Editing Photon (section)

== Physical properties ==
The photon has no [[electric charge]],<ref>{{cite book |last1=Frisch |first1=David H. |title=Elementary Particles |last2=Thorndike |first2=Alan M. |publisher=[[David Van Nostrand]] |year=1964 |location=Princeton, New Jersey |page=22 |language=en-us |author1-link=David H. Frisch}}</ref><ref name="chargeless">{{cite journal |last1=Kobychev |first1=V. V. |last2=Popov |first2=S. B. |year=2005 |title=Constraints on the photon charge from observations of extragalactic sources |journal=[[Astronomy Letters]] |volume=31 |issue=3 |pages=147–151 |arxiv=hep-ph/0411398 |bibcode=2005AstL...31..147K |doi=10.1134/1.1883345 |s2cid=119409823}}</ref> is generally considered to have zero [[rest mass]]<ref>{{cite web |first=John |last=Baez |author-link=John Baez |title=What is the mass of a photon? |publisher=[[University of California, Riverside|U.C. Riverside]] |type=pers. academic site |url=http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html |access-date=2009-01-13 |archive-date=2014-05-31 |archive-url=https://web.archive.org/web/20140531100537/http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html |url-status=live }}</ref> and is a [[stable particle]]. The experimental upper limit on the photon mass<ref>{{Cite journal |last1=Tu |first1=Liang-Cheng |last2=Luo |first2=Jun |last3=Gillies |first3=George T |date=2005-01-01 |title=The mass of the photon |url=https://iopscience.iop.org/article/10.1088/0034-4885/68/1/R02 |journal=Reports on Progress in Physics |volume=68 |issue=1 |pages=77–130 |doi=10.1088/0034-4885/68/1/R02 |bibcode=2005RPPh...68...77T |issn=0034-4885|url-access=subscription }}</ref><ref>{{Cite journal |last1=Goldhaber |first1=Alfred Scharff |last2=Nieto |first2=Michael Martin |date=2010-03-23 |title=Photon and graviton mass limits |url=https://link.aps.org/doi/10.1103/RevModPhys.82.939 |journal=Reviews of Modern Physics |language=en |volume=82 |issue=1 |pages=939–979 |doi=10.1103/RevModPhys.82.939 |issn=0034-6861 |arxiv=0809.1003 |bibcode=2010RvMP...82..939G |access-date=2024-02-01 |archive-date=2024-05-13 |archive-url=https://web.archive.org/web/20240513012520/https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.939 |url-status=live }}</ref> is very small, on the order of 10<sup>−50</sup> kg; its lifetime would be more than 10<sup>18</sup> years.<ref>{{Cite journal |last=Heeck |first=Julian |date=2013-07-11 |title=How Stable is the Photon? |url=https://link.aps.org/doi/10.1103/PhysRevLett.111.021801 |journal=Physical Review Letters |language=en |volume=111 |issue=2 |page=021801 |doi=10.1103/PhysRevLett.111.021801 |pmid=23889385 |issn=0031-9007 |arxiv=1304.2821 |bibcode=2013PhRvL.111b1801H |access-date=2024-02-01 |archive-date=2024-05-13 |archive-url=https://web.archive.org/web/20240513012534/https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.021801 |url-status=live }}</ref> For comparison the [[age of the universe]] is about {{convert|13.8e9|m|m|disp=number}} years. <!--convert does not support time units, using it only for number in scientific notation --> 

In a vacuum, a photon has two possible [[photon polarization|polarization]] states.<ref name="Schwartz2014">{{cite book |first=Matthew D. |last=Schwartz |title=Quantum Field Theory and the Standard Model |url=https://books.google.com/books?id=HbdEAgAAQBAJ&pg=PA66 |year=2014 |publisher=Cambridge University Press |isbn=978-1-107-03473-0 |pages=66}}</ref> The photon is the [[gauge boson]] for [[electromagnetism]],<ref>"Role as gauge boson and polarization" §5.1 in {{cite book |last1=Aitchison |first1=I.J.R. |last2=Hey |first2=A.J.G. |title=Gauge Theories in Particle Physics |publisher=[[IOP Publishing]] |year=1993 |url=https://books.google.com/books?id=ZJ-ZY8NW9TIC |isbn=978-0-85274-328-7 |access-date=2016-10-06 |archive-date=2023-01-17 |archive-url=https://web.archive.org/web/20230117203733/https://books.google.com/books?id=ZJ-ZY8NW9TIC |url-status=live }}</ref>{{rp|29–30}} and therefore all other quantum numbers of the photon (such as [[lepton number]], [[baryon number]], and [[flavor (particle physics)#Flavour quantum numbers|flavour quantum numbers]]) are zero.<ref>{{cite journal |doi=10.1016/j.physletb.2008.07.018 |pmid=10020536 |last=Amsler |first=C. |display-authors=etal |title=Review of Particle Physics |journal=[[Physics Letters B]] |volume=667 |issue=1–5 |page=31 |year=2008 |bibcode=2008PhLB..667....1A |url=http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf |hdl=1854/LU-685594 |s2cid=227119789 |hdl-access=free |access-date=2017-10-26 |archive-date=2020-06-01 |archive-url=https://web.archive.org/web/20200601115825/http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf |url-status=live }}</ref> Also, the photon obeys [[Bose–Einstein statistics]], and not [[Fermi–Dirac statistics]]. That is, they do ''not'' obey the [[Pauli exclusion principle]]<ref name=Halliday>{{cite book |last1=Halliday |first1=David |last2=Resnick |first2=Robert |last3=Walker |first3=Jerl |title=Fundamental of Physics |publisher=John Wiley and Sons, Inc. |edition=7th |isbn=978-0-471-23231-5 |year=2005 |url=https://archive.org/details/isbn_0471216437}}</ref>{{rp|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 [[acceleration|accelerated]] it emits [[synchrotron radiation]]. During a [[molecule|molecular]], [[atom]]ic or [[atomic nucleus|nuclear]] transition to a lower [[energy level]], photons of various energy will be emitted, ranging from [[radio wave]]s to [[gamma ray]]s. Photons can also be emitted when a particle and its corresponding [[antiparticle]] are [[annihilation|annihilated]] (for example, [[electron–positron annihilation]]).<ref name=Halliday/>{{rp|572,1114,1172}}

=== Relativistic energy and momentum ===
{{See also|Photon energy|Special relativity}}
[[File:Light cone colour.svg|thumb|right|The cone shows possible values of wave 4-vector of a photon. The "time" axis gives the angular frequency ([[radians per second|rad⋅s<sup>−1</sup>]]) and the "space" axis represents the angular wavenumber (rad⋅m<sup>−1</sup>). Green and indigo represent left and right<!-- I do not know a "correct" assignment --> polarization.]]
In empty space, the photon moves at {{mvar|c}} (the [[speed of light]]) and its [[energy]] and [[momentum]] are related by {{math|1=''E'' = ''pc''}}, where {{mvar|p}} is the [[magnitude (mathematics)|magnitude]] of the momentum vector {{math|'''''p'''''}}. This derives from the following relativistic relation, with {{math|1=''m'' = 0}}:<ref>See {{harvnb|Alonso|Finn|1968|loc=Section 1.6}}.</ref>
: <math>E^{2} = p^{2} c^{2} + m^{2} c^{4} ~.</math>

The energy and momentum of a photon depend only on its [[frequency]] (<math>\nu</math>) or inversely, its [[wavelength]] ({{mvar|λ}}):
: <math>E = \hbar \, \omega = h \nu = \frac{\, h\,c \,}{\lambda}</math>
: <math>\boldsymbol{p} = \hbar \boldsymbol{k} ~,</math>
where '''{{mvar|k}}''' is the [[wave vector]], where
* {{math| ''k'' ≡ {{abs|'''''k'''''}} {{=}} {{sfrac| 2''π'' |''λ''}} }} &emsp; is the [[wave number]], and
* {{math| ''ω'' ≡ 2 ''πν''}} &emsp; is the [[angular frequency]], and
* {{math| ''ħ'' ≡ {{sfrac|''h''| 2''π'' }} }} &emsp; is the [[reduced Planck constant]].<ref>{{cite web |first=Davison E. |last=Soper |title=Electromagnetic radiation is made of photons |department=Institute of Theoretical Science |publisher=[[University of Oregon]] |url=http://pages.uoregon.edu/soper/Light/photons.html |access-date=2024-03-21 |archive-date=2023-04-08 |archive-url=https://web.archive.org/web/20230408082934/https://pages.uoregon.edu/soper/Light/photons.html |url-status=live }}</ref>

Since <math>\boldsymbol{p}</math> points in the direction of the photon's propagation, the magnitude of its momentum is
: <math>p \equiv \left| \boldsymbol{p} \right| = \hbar k = \frac{\, h \nu \,}{c} = \frac{\, h \,}{\lambda} ~.</math>

=== Polarization and spin angular momentum ===
{{main|Photon polarization|Spin angular momentum of light}}
The photon also carries [[Spin angular momentum of light|spin angular momentum]], which is related to [[photon polarization]]. (Beams of light also exhibit properties described as [[orbital angular momentum of light]]).

The angular momentum of the photon has two possible values, either {{mvar|+ħ}} or {{mvar|−ħ}}. These two possible values correspond to the two possible pure states of [[circular polarization]]. 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.<ref name="Hecht">{{Cite book |last=Hecht |first=Eugene |title=Optics |date=1998 |publisher=Addison-Wesley |isbn=978-0-201-83887-9 |edition=3rd |location=Reading, Massachusetts; Harlow |language=en-us}}</ref>{{rp|325}}

The spin angular momentum of light does not depend on its frequency, and was experimentally verified by [[C. V. Raman]] and S. Bhagavantam in 1931.<ref name="spin">{{Cite journal |last1=Raman |first1=C. V. |author1-link=C. V. Raman |last2=Bhagavantam |first2=S. |year=1931 |title=Experimental proof of the spin of the photon |url=http://dspace.rri.res.in/bitstream/2289/2123/1/1931%20IJP%20V6%20p353.pdf |url-status=dead |journal=Indian Journal of Physics |volume=6 |issue=3244 |page=353 |bibcode=1932Natur.129...22R |doi=10.1038/129022a0 |s2cid=4064852 |archive-url=https://web.archive.org/web/20160603235132/http://dspace.rri.res.in/bitstream/2289/2123/1/1931%20IJP%20V6%20p353.pdf |archive-date=2016-06-03 |access-date=2008-12-28 |hdl-access=free |hdl=10821/664}}</ref>

=== Antiparticle annihilation ===
{{Main | Annihilation | Electron–positron annihilation}}
The collision of a particle with its antiparticle can create photons. In free space at least ''two'' photons must be created since, in the [[center of momentum frame]], 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, [[momentum|conservation of momentum]] (or equivalently, [[translational invariance]]) requires that at least two photons are created, with zero net momentum.<ref name=Griffiths2008>{{cite book |last=Griffiths |first=David J. |year=2008 |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |isbn=978-3-527-40601-2}}</ref>{{rp|64–65}} The energy of the two photons, or, equivalently, their frequency, may be determined from [[Conservation law (physics)|conservation of four-momentum]].

{{anchor |antiphoton}}Seen another way, the photon can be considered as its own antiparticle (thus an "antiphoton" is simply a normal photon with opposite momentum, equal polarization, and 180° out of phase). The reverse process, [[pair production]], is the dominant mechanism by which high-energy photons such as [[gamma ray]]s lose energy while passing through matter.<ref>{{harvnb|Alonso|Finn|1968|loc=Section 9.3}}.</ref> 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 [[electromagnetic radiation]] can be re-expressed in terms of photon events. For example, the [[radiation pressure|pressure of electromagnetic radiation]] 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 [[momentum]] per unit time.<ref>{{cite book |last1=Born |first1=Max |url={{google books |plainurl=y |id=NmM-KujxMtoC}} |title=Atomic Physics |last2=Blin-Stoyle |first2=Roger John |last3=Radcliffe |first3=J. M. |date=1989 |publisher=Courier Corporation |isbn=978-0-486-65984-8 |language=en |section=Appendix&nbsp;XXXII}}</ref>

=== Experimental checks on photon mass ===
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 [[upper bound]] on speed that any object could theoretically attain in spacetime.<ref>{{cite journal|author=Mermin, David|title=Relativity without light|doi=10.1119/1.13917|journal=American Journal of Physics|date=February 1984|volume=52|issue=2|pages=119–124|bibcode=1984AmJPh..52..119M }}</ref> Thus, it would still be the speed of spacetime ripples ([[gravitational waves]] and [[graviton]]s), but it would not be the speed of photons.

If a photon did have non-zero mass, there would be other effects as well. [[Coulomb's law]] would be modified and the [[electromagnetic field]] would have an extra physical [[degree of freedom]]. 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 [[electric field]] to exist within a hollow conductor when it is subjected to an external electric field. This provides a means for precision [[Tests of electromagnetism|tests of Coulomb's law]].<ref>{{cite journal|last1=Plimpton|first1=S.|last2=Lawton|first2=W.|title=A Very Accurate Test of Coulomb's Law of Force Between Charges|journal=Physical Review|volume=50|page=1066|year=1936|doi=10.1103/PhysRev.50.1066|bibcode=1936PhRv...50.1066P|issue=11 }}</ref> A null result of such an experiment has set a limit of {{nowrap|''m'' ≲ {{val|e=-14|u=eV/c2}}}}.<ref>{{cite journal|last1=Williams|first1=E.|last2=Faller|first2=J.|last3=Hill|first3=H.|title=New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass|journal=Physical Review Letters|volume=26|page=721|year=1971|doi=10.1103/PhysRevLett.26.721|bibcode=1971PhRvL..26..721W|issue=12}}</ref>

Sharper upper limits on the mass of light have been obtained in experiments designed to detect effects caused by the galactic [[magnetic vector potential|vector potential]]. Although the galactic vector potential is large because the galactic [[magnetic field]] 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 {{sfrac|1|2}}''m''{{sup|2}}''A''{{sub|''μ''}}''A''{{sup|''μ''}} would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of {{nowrap|''m'' &lt; {{val|3|e=-27|u=eV/c2}}}}.<ref>{{cite journal |last1=Chibisov |first1=G. V. |year=1976 |title=Astrophysical upper limits on the photon rest mass |journal=Soviet Physics Uspekhi |volume=19 |issue=7 |page=624 |bibcode=1976SvPhU..19..624C |doi=10.1070/PU1976v019n07ABEH005277}}</ref> The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.<ref>{{cite journal|last1=Lakes|first1=Roderic|title=Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential|journal=Physical Review Letters|volume=80|page=1826|year=1998|doi=10.1103/PhysRevLett.80.1826|bibcode=1998PhRvL..80.1826L|issue=9}}</ref> Such methods were used to obtain the sharper upper limit of {{val|1.07|e=-27|u=eV/c2}} ({{val|e=-36|ul=Da}}) given by the [[Particle Data Group]].<ref name=amsler>{{cite journal |last1=Amsler |first1=C |last2=Doser |first2=M |last3=Antonelli |first3=M |last4=Asner |first4=D |last5=Babu |first5=K |last6=Baer |first6=H |last7=Band |first7=H |last8=Barnett |first8=R |last9=Bergren |display-authors=8 |first9=E |title=Review of Particle Physics⁎ |journal=[[Physics Letters B]] |volume=667 |issue=1–5 |page=1 |year=2008 |doi=10.1016/j.physletb.2008.07.018 |bibcode=2008PhLB..667....1A |url=http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf |hdl=1854/LU-685594 |s2cid=227119789 |hdl-access=free |access-date=2017-10-26 |archive-date=2020-06-01 |archive-url=https://web.archive.org/web/20200601115825/http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf |url-status=live}} [http://pdg.lbl.gov/2009/tables/contents_tables.html Summary Table] {{webarchive |url=https://web.archive.org/web/20100109093036/http://pdg.lbl.gov/2009/tables/contents_tables.html |date=2010-01-09 }}</ref>

These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model-dependent.<ref>{{cite journal |last1=Adelberger |first1=Eric |last2=Dvali |first2=Gia |last3=Gruzinov |first3=Andrei |title=Photon-Mass Bound Destroyed by Vortices |journal=Physical Review Letters |volume=98 |issue=1 |page=010402 |year=2007 |pmid=17358459 |doi=10.1103/PhysRevLett.98.010402 |bibcode=2007PhRvL..98a0402A |arxiv=hep-ph/0306245 |s2cid=31249827 }}</ref> If the photon mass is generated via the [[Higgs mechanism]] then the upper limit of {{nowrap|''m'' ≲ {{val|e=-14|u=eV/c2}}}} from the test of Coulomb's law is valid.
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NOTE BEFORE DELETION:Don't confuse absorption and remission with a single photon. This is untrue, an overstretch, and may confuse:
Photons inside [[superconductors]] develop a nonzero [[effective mass (solid-state physics)|effective rest mass]]; as a result, electromagnetic forces become short-range inside superconductors.<ref>{{cite book
|last=Wilczek |first=Frank
|title=The Lightness of Being: Mass, Ether, and the Unification of Forces
|journal=Physics Today
|volume=62
|issue=4
|year=2010
|publisher=Basic Books
|page=212
|isbn=978-0-465-01895-6
|url={{google books |plainurl=y |id=22Z36Qoz664C|page=212}}
|bibcode=2009PhT....62d..61W
|doi=10.1063/1.3120899
}}</ref>
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