Photon

This article is about the elementary particle or quantum of light. For other uses, seePhoton (disambiguation).

Photon

Composition	Elementary particle
Statistics	Bosonic
Family	Gauge boson
Interactions	Electromagnetic,weak(andgravity)
Symbol	γ
Theorized	Albert Einstein(1905) The name "photon" is generally attributed toGilbert N. Lewis(1926)
Mass	0 (theoretical value) <1×10−18eV/c2(experimental limit)
Mean lifetime	Stable
Electric charge	0 <1×10−35e
Color charge	No
Spin	1ħ
Spin states	+1ħ,−1ħ
Parity	−1
C parity	−1
Condensed	I(JP C)=0,1(1−−)

Aphoton(fromAncient Greekφῶς,φωτός(phôs, phōtós)'light') is anelementary particlethat is aquantumof theelectromagnetic field,includingelectromagnetic radiationsuch aslightandradio waves,and theforce carrierfor theelectromagnetic force.Photons aremassless particlesthat always move at thespeed of lightmeasured in vacuum. The photon belongs to the class ofbosonparticles.

As with other elementary particles, photons are best explained byquantum mechanicsand exhibitwave–particle duality,their behavior featuring properties of bothwavesandparticles.The modern photon concept originated during the first two decades of the 20th century with the work ofAlbert Einstein,who built upon the research ofMax Planck.While Planck was trying to explain howmatterand electromagnetic radiation could be inthermal equilibriumwith one another, he proposed that the energy stored within amaterialobject should be regarded as composed of anintegernumber of discrete, equal-sized parts. To explain thephotoelectric effect,Einstein introduced the idea that light itself is made of discrete units of energy. In 1926,Gilbert N. Lewispopularized the termphotonfor these energy units.Subsequently, many other experiments validated Einstein's approach.

In theStandard Modelofparticle physics,photons and other elementary particles are described as a necessary consequence of physical laws having a certainsymmetryat every point inspacetime.The intrinsic properties of particles, such ascharge,mass,andspin,are determined bygauge symmetry.The photon concept has led to momentous advances in experimental and theoretical physics, includinglasers,Bose–Einstein condensation,quantum field theory,and theprobabilistic interpretationof quantum mechanics. It has been applied tophotochemistry,high-resolution microscopy,andmeasurements of molecular distances.Moreover, photons have been studied as elements ofquantum computers,and for applications inoptical imagingandoptical communicationsuch asquantum cryptography.

Nomenclature

Photoelectric effect:the emission of electrons from a metal plate caused by light quanta – photons

1926Gilbert N. Lewisletter which brought the word "photon" into common usage

The wordquanta(singularquantum,Latin forhow much) was used before 1900 to mean particles or amounts of differentquantities,includingelectricity.In 1900, the German physicistMax Planckwas studyingblack-body radiation,and he suggested that the experimental observations, specifically atshorter wavelengths,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".In 1905,Albert Einsteinpublished a paper in which he proposed that many light-related phenomena—including black-body radiation and thephotoelectric effect—would be better explained by modelling electromagnetic waves as consisting of spatially localized, discrete wave-packets.He called such a wave-packeta light quantum(German:ein Lichtquant).

The namephotonderives from theGreek wordfor light,φῶς(transliteratedphôs).Arthur Comptonusedphotonin 1928, referring toGilbert N. Lewis,who coined the term in a letter toNatureon 18 December 1926.The same name was used earlier but was never widely adopted before Lewis: in 1916 by the American physicist and psychologistLeonard T. Troland,in 1921 by the Irish physicistJohn Joly,in 1924 by the French physiologist René Wurmser (1890–1993), and in 1926 by the French physicist Frithiof Wolfers (1891–1971).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.

In physics, a photon is usually denoted by the symbolγ(theGreek lettergamma). This symbol for the photon probably derives fromgamma rays,which were discovered in 1900 byPaul Villard,named byErnest Rutherfordin 1903, and shown to be a form ofelectromagnetic radiationin 1914 by Rutherford andEdward Andrade.Inchemistryandoptical engineering,photons are usually symbolized byhν,which is thephoton energy,wherehis thePlanck constantand theGreek letterν(nu) is the photon'sfrequency.

Physical properties

The photon has noelectric charge,is generally considered to have zerorest massand is astable particle.The experimental upper limit on the photon massis very small, on the order of 10⁻⁵⁰kg; its lifetime would be more than 10¹⁸years.For comparison theage of the universeis about 1.38×10¹⁰years.

In a vacuum, a photon has two possiblepolarizationstates.The photon is thegauge bosonforelectromagnetism,and therefore all other quantum numbers of the photon (such aslepton number,baryon number,andflavour quantum numbers) are zero.Also, the photon obeysBose–Einstein statistics,and notFermi–Dirac statistics.That is, they donotobey thePauli exclusion principleand more than one can occupy the same bound quantum state.

Photons are emitted in many natural processes. For example, when a charge isacceleratedit emitssynchrotron radiation.During amolecular,atomicornucleartransition to a lowerenergy level,photons of various energy will be emitted, ranging fromradio wavestogamma rays.Photons can also be emitted when a particle and its correspondingantiparticleareannihilated(for example,electron–positron annihilation).

Relativistic energy and momentum

See also:Photon energyandSpecial relativity

The cone shows possible values of wave 4-vector of a photon. The "time" axis gives the angular frequency (rad⋅s⁻¹) and the "space" axis represents the angular wavenumber (rad⋅m⁻¹). Green and indigo represent left and right polarization.

In empty space, the photon moves atc(thespeed of light) and itsenergyandmomentumare related byE=pc,wherepis themagnitudeof the momentum vectorp.This derives from the following relativistic relation, withm= 0:

$E^{2}=p^{2}c^{2}+m^{2}c^{4}~.$

The energy and momentum of a photon depend only on itsfrequency($\nu$) or inversely, itswavelength(λ):

$E=\hbar \,\ Omega =h\nu ={\frac {\,h\,c\,}{\lambda }}$

${\boldsymbol {p}}=\hbar {\boldsymbol {k}}~,$

wherekis thewave vector,where

• k≡ |k| =⁠ 2π /λ⁠  is thewave number,and
• ω≡ 2πν  is theangular frequency,and
• ħ≡⁠h/ 2π ⁠  is thereduced Planck constant.

Since${\boldsymbol {p}}$points in the direction of the photon's propagation, the magnitude of its momentum is

$p\equiv \left|{\boldsymbol {p}}\right|=\hbar k={\frac {\,h\nu \,}{c}}={\frac {\,h\,}{\lambda }}~.$

Polarization and spin angular momentum

Main articles:Photon polarizationandSpin angular momentum of light

The photon also carriesspin angular momentum,which is related tophoton polarization.(Beams of light also exhibit properties described asorbital angular momentum of light).

The angular momentum of the photon has two possible values, either+ħor−ħ.These two possible values correspond to the two possible pure states ofcircular 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.

The spin angular momentum of light does not depend on its frequency, and was experimentally verified byC. V. Ramanand S. Bhagavantam in 1931.

Antiparticle annihilation

Main articles:AnnihilationandElectron-positron annihilation

The collision of a particle with its antiparticle can create photons. In free space at leasttwophotons must be created since, in thecenter 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,conservation of momentum(or equivalently,translational invariance) requires that at least two photons are created, with zero net momentum.The energy of the two photons, or, equivalently, their frequency, may be determined fromconservation of four-momentum.

Seen another way, the photon can be considered asits 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 asgamma rayslose energy while passing through matter.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 ofelectromagnetic radiationcan be re-expressed in terms of photon events. For example, thepressure of electromagnetic radiationon 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 inmomentumper unit time.

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 theupper boundon speed that any object could theoretically attain in spacetime.Thus, it would still be the speed of spacetime ripples (gravitational wavesandgravitons), 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 lawwould be modified and theelectromagnetic fieldwould have an extra physicaldegree 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 anelectric fieldto exist within a hollow conductor when it is subjected to an external electric field. This provides a means for precisiontests of Coulomb's law.A null result of such an experiment has set a limit ofm≲10⁻¹⁴eV/c².

Sharper upper limits on the mass of light have been obtained in experiments designed to detect effects caused by the galacticvector potential.Although the galactic vector potential is large because the galacticmagnetic fieldexists 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 term⁠1/2⁠m²A_μA^μwould affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass ofm<3×10⁻²⁷eV/c².The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.Such methods were used to obtain the sharper upper limit of1.07×10⁻²⁷eV/c²(the equivalent of10⁻³⁶daltons) given by theParticle Data Group.

These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model-dependent.If the photon mass is generated via theHiggs mechanismthen the upper limit ofm≲10⁻¹⁴eV/c²from the test of Coulomb's law is valid.

Historical development

Main article:Light

Thomas Young'sdouble-slit experimentin 1801 showed that light can act as awave,helping to invalidate earlyparticletheories of light.

In most theories up to the eighteenth century, light was pictured as being made of particles. Sinceparticlemodels cannot easily account for therefraction,diffractionandbirefringenceof light, wave theories of light were proposed byRené Descartes(1637),Robert Hooke(1665),andChristiaan Huygens(1678);however, particle models remained dominant, chiefly due to the influence ofIsaac Newton.In the early 19th century,Thomas YoungandAugust Fresnelclearly demonstrated theinterferenceand diffraction of light, and by 1850 wave models were generally accepted.James Clerk Maxwell's 1865predictionthat light was an electromagnetic wave – which was confirmed experimentally in 1888 byHeinrich Hertz's detection ofradio waves– seemed to be the final blow to particle models of light.

In 1900,Maxwell'stheoretical model of lightas oscillatingelectricandmagnetic fieldsseemed complete. However, several observations could not be explained by any wave model ofelectromagnetic radiation,leading to the idea that light-energy was packaged intoquantadescribed byE = hν.Later experiments showed that these light-quanta also carry momentum and, thus, can be consideredparticles:Thephotonconcept was born, leading to a deeper understanding of the electric and magnetic fields themselves.

TheMaxwell wave theory,however, does not account forallproperties of light. The Maxwell theory predicts that the energy of a light wave depends only on itsintensity,not on itsfrequency;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,some chemical reactionsare 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 (thephotoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.

At the same time, investigations ofblack-body radiationcarried out over four decades (1860–1900) by various researchersculminated inMax Planck'shypothesisthat the energy ofanysystem that absorbs or emits electromagnetic radiation of frequencyνis an integer multiple of an energy quantumE=hν.As shown byAlbert Einstein,some form of energy quantizationmustbe assumed to account for the thermal equilibrium observed between matter andelectromagnetic radiation;for this explanation of the photoelectric effect, Einstein received the 1921Nobel Prizein physics.

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.Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if theenergyof 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.In 1909and 1916,Einstein showed that, ifPlanck's lawregarding black-body radiation is accepted, the energy quanta must also carrymomentump =⁠ h / λ ⁠,making them full-fledged particles. This photon momentum was observed experimentally byArthur Compton,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,and was solved inquantum electrodynamicsand its successor, theStandard Model.(See§ Quantum field theoryand§ As a gauge boson,below.)

Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behaviour by quantizing onlymatter,as in theBohr modelof thehydrogen atom(shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led toquantum mechanics.

Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted inRobert Millikan's Nobel lecture.However, before Compton's experimentshowed that photons carried momentum proportional to theirwave number(1922),most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures ofWien,Planckand Millikan.)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 revealingCompton scattering,where it was much more difficult not to ascribe quantization to light itself to explain the observed results.

Even after Compton's experiment,Niels Bohr,Hendrik KramersandJohn Slatermade one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-calledBKS theory.An important feature of the BKS theory is how it treated theconservation of energyand theconservation of momentum.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.Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible".Nevertheless, the failures of the BKS model inspiredWerner Heisenbergin his development ofmatrix mechanics.

A few physicists persistedin developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws ofquantum mechanics.Although the evidence from chemical and physical experiments for the existence of photons was overwhelming by the 1970s, this evidence could not be considered asabsolutelydefinitive; 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,allsemiclassical theories were refuted definitively in the 1970s and 1980s by photon-correlation experiments.Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven.

Wave–particle duality and uncertainty principles

Photons in aMach–Zehnder interferometerexhibit wave-like interference and particle-like detection atsingle-photon detectors.

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, theprobabilityof detecting a photon is calculated by equations that describe waves. This combination of aspects is known aswave–particle duality.For example, theprobability distributionfor the location at which a photon might be detected displays clearly wave-like phenomena such asdiffractionandinterference.A single photon passing through adouble slithas its energy received at a point on the screen with a probability distribution given by its interference pattern determined byMaxwell's wave equations.However, experiments confirm that the photon isnota 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 abeam splitter.Rather, the received photon acts like apoint-like particlesince it is absorbed or emittedas a wholeby arbitrarily small systems, including systems much smaller than its wavelength, such as an atomic nucleus (≈10⁻¹⁵m across) or even the point-likeelectron.

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 zerorest mass,nowave functiondefined for a photon can have all the properties familiar from wave functions in non-relativistic quantum mechanics.In order to avoid these difficulties, physicists employ the second-quantized theory of photons described below,quantum electrodynamics,in which photons are quantized excitations of electromagnetic modes.

Another difficulty is finding the proper analogue for theuncertainty principle,an idea frequently attributed to Heisenberg, who introduced the concept in analyzing athought experimentinvolvingan electron and a high-energy photon.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 toKennard,Pauli,andWeyl.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.Acoherent stateminimizes the overall uncertainty as far as quantum mechanics allows.Quantum opticsmakes 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.This is sometimes informally expressed in terms of the uncertainty in the number of photons present in the electromagnetic wave,$\Delta N$,and the uncertainty in the phase of the wave,$\Delta \phi$.However, this cannot be an uncertainty relation of the Kennard–Pauli–Weyl type, since unlike position and momentum, the phase$\phi$cannot be represented by aHermitian operator.

Bose–Einstein model of a photon gas

Main articles:Bose gas,Bose–Einstein statistics,Spin-statistics theorem,Gas in a box,andPhoton gas

In 1924,Satyendra Nath BosederivedPlanck's law of black-body radiationwithout using any electromagnetism, but rather by using a modification of coarse-grained counting ofphase space.Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction",now understood as the requirement for asymmetric quantum mechanical state.This work led to the concept ofcoherent statesand 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 lowestquantum stateat low enough temperatures; thisBose–Einstein condensationwas observed experimentally in 1995.It was later used byLene Hauto slow, and then completely stop, light in 1999and 2001.

The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed tofermionswith half-integer spin). By thespin-statistics theorem,all bosons obey Bose–Einstein statistics (whereas all fermions obeyFermi–Dirac statistics).

Stimulated and spontaneous emission

Main articles:Stimulated emissionandLaser

Stimulated emission(in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of thelaser.Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.

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 inthermal equilibriumwith all parts of itself and filled withelectromagnetic radiationand that the atoms can emit and absorb that radiation. Thermal equilibrium requires that the energy density$\rho (\nu )$of photons with frequency$\nu$(which is proportional to theirnumber density) is, on average, constant in time; hence, the rate at which photons of any particular frequency areemittedmust equal the rate at which they areabsorbed.

Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate$R_{ji}$for a system toabsorba photon of frequency$\nu$and transition from a lower energy$E_{j}$to a higher energy$E_{i}$is proportional to the number$N_{j}$of atoms with energy$E_{j}$and to the energy density$\rho (\nu )$of ambient photons of that frequency,

$R_{ji}=N_{j}B_{ji}\rho (\nu )\!$

where$B_{ji}$is therate constantfor 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$R_{ij}$for the emission of photons of frequency$\nu$and transition from a higher energy$E_{i}$to a lower energy$E_{j}$is

$R_{ij}=N_{i}A_{ij}+N_{i}B_{ij}\rho (\nu )\!$

where$A_{ij}$is the rate constant foremitting a photon spontaneously,and$B_{ij}$is the rate constant for emissions in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state$i$and those in state$j$must, on average, be constant; hence, the rates$R_{ji}$and$R_{ij}$must be equal. Also, by arguments analogous to the derivation ofBoltzmann statistics,the ratio of$N_{i}$and$N_{j}$is$g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},$where$g_{i}$and$g_{j}$are thedegeneracyof the state$i$and that of$j$,respectively,$E_{i}$and$E_{j}$their energies,$k$theBoltzmann constantand$T$the system'stemperature.From this, it is readily derived that

$g_{i}B_{ij}=g_{j}B_{ji}$and

$A_{ij}={\frac {8\pi h\nu ^{3}}{c^{3}}}B_{ij}.$

The$A_{ij}$and$B_{ij}$are collectively known as theEinstein coefficients.

Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients$A_{ij}$,$B_{ji}$and$B_{ij}$once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".Not long thereafter, in 1926,Paul Diracderived the$B_{ij}$rate constants by using a semiclassical approach,and, in 1927, succeeded in derivingallthe rate constants from first principles within the framework of quantum theory.Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also calledsecond quantizationorquantum field theory;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 thedirectionof a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered byNewtonin his treatment ofbirefringenceand, 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.Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separationfrom quantum mechanics. Ironically,Max Born'sprobabilistic interpretationof thewave functionwas inspired by Einstein's later work searching for a more complete theory.

Quantum field theory

Quantization of the electromagnetic field

Main article:Quantum field theory

Differentelectromagnetic modes(such as those depicted here) can be treated as independentsimple harmonic oscillators.A photon corresponds to a unit of energyE=hνin its electromagnetic mode.

In 1910,Peter DebyederivedPlanck's law of black-body radiationfrom a relatively simple assumption.He decomposed the electromagnetic field in a cavity into itsFourier modes,and assumed that the energy in any mode was an integer multiple of$h\nu$,where$\nu$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.

In 1925,Born,HeisenbergandJordanreinterpreted Debye's concept in a key way.As may be shown classically, theFourier modesof theelectromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vectorkand polarization state—are equivalent to a set of uncoupledsimple harmonic oscillators.Treated quantum mechanically, the energy levels of such oscillators are known to be$E=nh\nu$,where$\nu$is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy$E=nh\nu$as a state with$n$photons, each of energy$h\nu$.This approach gives the correct energy fluctuation formula.

Feynman diagramof two electrons interacting by exchange of a virtual photon.

Diractook this one step further.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$A_{ij}$and$B_{ij}$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 derivedPlanck's law of black-body radiationbyassumingB–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics.

Dirac's second-orderperturbation theorycan involvevirtual photons,transient intermediate states of the electromagnetic field; the staticelectricandmagneticinteractions are mediated by such virtual photons. In suchquantum field theories,theprobability amplitudeof observable events is calculated by summing overallpossible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy$E=pc$,and may have extrapolarizationstates; depending on thegaugeused, 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.

Indeed, such second-order and higher-order perturbation calculations can give apparentlyinfinitecontributions to the sum. Such unphysical results are corrected for using the technique ofrenormalization.

Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtualelectron–positronpairs.Such photon–photon scattering (seetwo-photon physics), as well as electron–photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, theInternational Linear Collider.

Inmodern physicsnotation, thequantum stateof the electromagnetic field is written as aFock state,atensor productof the states for each electromagnetic mode

$|n_{k_{0}}\rangle \otimes |n_{k_{1}}\rangle \otimes \dots \otimes |n_{k_{n}}\rangle \dots$

where$|n_{k_{i}}\rangle$represents the state in which$\,n_{k_{i}}$photons are in the mode$k_{i}$.In this notation, the creation of a new photon in mode$k_{i}$(e.g., emitted from an atomic transition) is written as$|n_{k_{i}}\rangle \rightarrow |n_{k_{i}}+1\rangle$.This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.

As a gauge boson

Main article:Gauge theory

The electromagnetic field can be understood as agauge field,i.e., as a field that results from requiring that a gauge symmetry holds independently at every position inspacetime.For theelectromagnetic field,this gauge symmetry is theAbelianU(1) symmetryofcomplex numbersof absolute value 1, which reflects the ability to vary thephaseof a complex field without affectingobservablesorreal valued functionsmade from it, such as theenergyor theLagrangian.

The quanta of anAbelian gauge fieldmust be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zeroelectric chargeand integer spin. The particular form of theelectromagnetic interactionspecifies that the photon must havespin±1; thus, itshelicitymust be$\pm \hbar$.These two spin components correspond to the classical concepts ofright-handed and left-handed circularly polarizedlight. However, the transientvirtual photonsofquantum electrodynamicsmay also adopt unphysical polarization states.

In the prevailingStandard Modelof physics, the photon is one of four gauge bosons in theelectroweak interaction;theother threeare denoted W⁺,W⁻and Z⁰and are responsible for theweak interaction.Unlike the photon, these gauge bosons havemass,owing to amechanismthat breaks theirSU(2) gauge symmetry.The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished bySheldon Glashow,Abdus SalamandSteven Weinberg,for which they were awarded the 1979Nobel Prizein physics.Physicists continue to hypothesizegrand unified theoriesthat connect these four gauge bosons with the eightgluongauge bosons ofquantum chromodynamics;however, key predictions of these theories, such asproton decay,have not been observed experimentally.

Hadronic properties

Main article:Photon structure function

Measurements of the interaction between energetic photons andhadronsshow 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 neutronsin spite of the fact that the electric charge structures of protons and neutrons are substantially different. A theory calledVector Meson Dominance(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.However, if experimentally probed at very short distances, the intrinsic structure of the photon is recognized as a flux of quark and gluon components, quasi-free according to asymptotic freedom inQCDand described by thephoton structure function.A comprehensive comparison of data with theoretical predictions was presented in a review in 2000.

Contributions to the mass of a system

See also:Mass in special relativityandMass in general relativity

The energy of a system that emits a photon isdecreasedby the energy$E$of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount${E}/{c^{2}}$.Similarly, the mass of a system that absorbs a photon isincreasedby 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${E}/{c^{2}}$for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).

This concept is applied in key predictions ofquantum electrodynamics(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 asrenormalization.Such "radiative corrections"contribute to a number of predictions of QED, such as themagnetic dipole momentofleptons,theLamb shift,and thehyperfine structureof bound lepton pairs, such asmuoniumandpositronium.

Since photons contribute to thestress–energy tensor,they exert agravitational attractionon other objects, according to the theory ofgeneral relativity.Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warpedspacetime,as ingravitational lensing,andtheir frequencies may be loweredby moving to a highergravitational potential,as in thePound–Rebka experiment.However, these effects are not specific to photons; exactly the same effects would be predicted for classicalelectromagnetic waves.

In matter

See also:Refractive index,Group velocity,andPhotochemistry

Light that travels through transparent matter does so at a lower speed thanc,the speed of light in vacuum. The factor by which the speed is decreased is called therefractive indexof the material. In a classical wave picture, the slowing can be explained by the light inducingelectric polarizationin 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 producequasi-particlesknown aspolariton(seethis listfor some other quasi-particles); this polariton has a nonzeroeffective mass,which means that it cannot travel atc.Light of different frequencies may travel through matter atdifferent speeds;this is calleddispersion(not to be confused with scattering). In some cases, it can result inextremely slow speeds of lightin matter. The effects of photon interactions with other quasi-particles may be observed directly inRaman scatteringandBrillouin scattering.

Photons can be scattered by matter. For example, photons engage in so many collisions on the way from thecore of the Sunthatradiant energycan take about a million years to reach the surface;however, once in open space, a photon takes only 8.3 minutes to reach Earth.

Photons can also beabsorbedby nuclei, atoms or molecules, provoking transitions between theirenergy levels.A classic example is the molecular transition ofretinal(C₂₀H₂₈O), which is responsible forvision,as discovered in 1958 by Nobel laureatebiochemistGeorge Waldand co-workers. The absorption provokes acis–transisomerizationthat, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in thephotodissociationofchlorine;this is the subject ofphotochemistry.

Technological applications

Photons have many applications in technology. These examples are chosen to illustrate applications of photonsper 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 understimulated emission.

Individual photons can be detected by several methods. The classicphotomultipliertube exploits thephotoelectric effect:a photon of sufficient energy strikes a metal plate and knocks free an electron, initiating an ever-amplifying avalanche of electrons.Semiconductorcharge-coupled devicechips use a similar effect: an incident photon generates a charge on a microscopiccapacitorthat can be detected. Other detectors such asGeiger countersuse the ability of photons toionizegas molecules contained in the device, causing a detectable change ofconductivityof the gas.

Planck's energy formula$E=h\nu$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, theemission spectrumof agas-discharge lampcan be altered by filling it with (mixtures of) gases with different electronicenergy levelconfigurations.

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 (seetwo-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.

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 offluorescence resonance energy transfer,a technique that is used inmolecular biologyto study the interaction of suitableproteins.

Several different kinds ofhardware random number generatorsinvolve 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 abeam-splitter.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".

Quantum optics and computation

Much research has been devoted to applications of photons in the field ofquantum optics.Photons seem well-suited to be elements of an extremely fastquantum computer,and thequantum entanglementof photons is a focus of research.Nonlinear optical processesare another active research area, with topics such astwo-photon absorption,self-phase modulation,modulational instabilityandoptical parametric oscillators.However, such processes generally do not require the assumption of photonsper se;they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process ofspontaneous parametric down conversionis often used to produce single-photon states. Finally, photons are essential in some aspects ofoptical communication,especially forquantum cryptography.

Two-photon physicsstudies interactions between photons, which are rare. In 2018, Massachusetts Institute of Technology researchers announced the discovery of bound photon triplets, which may involvepolaritons.

See also

• Advanced Photon Sourceat Argonne National Laboratory
• Ballistic photon
• Dirac equation
• Doppler effect
• EPR paradox
• High energy X-ray imaging technology
• Luminiferous aether
• Medipix
• Phonon
• Photography
• Photon counting
• Photon epoch
• Photonic molecule
• Photonics
• Single-photon source
• Static forces and virtual-particle exchange
• Variable speed of light

Further reading

By date of publication

• Alonso, M.; Finn, E. J. (1968).Fundamental University Physics.Vol. III: Quantum and Statistical Physics. Addison-Wesley.ISBN978-0-201-00262-1.
• Clauser, J. F. (1974)."Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect".Physical Review D.9(4): 853–860.Bibcode:1974PhRvD...9..853C.doi:10.1103/PhysRevD.9.853.S2CID118320287.Archivedfrom the original on 2019-01-24.Retrieved2019-01-03.
• Pais, Abraham(1982).Subtle is the Lord: The Science and the Life of Albert Einstein.Oxford University Press.
• Feynman, Richard(1985).QED: The Strange Theory of Light and Matter.Princeton University Press.ISBN978-0-691-12575-6.
• 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".Europhysics Letters.1(4): 173–179.Bibcode:1986EL......1..173G.CiteSeerX10.1.1.178.4356.doi:10.1209/0295-5075/1/4/004.S2CID250837011.
• Lamb, Willis E.(1995). "Anti-photon".Applied Physics B.60(2–3): 77–84.Bibcode:1995ApPhB..60...77L.doi:10.1007/BF01135846.S2CID263785760.
• "Special supplemental issue"(PDF).Optics and Photonics News.Vol. 14. October 2003. Archived fromthe original(PDF)on June 5, 2022.
  • Roychoudhuri, C.; Rajarshi, R. (2003). "The nature of light: What is a photon?".Optics and Photonics News.Vol. 14. pp. S1 (Supplement).
  • Zajonc, A. (2003). "Light reconsidered".Optics and Photonics News.Vol. 14. pp. S2–S5 (Supplement).
  • Loudon, R. (2003). "What is a photon?".Optics and Photonics News.Vol. 14. pp. S6–S11 (Supplement).
  • Finkelstein, D. (2003). "What is a photon?".Optics and Photonics News.Vol. 14. pp. S12–S17 (Supplement).
  • Muthukrishnan, A.; Scully, M. O.; Zubairy, M. S. (2003). "The concept of the photon – revisited".Optics and Photonics News.Vol. 14. pp. S18–S27 (Supplement).
  • Mack, H.;Schleich, Wolfgang P.(2003). "A photon viewed from Wigner phase space".Optics and Photonics News.Vol. 14. pp. S28–S35 (Supplement).
• Glauber, R. (2005)."One Hundred Years of Light Quanta"(PDF).Nobel Prize.Physics Lecture. Archived fromthe original(PDF)on 2008-07-23.Retrieved2009-06-29.
• Hentschel, K. (2007)."Light quanta: The maturing of a concept by the stepwise accretion of meaning".Physics and Philosophy.1(2): 1–20.Archivedfrom the original on 2014-05-29.Retrieved2014-06-29.

Education with single photons

• Thorn, J. J.; Neel, M. S.; Donato, V. W.; Bergreen, G. S.; Davies, R. E.; Beck, M. (2004)."Observing the quantum behavior of light in an undergraduate laboratory"(PDF).American Journal of Physics.72(9): 1210–1219.Bibcode:2004AmJPh..72.1210T.doi:10.1119/1.1737397.Archived(PDF)from the original on 2016-02-01.Retrieved2009-06-29.
• Bronner, P.; Strunz, Andreas; Silberhorn, Christine; Meyn, Jan-Peter (2009)."Interactive screen experiments with single photons".European Journal of Physics.30(2): 345–353.Bibcode:2009EJPh...30..345B.doi:10.1088/0143-0807/30/2/014.S2CID38626417.Archivedfrom the original on 2019-07-01.Retrieved2009-07-17.

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