Progress in Optics">Progress in Optics</a>. Vol. 13. North-Holland. pp. 27–69. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1976PrOpt..13...27M">1976PrOpt..13...27M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0079-6638%2808%2970018-0">10.1016/S0079-6638(08)70018-0</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-10806-7" title="Special:BookSources/978-0-444-10806-7"><bdi>978-0-444-10806-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=II+the+Case+for+and+Against+Semiclassical+Radiation+Theory&rft.series=Progress+in+Optics&rft.pages=27-69&rft.pub=North-Holland&rft.date=1976&rft_id=info%3Adoi%2F10.1016%2FS0079-6638%2808%2970018-0&rft_id=info%3Abibcode%2F1976PrOpt..13...27M&rft.isbn=978-0-444-10806-7&rft.aulast=Mandel&rft.aufirst=Leonard&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> <code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: <code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>) </li> <li id="cite_note-68"><a href="#cite_ref-68">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrangierRogerAspect1986" class="citation journal cs1">Grangier, P.; Roger, G.; Aspect, A. (1986). "Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences". <a href="/wiki/EPL_(journal)" title="EPL (journal)">Europhysics Letters</a>. 1 (4): 173–179. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1986EL......1..173G">1986EL......1..173G</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.4356">10.1.1.178.4356</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1209%2F0295-5075%2F1%2F4%2F004">10.1209/0295-5075/1/4/004</a>. <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:250837011">250837011</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Europhysics+Letters&rft.atitle=Experimental+evidence+for+a+photon+anticorrelation+effect+on+a+beam+splitter%3A+A+new+light+on+single-photon+interferences&rft.volume=1&rft.issue=4&rft.pages=173-179&rft.date=1986&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.178.4356%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250837011%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1209%2F0295-5075%2F1%2F4%2F004&rft_id=info%3Abibcode%2F1986EL......1..173G&rft.aulast=Grangier&rft.aufirst=P.&rft.au=Roger%2C+G.&rft.au=Aspect%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-69"><a href="#cite_ref-69">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThornNeelDonatoBergreen2004" class="citation journal cs1">Thorn, J.J.; Neel, M.S.; Donato, V.W.; Bergreen, G.S.; Davies, R.E.; Beck, M. (2004). <a rel="nofollow" class="external text" href="http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf">"Observing the quantum behavior of light in an undergraduate laboratory"</a> (PDF). <a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a>. 72 (9): 1210–1219. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004AmJPh..72.1210T">2004AmJPh..72.1210T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1737397">10.1119/1.1737397</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160201214040/http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf">Archived</a> (PDF) from the original on 2016-02-01. Retrieved 2009-06-29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Observing+the+quantum+behavior+of+light+in+an+undergraduate+laboratory&rft.volume=72&rft.issue=9&rft.pages=1210-1219&rft.date=2004&rft_id=info%3Adoi%2F10.1119%2F1.1737397&rft_id=info%3Abibcode%2F2004AmJPh..72.1210T&rft.aulast=Thorn&rft.aufirst=J.J.&rft.au=Neel%2C+M.S.&rft.au=Donato%2C+V.W.&rft.au=Bergreen%2C+G.S.&rft.au=Davies%2C+R.E.&rft.au=Beck%2C+M.&rft_id=http%3A%2F%2Fpeople.whitman.edu%2F~beckmk%2FQM%2Fgrangier%2FThorn_ajp.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Taylor1909-71"><a href="#cite_ref-Taylor1909_71-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylor1909" class="citation conference cs1"><a href="/wiki/Geoffrey_Ingram_Taylor" class="mw-redirect" title="Geoffrey Ingram Taylor">Taylor, Geoffrey Ingram</a> (1909). Interference fringes with feeble light. Cambridge Philosophical Society. Proceedings of the Cambridge Philosophical Society. Vol. 15. pp. 114–115.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=conference&rft.jtitle=Proceedings+of+the+Cambridge+Philosophical+Society&rft.atitle=Interference+fringes+with+feeble+light&rft.volume=15&rft.pages=114-115&rft.date=1909&rft.aulast=Taylor&rft.aufirst=Geoffrey+Ingram&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Saleh-72"><a href="#cite_ref-Saleh_72-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSalehTeich2007" class="citation book cs1">Saleh, B. E. A. & Teich, M. C. (2007). Fundamentals of Photonics. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-35832-9" title="Special:BookSources/978-0-471-35832-9"><bdi>978-0-471-35832-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Photonics&rft.pub=Wiley&rft.date=2007&rft.isbn=978-0-471-35832-9&rft.aulast=Saleh&rft.aufirst=B.+E.+A.&rft.au=Teich%2C+M.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-73"><a href="#cite_ref-73">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewtonWigner1949" class="citation journal cs1">Newton, T.D.; <a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Wigner, E.P.</a> (1949). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/1062641/files/RevModPhys.21.400.pdf">"Localized states for elementary particles"</a> (PDF). <a href="/wiki/Reviews_of_Modern_Physics" title="Reviews of Modern Physics">Reviews of Modern Physics</a>. 21 (3): 400–406. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1949RvMP...21..400N">1949RvMP...21..400N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.21.400">10.1103/RevModPhys.21.400</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230516123629/http://cds.cern.ch/record/1062641/files/RevModPhys.21.400.pdf">Archived</a> (PDF) from the original on 2023-05-16. Retrieved 2023-06-21.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.atitle=Localized+states+for+elementary+particles&rft.volume=21&rft.issue=3&rft.pages=400-406&rft.date=1949&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.21.400&rft_id=info%3Abibcode%2F1949RvMP...21..400N&rft.aulast=Newton&rft.aufirst=T.D.&rft.au=Wigner%2C+E.P.&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F1062641%2Ffiles%2FRevModPhys.21.400.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-74"><a href="#cite_ref-74">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBialynicki-Birula1994" class="citation journal cs1">Bialynicki-Birula, I. (1994). <a rel="nofollow" class="external text" href="https://doi.org/10.12693%2FAPhysPolA.86.97">"On the wave function of the photon"</a>. <a href="/wiki/Acta_Physica_Polonica_A" class="mw-redirect" title="Acta Physica Polonica A">Acta Physica Polonica A</a>. 86 (1–2): 97–116. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994AcPPA..86...97B">1994AcPPA..86...97B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.12693%2FAPhysPolA.86.97">10.12693/APhysPolA.86.97</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Physica+Polonica+A&rft.atitle=On+the+wave+function+of+the+photon&rft.volume=86&rft.issue=1%E2%80%932&rft.pages=97-116&rft.date=1994&rft_id=info%3Adoi%2F10.12693%2FAPhysPolA.86.97&rft_id=info%3Abibcode%2F1994AcPPA..86...97B&rft.aulast=Bialynicki-Birula&rft.aufirst=I.&rft_id=https%3A%2F%2Fdoi.org%2F10.12693%252FAPhysPolA.86.97&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-75"><a href="#cite_ref-75">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSipe1995" class="citation journal cs1">Sipe, J.E. (1995). "Photon wave functions". Physical Review A. 52 (3): 1875–1883. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995PhRvA..52.1875S">1995PhRvA..52.1875S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.52.1875">10.1103/PhysRevA.52.1875</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9912446">9912446</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Photon+wave+functions&rft.volume=52&rft.issue=3&rft.pages=1875-1883&rft.date=1995&rft_id=info%3Apmid%2F9912446&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.52.1875&rft_id=info%3Abibcode%2F1995PhRvA..52.1875S&rft.aulast=Sipe&rft.aufirst=J.E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-76"><a href="#cite_ref-76">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBialynicki-Birula1996" class="citation book cs1">Bialynicki-Birula, I. 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Vol. 36. pp. 245–294. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996PrOpt..36..245B">1996PrOpt..36..245B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0079-6638%2808%2970316-0">10.1016/S0079-6638(08)70316-0</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-82530-8" title="Special:BookSources/978-0-444-82530-8"><bdi>978-0-444-82530-8</bdi></a>. <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:17695022">17695022</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=V+Photon+Wave+Function&rft.series=Progress+in+Optics&rft.pages=245-294&rft.date=1996&rft_id=info%3Adoi%2F10.1016%2FS0079-6638%2808%2970316-0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17695022%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1996PrOpt..36..245B&rft.isbn=978-0-444-82530-8&rft.aulast=Bialynicki-Birula&rft.aufirst=I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> <code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: <code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>) </li> <li id="cite_note-scully1997-78">^ <a href="#cite_ref-scully1997_78-0">a</a> <a href="#cite_ref-scully1997_78-1">b</a> <a href="#cite_ref-scully1997_78-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScullyZubairy1997" class="citation book cs1">Scully, M. 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Entropy. 18 (5): 174. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1602.09002">1602.09002</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016Entrp..18..174A">2016Entrp..18..174A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe18050174">10.3390/e18050174</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Entropy&rft.atitle=Quantum+Errors+and+Disturbances%3A+Response+to+Busch%2C+Lahti+and+Werner&rft.volume=18&rft.issue=5&rft.pages=174&rft.date=2016-05-06&rft_id=info%3Aarxiv%2F1602.09002&rft_id=info%3Adoi%2F10.3390%2Fe18050174&rft_id=info%3Abibcode%2F2016Entrp..18..174A&rft.aulast=Appleby&rft.aufirst=David+Marcus&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Fe18050174&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-L&L-81"><a href="#cite_ref-L&L_81-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandauLifschitz1977" class="citation book cs1"><a href="/wiki/Lev_Landau" title="Lev Landau">Landau, Lev D.</a>; <a href="/wiki/Evgeny_Lifshitz" title="Evgeny Lifshitz">Lifschitz, Evgeny M.</a> (1977). <a rel="nofollow" class="external text" href="https://archive.org/details/QuantumMechanics_104">Quantum Mechanics: Non-Relativistic Theory</a>. Vol. 3 (3rd ed.). <a href="/wiki/Pergamon_Press" title="Pergamon Press">Pergamon Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-020940-1" title="Special:BookSources/978-0-08-020940-1"><bdi>978-0-08-020940-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/2284121">2284121</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Mechanics%3A+Non-Relativistic+Theory&rft.edition=3rd&rft.pub=Pergamon+Press&rft.date=1977&rft_id=info%3Aoclcnum%2F2284121&rft.isbn=978-0-08-020940-1&rft.aulast=Landau&rft.aufirst=Lev+D.&rft.au=Lifschitz%2C+Evgeny+M.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FQuantumMechanics_104&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-82"><a href="#cite_ref-82">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBuschGrabowskiLahti1995" class="citation journal cs1">Busch, P.; Grabowski, M.; Lahti, P. 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"Strahlungs-emission und -absorption nach der Quantentheorie". <a href="/wiki/Verhandlungen_der_Deutschen_Physikalischen_Gesellschaft" class="mw-redirect" title="Verhandlungen der Deutschen Physikalischen Gesellschaft">Verhandlungen der Deutschen Physikalischen Gesellschaft</a> (in German). 18: 318–323. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1916DPhyG..18..318E">1916DPhyG..18..318E</a>. <q>p. 322: Die Konstanten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{m}^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{m}^{n}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8b2053eb5886463a57ecb067311875bf37ecd56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.418ex; height:2.509ex;" alt="{\displaystyle A_{m}^{n}}"></noscript><span class="lazy-image-placeholder" style="width: 3.418ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8b2053eb5886463a57ecb067311875bf37ecd56" data-alt="{\displaystyle A_{m}^{n}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{m}^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{m}^{n}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7683a70991a12e36b89eb071a5e98bf2b1e2e7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.439ex; height:2.509ex;" alt="{\displaystyle B_{m}^{n}}"></noscript><span class="lazy-image-placeholder" style="width: 3.439ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7683a70991a12e36b89eb071a5e98bf2b1e2e7e" data-alt="{\displaystyle B_{m}^{n}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  würden sich direkt berechnen lassen, wenn wir im Besitz einer im Sinne der Quantenhypothese modifizierten Elektrodynamik und Mechanik wären."</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Verhandlungen+der+Deutschen+Physikalischen+Gesellschaft&rft.atitle=Strahlungs-emission+und+-absorption+nach+der+Quantentheorie&rft.volume=18&rft.pages=318-323&rft.date=1916&rft_id=info%3Abibcode%2F1916DPhyG..18..318E&rft.aulast=Einstein&rft.aufirst=Albert&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Dirac1926-93"><a href="#cite_ref-Dirac1926_93-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDirac1926" class="citation journal cs1"><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac, Paul A. 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Proceedings of the Royal Society A. 112 (762): 661–677. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926RSPSA.112..661D">1926RSPSA.112..661D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1926.0133">10.1098/rspa.1926.0133</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+A&rft.atitle=On+the+Theory+of+Quantum+Mechanics&rft.volume=112&rft.issue=762&rft.pages=661-677&rft.date=1926&rft_id=info%3Adoi%2F10.1098%2Frspa.1926.0133&rft_id=info%3Abibcode%2F1926RSPSA.112..661D&rft.aulast=Dirac&rft.aufirst=Paul+A.+M.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frspa.1926.0133&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Dirac1927a-94">^ <a href="#cite_ref-Dirac1927a_94-0">a</a> <a href="#cite_ref-Dirac1927a_94-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDirac1927" class="citation journal cs1"><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac, Paul A. 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M.</a> (1927b). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1927.0071">"The Quantum Theory of Dispersion"</a>. Proceedings of the Royal Society A. 114 (769): 710–728. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1927RSPSA.114..710D">1927RSPSA.114..710D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1927.0071">10.1098/rspa.1927.0071</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+A&rft.atitle=The+Quantum+Theory+of+Dispersion&rft.volume=114&rft.issue=769&rft.pages=710-728&rft.date=1927&rft_id=info%3Adoi%2F10.1098%2Frspa.1927.0071&rft_id=info%3Abibcode%2F1927RSPSA.114..710D&rft.aulast=Dirac&rft.aufirst=Paul+A.+M.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frspa.1927.0071&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Heisenberg1929-96"><a href="#cite_ref-Heisenberg1929_96-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeisenbergPauli1929" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg, Werner</a>; <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli, Wolfgang</a> (1929). "Zur Quantentheorie der Wellenfelder". <a href="/wiki/European_Physical_Journal" title="European Physical Journal">Zeitschrift für Physik</a> (in German). 56 (1–2): 1. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1929ZPhy...56....1H">1929ZPhy...56....1H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01340129">10.1007/BF01340129</a>. <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:121928597">121928597</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Zur+Quantentheorie+der+Wellenfelder&rft.volume=56&rft.issue=1%E2%80%932&rft.pages=1&rft.date=1929&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121928597%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01340129&rft_id=info%3Abibcode%2F1929ZPhy...56....1H&rft.aulast=Heisenberg&rft.aufirst=Werner&rft.au=Pauli%2C+Wolfgang&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Heisenberg1930-97"><a href="#cite_ref-Heisenberg1930_97-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeisenbergPauli1930" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg, Werner</a>; <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli, Wolfgang</a> (1930). "Zur Quantentheorie der Wellenfelder". <a href="/wiki/European_Physical_Journal" title="European Physical Journal">Zeitschrift für Physik</a> (in German). 59 (3–4): 139. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1930ZPhy...59..168H">1930ZPhy...59..168H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01341423">10.1007/BF01341423</a>. <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:186219228">186219228</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Zur+Quantentheorie+der+Wellenfelder&rft.volume=59&rft.issue=3%E2%80%934&rft.pages=139&rft.date=1930&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A186219228%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01341423&rft_id=info%3Abibcode%2F1930ZPhy...59..168H&rft.aulast=Heisenberg&rft.aufirst=Werner&rft.au=Pauli%2C+Wolfgang&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Fermi1932-98"><a href="#cite_ref-Fermi1932_98-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFermi1932" class="citation journal cs1"><a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi, Enrico</a> (1932). "Quantum Theory of Radiation". <a href="/wiki/Reviews_of_Modern_Physics" title="Reviews of Modern Physics">Reviews of Modern Physics</a>. 4 (1): 87. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1932RvMP....4...87F">1932RvMP....4...87F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.4.87">10.1103/RevModPhys.4.87</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.atitle=Quantum+Theory+of+Radiation&rft.volume=4&rft.issue=1&rft.pages=87&rft.date=1932&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.4.87&rft_id=info%3Abibcode%2F1932RvMP....4...87F&rft.aulast=Fermi&rft.aufirst=Enrico&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Born1926a-99"><a href="#cite_ref-Born1926a_99-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBorn1926" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Max_Born" title="Max Born">Born, Max</a> (1926). "Zur Quantenmechanik der Stossvorgänge". <a href="/wiki/European_Physical_Journal" title="European Physical Journal">Zeitschrift für Physik</a> (in German). 37 (12): 863–867. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...37..863B">1926ZPhy...37..863B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01397477">10.1007/BF01397477</a>. <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:119896026">119896026</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Zur+Quantenmechanik+der+Stossvorg%C3%A4nge&rft.volume=37&rft.issue=12&rft.pages=863-867&rft.date=1926&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119896026%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01397477&rft_id=info%3Abibcode%2F1926ZPhy...37..863B&rft.aulast=Born&rft.aufirst=Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Born1926b-100"><a href="#cite_ref-Born1926b_100-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBorn1926" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Max_Born" title="Max Born">Born, Max</a> (1926). "Quantenmechanik der Stossvorgänge". <a href="/wiki/European_Physical_Journal" title="European Physical Journal">Zeitschrift für Physik</a> (in German). 38 (11–12): 803. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...38..803B">1926ZPhy...38..803B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01397184">10.1007/BF01397184</a>. <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:126244962">126244962</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Quantenmechanik+der+Stossvorg%C3%A4nge&rft.volume=38&rft.issue=11%E2%80%9312&rft.pages=803&rft.date=1926&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A126244962%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01397184&rft_id=info%3Abibcode%2F1926ZPhy...38..803B&rft.aulast=Born&rft.aufirst=Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-ghost_field-101"><a href="#cite_ref-ghost_field_101-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPais1986" class="citation book cs1"><a href="/wiki/Abraham_Pais" title="Abraham Pais">Pais, A.</a> (1986). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=mREnwpAqz-YC&pg=PA260">Inward Bound: Of Matter and Forces in the Physical World</a>. Oxford University Press. p. 260. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-851997-3" title="Special:BookSources/978-0-19-851997-3"><bdi>978-0-19-851997-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Inward+Bound%3A+Of+Matter+and+Forces+in+the+Physical+World&rft.pages=260&rft.pub=Oxford+University+Press&rft.date=1986&rft.isbn=978-0-19-851997-3&rft.aulast=Pais&rft.aufirst=A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DmREnwpAqz-YC%26pg%3DPA260&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> Specifically, Born claimed to have been inspired by Einstein's never-published attempts to develop a "ghost-field" theory, in which point-like photons are guided probabilistically by ghost fields that follow Maxwell's equations. </li> <li id="cite_note-Debye1910-102"><a href="#cite_ref-Debye1910_102-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDebye1910" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Peter_Debye" title="Peter Debye">Debye, Peter</a> (1910). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1424189">"Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung"</a>. <a href="/wiki/Annalen_der_Physik" title="Annalen der Physik">Annalen der Physik</a> (in German). 33 (16): 1427–1434. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1910AnP...338.1427D">1910AnP...338.1427D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19103381617">10.1002/andp.19103381617</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200314211718/https://zenodo.org/record/1424189">Archived</a> from the original on 2020-03-14. Retrieved 2019-08-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Der+Wahrscheinlichkeitsbegriff+in+der+Theorie+der+Strahlung&rft.volume=33&rft.issue=16&rft.pages=1427-1434&rft.date=1910&rft_id=info%3Adoi%2F10.1002%2Fandp.19103381617&rft_id=info%3Abibcode%2F1910AnP...338.1427D&rft.aulast=Debye&rft.aufirst=Peter&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1424189&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Born1925-103"><a href="#cite_ref-Born1925_103-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBornHeisenbergJordan1925" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Max_Born" title="Max Born">Born, Max</a>; <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg, Werner</a>; <a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Jordan, Pascual</a> (1925). "Quantenmechanik II". <a href="/wiki/European_Physical_Journal" title="European Physical Journal">Zeitschrift für Physik</a> (in German). 35 (8–9): 557–615. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1926ZPhy...35..557B">1926ZPhy...35..557B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01379806">10.1007/BF01379806</a>. <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:186237037">186237037</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Quantenmechanik+II&rft.volume=35&rft.issue=8%E2%80%939&rft.pages=557-615&rft.date=1925&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A186237037%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01379806&rft_id=info%3Abibcode%2F1926ZPhy...35..557B&rft.aulast=Born&rft.aufirst=Max&rft.au=Heisenberg%2C+Werner&rft.au=Jordan%2C+Pascual&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-104"><a href="#cite_ref-104">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJaeger2019" class="citation journal cs1">Jaeger, Gregg (2019). <a rel="nofollow" class="external text" href="http://philsci-archive.pitt.edu/15858/1/Jaeger%20Are%20Virtual%20Particles%20Less%20Real_%20entropy-21-00141-v3.pdf">"Are virtual particles less real?"</a> (PDF). Entropy. 21 (2): 141. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019Entrp..21..141J">2019Entrp..21..141J</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe21020141">10.3390/e21020141</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514619">7514619</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/33266857">33266857</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230611010352/http://philsci-archive.pitt.edu/15858/1/Jaeger%20Are%20Virtual%20Particles%20Less%20Real_%20entropy-21-00141-v3.pdf">Archived</a> (PDF) from the original on 2023-06-11. Retrieved 2021-05-19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Entropy&rft.atitle=Are+virtual+particles+less+real%3F&rft.volume=21&rft.issue=2&rft.pages=141&rft.date=2019&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7514619%23id-name%3DPMC&rft_id=info%3Apmid%2F33266857&rft_id=info%3Adoi%2F10.3390%2Fe21020141&rft_id=info%3Abibcode%2F2019Entrp..21..141J&rft.aulast=Jaeger&rft.aufirst=Gregg&rft_id=http%3A%2F%2Fphilsci-archive.pitt.edu%2F15858%2F1%2FJaeger%2520Are%2520Virtual%2520Particles%2520Less%2520Real_%2520entropy-21-00141-v3.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-105"><a href="#cite_ref-105">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZee2003" class="citation book cs1"><a href="/wiki/Anthony_Zee" title="Anthony Zee">Zee, Anthony</a> (2003). <a href="/wiki/Quantum_Field_Theory_in_a_Nutshell" title="Quantum Field Theory in a Nutshell">Quantum Field Theory in a Nutshell</a>. Princeton, New Jersey: <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-01019-6" title="Special:BookSources/0-691-01019-6"><bdi>0-691-01019-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/50479292">50479292</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Field+Theory+in+a+Nutshell&rft.place=Princeton%2C+New+Jersey&rft.pub=Princeton+University+Press&rft.date=2003&rft_id=info%3Aoclcnum%2F50479292&rft.isbn=0-691-01019-6&rft.aulast=Zee&rft.aufirst=Anthony&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-106"><a href="#cite_ref-106">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFItzyksonZuber1980" class="citation book cs1">Itzykson, C.; Zuber, J.-B. (1980). <a rel="nofollow" class="external text" href="https://archive.org/details/quantumfieldtheo0000itzy">Quantum Field Theory</a>. McGraw-Hill. Photon–photon-scattering section 7–3–1, renormalization chapter 8–2. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-032071-0" title="Special:BookSources/978-0-07-032071-0"><bdi>978-0-07-032071-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Field+Theory&rft.pages=Photon-photon-scattering+section+7-3-1%2C+renormalization+chapter+8-2&rft.pub=McGraw-Hill&rft.date=1980&rft.isbn=978-0-07-032071-0&rft.aulast=Itzykson&rft.aufirst=C.&rft.au=Zuber%2C+J.-B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fquantumfieldtheo0000itzy&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-107"><a href="#cite_ref-107">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeiglein2008" class="citation journal cs1">Weiglein, G. (2008). "Electroweak Physics at the ILC". <a href="/wiki/Journal_of_Physics:_Conference_Series" title="Journal of Physics: Conference Series">Journal of Physics: Conference Series</a>. 110 (4): 042033. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/0711.3003">0711.3003</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008JPhCS.110d2033W">2008JPhCS.110d2033W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1742-6596%2F110%2F4%2F042033">10.1088/1742-6596/110/4/042033</a>. <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:118517359">118517359</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physics%3A+Conference+Series&rft.atitle=Electroweak+Physics+at+the+ILC&rft.volume=110&rft.issue=4&rft.pages=042033&rft.date=2008&rft_id=info%3Aarxiv%2F0711.3003&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118517359%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F1742-6596%2F110%2F4%2F042033&rft_id=info%3Abibcode%2F2008JPhCS.110d2033W&rft.aulast=Weiglein&rft.aufirst=G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Ryder-108">^ <a href="#cite_ref-Ryder_108-0">a</a> <a href="#cite_ref-Ryder_108-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRyder1996" class="citation book cs1">Ryder, L. H. (1996). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nnuW_kVJ500C">Quantum field theory</a> (2nd ed.). England: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-47814-4" title="Special:BookSources/978-0-521-47814-4"><bdi>978-0-521-47814-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+field+theory&rft.place=England&rft.edition=2nd&rft.pub=Cambridge+University+Press&rft.date=1996&rft.isbn=978-0-521-47814-4&rft.aulast=Ryder&rft.aufirst=L.+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnnuW_kVJ500C&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-Glashow-109"><a href="#cite_ref-Glashow_109-0">^</a> <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1979/glashow-lecture.html">Sheldon Glashow Nobel lecture</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080418033045/http://nobelprize.org/nobel_prizes/physics/laureates/1979/glashow-lecture.html">Archived</a> 2008-04-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, delivered 8 December 1979. </li> <li id="cite_note-Salam-110"><a href="#cite_ref-Salam_110-0">^</a> <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1979/salam-lecture.html">Abdus Salam Nobel lecture</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080418033106/http://nobelprize.org/nobel_prizes/physics/laureates/1979/salam-lecture.html">Archived</a> 2008-04-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, delivered 8 December 1979. </li> <li id="cite_note-Weinberg-111"><a href="#cite_ref-Weinberg_111-0">^</a> <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/1979/weinberg-lecture.html">Steven Weinberg Nobel lecture</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080418033111/http://nobelprize.org/nobel_prizes/physics/laureates/1979/weinberg-lecture.html">Archived</a> 2008-04-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, delivered 8 December 1979. </li> <li id="cite_note-112"><a href="#cite_ref-112">^</a> E.g., chapter 14 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHughes1985" class="citation book cs1">Hughes, I.S. 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Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-26092-3" title="Special:BookSources/978-0-521-26092-3"><bdi>978-0-521-26092-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementary+particles&rft.edition=2nd&rft.pub=Cambridge+University+Press&rft.date=1985&rft.isbn=978-0-521-26092-3&rft.aulast=Hughes&rft.aufirst=I.S.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felementarypartic00hugh&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-113"><a href="#cite_ref-113">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBauerSpitalYenniePipkin1978" class="citation journal cs1">Bauer, T.H.; Spital, R.D.; Yennie, D. R.; Pipkin, F.M. (1978). 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Annals of Physics. 11 (1): 1–48. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960AnPhy..11....1S">1960AnPhy..11....1S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0003-4916%2860%2990126-3">10.1016/0003-4916(60)90126-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Physics&rft.atitle=Theory+of+strong+interactions&rft.volume=11&rft.issue=1&rft.pages=1-48&rft.date=1960&rft_id=info%3Adoi%2F10.1016%2F0003-4916%2860%2990126-3&rft_id=info%3Abibcode%2F1960AnPhy..11....1S&rft.aulast=Sakurai&rft.aufirst=J.J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-115"><a href="#cite_ref-115">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalshZerwas1973" class="citation journal cs1">Walsh, T.F.; Zerwas, P. (1973). "Two-photon processes in the parton model". <a href="/wiki/Physics_Letters_B" class="mw-redirect" title="Physics Letters B">Physics Letters B</a>. 44 (2): 195. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1973PhLB...44..195W">1973PhLB...44..195W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-2693%2873%2990520-0">10.1016/0370-2693(73)90520-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Two-photon+processes+in+the+parton+model&rft.volume=44&rft.issue=2&rft.pages=195&rft.date=1973&rft_id=info%3Adoi%2F10.1016%2F0370-2693%2873%2990520-0&rft_id=info%3Abibcode%2F1973PhLB...44..195W&rft.aulast=Walsh&rft.aufirst=T.F.&rft.au=Zerwas%2C+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-116"><a href="#cite_ref-116">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWitten1977" class="citation journal cs1">Witten, E. (1977). "Anomalous cross section for photon–photon scattering in gauge theories". <a href="/wiki/Nuclear_Physics_B" class="mw-redirect" title="Nuclear Physics B">Nuclear Physics B</a>. 120 (2): 189–202. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1977NuPhB.120..189W">1977NuPhB.120..189W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0550-3213%2877%2990038-4">10.1016/0550-3213(77)90038-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nuclear+Physics+B&rft.atitle=Anomalous+cross+section+for+photon%E2%80%93photon+scattering+in+gauge+theories&rft.volume=120&rft.issue=2&rft.pages=189-202&rft.date=1977&rft_id=info%3Adoi%2F10.1016%2F0550-3213%2877%2990038-4&rft_id=info%3Abibcode%2F1977NuPhB.120..189W&rft.aulast=Witten&rft.aufirst=E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-117"><a href="#cite_ref-117">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNisius2000" class="citation journal cs1">Nisius, R. (2000). "The photon structure from deep inelastic electron–photon scattering". <a href="/wiki/Physics_Reports" title="Physics Reports">Physics Reports</a>. 332 (4–6): 165–317. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-ex/9912049">hep-ex/9912049</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000PhR...332..165N">2000PhR...332..165N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0370-1573%2899%2900115-5">10.1016/S0370-1573(99)00115-5</a>. <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:119437227">119437227</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Reports&rft.atitle=The+photon+structure+from+deep+inelastic+electron%E2%80%93photon+scattering&rft.volume=332&rft.issue=4%E2%80%936&rft.pages=165-317&rft.date=2000&rft_id=info%3Aarxiv%2Fhep-ex%2F9912049&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119437227%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2FS0370-1573%2899%2900115-5&rft_id=info%3Abibcode%2F2000PhR...332..165N&rft.aulast=Nisius&rft.aufirst=R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-118"><a href="#cite_ref-118">^</a> E.g., section 10.1 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunlap2004" class="citation book cs1">Dunlap, R. A. (2004). An Introduction to the Physics of Nuclei and Particles. <a href="/wiki/Cengage_Learning#Brands/imprints" class="mw-redirect" title="Cengage Learning">Brooks/Cole</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-534-39294-9" title="Special:BookSources/978-0-534-39294-9"><bdi>978-0-534-39294-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+the+Physics+of+Nuclei+and+Particles&rft.pub=Brooks%2FCole&rft.date=2004&rft.isbn=978-0-534-39294-9&rft.aulast=Dunlap&rft.aufirst=R.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-119"><a href="#cite_ref-119">^</a> Radiative correction to electron mass section 7–1–2, anomalous magnetic moments section 7–2–1, Lamb shift section 7–3–2 and hyperfine splitting in positronium section 10–3 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFItzyksonZuber1980" class="citation book cs1">Itzykson, C.; Zuber, J.-B. (1980). <a rel="nofollow" class="external text" href="https://archive.org/details/quantumfieldtheo0000itzy">Quantum Field Theory</a>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-032071-0" title="Special:BookSources/978-0-07-032071-0"><bdi>978-0-07-032071-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Field+Theory&rft.pub=McGraw-Hill&rft.date=1980&rft.isbn=978-0-07-032071-0&rft.aulast=Itzykson&rft.aufirst=C.&rft.au=Zuber%2C+J.-B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fquantumfieldtheo0000itzy&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-120"><a href="#cite_ref-120">^</a> E.g. sections 9.1 (gravitational contribution of photons) and 10.5 (influence of gravity on light) in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStephaniStewart1990" class="citation book cs1">Stephani, H.; Stewart, J. (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=V04_vLQvstcC&pg=PA86">General Relativity: An Introduction to the Theory of Gravitational Field</a>. Cambridge University Press. pp. 86 ff, 108 ff. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-37941-0" title="Special:BookSources/978-0-521-37941-0"><bdi>978-0-521-37941-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=General+Relativity%3A+An+Introduction+to+the+Theory+of+Gravitational+Field&rft.pages=86+ff%2C+108+ff&rft.pub=Cambridge+University+Press&rft.date=1990&rft.isbn=978-0-521-37941-0&rft.aulast=Stephani&rft.aufirst=H.&rft.au=Stewart%2C+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DV04_vLQvstcC%26pg%3DPA86&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-121"><a href="#cite_ref-121">^</a> Polaritons section 10.10.1, Raman and Brillouin scattering section 10.11.3 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPattersonBailey2007" class="citation book cs1">Patterson, J. D.; Bailey, B. C. (2007). Solid-State Physics: Introduction to the Theory. <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-24115-7" title="Special:BookSources/978-3-540-24115-7"><bdi>978-3-540-24115-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solid-State+Physics%3A+Introduction+to+the+Theory&rft.pub=Springer&rft.date=2007&rft.isbn=978-3-540-24115-7&rft.aulast=Patterson&rft.aufirst=J.+D.&rft.au=Bailey%2C+B.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-122"><a href="#cite_ref-122">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNaeye1998" class="citation book cs1">Naeye, R. (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=06_9B7S_q_YC&pg=PA16">Through the Eyes of Hubble: Birth, Life and Violent Death of Stars</a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7503-0484-9" title="Special:BookSources/978-0-7503-0484-9"><bdi>978-0-7503-0484-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/40180195">40180195</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240512231320/https://books.google.com/books?id=06_9B7S_q_YC&pg=PA16#v=onepage&q&f=false">Archived</a> from the original on 2024-05-12. Retrieved 2016-10-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Through+the+Eyes+of+Hubble%3A+Birth%2C+Life+and+Violent+Death+of+Stars&rft.pub=CRC+Press&rft.date=1998&rft_id=info%3Aoclcnum%2F40180195&rft.isbn=978-0-7503-0484-9&rft.aulast=Naeye&rft.aufirst=R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D06_9B7S_q_YC%26pg%3DPA16&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-123"><a href="#cite_ref-123">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKoupelisKuhn2007" class="citation book cs1">Koupelis, Theo; Kuhn, Karl F. (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6rTttN4ZdyoC&pg=PA102">In Quest of the Universe</a>. Jones and Bartlett Canada. p. 102. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780763743871" title="Special:BookSources/9780763743871"><bdi>9780763743871</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240512231402/https://books.google.com/books?id=6rTttN4ZdyoC&pg=PA102#v=onepage&q&f=false">Archived</a> from the original on 2024-05-12. Retrieved 2020-11-29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=In+Quest+of+the+Universe&rft.pages=102&rft.pub=Jones+and+Bartlett+Canada&rft.date=2007&rft.isbn=9780763743871&rft.aulast=Koupelis&rft.aufirst=Theo&rft.au=Kuhn%2C+Karl+F.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D6rTttN4ZdyoC%26pg%3DPA102&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-124"><a href="#cite_ref-124">^</a> E.g. section 11-5 C in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPineHendricksonCramHammond1980" class="citation book cs1">Pine, S. H.; Hendrickson, J. B.; Cram, D. J.; Hammond, G. S. (1980). Organic Chemistry (4th ed.). McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-050115-7" title="Special:BookSources/978-0-07-050115-7"><bdi>978-0-07-050115-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Organic+Chemistry&rft.edition=4th&rft.pub=McGraw-Hill&rft.date=1980&rft.isbn=978-0-07-050115-7&rft.aulast=Pine&rft.aufirst=S.+H.&rft.au=Hendrickson%2C+J.+B.&rft.au=Cram%2C+D.+J.&rft.au=Hammond%2C+G.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-125"><a href="#cite_ref-125">^</a> Nobel lecture given by G. Wald on December 12, 1967, online at nobelprize.org: <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/medicine/laureates/1967/wald-lecture.html">The Molecular Basis of Visual Excitation</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160423182216/http://www.nobelprize.org/nobel_prizes/medicine/laureates/1967/wald-lecture.html">Archived</a> 2016-04-23 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. </li> <li id="cite_note-126"><a href="#cite_ref-126">^</a> Photomultiplier section 1.1.10, CCDs section 1.1.8, Geiger counters section 1.3.2.1 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKitchin2008" class="citation book cs1">Kitchin, C. R. (2008). Astrophysical Techniques. Boca Raton, Florida: CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4200-8243-2" title="Special:BookSources/978-1-4200-8243-2"><bdi>978-1-4200-8243-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astrophysical+Techniques&rft.place=Boca+Raton%2C+Florida&rft.pub=CRC+Press&rft.date=2008&rft.isbn=978-1-4200-8243-2&rft.aulast=Kitchin&rft.aufirst=C.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-127"><a href="#cite_ref-127">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWaymouth1971" class="citation book cs1">Waymouth, John (1971). <a rel="nofollow" class="external text" href="https://archive.org/details/electricdischarg00waym">Electric Discharge Lamps</a>. Cambridge, Massachusetts: The M.I.T. Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-23048-3" title="Special:BookSources/978-0-262-23048-3"><bdi>978-0-262-23048-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electric+Discharge+Lamps&rft.place=Cambridge%2C+Massachusetts&rft.pub=The+M.I.T.+Press&rft.date=1971&rft.isbn=978-0-262-23048-3&rft.aulast=Waymouth&rft.aufirst=John&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectricdischarg00waym&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-128"><a href="#cite_ref-128">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDenk,_W.Svoboda,_K.1997" class="citation journal cs1"><a href="/wiki/Winfried_Denk" title="Winfried Denk">Denk, W.</a>; <a href="/wiki/Karel_Svoboda_(scientist)" title="Karel Svoboda (scientist)">Svoboda, K.</a> (1997). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0896-6273%2800%2981237-4">"Photon upmanship: Why multiphoton imaging is more than a gimmick"</a>. <a href="/wiki/Neuron_(journal)" title="Neuron (journal)">Neuron</a>. 18 (3): 351–357. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0896-6273%2800%2981237-4">10.1016/S0896-6273(00)81237-4</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9115730">9115730</a>. <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:2414593">2414593</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Neuron&rft.atitle=Photon+upmanship%3A+Why+multiphoton+imaging+is+more+than+a+gimmick&rft.volume=18&rft.issue=3&rft.pages=351-357&rft.date=1997&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A2414593%23id-name%3DS2CID&rft_id=info%3Apmid%2F9115730&rft_id=info%3Adoi%2F10.1016%2FS0896-6273%2800%2981237-4&rft.au=Denk%2C+W.&rft.au=Svoboda%2C+K.&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252FS0896-6273%252800%252981237-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-129"><a href="#cite_ref-129">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLakowicz2006" class="citation book cs1">Lakowicz, J. R. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-PSybuLNxcAC&pg=PA529">Principles of Fluorescence Spectroscopy</a>. Springer. pp. 529 ff. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-31278-1" title="Special:BookSources/978-0-387-31278-1"><bdi>978-0-387-31278-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Fluorescence+Spectroscopy&rft.pages=529+ff&rft.pub=Springer&rft.date=2006&rft.isbn=978-0-387-31278-1&rft.aulast=Lakowicz&rft.aufirst=J.+R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-PSybuLNxcAC%26pg%3DPA529&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-130"><a href="#cite_ref-130">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJenneweinAchleitnerWeihsWeinfurter2000" class="citation journal cs1">Jennewein, T.; Achleitner, U.; Weihs, G.; Weinfurter, H.; Zeilinger, A. (2000). "A fast and compact quantum random number generator". <a href="/wiki/Review_of_Scientific_Instruments" title="Review of Scientific Instruments">Review of Scientific Instruments</a>. 71 (4): 1675–1680. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/9912118">quant-ph/9912118</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000RScI...71.1675J">2000RScI...71.1675J</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1150518">10.1063/1.1150518</a>. <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:13118587">13118587</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Review+of+Scientific+Instruments&rft.atitle=A+fast+and+compact+quantum+random+number+generator&rft.volume=71&rft.issue=4&rft.pages=1675-1680&rft.date=2000&rft_id=info%3Aarxiv%2Fquant-ph%2F9912118&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A13118587%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1063%2F1.1150518&rft_id=info%3Abibcode%2F2000RScI...71.1675J&rft.aulast=Jennewein&rft.aufirst=T.&rft.au=Achleitner%2C+U.&rft.au=Weihs%2C+G.&rft.au=Weinfurter%2C+H.&rft.au=Zeilinger%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-131"><a href="#cite_ref-131">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStefanovGisinGuinnardGuinnard2000" class="citation journal cs1">Stefanov, A.; Gisin, N.; Guinnard, O.; Guinnard, L.; Zbiden, H. (2000). "Optical quantum random number generator". <a href="/wiki/Journal_of_Modern_Optics" title="Journal of Modern Optics">Journal of Modern Optics</a>. 47 (4): 595–598. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F095003400147908">10.1080/095003400147908</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Modern+Optics&rft.atitle=Optical+quantum+random+number+generator&rft.volume=47&rft.issue=4&rft.pages=595-598&rft.date=2000&rft_id=info%3Adoi%2F10.1080%2F095003400147908&rft.aulast=Stefanov&rft.aufirst=A.&rft.au=Gisin%2C+N.&rft.au=Guinnard%2C+O.&rft.au=Guinnard%2C+L.&rft.au=Zbiden%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-132"><a href="#cite_ref-132">^</a> Introductory-level material on the various sub-fields of quantum optics can be found in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFox2006" class="citation book cs1">Fox, M. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Q-4dIthPuL4C">Quantum Optics: An introduction</a>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-856673-1" title="Special:BookSources/978-0-19-856673-1"><bdi>978-0-19-856673-1</bdi></a> – via Google Books.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Optics%3A+An+introduction&rft.pub=Oxford+University+Press&rft.date=2006&rft.isbn=978-0-19-856673-1&rft.aulast=Fox&rft.aufirst=M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQ-4dIthPuL4C&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-NW-20180216-133"><a href="#cite_ref-NW-20180216_133-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHignett2018" class="citation news cs1">Hignett, Katherine (16 February 2018). <a rel="nofollow" class="external text" href="http://www.newsweek.com/photons-light-physics-808862">"Physics creates new form of light that could drive the quantum computing revolution"</a>. <a href="/wiki/Newsweek" title="Newsweek">Newsweek</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210425041617/https://www.newsweek.com/photons-light-physics-808862">Archived</a> from the original on 25 April 2021. Retrieved 17 February 2018.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Newsweek&rft.atitle=Physics+creates+new+form+of+light+that+could+drive+the+quantum+computing+revolution&rft.date=2018-02-16&rft.aulast=Hignett&rft.aufirst=Katherine&rft_id=http%3A%2F%2Fwww.newsweek.com%2Fphotons-light-physics-808862&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> <li id="cite_note-SCI-20180216-134"><a href="#cite_ref-SCI-20180216_134-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiang2018" class="citation journal cs1">Liang, Qi-Yu; et al. (16 February 2018). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6467536">"Observation of three-photon bound states in a quantum nonlinear medium"</a>. <a href="/wiki/Science_(journal)" title="Science (journal)">Science</a>. 359 (6377): 783–786. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1709.01478">1709.01478</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018Sci...359..783L">2018Sci...359..783L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.aao7293">10.1126/science.aao7293</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6467536">6467536</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/29449489">29449489</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Observation+of+three-photon+bound+states+in+a+quantum+nonlinear+medium&rft.volume=359&rft.issue=6377&rft.pages=783-786&rft.date=2018-02-16&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6467536%23id-name%3DPMC&rft_id=info%3Abibcode%2F2018Sci...359..783L&rft_id=info%3Aarxiv%2F1709.01478&rft_id=info%3Apmid%2F29449489&rft_id=info%3Adoi%2F10.1126%2Fscience.aao7293&rft.aulast=Liang&rft.aufirst=Qi-Yu&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6467536&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> </li> </ol></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(14)"><h2 id="Further_reading">Further reading</h2> <a role="button" href="/w/index.php?title=Photon&action=edit&section=22" title="Edit section: Further reading" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-14 collapsible-block" id="mf-section-14"> <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=""> <dl><dt>By date of publication</dt> <dd></dd></dl> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlonsoFinn1968" class="citation book cs1 cs1-prop-long-vol">Alonso, M.; Finn, E. J. (1968). Fundamental University Physics. Vol. III: Quantum and Statistical Physics. Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-00262-1" title="Special:BookSources/978-0-201-00262-1"><bdi>978-0-201-00262-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamental+University+Physics&rft.pub=Addison-Wesley&rft.date=1968&rft.isbn=978-0-201-00262-1&rft.aulast=Alonso&rft.aufirst=M.&rft.au=Finn%2C+E.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClauser1974" class="citation journal cs1">Clauser, J. F. (1974). <a rel="nofollow" class="external text" href="http://www.escholarship.org/uc/item/3wm0v847">"Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect"</a>. <a href="/wiki/Physical_Review_D" class="mw-redirect" title="Physical Review D">Physical Review D</a>. 9 (4): 853–860. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1974PhRvD...9..853C">1974PhRvD...9..853C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.9.853">10.1103/PhysRevD.9.853</a>. <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:118320287">118320287</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190124203753/https://escholarship.org/uc/item/3wm0v847">Archived</a> from the original on 2019-01-24. Retrieved 2019-01-03.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Experimental+distinction+between+the+quantum+and+classical+field-theoretic+predictions+for+the+photoelectric+effect&rft.volume=9&rft.issue=4&rft.pages=853-860&rft.date=1974&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118320287%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.9.853&rft_id=info%3Abibcode%2F1974PhRvD...9..853C&rft.aulast=Clauser&rft.aufirst=J.+F.&rft_id=http%3A%2F%2Fwww.escholarship.org%2Fuc%2Fitem%2F3wm0v847&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPais1982" class="citation book cs1"><a href="/wiki/Abraham_Pais" title="Abraham Pais">Pais, Abraham</a> (1982). <a href="/wiki/Subtle_is_the_Lord:_The_Science_and_the_Life_of_Albert_Einstein" class="mw-redirect" title="Subtle is the Lord: The Science and the Life of Albert Einstein">Subtle is the Lord: The Science and the Life of Albert Einstein</a>. Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Subtle+is+the+Lord%3A+The+Science+and+the+Life+of+Albert+Einstein&rft.pub=Oxford+University+Press&rft.date=1982&rft.aulast=Pais&rft.aufirst=Abraham&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynman1985" class="citation book cs1"><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman, Richard</a> (1985). <a href="/wiki/QED:_The_Strange_Theory_of_Light_and_Matter" title="QED: The Strange Theory of Light and Matter">QED: The Strange Theory of Light and Matter</a>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-12575-6" title="Special:BookSources/978-0-691-12575-6"><bdi>978-0-691-12575-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=QED%3A+The+Strange+Theory+of+Light+and+Matter&rft.pub=Princeton+University+Press&rft.date=1985&rft.isbn=978-0-691-12575-6&rft.aulast=Feynman&rft.aufirst=Richard&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrangierRogerAspect1986" class="citation journal cs1">Grangier, P.; Roger, G.; Aspect, A. (1986). "Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences". <a href="/wiki/EPL_(journal)" title="EPL (journal)">Europhysics Letters</a>. 1 (4): 173–179. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1986EL......1..173G">1986EL......1..173G</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.4356">10.1.1.178.4356</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1209%2F0295-5075%2F1%2F4%2F004">10.1209/0295-5075/1/4/004</a>. <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:250837011">250837011</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Europhysics+Letters&rft.atitle=Experimental+evidence+for+a+photon+anticorrelation+effect+on+a+beam+splitter%3A+A+new+light+on+single-photon+interferences&rft.volume=1&rft.issue=4&rft.pages=173-179&rft.date=1986&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.178.4356%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250837011%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1209%2F0295-5075%2F1%2F4%2F004&rft_id=info%3Abibcode%2F1986EL......1..173G&rft.aulast=Grangier&rft.aufirst=P.&rft.au=Roger%2C+G.&rft.au=Aspect%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLamb1995" class="citation journal cs1"><a href="/wiki/Willis_Lamb" title="Willis Lamb">Lamb, Willis E.</a> (1995). "Anti-photon". <a href="/wiki/Applied_Physics_B" title="Applied Physics B">Applied Physics B</a>. 60 (2–3): 77–84. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995ApPhB..60...77L">1995ApPhB..60...77L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01135846">10.1007/BF01135846</a>. <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:263785760">263785760</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Physics+B&rft.atitle=Anti-photon&rft.volume=60&rft.issue=2%E2%80%933&rft.pages=77-84&rft.date=1995&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A263785760%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01135846&rft_id=info%3Abibcode%2F1995ApPhB..60...77L&rft.aulast=Lamb&rft.aufirst=Willis+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation magazine cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220605130152/http://www.sheffield.ac.uk/polopoly_fs/1.14183!/file/photon.pdf">"Special supplemental issue"</a> (PDF). Optics and Photonics News. Vol. 14. October 2003. Archived from <a rel="nofollow" class="external text" href="http://www.sheffield.ac.uk/polopoly_fs/1.14183!/file/photon.pdf">the original</a> (PDF) on June 5, 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+and+Photonics+News&rft.atitle=Special+supplemental+issue&rft.volume=14&rft.date=2003-10&rft_id=http%3A%2F%2Fwww.sheffield.ac.uk%2Fpolopoly_fs%2F1.14183%21%2Ffile%2Fphoton.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoychoudhuriRajarshi2003" class="citation magazine cs1">Roychoudhuri, C.; Rajarshi, R. (2003). "The nature of light: What is a photon?". <a href="/wiki/Optics_and_Photonics_News" title="Optics and Photonics News">Optics and Photonics News</a>. Vol. 14. pp. S1 (Supplement).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+and+Photonics+News&rft.atitle=The+nature+of+light%3A+What+is+a+photon%3F&rft.volume=14&rft.pages=S1+%28Supplement%29&rft.date=2003&rft.aulast=Roychoudhuri&rft.aufirst=C.&rft.au=Rajarshi%2C+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZajonc2003" class="citation magazine cs1">Zajonc, A. (2003). "Light reconsidered". <a href="/wiki/Optics_and_Photonics_News" title="Optics and Photonics News">Optics and Photonics News</a>. 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Archived from <a rel="nofollow" class="external text" href="http://nobelprize.org/nobel_prizes/physics/laureates/2005/glauber-lecture.pdf">the original</a> (PDF) on 2008-07-23. Retrieved 2009-06-29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Nobel+Prize&rft.atitle=One+Hundred+Years+of+Light+Quanta&rft.date=2005&rft.aulast=Glauber&rft.aufirst=R.&rft_id=http%3A%2F%2Fnobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F2005%2Fglauber-lecture.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHentschel2007" class="citation journal cs1">Hentschel, K. (2007). <a rel="nofollow" class="external text" href="https://eldorado.tu-dortmund.de/handle/2003/24257">"Light quanta: The maturing of a concept by the stepwise accretion of meaning"</a>. Physics and Philosophy. 1 (2): 1–20. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140529085134/https://eldorado.tu-dortmund.de/handle/2003/24257">Archived</a> from the original on 2014-05-29. Retrieved 2014-06-29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+and+Philosophy&rft.atitle=Light+quanta%3A+The+maturing+of+a+concept+by+the+stepwise+accretion+of+meaning&rft.volume=1&rft.issue=2&rft.pages=1-20&rft.date=2007&rft.aulast=Hentschel&rft.aufirst=K.&rft_id=https%3A%2F%2Feldorado.tu-dortmund.de%2Fhandle%2F2003%2F24257&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li></ul> <dl><dt>Education with single photons</dt> <dd></dd></dl> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThornNeelDonatoBergreen2004" class="citation journal cs1">Thorn, J. J.; Neel, M. S.; Donato, V. W.; Bergreen, G. S.; Davies, R. E.; Beck, M. (2004). <a rel="nofollow" class="external text" href="http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf">"Observing the quantum behavior of light in an undergraduate laboratory"</a> (PDF). <a href="/wiki/American_Journal_of_Physics" title="American Journal of Physics">American Journal of Physics</a>. 72 (9): 1210–1219. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004AmJPh..72.1210T">2004AmJPh..72.1210T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1737397">10.1119/1.1737397</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160201214040/http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf">Archived</a> (PDF) from the original on 2016-02-01. Retrieved 2009-06-29.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Observing+the+quantum+behavior+of+light+in+an+undergraduate+laboratory&rft.volume=72&rft.issue=9&rft.pages=1210-1219&rft.date=2004&rft_id=info%3Adoi%2F10.1119%2F1.1737397&rft_id=info%3Abibcode%2F2004AmJPh..72.1210T&rft.aulast=Thorn&rft.aufirst=J.+J.&rft.au=Neel%2C+M.+S.&rft.au=Donato%2C+V.+W.&rft.au=Bergreen%2C+G.+S.&rft.au=Davies%2C+R.+E.&rft.au=Beck%2C+M.&rft_id=http%3A%2F%2Fpeople.whitman.edu%2F~beckmk%2FQM%2Fgrangier%2FThorn_ajp.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhoton" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBronnerStrunzSilberhornMeyn2009" class="citation journal cs1">Bronner, P.; Strunz, Andreas; Silberhorn, Christine; Meyn, Jan-Peter (2009). <a rel="nofollow" class="external text" href="http://www.quantumlab.de/">"Interactive screen experiments with single photons"</a>. <a href="/wiki/European_Journal_of_Physics" title="European Journal of Physics">European Journal of Physics</a>. 30 (2): 345–353. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009EJPh...30..345B">2009EJPh...30..345B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0143-0807%2F30%2F2%2F014">10.1088/0143-0807/30/2/014</a>. <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:38626417">38626417</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190701002242/http://www.quantumlab.de/">Archived</a> from the original on 2019-07-01. 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href="https://en.wikipedia.org/w/index.php?title=Photon&oldid=1258813945">https://en.wikipedia.org/w/index.php?title=Photon&oldid=1258813945</a>"</div></div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"> <a class="last-modified-bar" href="/w/index.php?title=Photon&action=history"> <div class="post-content last-modified-bar__content"> Last edited on 21 November 2024, at 19:42 </div> </a> <div class="post-content footer-content"> <div id='mw-data-after-content'> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Languages</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Foton" title="Foton – Afrikaans" lang="af" hreflang="af" data-title="Foton" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D9%88%D8%AA%D9%88%D9%86" title="فوتون – Arabic" lang="ar" hreflang="ar" data-title="فوتون" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Fot%C3%B3n" title="Fotón – Aragonese" lang="an" hreflang="an" data-title="Fotón" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Fot%C3%B3n" title="Fotón – Asturian" lang="ast" hreflang="ast" data-title="Fotón" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Foton" title="Foton – Azerbaijani" lang="az" hreflang="az" data-title="Foton" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AB%E0%A7%8B%E0%A6%9F%E0%A6%A8" title="ফোটন – Bangla" lang="bn" hreflang="bn" data-title="ফোটন" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Kng-ch%C3%BA" title="Kng-chú – Minnan" lang="nan" hreflang="nan" data-title="Kng-chú" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D0%B0%D1%82%D0%BE%D0%BD" title="Фатон – Belarusian" lang="be" hreflang="be" data-title="Фатон" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A4%D0%B0%D1%82%D0%BE%D0%BD" title="Фатон – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Фатон" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Bulgarian" lang="bg" hreflang="bg" data-title="Фотон" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Photon" title="Photon – Bavarian" lang="bar" hreflang="bar" data-title="Photon" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target">Boarisch</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Foton" title="Foton – Bosnian" lang="bs" hreflang="bs" data-title="Foton" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Fot%C3%B3" title="Fotó – Catalan" lang="ca" hreflang="ca" data-title="Fotó" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Chuvash" lang="cv" hreflang="cv" data-title="Фотон" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Foton" title="Foton – Czech" lang="cs" hreflang="cs" data-title="Foton" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ffoton" title="Ffoton – Welsh" lang="cy" hreflang="cy" data-title="Ffoton" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Foton" title="Foton – Danish" lang="da" hreflang="da" data-title="Foton" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%81%D9%88%D8%B7%D9%88%D9%86" title="فوطون – Moroccan Arabic" lang="ary" hreflang="ary" data-title="فوطون" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target">الدارجة</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Photon" title="Photon – German" lang="de" hreflang="de" data-title="Photon" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Footon" title="Footon – Estonian" lang="et" hreflang="et" data-title="Footon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A6%CF%89%CF%84%CF%8C%CE%BD%CE%B9%CE%BF" title="Φωτόνιο – Greek" lang="el" hreflang="el" data-title="Φωτόνιο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Fot%C3%B3n" title="Fotón – Spanish" lang="es" hreflang="es" data-title="Fotón" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Fotono" title="Fotono – Esperanto" lang="eo" hreflang="eo" data-title="Fotono" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Fotoi" title="Fotoi – Basque" lang="eu" hreflang="eu" data-title="Fotoi" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D9%88%D8%AA%D9%88%D9%86" title="فوتون – Persian" lang="fa" hreflang="fa" data-title="فوتون" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Photon" title="Photon – French" lang="fr" hreflang="fr" data-title="Photon" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/F%C3%B3t%C3%B3n" title="Fótón – Irish" lang="ga" hreflang="ga" data-title="Fótón" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Fot%C3%B3n" title="Fotón – Galician" lang="gl" hreflang="gl" data-title="Fotón" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AB%E0%AB%8B%E0%AA%9F%E0%AB%89%E0%AA%A8" title="ફોટૉન – Gujarati" lang="gu" hreflang="gu" data-title="ફોટૉન" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target">ગુજરાતી</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B4%91%EC%9E%90" title="광자 – Korean" lang="ko" hreflang="ko" data-title="광자" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%B8%D5%BF%D5%B8%D5%B6" title="Ֆոտոն – Armenian" lang="hy" hreflang="hy" data-title="Ֆոտոն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AB%E0%A5%8B%E0%A4%9F%E0%A5%89%E0%A4%A8" title="फोटॉन – Hindi" lang="hi" hreflang="hi" data-title="फोटॉन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Foton" title="Foton – Croatian" lang="hr" hreflang="hr" data-title="Foton" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Fotono" title="Fotono – Ido" lang="io" hreflang="io" data-title="Fotono" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target">Ido</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Foton" title="Foton – Indonesian" lang="id" hreflang="id" data-title="Foton" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Photon" title="Photon – Interlingua" lang="ia" hreflang="ia" data-title="Photon" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ibane" title="Ibane – Zulu" lang="zu" hreflang="zu" data-title="Ibane" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target">IsiZulu</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Lj%C3%B3seind" title="Ljóseind – Icelandic" lang="is" hreflang="is" data-title="Ljóseind" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Fotone" title="Fotone – Italian" lang="it" hreflang="it" data-title="Fotone" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%95%D7%98%D7%95%D7%9F" title="פוטון – Hebrew" lang="he" hreflang="he" data-title="פוטון" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Foton" title="Foton – Javanese" lang="jv" hreflang="jv" data-title="Foton" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target">Jawa</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AB%E0%B3%8B%E0%B2%9F%E0%B2%BE%E0%B2%A8%E0%B3%8D" title="ಫೋಟಾನ್ – Kannada" lang="kn" hreflang="kn" data-title="ಫೋಟಾನ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A4%E1%83%9D%E1%83%A2%E1%83%9D%E1%83%9C%E1%83%98" title="ფოტონი – Georgian" lang="ka" hreflang="ka" data-title="ფოტონი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%D9%BE%DA%BE%D9%88%D9%B9%D8%A7%D9%86" title="پھوٹان – Kashmiri" lang="ks" hreflang="ks" data-title="پھوٹان" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="Kashmiri" class="interlanguage-link-target">कॉशुर / کٲشُر</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Kazakh" lang="kk" hreflang="kk" data-title="Фотон" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Fotoni" title="Fotoni – Swahili" lang="sw" hreflang="sw" data-title="Fotoni" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Foton" title="Foton – Haitian Creole" lang="ht" hreflang="ht" data-title="Foton" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Foton" title="Foton – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Foton" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target">Kriyòl gwiyannen</a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Foton" title="Foton – Kurdish" lang="ku" hreflang="ku" data-title="Foton" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target">Kurdî</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Kyrgyz" lang="ky" hreflang="ky" data-title="Фотон" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Photon" title="Photon – Latin" lang="la" hreflang="la" data-title="Photon" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Fotons" title="Fotons – Latvian" lang="lv" hreflang="lv" data-title="Fotons" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Fotonas" title="Fotonas – Lithuanian" lang="lt" hreflang="lt" data-title="Fotonas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Foton" title="Foton – Limburgish" lang="li" hreflang="li" data-title="Foton" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target">Limburgs</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Fut%C3%B9n" title="Futùn – Lombard" lang="lmo" hreflang="lmo" data-title="Futùn" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Foton" title="Foton – Hungarian" lang="hu" hreflang="hu" data-title="Foton" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Macedonian" lang="mk" hreflang="mk" data-title="Фотон" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Voankazavana" title="Voankazavana – Malagasy" lang="mg" hreflang="mg" data-title="Voankazavana" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target">Malagasy</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AB%E0%B5%8B%E0%B4%9F%E0%B5%8D%E0%B4%9F%E0%B5%8B%E0%B5%BA" title="ഫോട്ടോൺ – Malayalam" lang="ml" hreflang="ml" data-title="ഫോട്ടോൺ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AB%E0%A5%8B%E0%A4%9F%E0%A5%89%E0%A4%A8" title="फोटॉन – Marathi" lang="mr" hreflang="mr" data-title="फोटॉन" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Foton" title="Foton – Malay" lang="ms" hreflang="ms" data-title="Foton" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Mongolian" lang="mn" hreflang="mn" data-title="Фотон" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target">Монгол</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%96%E1%80%AD%E1%80%AF%E1%80%90%E1%80%BD%E1%80%94%E1%80%BA" title="ဖိုတွန် – Burmese" lang="my" hreflang="my" data-title="ဖိုတွန်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Foton" title="Foton – Dutch" lang="nl" hreflang="nl" data-title="Foton" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AB%E0%A5%8B%E0%A4%9F%E0%A5%8B%E0%A4%A8" title="फोटोन – Nepali" lang="ne" hreflang="ne" data-title="फोटोन" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target">नेपाली</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%85%89%E5%AD%90" title="光子 – Japanese" lang="ja" hreflang="ja" data-title="光子" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Foton" title="Foton – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Foton" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Foton" title="Foton – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Foton" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Foton" title="Foton – Occitan" lang="oc" hreflang="oc" data-title="Foton" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AB%E0%AD%8B%E0%AC%9F%E0%AC%A8%E0%AD%8D%E2%80%8C" title="ଫୋଟନ୍‌ – Odia" lang="or" hreflang="or" data-title="ଫୋଟନ୍‌" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target">ଓଡ଼ିଆ</a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Suudifa" title="Suudifa – Oromo" lang="om" hreflang="om" data-title="Suudifa" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target">Oromoo</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Foton" title="Foton – Uzbek" lang="uz" hreflang="uz" data-title="Foton" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AB%E0%A8%BC%E0%A9%8B%E0%A8%9F%E0%A9%8C%E0%A8%A8" title="ਫ਼ੋਟੌਨ – Punjabi" lang="pa" hreflang="pa" data-title="ਫ਼ੋਟੌਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%81%D9%88%D9%B9%D9%88%D9%86" title="فوٹون – Western Punjabi" lang="pnb" hreflang="pnb" data-title="فوٹون" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%81%D9%88%D9%BC%D9%88%D9%86" title="فوټون – Pashto" lang="ps" hreflang="ps" data-title="فوټون" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Fuotan" title="Fuotan – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Fuotan" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Photon" title="Photon – Low German" lang="nds" hreflang="nds" data-title="Photon" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target">Plattdüütsch</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Foton" title="Foton – Polish" lang="pl" hreflang="pl" data-title="Foton" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fot%C3%A3o" title="Fotão – Portuguese" lang="pt" hreflang="pt" data-title="Fotão" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Foton" title="Foton – Romanian" lang="ro" hreflang="ro" data-title="Foton" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Phutun" title="Phutun – Quechua" lang="qu" hreflang="qu" data-title="Phutun" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target">Runa Simi</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Rusyn" lang="rue" hreflang="rue" data-title="Фотон" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Russian" lang="ru" hreflang="ru" data-title="Фотон" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%95%E0%A4%BE%E0%A4%B6%E0%A4%BE%E0%A4%A3%E0%A5%81" title="प्रकाशाणु – Sanskrit" lang="sa" hreflang="sa" data-title="प्रकाशाणु" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskrit" class="interlanguage-link-target">संस्कृतम्</a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Photon" title="Photon – Saterland Frisian" lang="stq" hreflang="stq" data-title="Photon" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target">Seeltersk</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Fotoni" title="Fotoni – Albanian" lang="sq" hreflang="sq" data-title="Fotoni" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Fotoni" title="Fotoni – Sicilian" lang="scn" hreflang="scn" data-title="Fotoni" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Photon" title="Photon – Simple English" lang="en-simple" hreflang="en-simple" data-title="Photon" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%81%D9%88%D9%BD%D8%A7%D9%86" title="فوٽان – Sindhi" lang="sd" hreflang="sd" data-title="فوٽان" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target">سنڌي</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Fot%C3%B3n" title="Fotón – Slovak" lang="sk" hreflang="sk" data-title="Fotón" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Foton" title="Foton – Slovenian" lang="sl" hreflang="sl" data-title="Foton" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%81%DB%86%D8%AA%DB%86%D9%86" title="فۆتۆن – Central Kurdish" lang="ckb" hreflang="ckb" data-title="فۆتۆن" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-sr badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Serbian" lang="sr" hreflang="sr" data-title="Фотон" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Foton" title="Foton – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Foton" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Foton" title="Foton – Sundanese" lang="su" hreflang="su" data-title="Foton" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target">Sunda</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Fotoni" title="Fotoni – Finnish" lang="fi" hreflang="fi" data-title="Fotoni" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Foton" title="Foton – Swedish" lang="sv" hreflang="sv" data-title="Foton" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Photon" title="Photon – Tagalog" lang="tl" hreflang="tl" data-title="Photon" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%92%E0%AE%B3%E0%AE%BF%E0%AE%AF%E0%AE%A3%E0%AF%81" title="ஒளியணு – Tamil" lang="ta" hreflang="ta" data-title="ஒளியணு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Tatar" lang="tt" hreflang="tt" data-title="Фотон" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AB%E0%B1%8B%E0%B0%9F%E0%B0%BE%E0%B0%A8%E0%B1%8D" title="ఫోటాన్ – Telugu" lang="te" hreflang="te" data-title="ఫోటాన్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%82%E0%B8%9F%E0%B8%95%E0%B8%AD%E0%B8%99" title="โฟตอน – Thai" lang="th" hreflang="th" data-title="โฟตอน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Foton" title="Foton – Turkish" lang="tr" hreflang="tr" data-title="Foton" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D0%BE%D1%82%D0%BE%D0%BD" title="Фотон – Ukrainian" lang="uk" hreflang="uk" data-title="Фотон" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%81%D9%88%D9%B9%D9%88%D9%86" title="فوٹون – Urdu" lang="ur" hreflang="ur" data-title="فوٹون" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-vi badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://vi.wikipedia.org/wiki/Photon" title="Photon – Vietnamese" lang="vi" hreflang="vi" data-title="Photon" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Foodon" title="Foodon – Võro" lang="vro" hreflang="vro" data-title="Foodon" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target">Võro</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Photon" title="Photon – Waray" lang="war" hreflang="war" data-title="Photon" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%85%89%E5%AD%90" title="光子 – Wu" lang="wuu" hreflang="wuu" data-title="光子" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%90%D7%98%D7%90%D7%9F" title="פאטאן – Yiddish" lang="yi" hreflang="yi" data-title="פאטאן" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%85%89%E5%AD%90" title="光子 – Cantonese" lang="yue" hreflang="yue" data-title="光子" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://zh.wikipedia.org/wiki/%E5%85%89%E5%AD%90" title="光子 – Chinese" lang="zh" hreflang="zh" data-title="光子" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li></ul> </section> </div> <div class="minerva-footer-logo"><img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 1.125em;"/> </div> <ul id="footer-info" class="footer-info hlist hlist-separated"> <li id="footer-info-lastmod"> This page was last edited on 21 November 2024, at 19:42 (UTC).</li> <li id="footer-info-copyright">Content is available under <a class="external" rel="nofollow" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">CC BY-SA 4.0</a> unless otherwise noted.</li> </ul> <ul id="footer-places" class="footer-places hlist hlist-separated"> <li id="footer-places-privacy"><a 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<script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-f69cdc8f6-qfk9f","wgBackendResponseTime":269,"wgPageParseReport":{"limitreport":{"cputime":"2.228","walltime":"2.635","ppvisitednodes":{"value":13611,"limit":1000000},"postexpandincludesize":{"value":422315,"limit":2097152},"templateargumentsize":{"value":13091,"limit":2097152},"expansiondepth":{"value":17,"limit":100},"expensivefunctioncount":{"value":26,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":552000,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 2106.737 1 -total"," 39.28% 827.518 3 Template:Reflist"," 19.97% 420.651 73 Template:Cite_journal"," 16.56% 348.873 45 Template:Cite_book"," 6.94% 146.265 1 Template:Etymology"," 6.83% 143.905 11 Template:Navbox"," 6.55% 137.900 6 Template:Efn"," 5.55% 116.982 1 Template:Particles"," 5.37% 113.102 1 Template:Harvp"," 5.28% 111.235 2 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1,\n [\"CITEREFLiang2018\"] = 1,\n [\"CITEREFLiddle2015\"] = 1,\n [\"CITEREFLoudon2003\"] = 1,\n [\"CITEREFMackSchleich2003\"] = 1,\n [\"CITEREFMandel1976\"] = 1,\n [\"CITEREFMaxwell1865\"] = 1,\n [\"CITEREFMermin,_David1984\"] = 1,\n [\"CITEREFMillikan1924\"] = 1,\n [\"CITEREFMuthukrishnanScullyZubairy2003\"] = 1,\n [\"CITEREFNaeye1998\"] = 1,\n [\"CITEREFNewton1952\"] = 1,\n [\"CITEREFNewtonWigner1949\"] = 1,\n [\"CITEREFNisius2000\"] = 1,\n [\"CITEREFPais1982\"] = 2,\n [\"CITEREFPais1986\"] = 1,\n [\"CITEREFPattersonBailey2007\"] = 1,\n [\"CITEREFPineHendricksonCramHammond1980\"] = 1,\n [\"CITEREFPlanck1901\"] = 1,\n [\"CITEREFPlanck1920\"] = 1,\n [\"CITEREFPlanck1922\"] = 1,\n [\"CITEREFPlimptonLawton1936\"] = 1,\n [\"CITEREFRamanBhagavantam1931\"] = 1,\n [\"CITEREFRoychoudhuriRajarshi2003\"] = 1,\n [\"CITEREFRutherfordAndrade1914\"] = 1,\n [\"CITEREFRyder1996\"] = 1,\n [\"CITEREFSakurai1960\"] = 1,\n [\"CITEREFSalehTeich2007\"] = 1,\n [\"CITEREFSchwartz2014\"] = 1,\n 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[\"Cite news\"] = 1,\n [\"Cite web\"] = 11,\n [\"Commons category-inline\"] = 1,\n [\"Convert\"] = 1,\n [\"Div col\"] = 1,\n [\"Efn\"] = 6,\n [\"Etymology\"] = 1,\n [\"Full citation needed\"] = 1,\n [\"Google books\"] = 12,\n [\"Grc-transl\"] = 1,\n [\"Harvnb\"] = 3,\n [\"Harvp\"] = 1,\n [\"Infobox particle\"] = 1,\n [\"Lang\"] = 1,\n [\"Main\"] = 8,\n [\"Math\"] = 7,\n [\"Mvar\"] = 14,\n [\"Nobr\"] = 3,\n [\"Notelist\"] = 1,\n [\"Nowrap\"] = 6,\n [\"Particles\"] = 1,\n [\"Portal\"] = 1,\n [\"QED\"] = 1,\n [\"Refbegin\"] = 1,\n [\"Refend\"] = 1,\n [\"Reflist\"] = 2,\n [\"Rp\"] = 6,\n [\"Section link\"] = 2,\n [\"See also\"] = 3,\n [\"Sfrac\"] = 4,\n [\"Short description\"] = 1,\n [\"Sub\"] = 1,\n [\"Sup\"] = 2,\n [\"Val\"] = 7,\n [\"Webarchive\"] = 6,\n [\"Wikiquote-inline\"] = 1,\n [\"Wikt-lang\"] = 2,\n [\"Wiktionary-inline\"] = 1,\n}\narticle_whitelist = table#1 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