As with other elementary particles, photons are best explained byquantum mechanics and exhibitwave–particle duality, their behavior featuring properties of bothwaves andparticles.[2] 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 howmatter and electromagnetic radiation could be inthermal equilibrium with one another, he proposed that the energy stored within amaterial object should be regarded as composed of aninteger number 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. Lewis popularized the termphoton for these energy units.[3][4][5] Subsequently, many other experiments validated Einstein's approach.[6][7][8]
The photon has noelectric charge,[9][10] is generally considered to have zerorest mass,[11] and is astable particle. The experimental upper limit on the photon mass[12][13] is very small, on the order of 10−53 g; its lifetime would be more than 1018 years.[14] For comparison, theage of the universe is about 1.38×1010 years.
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 a quantum mechanical model, electromagnetic waves transfer energy in photons withenergy proportional tofrequency ()[19]: 325
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 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.[19]: 325
The spin angular momentum of light does not depend on its frequency, and was experimentally verified byC. V. Raman andSuri Bhagavantam in 1931.[22]
The collision of a particle with its antiparticle can create photons. In free space at leasttwo photons 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.[23]: 64–65 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 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 asgamma rays lose energy while passing through matter.[24] 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 radiation can be re-expressed in terms of photon events. For example, thepressure 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 inmomentum per unit time.[25]
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 bound on speed that any object could theoretically attain in spacetime.[26] Thus, it would still be the speed of spacetime ripples (gravitational waves andgravitons), 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 theelectromagnetic field would 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 field to exist within a hollow conductor when it is subjected to an external electric field. This provides a means for precisiontests of Coulomb's law.[27] A null result of such an experiment has set a limit ofm ≲10−14 eV/c2.[28]
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 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 term1/2m2AμAμ would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass ofm <3×10−27 eV/c2.[29] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.[30] Such methods were used to obtain the sharper upper limit of1.07×10−27 eV/c2 (10−36Da) given by theParticle Data Group.[31]
These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model-dependent.[32] If the photon mass is generated via theHiggs mechanism then the upper limit ofm ≲10−14 eV/c2 from the test of Coulomb's law is valid.
Thomas Young's sketch of interference based on observations of water waves.[33] Young reasoned that the similar effects observed with light supported a wave model and not Newton'sparticle theory of light.[18]: 964
In 1900,Maxwell'stheoretical model of light as oscillatingelectric andmagnetic fields seemed complete. However, several observations could not be explained by any wave model ofelectromagnetic radiation, leading to the idea that light-energy was packaged intoquanta described byE = hν. Later experiments showed that these light-quanta also carry momentum and, thus, can be consideredparticles: Thephoton concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.
TheMaxwell wave theory, however, does not account forall properties 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 reactions 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 (thephotoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.[41]
At the same time, investigations ofblack-body radiation carried out over four decades (1860–1900) by various researchers[42] culminated inMax Planck'shypothesis[43][44] that the energy ofany system that absorbs or emits electromagnetic radiation of frequencyν is an integer multiple of an energy quantumE =hν . As shown byAlbert Einstein,[45][46] some form of energy quantizationmust be assumed to account for the thermal equilibrium observed between matter andelectromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921Nobel Prize in physics.[47]
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.[45] Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if theenergy 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.[45] In 1909[46] and 1916,[48] Einstein showed that, ifPlanck's law regarding black-body radiation is accepted, the energy quanta must also carrymomentum p = h / λ , making them full-fledged particles.
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 model of 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.
As recounted inRobert Millikan's 1923 Nobel lecture, Einstein's 1905 predicted energy relationship was verified experimentally by 1916 but the local concept of the quanta remained unsettled.[49]Most physicists were reluctant to believe that electromagnetic radiation itself might be particulate and thus an example of wave-particle duality.[50] Then in 1922Arthur Compton experiment[51] showed that photons carried momentum proportional to theirwave number (1922) in an experiment now calledCompton scattering that appeared to clearly support a localized quantum model. At least for Millikan, this settled the matter.[49] Compton received the Nobel Prize in 1927 for his scattering work.
Even after Compton's experiment,Niels Bohr,Hendrik Kramers andJohn Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-calledBKS theory.[52] An important feature of the BKS theory is how it treated theconservation of energy and 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.[53] Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible".[54] Nevertheless, the failures of the BKS model inspiredWerner Heisenberg in his development ofmatrix mechanics.[55]
By the late 1920, the pivotal question 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,[54] and was solved inquantum electrodynamics and its successor, theStandard Model. (See§ Quantum field theory and§ As a gauge boson, below.)
A few physicists persisted[56] in 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 asabsolutely 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.
In the 1970s and 1980s photon-correlation experiments definitively demonstrated quantum photon effects.These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from thequantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classicalCauchy–Schwarz inequality. In 1977, Kimbleet 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);[57] This work is reviewed and simplified further in Thorn, Neel,et al. (2004).[58]
Photoelectric effect: the emission of electrons from a metal plate caused by light quanta – photons
The wordquanta (singularquantum, Latin forhow much) was used before 1900 to mean particles or amounts of differentquantities, includingelectricity. In 1900, the German physicistMax Planck was studyingblack-body radiation, and he suggested that the experimental observations, specifically atshorter wavelengths, would be explained if the energy was "made up of a completely determinate number of finite equal parts", which he called "energy elements".[59] In 1905,Albert Einstein published 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 energy quanta.[45] He called thesea light quantum (German:ein Lichtquant).[60]
The namephoton derives from theGreek word for light,φῶς (transliteratedphôs). The name was used 1916 by the American physicist and psychologistLeonard T. Troland for a unit of illumination of theretina and in several other contexts before being adopted for physics.[5] The use of the termphoton for the light quantum was popularized byGilbert N. Lewis, who used the term in a letter toNature on 18 December 1926.[61] Arthur Compton, who had performed a key experiment demonstrating light quanta, cited Lewis in the 1927Solvay conference proceedings for suggesting the namephoton. Einstein never did use the term.[5]
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, theprobability of detecting a photon is calculated by equations that describe waves. This combination of aspects is known aswave–particle duality. For example, theprobability distribution for the location at which a photon might be detected displays clearly wave-like phenomena such asdiffraction andinterference. A single photon passing through adouble slit has its energy received at a point on the screen with a probability distribution given by its interference pattern determined byMaxwell's wave equations.[66] However, experiments confirm that the photon isnot 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 abeam splitter.[67] Rather, the received photon acts like apoint-like particle since it is absorbed or emittedas 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-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 function defined for a photon can have all the properties familiar from wave functions in non-relativistic quantum mechanics.[a] 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.[72]
Another difficulty is finding the proper analogue for theuncertainty principle, an idea frequently attributed to Heisenberg, who introduced the concept in analyzing athought experiment involvingan 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.[73][74] 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.[75] Acoherent state minimizes the overall uncertainty as far as quantum mechanics allows.[72]Quantum optics 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.[72] This is sometimes informally expressed in terms of the uncertainty in the number of photons present in the electromagnetic wave,, and the uncertainty in the phase of the wave,. However, this cannot be an uncertainty relation of the Kennard–Pauli–Weyl type, since unlike position and momentum, the phase cannot be represented by aHermitian operator.[76]
In 1924,Satyendra Nath Bose derivedPlanck's law of black-body radiation without using any electromagnetism, but rather by using a modification of coarse-grained counting ofphase space.[77] Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction",[78][79] now understood as the requirement for asymmetric quantum mechanical state. This work led to the concept ofcoherent states 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 lowestquantum state at low enough temperatures; thisBose–Einstein condensation was observed experimentally in 1995.[80] It was later used byLene Hau to slow, and then completely stop, light in 1999[81] and 2001.[82]
The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed tofermions with half-integer spin). By thespin-statistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obeyFermi–Dirac statistics).[83]
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 equilibrium with all parts of itself and filled withelectromagnetic radiation and that the atoms can emit and absorb that radiation. Thermal equilibrium requires that the energy density of photons with frequency (which is proportional to theirnumber density) is, on average, constant in time; hence, the rate at which photons of any particular frequency areemitted must equal the rate at which they areabsorbed.[84]
Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate for a system toabsorb a photon of frequency and transition from a lower energy to a higher energy is proportional to the number of atoms with energy and to the energy density of ambient photons of that frequency,
where is therate constant 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 for the emission of photons of frequency and transition from a higher energy to a lower energy is
where is the rate constant foremitting a photon spontaneously, and is the rate constant for emissions in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state and those in state must, on average, be constant; hence, the rates and must be equal. Also, by arguments analogous to the derivation ofBoltzmann statistics, the ratio of and is where and are thedegeneracy of the state and that of, respectively, and their energies, theBoltzmann constant and the system'stemperature. From this, it is readily derived that
and
The and are collectively known as theEinstein coefficients.[85]
Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients, and once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".[86] Not long thereafter, in 1926,Paul Dirac derived the rate constants by using a semiclassical approach,[87] and, in 1927, succeeded in derivingall the rate constants from first principles within the framework of quantum theory.[88][89] Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also calledsecond quantization orquantum field theory;[90][91][92] 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 thedirection of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered byNewton in his treatment ofbirefringence 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.[37] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation[54] from quantum mechanics. Ironically,Max Born'sprobabilistic interpretation of thewave function[93][94] was inspired by Einstein's later work searching for a more complete theory.[95]
Differentelectromagnetic modes (such as those depicted here) can be treated as independentsimple harmonic oscillators. A photon corresponds to a unit of energyE = hν in its electromagnetic mode.
In 1910,Peter Debye derivedPlanck's law of black-body radiation from a relatively simple assumption.[96] He decomposed the electromagnetic field in a cavity into itsFourier modes, and assumed that the energy in any mode was an integer multiple of, where 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.[46]
In 1925,Born,Heisenberg andJordan reinterpreted Debye's concept in a key way.[97] As may be shown classically, theFourier modes of theelectromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vectork and polarization state—are equivalent to a set of uncoupledsimple harmonic oscillators. Treated quantum mechanically, the energy levels of such oscillators are known to be, where is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy as a state with photons, each of energy. This approach gives the correct energy fluctuation formula.
Feynman diagram of two electrons interacting by exchange of a virtual photon
Dirac took this one step further.[88][89] 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 and 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 radiation byassuming B–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics.[citation needed]
Dirac's second-orderperturbation theory can involvevirtual photons, transient intermediate states of the electromagnetic field; the staticelectric andmagnetic interactions are mediated by such virtual photons. In suchquantum field theories, theprobability amplitude of observable events is calculated by summing overall possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy, and may have extrapolarization states; depending on thegauge 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.[98]
Second-order and higher-order perturbation calculations can giveinfinite contributions to the sum. Such unphysical results are corrected for using the technique ofrenormalization.[99]
Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtualelectron–positronpairs.[100] 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.[101]
where represents the state in which photons are in the mode. In this notation, the creation of a new photon in mode (e.g., emitted from an atomic transition) is written as. This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.
Measurements of the interaction between energetic photons andhadrons 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[107] in spite of the fact that the electrical 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, which mediate the residualnuclear force.[108] 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 inQCD. That flux is described by thephoton structure function.[109][110] A review byNisius (2000) presented a comprehensive comparison of data with theoretical predictions.[111]
The energy of a system that emits a photon isdecreased by the energy of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount. Similarly, the mass of a system that absorbs a photon isincreased 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 for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).[112]
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 index of the material. In a classical wave picture, the slowing can be explained by the light inducingelectric polarization 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 producequasi-particles known aspolaritons. Polaritons have a nonzeroeffective mass, which means that they 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 light in matter. The effects of photon interactions with other quasi-particles may be observed directly inRaman scattering andBrillouin scattering.[115]
Photons can also beabsorbed by 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 Wald and co-workers. The absorption provokes acis–transisomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in thephotodissociation ofchlorine; this is the subject ofphotochemistry.[118][119]
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 classicphotomultiplier tube 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 device chips use a similar effect: an incident photon generates a charge on a microscopiccapacitor that can be detected. Other detectors such asGeiger counters use the ability of photons toionize gas molecules contained in the device, causing a detectable change ofconductivity of the gas.[120]
Planck's energy formula 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 spectrum of agas-discharge lamp can be altered by filling it with (mixtures of) gases with different electronicenergy level configurations.[121]
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.[122]
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 biology to study the interaction of suitableproteins.[123]
Several different kinds ofhardware random number generators 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 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.[124][125]
Two-photon physics studies interactions between photons, which are rare. In 2018, Massachusetts Institute of Technology researchers announced the discovery of bound photon triplets, which may involvepolaritons.[127][128]
^The issue was first formulated by Theodore Duddell Newton andEugene Wigner.[68][69][70] The challenges arise from the fundamental nature of theLorentz group, which describes the symmetries ofspacetime in special relativity. Unlike the generators ofGalilean transformations, the generators ofLorentz boosts do not commute, and so simultaneously assigning low uncertainties to all coordinates of a relativistic particle's position becomes problematic.[71]
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^Polaritons section 10.10.1, Raman and Brillouin scattering section 10.11.3 inPatterson, J. D.; Bailey, B. C. (2007).Solid-State Physics: Introduction to the Theory.Springer.ISBN978-3-540-24115-7.
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