# Photon

Last updated
 Composition Photons are emitted in a threaded laser beam Elementary particle Bose–Einstein Electromagnetic, Weak, Gravity γ Albert Einstein (1905) The name of "photon" is generally attributed to Gilbert N. Lewis (1926) 0 <1×10−18  eV/c2 [1] Stable [1] 0 <1×10−35  e [1] 1 −1 [1] −1 [1] I ( J P C )=0,1(1−−) [1]

The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force (even when static via virtual particles). The invariant mass of the photon is zero; it always moves at the speed of light within a vacuum.

In particle physics, an elementary particle or fundamental particle is a subatomic particle with no sub structure, thus not composed of other particles. Particles currently thought to be elementary include the fundamental fermions, which generally are "matter particles" and "antimatter particles", as well as the fundamental bosons, which generally are "force particles" that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.

In physics, a quantum is the minimum amount of any physical entity involved in an interaction. The fundamental notion that a physical property may be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.

An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of non-comoving charged objects at any distance of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature.

## Contents

Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a single photon may be refracted by a lens and exhibit wave interference with itself, and it can behave as a particle with definite and finite measurable position or momentum, though not both at the same time as per Heisenberg's uncertainty principle. The photon's wave and quantum qualities are two observable aspects of a single phenomenon—they cannot be described by any mechanical model; [2] a representation of this dual property of light that assumes certain points on the wavefront to be the seat of the energy is not possible. The quanta in a light wave are not spatially localized.

Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be partly described in terms not only of particles, but also of waves. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote:

It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.

In physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.

The modern concept of the photon was developed gradually by Albert Einstein in the early 20th century to explain experimental observations that did not fit the classical wave model of light. The benefit of the photon model is that it accounts for the frequency dependence of light's energy, and explains the ability of matter and electromagnetic radiation to be in thermal equilibrium. The photon model accounts for anomalous observations, including the properties of black-body radiation, that others (notably Max Planck) had tried to explain using semiclassical models. In that model, light is described by Maxwell's equations, but material objects emit and absorb light in quantized amounts (i.e., they change energy only by certain particular discrete amounts). Although these semiclassical models contributed to the development of quantum mechanics, many further experiments [3] [4] beginning with the phenomenon of Compton scattering of single photons by electrons, validated Einstein's hypothesis that light itself is quantized. [5] In December 1926, American physical chemist Gilbert N. Lewis coined the widely adopted name "photon" for these particles in a letter to Nature . [6] [7] [8] After Arthur H. Compton won the Nobel Prize in 1927 for his scattering studies, [9] most scientists accepted that light quanta have an independent existence, and the term "photon" was accepted.

Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics. His work is also known for its influence on the philosophy of science. He is best known to the general public for his mass–energy equivalence formula , which has been dubbed "the world's most famous equation". He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory.

The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:

In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states. These include classical everyday phases such as solid, liquid, and gas – for example water exists as ice, liquid water, and gaseous steam – but other states are possible, including plasma, Bose–Einstein condensates, fermionic condensates, and quark–gluon plasma.

In the Standard Model of particle physics, photons and other elementary particles are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of particles, such as charge, mass, and spin, are determined by this gauge symmetry. The photon concept has led to momentous advances in experimental and theoretical physics, including lasers, Bose–Einstein condensation, quantum field theory, and the probabilistic interpretation of quantum mechanics. It has been applied to photochemistry, high-resolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers, and for applications in optical imaging and optical communication such as quantum cryptography.

The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe, as well as classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists around the world, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, confirmation of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.

Particle physics is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word particle can refer to various types of very small objects, particle physics usually investigates the irreducibly smallest detectable particles and the fundamental interactions necessary to explain their behaviour. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, the Higgs boson, or even to the oldest known force field, gravity.

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur differently.

## Nomenclature

The word quanta (singular quantum, Latin for how much ) was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1900, the German physicist Max Planck was studying black-body radiation, and specifically the Ultraviolet Catastrophe: he suggested that the experimental observations would be explained if the energy carried by electromagnetic waves could only be released in "packets" of energy. In his 1901 article [10] in Annalen der Physik he called these packets "energy elements". In 1905, Albert Einstein published a paper in which he proposed that many light-related phenomena—including black-body radiation and the photoelectric effect—would be better explained by modelling electromagnetic waves as consisting of spatially localized, discrete wave-packets. [11] He called such a wave-packet the light quantum (German: das Lichtquant). [lower-alpha 1]

Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Mass, time, distance, heat, and angular separation are among the familiar examples of quantitative properties.

The electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

Max Karl Ernst Ludwig Planck, ForMemRS was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.

The name photon derives from the Greek word for light, φῶς (transliterated phôs). Arthur Compton used photon in 1928, referring to Gilbert N. Lewis, who coined the term in a letter to Nature on December 18, 1926. [6] [12] In fact, the same name was used earlier but was never widely adopted before Lewis: in 1916 by the American physicist and psychologist Leonard T. Troland, in 1921 by the Irish physicist John Joly, in 1924 by the French physiologist René Wurmser (1890–1993), and in 1926 by the French physicist Frithiof Wolfers (1891–1971). [8] 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 very soon by most physicists after Compton used it. [8] [lower-alpha 2]

Greek is an independent branch of the Indo-European family of languages, native to Greece, Cyprus and other parts of the Eastern Mediterranean and the Black Sea. It has the longest documented history of any living Indo-European language, spanning more than 3000 years of written records. Its writing system has been the Greek alphabet for the major part of its history; other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic, and many other writing systems.

Arthur Holly Compton was an American physicist who won the Nobel Prize in Physics in 1927 for his 1923 discovery of the Compton effect, which demonstrated the particle nature of electromagnetic radiation. It was a sensational discovery at the time: the wave nature of light had been well-demonstrated, but the idea that light had both wave and particle properties was not easily accepted. He is also known for his leadership of the Manhattan Project's Metallurgical Laboratory at the University of Chicago, and served as Chancellor of Washington University in St. Louis from 1945 to 1953.

Gilbert Newton Lewis was an American physical chemist and a former Dean of the College of Chemistry at University of California, Berkeley. Lewis was best known for his discovery of the covalent bond and his concept of electron pairs; his Lewis dot structures and other contributions to valence bond theory have shaped modern theories of chemical bonding. Lewis successfully contributed to chemical thermodynamics, photochemistry, and isotope separation, and is also known for his concept of acids and bases. Lewis also researched on relativity and quantum physics, and in 1926 he coined the term "photon" for the smallest unit of radiant energy.

In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma). This symbol for the photon probably derives from gamma rays, which were discovered in 1900 by Paul Villard, [14] [15] named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade. [16] In chemistry and optical engineering, photons are usually symbolized by , which is the photon energy, where h is Planck constant and the Greek letter ν (nu) is the photon's frequency. [17] Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f.

## Physical properties

A photon is massless, [lower-alpha 3] has no electric charge, [18] [19] and is a stable particle. A photon has two possible polarization states. [20] In the momentum representation of the photon, which is preferred in quantum field theory, a photon is described by its wave vector, which determines its wavelength λ and its direction of propagation. A photon's wave vector may not be zero and can be represented either as a spatial 3-vector or as a (relativistic) four-vector; in the latter case it belongs to the light cone (pictured). Different signs of the four-vector denote different circular polarizations, but in the 3-vector representation one should account for the polarization state separately; it actually is a spin quantum number. In both cases the space of possible wave vectors is three-dimensional.

The photon is the gauge boson for electromagnetism, [21] :29–30 and therefore all other quantum numbers of the photon (such as lepton number, baryon number, and flavour quantum numbers) are zero. [22] Also, the photon does not obey the Pauli exclusion principle, [23] :1221 but instead obeys Bose–Einstein statistics.

Photons are emitted in many natural processes. For example, when a charge is accelerated it emits synchrotron radiation. During a molecular, atomic or nuclear transition to a lower energy level, photons of various energy will be emitted, ranging from radio waves to gamma rays. Photons can also be emitted when a particle and its corresponding antiparticle are annihilated (for example, electron–positron annihilation). [23] :572,1114,1172

In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0: [24]

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

The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ):

${\displaystyle E=\hbar \omega =h\nu ={\frac {hc}{\lambda }}}$
${\displaystyle {\boldsymbol {p}}=\hbar {\boldsymbol {k}},}$

where k is the wave vector (where the wave number k = |k| = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant. [25]

Since p points in the direction of the photon's propagation, the magnitude of the momentum is

${\displaystyle p=\hbar k={\frac {h\nu }{c}}={\frac {h}{\lambda }}.}$

The photon also carries a quantity called spin angular momentum that does not depend on its frequency. [26] The magnitude of its spin is 2ħ and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called right-handed and left-handed, correspond to the two possible circular polarization states of the photon. [27]

To illustrate the significance of these formulae, the annihilation of a particle with its antiparticle in free space must result in the creation of at least two photons for the following reason. In the center of momentum frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since, as we have seen, it is 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. (However, it is possible if the system interacts with another particle or field for the annihilation to produce one photon, as when a positron annihilates with a bound atomic electron, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry.) [28] :64–65 The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of four-momentum.

Seen another way, the photon can be considered as its own antiparticle (thus an "antiphoton" is simply a normal photon). The reverse process, pair production, is the dominant mechanism by which high-energy photons such as gamma rays lose energy while passing through matter. [29] 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 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. [30]

Each photon carries two distinct and independent forms of angular momentum of light. The spin angular momentum of light of a particular photon is always either +ħ or −ħ. The light orbital angular momentum of a particular photon can be any integer N, including zero. [31]

### Experimental checks on photon mass

Current commonly accepted physical theories imply or assume the photon to be strictly massless. If the photon is not a strictly massless particle, it would not move at the exact speed of light, c, in vacuum. Its speed would be lower and depend on its frequency. 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. [32] Thus, it would still be the speed of spacetime ripples (gravitational waves and gravitons), 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 thus allows one to test Coulomb's law to very high precision. [33] A null result of such an experiment has set a limit of m10−14 eV/c2. [34]

Sharper upper limits on the speed of light have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very 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 1/2m2AμAμ would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m<3×10−27 eV/c2. [35] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring. [36] Such methods were used to obtain the sharper upper limit of 1.07×10−27 eV/c2 (the equivalent of 10−18 atomic mass units) given by the Particle Data Group. [37]

These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model-dependent. [38] If the photon mass is generated via the Higgs mechanism then the upper limit of m10−14 eV/c2 from the test of Coulomb's law is valid.

Photons inside superconductors develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors. [39]

## Historical development

In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637), [40] Robert Hooke (1665), [41] and Christiaan Huygens (1678); [42] however, particle models remained dominant, chiefly due to the influence of Isaac Newton. [43] In the early nineteenth century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted. [44] In 1865, James Clerk Maxwell's prediction [45] that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves [46] —seemed to be the final blow to particle models of light.

The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; 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 (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity. [47] [lower-alpha 4]

At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers [48] culminated in Max Planck's hypothesis [10] [49] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E = . As shown by Albert Einstein, [11] [50] some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics. [51]

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. [11] Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over space. [11] In 1909 [50] and 1916, [52] Einstein showed that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentum p = h/λ, making them full-fledged particles. This photon momentum was observed experimentally [53] by Arthur Compton, for which he received the Nobel Prize in 1927. The pivotal question was then: 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 in quantum electrodynamics and its successor, the Standard Model (see § Second quantization and § The photon as a gauge boson , below).

## Einstein's light quantum

Unlike Planck, Einstein entertained the possibility that there might be actual physical quanta of light—what we now call photons. He noticed that a light quantum with energy proportional to its frequency would explain a number of troubling puzzles and paradoxes, including an unpublished law by Stokes, the ultraviolet catastrophe, and the photoelectric effect. Stokes's law said simply that the frequency of fluorescent light cannot be greater than the frequency of the light (usually ultraviolet) inducing it. Einstein eliminated the ultraviolet catastrophe by imagining a gas of photons behaving like a gas of electrons that he had previously considered. He was advised by a colleague to be careful how he wrote up this paper, in order to not challenge Planck, a powerful figure in physics, too directly, and indeed the warning was justified, as Planck never forgave him for writing it. [55]

## Early objections

Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture. [56] However, before Compton's experiment [53] showed that photons carried momentum proportional to their wave number (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien, [48] Planck [49] and Millikan. [56] ) 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 Compton scattering, where it was much more difficult not to ascribe quantization to light itself to explain the observed results. [57]

Even after Compton's experiment, Niels Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model. [58] To account for the data then available, two drastic hypotheses had to be made:

1. Energy and momentum are conserved only on the average in interactions between matter and radiation, but not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (the jump between energy states) with the continuous release of energy as radiation.
2. Causality is abandoned. For example, spontaneous emissions are merely emissions stimulated by a "virtual" electromagnetic field.

However, refined Compton experiments showed that energy–momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible". [54] Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics. [59]

A few physicists persisted [60] in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of quantum 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 as absolutely definitive; since it relied on the interaction of light with matter, and a sufficiently complete theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photon-correlation experiments. [lower-alpha 5] Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven.

## Wave–particle duality and uncertainty principles

Photons, like all quantum objects, exhibit wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment exhibits interference phenomena but only if no measure was made at the slit. A single photon passing through a double-slit experiment lands on the screen with a probability distribution given by its interference pattern determined by Maxwell's equations. [61] However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter. [62] Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see § Second quantization and § The photon as a gauge boson below).

A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum.

An elegant illustration of the uncertainty principle is Heisenberg's thought experiment for locating an electron with an ideal microscope. [63] The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics

${\displaystyle \Delta x\sim {\frac {\lambda }{\sin \theta }}}$

where θ is the aperture angle of the microscope and λ is the wavelength of the light used to observe the electron. Thus, the position uncertainty ${\displaystyle \Delta x}$ can be made arbitrarily small by reducing the wavelength λ. Even if the momentum of the electron is initially known, the light impinging on the electron will give it a momentum "kick" ${\displaystyle \Delta p}$ of some unknown amount, rendering the momentum of the electron uncertain. If light were not quantized into photons, the uncertainty ${\displaystyle \Delta p}$ could be made arbitrarily small by reducing the light's intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty principle. By contrast, Einstein's formula for photon momentum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals

${\displaystyle \Delta p\sim p_{\text{photon}}\sin \theta ={\frac {h}{\lambda }}\sin \theta }$

giving the product ${\displaystyle \Delta x\Delta p\,\sim \,h}$, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized. [64]

The analogous uncertainty principle for photons forbids the simultaneous measurement of the number ${\displaystyle n}$ of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase ${\displaystyle \phi }$ of that wave

${\displaystyle \Delta n\Delta \phi >1}$

See coherent state and squeezed coherent state for more details.

Both photons and electrons create analogous interference patterns when passed through a double-slit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles (electron), this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell's equations describing the photon's electromagnetic wave are simply Schrödinger's equation for photons, most physicists do not agree. [65] [66] For one thing, they are mathematically different; most obviously, Schrödinger's one equation for the electron solves for a complex field, whereas Maxwell's four equations solve for real fields. More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons. [67] As photons are massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate ${\displaystyle |\mathbf {r} \rangle }$, and, thus, the normal Heisenberg uncertainty principle ${\displaystyle \Delta x\Delta p>h/2}$ does not pertain to photons. A few substitute wave functions have been suggested for the photon, [68] [69] [70] [71] but they have not come into general use. Instead, physicists generally accept the second-quantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.

Another interpretation, that avoids duality, is the De Broglie–Bohm theory: known also as the pilot-wave model. In that theory, the photon is both, wave and particle. [72] "This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored", J.S. Bell. [73]

## Bose–Einstein model of a photon gas

In 1924, Satyendra Nath Bose derived Planck's law of black-body radiation without using any electromagnetism, but rather by using a modification of coarse-grained counting of phase space. [74] Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction", [75] [76] now understood as the requirement for a symmetric quantum mechanical state. This work led to the concept of coherent 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 lowest quantum state at low enough temperatures; this Bose–Einstein condensation was observed experimentally in 1995. [77] It was later used by Lene Hau to slow, and then completely stop, light in 1999 [78] and 2001. [79]

The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with half-integer spin). By the spin-statistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi–Dirac statistics). [80]

## Stimulated and spontaneous emission

In 1916, Albert Einstein showed that Planck's radiation law could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a link between the rates at which atoms emit and absorb photons. The condition follows from the assumption that functions of the emission and absorption of radiation by the atoms are independent of each other, and that thermal equilibrium is made by way of the radiation's interaction with the atoms. Consider a cavity in thermal equilibrium with all parts of itself and filled with electromagnetic radiation and that the atoms can emit and absorb that radiation. Thermal equilibrium requires that the energy density ${\displaystyle \rho (\nu )}$ of photons with frequency ${\displaystyle \nu }$ (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate at which they absorb them. [81]

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

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

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

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

where ${\displaystyle A_{ij}}$ is the rate constant for emitting a photon spontaneously, and ${\displaystyle B_{ij}}$ 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 ${\displaystyle R_{ji}}$ and ${\displaystyle R_{ij}}$ must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of ${\displaystyle N_{i}}$ and ${\displaystyle N_{j}}$ is ${\displaystyle g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},}$ where ${\displaystyle g_{i,j}}$ are the degeneracy of the state i and that of j, respectively, ${\displaystyle E_{i,j}}$ their energies, k the Boltzmann constant and T the system's temperature. From this, it is readily derived that ${\displaystyle g_{i}B_{ij}=g_{j}B_{ji}}$ and

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

The A and Bs are collectively known as the Einstein coefficients. [82]

Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients ${\displaystyle A_{ij}}$, ${\displaystyle B_{ji}}$ and ${\displaystyle B_{ij}}$ once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis". [83] In fact, in 1926, Paul Dirac derived the ${\displaystyle B_{ij}}$ rate constants by using a semiclassical approach, [84] and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory. [85] [86] Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory; [87] [88] [89] earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field.

Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered by Newton in his treatment of birefringence 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. [43] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation [54] from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function [90] [91] was inspired by Einstein's later work searching for a more complete theory. [92]

## Second quantization and high energy photon interactions

In 1910, Peter Debye derived Planck's law of black-body radiation from a relatively simple assumption. [93] He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of ${\displaystyle h\nu }$, where ${\displaystyle \nu }$ 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 blackbody radiation, which were derived by Einstein in 1909. [50]

In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way. [94] As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. Treated quantum mechanically, the energy levels of such oscillators are known to be ${\displaystyle E=nh\nu }$, where ${\displaystyle \nu }$ is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy ${\displaystyle E=nh\nu }$ as a state with ${\displaystyle n}$ photons, each of energy ${\displaystyle h\nu }$. This approach gives the correct energy fluctuation formula.

Dirac took this one step further. [85] [86] 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 ${\displaystyle A_{ij}}$ and ${\displaystyle B_{ij}}$ 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 derived Planck's law of black-body radiation by assuming B–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics.

Dirac's second-order perturbation theory can involve virtual photons, transient intermediate states of the electromagnetic field; the static electric and magnetic interactions are mediated by such virtual photons. In such quantum field theories, the probability amplitude of observable events is calculated by summing over all possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy ${\displaystyle E=pc}$, and may have extra polarization states; depending on the gauge 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. Indeed, such second-order and higher-order perturbation calculations can give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization.

Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electronpositron pairs. [95] In fact, such photon–photon scattering (see two-photon physics), as well as electron–photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider. [96]

In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode

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

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

## The hadronic properties of the photon

Measurements of the interaction between energetic photons and hadrons 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 [97] in spite of the fact that the electric charge structures of protons and neutrons are substantially different. A theory called Vector 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. [98] 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 in QCD and described by the photon structure function. [99] [100] A comprehensive comparison of data with theoretical predictions was presented in a review in 2000. [101]

## The photon as a gauge boson

The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime. [102] For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of complex numbers of absolute value 1, which reflects the ability to vary the phase of a complex field without affecting observables or real valued functions made from it, such as the energy or the Lagrangian.

The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be ${\displaystyle \pm \hbar }$. These two spin components correspond to the classical concepts of right-handed and left-handed circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states. [102]

In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W+, W and Z0 and are responsible for the weak interaction. Unlike the photon, these gauge bosons have mass, owing to a mechanism that breaks their SU(2) gauge symmetry. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics. [103] [104] [105] Physicists continue to hypothesize grand unified theories that connect these four gauge bosons with the eight gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally. [106]

## Contributions to the mass of a system

The energy of a system that emits a photon is decreased by the energy ${\displaystyle E}$ of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount ${\displaystyle {E}/{c^{2}}}$. Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form ${\displaystyle {E}/{c^{2}}}$ for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei). [107]

This concept is applied in key predictions of quantum 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 as renormalization. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium. [108]

Since photons contribute to the stress–energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound–Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves. [109]

## Photons in matter

Light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. For example, photons engage in so many collisions on the way from the core of the sun that radiant energy can take about a million years to reach the surface; [110] however, once in open space, a photon takes only 8.3 minutes to reach Earth. The factor by which the speed is decreased is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric 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 produce quasi-particles known as polariton (other quasi-particles are phonons and excitons); this polariton has a nonzero effective mass, which means that it cannot travel at c. Light of different frequencies may travel through matter at different speeds; this is called dispersion (not to be confused with scattering). In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering. [111]

Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal (C20H28O), which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and co-workers. The absorption provokes a cis-trans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry. [112] [113]

## Technological applications

Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission.

Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon of sufficient energy strikes a metal plate and knocks free an electron, initiating an ever-amplifying avalanche of electrons. Semiconductor charge-coupled device chips use a similar effect: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules contained in the device, causing a detectable change of conductivity of the gas. [114]

Planck's energy formula ${\displaystyle E=h\nu }$ 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, the emission spectrum of a gas-discharge lamp can be altered by filling it with (mixtures of) gases with different electronic energy level configurations.

Under some conditions, an energy transition can be excited by "two" photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the spectrum where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see two-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy. [115]

In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins. [116]

Several different kinds of hardware 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 a beam-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". [117] [118]

## Recent research

Much research has been devoted to applications of photons in the field of quantum optics. Photons seem well-suited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as two-photon absorption, self-phase modulation, modulational instability and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography. [lower-alpha 6]

Two-photon physics studies interactions between photons, which are rare. In 2018, MIT researchers announced the discovery of bound photon triplets, which may involve polaritons. [119] [120]

## Notes

1. Although the 1967 Elsevier translation of Planck's Nobel Lecture interprets Planck's Lichtquant as "photon", the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein Planck, Max (1922). The Origin and Development of the Quantum Theory. Clarendon Press. (here) uses "light-quantum". No evidence is known that Planck himself used the term "photon" by 1926 (see also).
2. Isaac Asimov credits Arthur Compton with defining quanta of energy as photons in 1923. [13]
3. The mass of the photon is believed to be exactly zero. Some sources also refer to the relativistic mass , which is just the energy scaled to units of mass. For a photon with wavelength λ or energy E, this is h/λc or E/c2. This usage for the term "mass" is no longer common in scientific literature. Further info: What is the mass of a photon?
4. The phrase "no matter how intense" refers to intensities below approximately 1013 W/cm2 at which point perturbation theory begins to break down. In contrast, in the intense regime, which for visible light is above approximately 1014 W/cm2, the classical wave description correctly predicts the energy acquired by electrons, called ponderomotive energy. (See also: Boreham et al. (1996). "Photon density and the correspondence principle of electromagnetic interaction".) By comparison, sunlight is only about 0.1 W/cm2.
5. These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality. In 1977, Kimble et al. demonstrated an analogous anti-bunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photon-anticorrelation experiment of Grangier et al. (1986). This work is reviewed and simplified further in Thorn et al. (2004). (These references are listed below.)
6. Introductory-level material on the various sub-fields of quantum optics can be found in Fox, M. (2006). Quantum Optics: An Introduction. Oxford University Press. ISBN   978-0-19-856673-1.

## Related Research Articles

In atomic physics, the Rutherford–Bohr model or Bohr model or Bohr diagram, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by revolving electrons —similar to the structure of the Solar System, but with attraction provided by electrostatic forces rather than gravity. After the cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911) came the Rutherford–Bohr model or just Bohr model for short (1913). The improvement to the Rutherford model is mostly a quantum physical interpretation of it. The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants.

In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

The photoelectric effect is the emission of electrons or other free carriers when light hits a material. Electrons emitted in this manner can be called photoelectrons. This phenomenon is commonly studied in electronic physics, as well as in fields of chemistry, such as quantum chemistry and electrochemistry.

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics and is used to construct physical models of subatomic particles and quasiparticles.

Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO theory includes classical, semi-classical and quantum treatments. Typically, the theory and applications of emission, absorption, scattering of electromagnetic radiation (light) from excited atoms and molecules, analysis of spectroscopy, generation of lasers and masers, and the optical properties of matter in general, fall into these categories.

Compton scattering, discovered by Arthur Holly Compton, is the scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy of the photon, called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering occurs when a charged particle transfers part of its energy to a photon.

Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. As well as atoms and molecules, the empty space of the vacuum has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions, and force fields, whose quanta are bosons. All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics, since some systems can detect the existence of this energy. However this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein's theory of special relativity.

In the physical sciences, the wavenumber is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.

Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter can exhibit wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. The concept that matter behaves like a wave was proposed by Louis de Broglie in 1924. It is also referred to as the de Broglie hypothesis. Matter waves are referred to as de Broglie waves.

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify the elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.

Quantum optics (QO) is a field of research that uses semi-classical and quantum-mechanical physics to investigate phenomena involving light and its interactions with matter at submicroscopic levels. In other words it is quantum mechanics applied to photons or light.

The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as the semi-classical approximation to modern quantum mechanics.

The Abraham–Minkowski controversy is a physics debate concerning electromagnetic momentum within dielectric media. Traditionally, it is argued that in the presence of matter the electromagnetic stress-energy tensor by itself is not conserved (divergenceless). Only the total stress-energy tensor carries unambiguous physical significance, and how one apportions it between an "electromagnetic" part and a "matter" part depends on context and convenience. In other words, the electromagnetic part and the matter part in the total momentum can be arbitrarily distributed as long as the total momentum is kept the same. There are two incompatible equations to describe momentum transfer between matter and electromagnetic fields. These two equations were first suggested by Hermann Minkowski (1908) and Max Abraham (1909), from which the controversy's name derives. Both were claimed to be supported by experimental data. Theoretically, it is usually argued that Abraham's version of momentum "does indeed represent the true momentum density of electromagnetic fields" for electromagnetic waves, while Minkowski's version of momentum is "pseudomomentum" or "wave momentum".

Quantum mechanics is the science of the very small. It explains the behavior of matter and its interactions with energy on the scale of atoms and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that created a shift in the original scientific paradigm: the theory of relativity and the development of quantum mechanics. This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century. It describes these concepts in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics.

The history of quantum mechanics is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" ε (epsilon) such that each of these energy elements is proportional to the frequency ν with which each of them individually radiate energy, as defined by the following formula:

The Planck constant is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

The Planck–Einstein relation is also referred to as the Einstein relation, Planck's energy–frequency relation, the Planck relation, and the Planck equation. Also the eponym Planck formula belongs on this list, but also often refers to Planck's law instead. These various eponyms are far from standard; they are used only sporadically, neither regularly nor very widely. They refer to a formula integral to quantum mechanics, which states that the energy of a photon, E, known as photon energy, is proportional to its frequency, ν:

In 1922 American physicist William Duane presented a discrete momentum-exchange model of the reflection of X-Ray photons by a crystal lattice. Duane showed that such a model gives the same scattering angles as the ones calculated via a wave diffraction model, see Bragg's Law.

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79. Section 1.4 in Wilson, J.; Hawkes, F.J.B. (1987). Lasers: Principles and Applications. New York: Prentice Hall. ISBN   978-0-13-523705-2.
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89. Pais, A. (1986). Inward Bound: Of Matter and Forces in the Physical World. Oxford University Press. p. 260. ISBN   978-0-19-851997-3. Specifically, Born claimed to have been inspired by Einstein's never-published attempts to develop a "ghost-field" theory, in which point-like photons are guided probabilistically by ghost fields that follow Maxwell's equations.
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92. Photon-photon-scattering section 7-3-1, renormalization chapter 8-2 in Itzykson, C.; Zuber, J.-B. (1980). Quantum Field Theory. McGraw-Hill. ISBN   978-0-07-032071-0.
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94. Bauer, T.H.; Spital, R.D.; Yennie, D.R.; Pipkin, F.M. (1978). "The hadronic properties of the photon in high-energy interactions". Reviews of Modern Physics. 50 (2): 261. Bibcode:1978RvMP...50..261B. doi:10.1103/RevModPhys.50.261.
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99. Ryder, L.H. (1996). Quantum field theory (2nd ed.). Cambridge University Press. ISBN   978-0-521-47814-4.
100. Sheldon Glashow Nobel lecture, delivered 8 December 1979.
101. Abdus Salam Nobel lecture, delivered 8 December 1979.
102. Steven Weinberg Nobel lecture, delivered 8 December 1979.
103. E.g., chapter 14 in Hughes, I.S. (1985). Elementary particles (2nd ed.). Cambridge University Press. ISBN   978-0-521-26092-3.
104. E.g., section 10.1 in Dunlap, R.A. (2004). An Introduction to the Physics of Nuclei and Particles. Brooks/Cole. ISBN   978-0-534-39294-9.
105. Radiative correction to electron mass section 7-1-2, anomalous magnetic moments section 7-2-1, Lamb shift section 7-3-2 and hyperfine splitting in positronium section 10-3 in Itzykson, C.; Zuber, J.-B. (1980). Quantum Field Theory. McGraw-Hill. ISBN   978-0-07-032071-0.
106. E.g. sections 9.1 (gravitational contribution of photons) and 10.5 (influence of gravity on light) in Stephani, H.; Stewart, J. (1990). General Relativity: An Introduction to the Theory of Gravitational Field. Cambridge University Press. pp. 86 ff, 108 ff. ISBN   978-0-521-37941-0.
107. Naeye, R. (1998). Through the Eyes of Hubble: Birth, Life and Violent Death of Stars. CRC Press. ISBN   978-0-7503-0484-9. OCLC   40180195.
108. Polaritons section 10.10.1, Raman and Brillouin scattering section 10.11.3 in Patterson, J.D.; Bailey, B.C. (2007). Solid-State Physics: Introduction to the Theory. Springer. ISBN   978-3-540-24115-7.
109. E.g. section 11-5 C in Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond, G.S. (1980). Organic Chemistry (4th ed.). McGraw-Hill. ISBN   978-0-07-050115-7.
110. Nobel lecture given by G. Wald on December 12, 1967, online at nobelprize.org: The Molecular Basis of Visual Excitation.
111. Photomultiplier section 1.1.10, CCDs section 1.1.8, Geiger counters section 1.3.2.1 in Kitchin, C.R. (2008). Astrophysical Techniques. Boca Raton, FL: CRC Press. ISBN   978-1-4200-8243-2.
112. Denk, W.; Svoboda, K. (1997). "Photon upmanship: Why multiphoton imaging is more than a gimmick". Neuron . 18 (3): 351–357. doi:10.1016/S0896-6273(00)81237-4. PMID   9115730.
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117. Liang, Qi-Yu; et al. (16 February 2018). "Observation of three-photon bound states in a quantum nonlinear medium". Science . 359 (6377): 783–786. arXiv:. Bibcode:2018Sci...359..783L. doi:10.1126/science.aao7293. PMID   29449489 . Retrieved 17 February 2018.

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