Editing Photon (section)

== Bose–Einstein model of a photon gas ==
{{Main|Bose gas|Bose–Einstein statistics|Spin-statistics theorem|Gas in a box|Photon gas}}

In 1924, [[Satyendra Nath Bose]] derived [[Planck's law of black-body radiation]] without using any electromagnetism, but rather by using a modification of coarse-grained counting of [[phase space]].<ref name="Bose1924">{{cite journal |last=Bose |first=Satyendra Nath |author-link=Satyendra Nath Bose |year=1924 |title=Plancks Gesetz und Lichtquantenhypothese |journal=[[European Physical Journal|Zeitschrift für Physik]] |language=de |volume=26 |issue=1 |pages=178–181 |bibcode=1924ZPhy...26..178B |doi=10.1007/BF01327326 |s2cid=186235974}}</ref> Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction",<ref name="Einstein1924">{{cite journal |last=Einstein |first=Albert |author-link=Albert Einstein |year=1924 |title=Quantentheorie des einatomigen idealen Gases |journal=Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalisch-mathematische Klasse |language=de |volume=1924 |pages=261–267}}</ref><ref name="Einstein1925">{{cite book |last=Einstein |first=Albert |title=Quantentheorie des einatomigen idealen Gases, Zweite Abhandlung |journal=Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalisch-mathematische Klasse |year=1925 |isbn=978-3-527-60895-9 |volume=1925 |pages=3–14 |language=de |doi=10.1002/3527608958.ch28 |author-link=Albert Einstein}}</ref> now understood as the requirement for a [[identical particles|symmetric quantum mechanical state]]. This work led to the concept of [[coherent state]]s 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 [[quantum state]] at low enough temperatures; this [[Bose–Einstein condensate|Bose–Einstein condensation]] was observed experimentally in 1995.<ref>{{cite journal |last1=Anderson |first1=M. H. |last2=Ensher |first2=J. R. |last3=Matthews |first3=M. R. |last4=Wieman |first4=Carl E. |author4-link=Carl Wieman |last5=Cornell |first5=Eric Allin |author5-link=Eric Allin Cornell |year=1995 |title=Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor |journal=[[Science (journal)|Science]] |volume=269 |issue=5221 |pages=198–201 |bibcode=1995Sci...269..198A |doi=10.1126/science.269.5221.198 |jstor=2888436 |pmid=17789847 |s2cid=540834 |doi-access=}}</ref> It was later used by [[Lene Hau]] to slow, and then completely stop, light in 1999<ref>{{Cite web |last=Cuneo |first=Michael |date=1999-02-18 |title=Physicists Slow Speed of Light |url=https://news.harvard.edu/gazette/story/1999/02/physicists-slow-speed-of-light/ |access-date=2023-12-07 |website=Harvard Gazette |language=en-US |archive-date=2000-10-15 |archive-url=https://web.archive.org/web/20001015232230/http://www.news.harvard.edu/gazette/1999/02.18/light.html |url-status=live }}</ref> and 2001.<ref>{{Cite web |title=Light Changed to Matter, Then Stopped and Moved |url=https://www.photonics.com/Articles/Light_Changed_to_Matter_Then_Stopped_and_Moved/a28520 |access-date=2023-12-07 |website=www.photonics.com |archive-date=2019-04-02 |archive-url=https://web.archive.org/web/20190402130851/https://www.photonics.com/Articles/Light_Changed_to_Matter_Then_Stopped_and_Moved/a28520 |url-status=live }}</ref>

The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to [[fermion]]s with half-integer spin). By the [[spin-statistics theorem]], all bosons obey Bose–Einstein statistics (whereas all fermions obey [[Fermi–Dirac statistics]]).<ref>{{Cite book |last1=Streater |first1=R. F. |title=PCT, Spin and Statistics, and All That |last2=Wightman |first2=A. S. |publisher=Addison-Wesley |year=1989 |isbn=978-0-201-09410-7 |language=en}}</ref>