Photon

Overview

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a

**photon**is an elementary particle

Elementary particle

In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

, the quantum

Quantum

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

of the electromagnetic interaction and the basic unit of light

Light

Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

and all other forms of electromagnetic radiation

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

. It is also the force carrier

Force carrier

In particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type...

for the electromagnetic force. The effects of this force

Force

In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

are easily observable at both the microscopic and macroscopic level, because the photon has no rest mass; this allows for interaction

Fundamental interaction

In particle physics, fundamental interactions are the ways that elementary particles interact with one another...

s at long distances. Like all elementary particles, photons are currently best explained by quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

and will exhibit wave–particle duality

Wave–particle duality

Wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects...

, exhibiting properties of both wave

Wave

In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

s and particles.

Unanswered Questions

Encyclopedia

In physics

, a

, the quantum

of the electromagnetic interaction and the basic unit of light

and all other forms of electromagnetic radiation

. It is also the force carrier

for the electromagnetic force. The effects of this force

are easily observable at both the microscopic and macroscopic level, because the photon has no rest mass; this allows for interaction

s at long distances. Like all elementary particles, photons are currently best explained by quantum mechanics

and will exhibit wave–particle duality

, exhibiting properties of both wave

s and particles. For example, a single photon may be refracted

by a lens

or exhibit wave interference with itself, but also act as a particle giving a definite result when quantitative momentum (quantized angular momentum

) is measured.

The modern concept of the photon was developed gradually by Albert Einstein

to explain experimental observations that did not fit the classical wave model

of light. In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter

and radiation

to be in thermal equilibrium

. It also accounted for anomalous observations, including the properties of black body radiation, that other physicists, most notably Max Planck

, had sought to explain using

, but the material objects that emit and absorb light are quantized. Although these semiclassical models contributed to the development of quantum mechanics, further experiments validated Einstein's hypothesis that

; the quanta

of light are photons.

In the Standard Model

of particle physics

, photons are described as a necessary consequence of physical laws having a certain symmetry

at every point in spacetime

. The intrinsic properties of photons, such as charge

, mass

and spin

, are determined by the properties of this gauge symmetry

. The neutrino theory of light

, which attempts to describe the photon as a composite structure, has been unsuccessful so far.

The photon concept has led to momentous advances in experimental and theoretical physics, such as laser

s, 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 computer

s and for sophisticated applications in optical communication

such as quantum cryptography

.

he called these packets "energy elements". The wordIn physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

(singular

, including electricity

. Later, in 1905 Albert Einstein

went further by suggesting that electromagnetic waves could only exist in these discrete wave-packets. He called such a wave

-packet

for light, (transliterated

, who published a speculative theory in which photons were "uncreatable and indestructible". Although Lewis' theory was never accepted as it was contradicted by many experiments, his new name,

credits Arthur Compton

with defining quanta of energy as photons in 1923.

In physics, a photon is usually denoted by the symbol

gamma

). This symbol for the photon probably derives from gamma ray

s, which were discovered in 1900 by Paul Villard

, named by Ernest Rutherford

in 1903, and shown to be a form of electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

in 1914 by Rutherford and Edward Andrade

. In chemistry

and optical engineering

, photons are usually symbolized by

) is the photon's frequency

. Much less commonly, the photon can be symbolized by

of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the

, and does not decay spontaneously

in empty space. A photon has two possible polarization

states and is described by exactly three continuous parameters: the components of its wave vector

, which determine its wavelength

for electromagnetism

, and therefore all other quantum numbers of the photon (such as lepton number

, baryon number, and flavour quantum numbers) are zero.

Photons are emitted in many natural processes. For example, when a charge is accelerated

it emits synchrotron radiation

. During a molecular

, atom

ic or nuclear

transition to a lower energy level

, photons of various energy will be emitted, from infrared light to gamma ray

s. A photon can also be emitted when a particle and its corresponding antiparticle

are annihilated

(for example, electron-positron annihilation

).

In empty space, the photon moves at

) and its energy

and momentum

are related by , where

of the momentum vector

The energy and momentum of a photon depend only on its frequency

(

(

where

(where the wave number ), is the angular frequency

, and is the reduced Planck constant

.

Since

The photon also carries spin angular momentum

that does not depend on its frequency. The magnitude of its spin is 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.

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

frame

, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since it is determined, as we have seen, only 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 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.) 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. The reverse process, pair production

, is the dominant mechanism by which high-energy photons such as gamma ray

s lose energy while passing through matter. 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 radiationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

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.

s), but it would not be the speed of photons.

A massive photon would have 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 cause the presence of an electric field

inside 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. A null result of such an experiment has set a limit of

Sharper upper limits 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 long length scales, only the magnetic field is observable if the photon is massless. In case of a massive photon, the mass term would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of

These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent. If the photon mass is generated via the Higgs mechanism

then the upper limit of

Photons inside superconductors

models cannot easily account for the refraction

, diffraction

and birefringence

of light, wave theories of light were proposed by René Descartes

(1637), Robert Hooke

(1665), and Christian Huygens (1678); however, particle models remained dominant, chiefly due to the influence of Isaac Newton

. 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. In 1865, James Clerk Maxwell

's prediction

that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves

—seemed to be the final blow to particle models of light.

The Maxwell wave theory

, however, does not account for

, 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.The phrase "no matter how intense" refers to intensities below approximately 10

begins to break down. In contrast, in the intense regime, which for visible light is above approximately 10

. (See also: Boreham

At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers culminated in Max Planck

's hypothesis that the energy of

, some form of energy quantizationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

; for this explanation of the photoelectric effect

, Einstein received the 1921 Nobel Prize

in physics.

Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself. Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if theIn classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

. This photon momentum was observed experimentally 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 EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

for the rest of his life, and was solved in quantum electrodynamics

and its successor, the Standard Model

(see Second quantization and The photon as a gauge boson, below).

's Nobel lecture. However, before Compton's experiment

showing that photons carried momentumIn classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

proportional to their wave number (or frequency) (1922), most physicists were reluctant to believe that electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

itself might be particulate. (See, for example, the Nobel lectures of Wien

, Planck

and Millikan.). Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits 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.

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

. To account for the data then available, two drastic hypotheses had to be made:

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". Nevertheless, the failures of the BKS model inspired Werner Heisenberg

in his development of matrix mechanics

.

A few physicists persisted in developing semiclassical models in which electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

is not quantized, but matter appears to obey the laws of quantum mechanics

. Although the evidence for photons from chemical and physical experiments was overwhelming by the 1970s, this evidence could not be considered as

. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality

. In 1977, Kimble

and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment

lands on the screen exhibiting interference phenomena but only if no measure was made on the actual slit being run across. To account for the particle interpretation that phenomenon is called probability distribution

but behaves according to the Maxwell's equations

. However, experiments confirm that the photon is

. Rather, the photon seems to be a point-like particle since it is absorbed or emitted

. Nevertheless, the photon is

, as conceived by EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

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 the Second quantization and Gauge boson sections below).

A key element of quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

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

for locating an electron with an ideal microscope. 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

where is the aperture angle

of the microscope. Thus, the position uncertainty can be made arbitrarily small by reducing the wavelength λ. The momentum of the electron is uncertain, since it received a "kick" from the light scattering from it into the microscope. If light were

. 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

giving the product , 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.

The analogous uncertainty principle for photons forbids the simultaneous measurement of the number of photons (see Fock state

and the Second quantization section below) in an electromagnetic wave and the phase of that wave

See coherent state

and squeezed coherent state for more details.

Both photons and material particles such as electrons create analogous interference patterns when passing through a double-slit experiment

. For photons, this corresponds to the interference of a Maxwell light wave

whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation

. Although this similarity might suggest that Maxwell's equationsMaxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

are simply Schrödinger's equation for photons, most physicists do not agree. For one thing, they are mathematically different; most obviously, Schrödinger's one equation 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. Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate , and, thus, the normal Heisenberg uncertainty principle does not pertain to photons. A few substitute wave functions have been suggested for the photon, 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.

derived Planck's law of black-body radiation without using any electromagnetism, but rather a modification of coarse-grained counting of phase space

. Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction", now understood as the requirement for a symmetric quantum mechanical state

. This work led to the concept of coherent state

s and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (boson

s) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation

was observed experimentally in 1995.

The modern view on this is that photons are, by virtue of their integer spin, boson

s (as opposed to fermion

s with half-integer spin). By the spin-statistics theorem

, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi-Dirac statistics

).

and filled with electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density of photons with frequency (which is proportional to their number density

) is, on average, constant in time; hence, the rate at which photons of any particular frequency are

Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate for a system to

where is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lower-energy state that is initiated by the interaction with a passing photon. 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 for emitting a photon spontaneously

, and is the rate constant for emitting it in response to ambient photons (induced or stimulated emission

). In thermodynamic equilibrium, the number of atoms in state i and that of atoms in state j must, on average, be constant; hence, the rates and must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of and is where are the degeneracy

of the state i and that of j, respectively, their energies, k the Boltzmann constant and T the system's temperature

. From this, it is readily derived that

and

The A and Bs are collectively known as the

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". In fact, in 1926, Paul Dirac

derived the rate constants in using a semiclassical approach, and, in 1927, succeeded in deriving

; 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

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 path it would follow. Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation from quantum mechanics. Ironically, Max Born

's probabilistic interpretation

of the wave function was inspired by Einstein's later work searching for a more complete theory.

derived Planck's law of black-body radiation from a relatively simple assumption. 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 , 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 blackbody radiation, which were derived by Einstein in 1909.

In 1925, Born

, Heisenberg

and Jordan

reinterpreted Debye's concept in a key way. As may be shown classically, the Fourier modes

of the electromagnetic field

—a complete set of electromagnetic plane waves indexed by their wave vector

Dirac

took this one step further. He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's 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 derived Planck's law of black body radiation

by

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 theoriesQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, the probability amplitudeIn quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...

of observable events is calculated by summing over

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 electron

-positron

pairs

. In fact, such photon-photon scattering, 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

.

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

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.

. For the electromagnetic field

, this gauge symmetry is the Abelian

U(1) symmetry

of a complex number

, which reflects the ability to vary the phase

of a complex number 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 . 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.

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

. 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. 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.

This concept is applied in key predictions of quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

(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 lepton

s, the Lamb shift, and the hyperfine structure

of bound lepton pairs, such as muonium

and positronium

.

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 wavesElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

.

. In addition, light can also undergo scattering

and absorption

. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. An example would be in the core

of the Sun. Energy can take about a million years to reach the surface. However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibration between the radiation and the temperature. Thus, the time is how long it takes the

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 the 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 (quasi-particles such as phonon

s and exciton

s) to form a polariton

; this polariton has a nonzero effective mass, which means that it cannot travel at

Alternatively, photons may be viewed as

Light of different frequencies may travel through matter at different speeds

; this is called dispersion

. 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

.

Photons can also be absorbed

by nuclei, atoms or molecules, provoking transitions between their energy level

s. A classic example is the molecular transition of retinal

C

, 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

. Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration

.

.

Individual photons can be detected by several methods. The classic photomultiplier

tube exploits the photoelectric effect

: a photon landing on a metal plate ejects an electron, initiating an ever-amplifying avalanche of electrons. Charge-coupled device

chips use a similar effect in semiconductor

s: an incident photon generates a charge on a microscopic capacitor

that can be detected. Other detectors such as Geiger counter

s use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.

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 predict the frequency of the light emitted for a given energy transition. For example, the emission spectrum

of a fluorescent light bulb

can be designed using gas molecules with different electronic energy levels and adjusting the typical energy with which an electron hits the gas molecules within the bulb.An example is US Patent Nr. 5212709.

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 region 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.

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 protein

s.

Several different kinds of hardware random number generator

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".

. 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 oscillator

s. However, such processes generally do not require the assumption of photons

is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication

, especially for quantum cryptography

.Introductory-level material on the various sub-fields of quantum optics can be found in

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a

**photon**is an elementary particleElementary particle

In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

, the quantum

Quantum

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

of the electromagnetic interaction and the basic unit of light

Light

Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

and all other forms of electromagnetic radiation

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

. It is also the force carrier

Force carrier

In particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type...

for the electromagnetic force. The effects of this force

Force

In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

are easily observable at both the microscopic and macroscopic level, because the photon has no rest mass; this allows for interaction

Fundamental interaction

In particle physics, fundamental interactions are the ways that elementary particles interact with one another...

s at long distances. Like all elementary particles, photons are currently best explained by quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

and will exhibit wave–particle duality

Wave–particle duality

Wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects...

, exhibiting properties of both wave

Wave

In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

s and particles. For example, a single photon may be refracted

Refraction

Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

by a lens

Lens (optics)

A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

or exhibit wave interference with itself, but also act as a particle giving a definite result when quantitative momentum (quantized angular momentum

Angular momentum

In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

) is measured.

The modern concept of the photon was developed gradually by Albert Einstein

Albert Einstein

Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

to explain experimental observations that did not fit the classical wave model

Electromagnetic wave equation

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...

of light. In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter

Matter

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

and radiation

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

to be in thermal equilibrium

Thermal equilibrium

Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

. It also accounted for anomalous observations, including the properties of black body radiation, that other physicists, most notably Max Planck

Max Planck

Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

, had sought to explain using

*semiclassical models*, in which light is still described by Maxwell's equationsMaxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

, but the material objects that emit and absorb light are quantized. Although these semiclassical models contributed to the development of quantum mechanics, further experiments validated Einstein's hypothesis that

*light itself*is quantizedQuantization (physics)

In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...

; the quanta

Quantum

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

of light are photons.

In the Standard Model

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

of particle physics

Particle physics

Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

, photons are described as a necessary consequence of physical laws having a certain symmetry

Symmetry in physics

In physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation...

at every point in spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

. The intrinsic properties of photons, such as charge

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

, mass

Invariant mass

The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

and spin

Spin (physics)

In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

, are determined by the properties of this gauge symmetry

Gauge theory

In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...

. The neutrino theory of light

Neutrino theory of light

The neutrino theory of light is the proposal that the photon is a composite particle formed of a neutrino-antineutrino pair. It is based on the idea that emission and absorption of a photon corresponds to the creation and annihilation of a particle-antiparticle pair...

, which attempts to describe the photon as a composite structure, has been unsuccessful so far.

The photon concept has led to momentous advances in experimental and theoretical physics, such as laser

Laser

A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

s, Bose–Einstein condensation, quantum field theory

Quantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, and the probabilistic interpretation

Probability amplitude

In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...

of quantum mechanics. It has been applied to photochemistry

Photochemistry

Photochemistry, a sub-discipline of chemistry, is the study of chemical reactions that proceed with the absorption of light by atoms or molecules.. Everyday examples include photosynthesis, the degradation of plastics and the formation of vitamin D with sunlight.-Principles:Light is a type of...

, high-resolution microscopy

Two-photon excitation microscopy

Two-photon excitation microscopy is a fluorescence imaging technique that allows imaging of living tissue up to a very high depth, that is up to about one millimeter. Being a special variant of the multiphoton fluorescence microscope, it uses red-shifted excitation light which can also excite...

, and measurements of molecular distances

Fluorescence resonance energy transfer

Förster resonance energy transfer , also known as fluorescence resonance energy transfer, resonance energy transfer or electronic energy transfer , is a mechanism describing energy transfer between two chromophores.A donor chromophore, initially in its electronic excited state, may transfer energy...

. Recently, photons have been studied as elements of quantum computer

Quantum computer

A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...

s and for sophisticated applications in optical communication

Optical communication

Optical communication is any form of telecommunication that uses light as the transmission medium.An optical communication system consists of a transmitter, which encodes a message into an optical signal, a channel, which carries the signal to its destination, and a receiver, which reproduces the...

such as quantum cryptography

Quantum cryptography

Quantum key distribution uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages...

.

## Nomenclature

In 1900, Max Planck was working on black-body radiation and suggested that the energy in electromagnetic waves could only be released in "packets" of energy. In his 1901 article in Annalen der PhysikAnnalen der Physik

Annalen der Physik is one of the oldest physics journals worldwide. The journal publishes original, peer-reviewed papers in the areas of experimental, theoretical, applied and mathematical physics and related areas...

he called these packets "energy elements". The word

*quanta*Quantum

(singular

*quantum*) was used even before 1900 to mean particles or amounts of different quantitiesQuantity

Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...

, including electricity

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

. Later, in 1905 Albert Einstein

Albert Einstein

Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

went further by suggesting that electromagnetic waves could only exist in these discrete wave-packets. He called such a wave

Wave

In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

-packet

*the light quantum*(German:*das Lichtquant*). The name*photon*derives from the Greek wordGreek language

Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

for light, (transliterated

*phôs*), and was coinedAlthough 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*The origin and development of the quantum theory*, The Clarendon Press, 1922 (here http://www.readanybook.com/ebook/the-origin-and-development-of-the-quantum-theory-48217#downloadable) uses "light-quantum". No evidence is known that Planck himself used the term "photon" by 1926 (see also this note). in 1926 by the physical chemist Gilbert LewisGilbert N. Lewis

Gilbert Newton Lewis was an American physical chemist known for the discovery of the covalent bond , his purification of heavy water, his reformulation of chemical thermodynamics in a mathematically rigorous manner accessible to ordinary chemists, his theory of Lewis acids and...

, who published a speculative theory in which photons were "uncreatable and indestructible". Although Lewis' theory was never accepted as it was contradicted by many experiments, his new name,

*photon*, was adopted immediately by most physicists. Isaac AsimovIsaac Asimov

Isaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...

credits Arthur Compton

Arthur Compton

Arthur Holly Compton was an American physicist and Nobel laureate in physics for his discovery of the Compton effect. He served as Chancellor of Washington University in St. Louis from 1945 to 1953.-Early years:...

with defining quanta of energy as photons in 1923.

In physics, a photon is usually denoted by the symbol

*γ*(the Greek letterGreek alphabet

The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

gamma

Gamma

Gamma is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. It was derived from the Phoenician letter Gimel . Letters that arose from Gamma include the Roman C and G and the Cyrillic letters Ge Г and Ghe Ґ.-Greek:In Ancient Greek, gamma represented a...

). This symbol for the photon probably derives from gamma ray

Gamma ray

Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

s, which were discovered in 1900 by Paul Villard

Paul Ulrich Villard

Paul Ulrich Villard was a French chemist and physicist, born in Saint-Germain-au-Mont-d'Or, Rhône, 28 September 1860...

, named by Ernest Rutherford

Ernest Rutherford

Ernest Rutherford, 1st Baron Rutherford of Nelson OM, FRS was a New Zealand-born British chemist and physicist who became known as the father of nuclear physics...

in 1903, and shown to be a form of electromagnetic radiation

Electromagnetic radiation

in 1914 by Rutherford and Edward Andrade

Edward Andrade

Edward Neville da Costa Andrade FRS was an English physicist, writer, and poet.-Background:Andrade was a Sephardi Jew and is a descendant Moses da Costa Andrade...

. In chemistry

Chemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

and optical engineering

Optical engineering

Optical engineering is the field of study that focuses on applications of optics. Optical engineers design components of optical instruments such as lenses, microscopes, telescopes, and other equipment that utilizes the properties of light. Other devices include optical sensors and measurement...

, photons are usually symbolized by

*hν*, the energy of a photon, where*h*is Planck's constant and the Greek letterGreek alphabet

The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

*ν*(nuNu (letter)

Nu , is the 13th letter of the Greek alphabet. In the system of Greek numerals it has a value of 50...

) is the photon's frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

. Much less commonly, the photon can be symbolized by

*hf*, where its frequency is denoted by*f*.## Physical properties

The photon is massless,The massInvariant mass

The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the

*relativistic mass*concept, 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*/*c*^{2}. This usage for the term "mass" is no longer common in scientific literature. Further info: What is the mass of a photon? http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html has no electric chargeElectric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

, and does not decay spontaneously

Particle decay

Particle decay is the spontaneous process of one elementary particle transforming into other elementary particles. During this process, an elementary particle becomes a different particle with less mass and an intermediate particle such as W boson in muon decay. The intermediate particle then...

in empty space. A photon has two possible polarization

Photon polarization

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized...

states and is described by exactly three continuous parameters: the components of its wave vector

Wave vector

In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...

, which determine its wavelength

*λ*and its direction of propagation. The photon is the gauge bosonGauge boson

In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...

for electromagnetism

Electromagnetism

Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

, and therefore all other quantum numbers of the photon (such as lepton number

Lepton number

In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0...

, baryon number, and flavour quantum numbers) are zero.

Photons are emitted in many natural processes. For example, when a charge is accelerated

Acceleration

In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

it emits synchrotron radiation

Synchrotron radiation

The electromagnetic radiation emitted when charged particles are accelerated radially is called synchrotron radiation. It is produced in synchrotrons using bending magnets, undulators and/or wigglers...

. During a molecular

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

, atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

ic or nuclear

Atomic nucleus

The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

transition to a lower energy level

Energy level

A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...

, photons of various energy will be emitted, from infrared light to gamma ray

Gamma ray

Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

s. A photon can also be emitted when a particle and its corresponding antiparticle

Antiparticle

Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...

are annihilated

Annihilation

Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....

(for example, electron-positron annihilation

Electron-positron annihilation

Electron–positron annihilation occurs when an electron and a positron collide. The result of the collision is the annihilation of the electron and positron, and the creation of gamma ray photons or, at higher energies, other particles:...

).

In empty space, the photon moves at

*c*(the speed of lightSpeed of light

The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

) and its energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

and momentum

Momentum

In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

are related by , where

*p*is the magnitudeMagnitude (mathematics)

The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....

of the momentum vector

**p**. This derives from the following relativistic relation, with :The energy and momentum of a photon depend only on its frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

(

*ν*) or inversely, its wavelengthWavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

(

*λ*):where

**k**is the wave vectorWave vector

In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...

(where the wave number ), is the angular frequency

Angular frequency

In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...

, and is the reduced Planck constant

Planck constant

The Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

.

Since

**p**points in the direction of the photon's propagation, the magnitude of the momentum isThe photon also carries spin angular momentum

Spin (physics)

In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

that does not depend on its frequency. The magnitude of its spin is 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

Circular polarization

In electrodynamics, circular polarization of an electromagnetic wave is a polarization in which the electric field of the passing wave does not change strength but only changes direction in a rotary type manner....

states of the photon.

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 massCenter of mass

In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...

frame

Frame of reference

A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...

, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since it is determined, as we have seen, only by the photon's frequency or wavelength—which cannot be zero). Hence, conservation of momentum

Momentum

In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

(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 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.) The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of four-momentum

Conservation law

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....

. Seen another way, the photon can be considered as its own antiparticle. The reverse process, pair production

Pair production

Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...

, is the dominant mechanism by which high-energy photons such as gamma ray

Gamma ray

Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

s lose energy while passing through matter. That process is the reverse of "annihilation to one photon" allowed in the electric field of an atomic nucleus.

The classical formulae for the energy and momentum of electromagnetic radiation

Electromagnetic radiation

can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation

Radiation pressure

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...

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

Momentum

In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

per unit time.

### Experimental checks on photon mass

The photon is currently understood to be strictly massless, but this is an experimental question. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum,*c*. 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 maximum speed that any object could theoretically attain in space-time. Thus, it would still be the speed of space-time ripples (gravitational waves and gravitonGraviton

In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...

s), but it would not be the speed of photons.

A massive photon would have other effects as well. Coulomb's law

Coulomb's law

Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

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 cause the presence of an electric field

Electric field

In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

inside 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. A null result of such an experiment has set a limit of

*m*≲ 10^{−14}eV/c^{2}.Sharper upper limits have been obtained in experiments designed to detect effects caused by the Galactic vector potential

Magnetic potential

The term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, A, and the magnetic scalar potential, ψ...

. Although the galactic vector potential is very large because the galactic magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

exists on very long length scales, only the magnetic field is observable if the photon is massless. In case of a massive photon, the mass term would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of

*m*< . The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring. Such methods were used to obtain the sharper upper limit of 10^{−18}eV/c^{2}given by the Particle Data Group.These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent. If the photon mass is generated via the Higgs mechanism

Higgs mechanism

In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....

then the upper limit of

*m*≲10^{−14}eV/c^{2}from the test of Coulomb's law is valid.Photons inside superconductors

*do*develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors.## Historical development

In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particleSubatomic particle

In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...

models cannot easily account for the refraction

Refraction

Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

, diffraction

Diffraction

Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

and birefringence

Birefringence

Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...

of light, wave theories of light were proposed by René Descartes

René Descartes

René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...

(1637), Robert Hooke

Robert Hooke

Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...

(1665), and Christian Huygens (1678); however, particle models remained dominant, chiefly due to the influence of Isaac Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

. In the early nineteenth century, Thomas Young

Thomas Young (scientist)

Thomas Young was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphics before Jean-François Champollion eventually expanded on his work...

and August Fresnel

Augustin-Jean Fresnel

Augustin-Jean Fresnel , was a French engineer who contributed significantly to the establishment of the theory of wave optics. Fresnel studied the behaviour of light both theoretically and experimentally....

clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted. In 1865, James Clerk Maxwell

James Clerk Maxwell

James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

's prediction

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves

Radio

Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...

—seemed to be the final blow to particle models of light.

The Maxwell wave theory

Electromagnetic wave equation

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...

, however, does not account for

*all*properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensityIntensity (physics)

In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...

, not on its frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the 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

Photochemistry

Photochemistry, a sub-discipline of chemistry, is the study of chemical reactions that proceed with the absorption of light by atoms or molecules.. Everyday examples include photosynthesis, the degradation of plastics and the formation of vitamin D with sunlight.-Principles:Light is a type of...

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

Photoelectric effect

In the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...

); the energy of the ejected electron is related only to the light's frequency, not to its intensity.The phrase "no matter how intense" refers to intensities below approximately 10

^{13}W/cm^{2}at which point perturbation theoryPerturbation theory

Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...

begins to break down. In contrast, in the intense regime, which for visible light is above approximately 10

^{14}W/cm^{2}, the classical wave description correctly predicts the energy acquired by electrons, called ponderomotive energyPonderomotive energy

In strong field laser physics, the term Ponderomotive Energy refers to the cycle averaged quiver energy of a free electron in an E-field as given by,U_p=e^2E_a^2/4m\omega_0^2...

. (See also: Boreham

*et al.*(1996). "Photon density and the correspondence principle of electromagnetic interaction".) By comparison, sunlight is only about 0.1 W/cm^{2}.At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers culminated in Max Planck

Max Planck

Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

's hypothesis that the energy of

*any*system that absorbs or emits electromagnetic radiation of frequency*ν*is an integer multiple of an energy quantum*E=hν*. As shown by Albert EinsteinAlbert Einstein

Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

, some form of energy quantization

*must*be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiationElectromagnetic radiation

; for this explanation of the photoelectric effect

Photoelectric effect

In the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...

, Einstein received the 1921 Nobel Prize

Nobel Prize

The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

in physics.

Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself. Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if 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. In 1909 and 1916, Einstein showed that, if Planck's law of black-body radiation is accepted, the energy quanta must also carry momentumMomentum

*p=h/λ*, making them full-fledged particlesElementary particle

In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

. This photon momentum was observed experimentally by Arthur Compton

Arthur Compton

Arthur Holly Compton was an American physicist and Nobel laureate in physics for his discovery of the Compton effect. He served as Chancellor of Washington University in St. Louis from 1945 to 1953.-Early years:...

, for which he received the Nobel Prize

Nobel Prize

The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

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

Albert Einstein

for the rest of his life, and was solved in quantum electrodynamics

Quantum electrodynamics

Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

and its successor, the Standard Model

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

(see Second quantization and The photon as a gauge boson, below).

## 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 MillikanRobert Millikan

Robert A. Millikan was an American experimental physicist, and Nobel laureate in physics for his measurement of the charge on the electron and for his work on the photoelectric effect. He served as president of Caltech from 1921 to 1945...

's Nobel lecture. However, before Compton's experiment

Compton scattering

In physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...

showing that photons carried momentum

Momentum

proportional to their wave number (or frequency) (1922), most physicists were reluctant to believe that electromagnetic radiation

Electromagnetic radiation

itself might be particulate. (See, for example, the Nobel lectures of Wien

Wilhelm Wien

Wilhelm Carl Werner Otto Fritz Franz Wien was a German physicist who, in 1893, used theories about heat and electromagnetism to deduce Wien's displacement law, which calculates the emission of a blackbody at any temperature from the emission at any one reference temperature.He also formulated an...

, Planck

Max Planck

Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

and Millikan.). Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Attitudes changed over time. In part, the change can be traced to experiments such as Compton scattering

Compton scattering

In physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...

, where it was much more difficult not to ascribe quantization to light itself to explain the observed results.

Even after Compton's experiment, Niels Bohr

Niels Bohr

Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

, Hendrik Kramers

Hendrik Anthony Kramers

Hendrik Anthony "Hans" Kramers was a Dutch physicist.-Background and education:...

and John Slater

John C. Slater

John Clarke Slater was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids. This work is of ongoing importance in chemistry, as well as in many areas of physics. He also made major contributions to microwave electronics....

made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model

BKS theory

The Bohr-Kramers-Slater theory was perhaps the final attempt at understanding the interaction of matter and electromagnetic radiation on the basis of the so-called Old quantum theory, in which quantum phenomena are treated by imposing quantum restrictions on classically describable behaviour...

. To account for the data then available, two drastic hypotheses had to be made:

**Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission.**This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuous release of energy into radiation.**Causality is abandoned**. For example, spontaneous emissionSpontaneous emissionSpontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...

s are merely emissions inducedStimulated emissionIn optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...

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

Compton scattering

In physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...

obey causality to within 10 ps

Picosecond

A picosecond is 10−12 of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 001 seconds. A picosecond is to one second as one second is to 31,700 years....

. Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible". Nevertheless, the failures of the BKS model inspired Werner Heisenberg

Werner Heisenberg

Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

in his development of matrix mechanics

Matrix mechanics

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps...

.

A few physicists persisted in developing semiclassical models in which electromagnetic radiation

Electromagnetic radiation

is not quantized, but matter appears to obey the laws of quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. Although the evidence for photons from chemical and physical experiments was overwhelming by the 1970s, this evidence could not be considered as

*absolutely*definitive; since it relied on the interaction of light with matter, a sufficiently complicated 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.These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement processMeasurement in quantum mechanics

The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....

. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality

Cauchy–Schwarz inequality

In mathematics, the Cauchy–Schwarz inequality , is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, and other areas...

. 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 under**Additional references**.) 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 both 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 diffractionDiffraction

Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment

Double-slit experiment

The double-slit experiment, sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles...

lands on the screen exhibiting interference phenomena but only if no measure was made on the actual slit being run across. To account for the particle interpretation that phenomenon is called probability distribution

Probability distribution

In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

but behaves according to the Maxwell's equations

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

. 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 splitterBeam splitter

A beam splitter is an optical device that splits a beam of light in two. It is the crucial part of most interferometers.In its most common form, a rectangle, it is made from two triangular glass prisms which are glued together at their base using Canada balsam...

. 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 electronElectron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

. Nevertheless, the photon is

*not*a point-like particle whose trajectory is shaped probabilistically by the electromagnetic fieldElectromagnetic field

An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...

, as conceived by Einstein

Albert 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

Quantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

(see the Second quantization and Gauge boson sections below).

A key element of quantum mechanics

Quantum mechanics

is Heisenberg's

Werner Heisenberg

Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

uncertainty principle

Uncertainty principle

In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

, 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 is Heisenberg's thought experimentThought experiment

A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

for locating an electron with an ideal microscope. The position of the electron can be determined to within the resolving power

Angular resolution

Angular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object...

of the microscope, which is given by a formula from classical optics

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

where is the aperture angle

Angular aperture

The angular aperture of a lens is the apparent angle of the lens aperture as seen from the focal point:a = 2 \arctan \leftwheref is the focal lengthD is the diameter of the aperture.- Relation to numerical aperture :...

of the microscope. Thus, the position uncertainty can be made arbitrarily small by reducing the wavelength λ. The momentum of the electron is uncertain, since it received a "kick" from the light scattering from it into the microscope. If light were

*not*quantized into photons, the uncertainty 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 principleUncertainty principle

In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

. 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

giving the product , 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.

The analogous uncertainty principle for photons forbids the simultaneous measurement of the number of photons (see Fock state

Fock state

A Fock state , in quantum mechanics, is any element of a Fock space with a well-defined number of particles . These states are named after the Soviet physicist, V. A. Fock.-Definition:...

and the Second quantization section below) in an electromagnetic wave and the phase of that wave

See coherent state

Coherent state

In quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator...

and squeezed coherent state for more details.

Both photons and material particles such as electrons create analogous interference patterns when passing through a double-slit experiment

Double-slit experiment

The double-slit experiment, sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles...

. For photons, this corresponds to the interference of a Maxwell light wave

Electromagnetic wave equation

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...

whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation

Schrödinger equation

The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

. Although this similarity might suggest that Maxwell's equations

Maxwell's equations

are simply Schrödinger's equation for photons, most physicists do not agree. For one thing, they are mathematically different; most obviously, Schrödinger's one equation solves for a complex

Complex number

A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...

field

Field (physics)

In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...

, whereas Maxwell's four equations solve for real

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

fields. More generally, the normal concept of a Schrödinger probability

Probability amplitude

In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...

wave function cannot be applied to photons. Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate , and, thus, the normal Heisenberg uncertainty principle does not pertain to photons. A few substitute wave functions have been suggested for the photon, but they have not come into general use. Instead, physicists generally accept the second-quantized theory of photons described below, quantum electrodynamics

Quantum electrodynamics

Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

, in which photons are quantized excitations of electromagnetic modes.

## Bose–Einstein model of a photon gas

In 1924, Satyendra Nath BoseSatyendra Nath Bose

Satyendra Nath Bose FRS was an Indian mathematician and physicist noted for his collaboration with Albert Einstein in developing a theory regarding the gaslike qualities of electromagnetic radiation. He is best known for his work on quantum mechanics in the early 1920s, providing the foundation...

derived Planck's law of black-body radiation without using any electromagnetism, but rather a modification of coarse-grained counting of phase space

Phase space

In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space...

. Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction", now understood as the requirement for a symmetric quantum mechanical state

Identical particles

Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. Species of identical particles include elementary particles such as electrons, and, with some clauses, composite particles such as atoms and molecules.There are two...

. This work led to the concept of coherent state

Coherent state

In quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator...

s and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (boson

Boson

In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....

s) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation

Bose–Einstein condensate

A Bose–Einstein condensate is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero . Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at...

was observed experimentally in 1995.

The modern view on this is that photons are, by virtue of their integer spin, boson

Boson

In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....

s (as opposed to fermion

Fermion

In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

s with half-integer spin). By the spin-statistics theorem

Spin-statistics theorem

In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum...

, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi-Dirac statistics

Fermi-Dirac statistics

Fermi–Dirac statistics is a part of the science of physics that describes the energies of single particles in a system comprising many identical particles that obey the Pauli Exclusion Principle...

).

## Stimulated and spontaneous emission

In 1916, Einstein showed that Planck's radiation law could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a relation between the rates at which atoms emit and absorb photons. The condition follows from the assumption that light is emitted and absorbed by atoms independently, and that the thermal equilibrium is preserved by interaction with atoms. Consider a cavity in thermal equilibriumThermal equilibrium

Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

and filled with electromagnetic radiation

Electromagnetic radiation

and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density of photons with frequency (which is proportional to their number density

Number density

In physics, astronomy, and chemistry, number density is an intensive quantity used to describe the degree of concentration of countable objects in the three-dimensional physical space...

) is, on average, constant in time; hence, the rate at which photons of any particular frequency are

*emitted*must equal the rate of*absorbing*them.Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate for a system to

*absorb*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 with that frequency,where is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lower-energy state that is initiated by the interaction with a passing photon. 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 for emitting a photon spontaneously

Spontaneous emission

Spontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...

, and is the rate constant for emitting it in response to ambient photons (induced or stimulated emission

Stimulated emission

In optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...

). In thermodynamic equilibrium, the number of atoms in state i and that of atoms in state j must, on average, be constant; hence, the rates and must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of and is where are the degeneracy

Degenerate energy level

In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled, and in Quantum Mechanics it is represented mathematically by the Hamiltonian for the system having more...

of the state i and that of j, respectively, their energies, k the Boltzmann constant and T the system's temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

. From this, it is readily derived that

and

The A and Bs are collectively known as the

*Einstein coefficients*.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". In fact, in 1926, Paul Dirac

Paul Dirac

Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

derived the rate constants in using a semiclassical approach, and, in 1927, succeeded in deriving

*all*the rate constants from first principles within the framework of quantum theory. Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called*second quantization*or quantum field theoryQuantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

; 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 NewtonIsaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

in his treatment of birefringence

Birefringence

Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...

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 path it would follow. Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation from quantum mechanics. Ironically, Max Born

Max Born

Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...

's probabilistic interpretation

Probability amplitude

In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...

of the wave function was inspired by Einstein's later work searching for a more complete theory.

## Second quantization

In 1910, Peter DebyePeter Debye

Peter Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.-Early life:...

derived Planck's law of black-body radiation from a relatively simple assumption. He correctly decomposed the electromagnetic field in a cavity into its Fourier modes

Fourier series

In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

, 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 blackbody radiation, which were derived by Einstein in 1909.

In 1925, Born

Max Born

Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...

, Heisenberg

Werner Heisenberg

Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

and Jordan

Pascual Jordan

-Further reading:...

reinterpreted Debye's concept in a key way. As may be shown classically, the Fourier modes

Fourier series

In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

of the electromagnetic field

Electromagnetic four-potential

The electromagnetic four-potential is a potential from which the electromagnetic field can be derived. It combines both the electric scalar potential and the magnetic vector potential into a single space-time four-vector. In a given reference frame, the first component is the scalar potential and...

—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 , 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.Dirac

Paul Dirac

Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

took this one step further. He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's 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 derived Planck's law of black body radiation

Planck's law of black body radiation

In physics, Planck's law describes the amount of energy emitted by a black body in radiation of a certain wavelength . The law is named after Max Planck, who originally proposed it in 1900. The law was the first to accurately describe black body radiation, and resolved the ultraviolet catastrophe...

by

*assuming*BE statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey BE statistics.Dirac's second-order perturbation theory

Perturbation theory (quantum mechanics)

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...

can involve virtual photons

Virtual particle

In physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...

, transient intermediate states of the electromagnetic field; the static electric

Coulomb's law

Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

and magnetic

Magnetism

Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...

interactions are mediated by such virtual photons. In such quantum field theories

Quantum field theory

, the probability amplitude

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 , and may have extra polarization states; depending on the gaugeGauge fixing

In the physics of gauge theories, gauge fixing denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field...

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

Infinity

Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...

contributions to the sum. Such unphysical results are corrected for using the technique of renormalization

Renormalization

In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

. Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

-positron

Positron

The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

pairs

Pair production

Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...

. In fact, such photon-photon scattering, 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

International Linear Collider

The International Linear Collider is a proposed linear particle accelerator. It is planned to have a collision energy of 500 GeV initially, and, if approved after the project has published its Technical Design Report, planned for 2012, could be completed in the late 2010s. A later upgrade to 1000...

.

In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state

Fock state

A Fock state , in quantum mechanics, is any element of a Fock space with a well-defined number of particles . These states are named after the Soviet physicist, V. A. Fock.-Definition:...

, a tensor product

Tensor product

In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects. In each case the significance of the symbol is the same: the most general...

of the states for each electromagnetic mode

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.

## 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 spacetimeSpacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

. For the electromagnetic field

Electromagnetic field

An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...

, this gauge symmetry is the Abelian

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order . Abelian groups generalize the arithmetic of addition of integers...

U(1) symmetry

Unitary group

In mathematics, the unitary group of degree n, denoted U, is the group of n×n unitary matrices, with the group operation that of matrix multiplication. The unitary group is a subgroup of the general linear group GL...

of a complex number

Complex number

A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...

, which reflects the ability to vary the phase

Complex geometry

In mathematics, complex geometry is the study of complex manifolds and functions of many complex variables. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric chapters of complex analysis....

of a complex number without affecting observables or real valued functions

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

made from it, such as the energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

or the Lagrangian

Lagrangian

The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

.

The quanta of an Abelian gauge field

Gauge theory

In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...

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

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin

Spin (physics)

In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

±1; thus, its helicity must be . These two spin components correspond to the classical concepts of right-handed and left-handed circularly polarized

Circular polarization

In electrodynamics, circular polarization of an electromagnetic wave is a polarization in which the electric field of the passing wave does not change strength but only changes direction in a rotary type manner....

light. However, the transient virtual photons of quantum electrodynamics

Quantum electrodynamics

Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

may also adopt unphysical polarization states.

In the prevailing Standard Model

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

of physics, the photon is one of four gauge bosons in the electroweak interaction

Electroweak interaction

In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...

; the other three

W and Z bosons

The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...

are denoted W

^{+}, W^{−}and Z^{0}and are responsible for the weak interactionWeak interaction

Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

. Unlike the photon, these gauge bosons have mass

Invariant mass

The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

, owing to a mechanism

Higgs mechanism

In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....

that breaks their SU(2) gauge symmetry

Special unitary group

The special unitary group of degree n, denoted SU, is the group of n×n unitary matrices with determinant 1. The group operation is that of matrix multiplication...

. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam

Abdus Salam

Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...

and Steven Weinberg

Steven Weinberg

Steven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....

, for which they were awarded the 1979 Nobel Prize

Nobel Prize

The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

in physics. Physicists continue to hypothesize grand unified theories

Grand unification theory

The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...

that connect these four gauge bosons with the eight gluon

Gluon

Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....

gauge bosons of quantum chromodynamics

Quantum chromodynamics

In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...

; however, key predictions of these theories, such as proton decay

Proton decay

In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...

, have not been observed experimentally.

## Contributions to the mass of a system

The energy of a system that emits a photon is*decreased*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 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 for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).This concept is applied in key predictions of quantum electrodynamics

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

Renormalization

In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment

Anomalous magnetic dipole moment

In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle...

of lepton

Lepton

A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...

s, the Lamb shift, and the hyperfine structure

Hyperfine structure

The term hyperfine structure refers to a collection of different effects leading to small shifts and splittings in the energy levels of atoms, molecules and ions. The name is a reference to the fine structure which results from the interaction between the magnetic moments associated with electron...

of bound lepton pairs, such as muonium

Muonium

Muonium is an exotic atom made up of an antimuon and an electron, which was discovered in 1960 and is given the chemical symbol . During the muon's lifetime, muonium can enter into compounds such as muonium chloride or sodium muonide . Due to the mass difference between the antimuon and the...

and positronium

Positronium

Positronium is a system consisting of an electron and its anti-particle, a positron, bound together into an "exotic atom". Being unstable, the two particles annihilate each other to produce two gamma ray photons after an average lifetime of 125 ps or three gamma ray photons after 142 ns in...

.

Since photons contribute to the stress-energy tensor

Stress-energy tensor

The stress–energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields...

, they exert a gravitational attraction on other objects, according to the theory of general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

, as in gravitational lensing, and their frequencies may be lowered

Gravitational redshift

In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...

by moving to a higher gravitational potential

Potential energy

In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

, as in the Pound-Rebka experiment

Pound-Rebka experiment

The Pound–Rebka experiment is a well known experiment to test Albert Einstein's theory of general relativity. It was proposed by Robert Pound and his graduate student Glen A. Rebka Jr. in 1959, and was the last of the classical tests of general relativity to be verified...

. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves

Electromagnetic radiation

.

## Photons in matter

Light that travels through transparent matter does so at a lower speed than*c*, the speed of light in a vacuum. X-rays, on the other hand, usually have a phase velocity above c, as evidenced by total external reflectionTotal external reflection

Total external reflection is an optical phenomenon where electromagnetic radiation can, at certain angles, be totally reflected from an interface between two media of different indices of refraction...

. In addition, light can also undergo scattering

Scattering

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

and absorption

Absorption (electromagnetic radiation)

In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. An example would be in the core

Solar core

The core of the Sun is considered to extend from the center to about 0.2 to 0.25 solar radius. It is the hottest part of the Sun and of the Solar System. It has a density of up to 150 g/cm³ and a temperature of close to 15,000,000 kelvin...

of the Sun. Energy can take about a million years to reach the surface. However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibration between the radiation and the temperature. Thus, the time is how long it takes the

*energy*to be transferred, not the*photons*themselves. Once in open space, a photon from the Sun takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased in a material is called the refractive indexRefractive index

In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

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 the 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 (quasi-particles such as phonon

Phonon

In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

s and exciton

Exciton

An exciton is a bound state of an electron and hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and some liquids...

s) to form a polariton

Polariton

In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also known as the anti-crossing principle...

; this polariton has a nonzero effective mass, which means that it cannot travel at

*c*.Alternatively, photons may be viewed as

*always*traveling at*c*, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed. A light wave made up of these photons does travel slower than the speed of light. In this view the photons are "bare", and are scattered and phase shifted, while in the view of the preceding paragraph the photons are "dressed" by their interaction with matter, and move without scattering or phase shifting, but at a lower speed.Light of different frequencies may travel through matter at different speeds

Variable speed of light

The variable speed of light concept states that the speed of light in a vacuum, usually denoted by c, may not be constant in most cases. In most situations in condensed matter physics when light is traveling through a medium, it effectively has a slower speed...

; this is called dispersion

Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

. In some cases, it can result in extremely slow speeds of light

Slow light

Slow light is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity. Slow light occurs when a propagating pulse is substantially slowed down by the interaction with the medium in which the propagation take place.Researchers at the Rowland...

in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering

Raman scattering

Raman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa Krishnan in liquids, and by Grigory Landsberg and Leonid Mandelstam in crystals....

and Brillouin scattering

Brillouin scattering

Brillouin scattering, named after Léon Brillouin, occurs when light in a medium interacts with time dependent optical density variations and changes its energy and path. The density variations may be due to acoustic modes, such as phonons, magnetic modes, such as magnons, or temperature gradients...

.

Photons can also be absorbed

Absorption (electromagnetic radiation)

In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

by nuclei, atoms or molecules, provoking transitions between their energy level

Energy level

A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...

s. A classic example is the molecular transition of retinal

Retinal

Retinal, also called retinaldehyde or vitamin A aldehyde, is one of the many forms of vitamin A . Retinal is a polyene chromophore, and bound to proteins called opsins, is the chemical basis of animal vision...

C

_{20}H_{28}O, which is responsible for visionVisual perception

Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...

, as discovered in 1958 by Nobel laureate biochemist

Biochemistry

Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...

George Wald

George Wald

George Wald was an American scientist who is best known for his work with pigments in the retina. He won a share of the 1967 Nobel Prize in Physiology or Medicine with Haldan Keffer Hartline and Ragnar Granit.- Research :...

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

Photodissociation

Photodissociation, photolysis, or photodecomposition is a chemical reaction in which a chemical compound is broken down by photons. It is defined as the interaction of one or more photons with one target molecule....

of chlorine

Chlorine

Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

; this is the subject of photochemistry

Photochemistry

Photochemistry, a sub-discipline of chemistry, is the study of chemical reactions that proceed with the absorption of light by atoms or molecules.. Everyday examples include photosynthesis, the degradation of plastics and the formation of vitamin D with sunlight.-Principles:Light is a type of...

. Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration

Photodisintegration

Photodisintegration is a physical process in which an extremely high energy gamma ray interacts with an atomic nucleus and causes it to enter an excited state, which immediately decays by emitting a subatomic particle. A single proton or neutron is effectively knocked out of the nucleus by the...

.

## 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 emissionStimulated emission

In optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...

.

Individual photons can be detected by several methods. The classic photomultiplier

Photomultiplier

Photomultiplier tubes , members of the class of vacuum tubes, and more specifically phototubes, are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum...

tube exploits the photoelectric effect

Photoelectric effect

In the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...

: a photon landing on a metal plate ejects an electron, initiating an ever-amplifying avalanche of electrons. Charge-coupled device

Charge-coupled device

A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...

chips use a similar effect in semiconductor

Semiconductor

A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...

s: an incident photon generates a charge on a microscopic capacitor

Capacitor

A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

that can be detected. Other detectors such as Geiger counter

Geiger counter

A Geiger counter, also called a Geiger–Müller counter, is a type of particle detector that measures ionizing radiation. They detect the emission of nuclear radiation: alpha particles, beta particles or gamma rays. A Geiger counter detects radiation by ionization produced in a low-pressure gas in a...

s use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.

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 predict the frequency of the light emitted for a given energy transition. For example, the emission spectrum

Emission spectrum

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....

of a fluorescent light bulb

Fluorescent lamp

A fluorescent lamp or fluorescent tube is a gas-discharge lamp that uses electricity to excite mercury vapor. The excited mercury atoms produce short-wave ultraviolet light that then causes a phosphor to fluoresce, producing visible light. A fluorescent lamp converts electrical power into useful...

can be designed using gas molecules with different electronic energy levels and adjusting the typical energy with which an electron hits the gas molecules within the bulb.An example is US Patent Nr. 5212709.

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 region 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

Two-photon excitation microscopy

Two-photon excitation microscopy is a fluorescence imaging technique that allows imaging of living tissue up to a very high depth, that is up to about one millimeter. Being a special variant of the multiphoton fluorescence microscope, it uses red-shifted excitation light which can also excite...

). Moreover, these photons cause less damage to the sample, since they are of lower energy.

In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer

Fluorescence resonance energy transfer

Förster resonance energy transfer , also known as fluorescence resonance energy transfer, resonance energy transfer or electronic energy transfer , is a mechanism describing energy transfer between two chromophores.A donor chromophore, initially in its electronic excited state, may transfer energy...

, a technique that is used in molecular biology

Molecular biology

Molecular biology is the branch of biology that deals with the molecular basis of biological activity. This field overlaps with other areas of biology and chemistry, particularly genetics and biochemistry...

to study the interaction of suitable protein

Protein

Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s.

Several different kinds of hardware random number generator

Hardware random number generator

In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. Such devices are often based on microscopic phenomena that generate a low-level, statistically random "noise" signal, such as thermal noise or the photoelectric effect or other...

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".

## Recent research

Much research has been devoted to applications of photons in the field of quantum opticsQuantum optics

Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...

. Photons seem well-suited to be elements of an extremely fast quantum computer

Quantum computer

A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...

, and the quantum entanglement

Quantum entanglement

Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

of photons is a focus of research. Nonlinear optical processes

Nonlinear optics

Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...

are another active research area, with topics such as two-photon absorption

Two-photon absorption

Two-photon absorption is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state to a higher energy electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the...

, self-phase modulation

Self-phase modulation

Self-phase modulation is a nonlinear optical effect of light-matter interaction.An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect...

, modulational instability

Modulational instability

In the field of nonlinear optics, modulational instability is a phenomenon whereby deviations from an optical waveform are reinforced by nonlinearity, leading to the generation of spectral-sidebands and the eventual breakup of the waveform into a train of pulses.-Initial instability and...

and optical parametric oscillator

Optical parametric oscillator

An optical parametric oscillator is a parametric oscillator which oscillates at optical frequencies. It converts an input laser wave into two output waves of lower frequency by means of second order nonlinear optical interaction. The sum of the output waves frequencies is equal to the input wave...

s. 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 conversionSpontaneous parametric down conversion

Spontaneous parametric down-conversion is an important process in quantum optics, used especially as a source of entangled photon pairs, and of single photons.-Basic process:...

is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication

Optical communication

Optical communication is any form of telecommunication that uses light as the transmission medium.An optical communication system consists of a transmitter, which encodes a message into an optical signal, a channel, which carries the signal to its destination, and a receiver, which reproduces the...

, especially for quantum cryptography

Quantum cryptography

Quantum key distribution uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages...

.Introductory-level material on the various sub-fields of quantum optics can be found in

## See also

- Doppler shift
- LightLightLight or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
- Luminiferous aetherLuminiferous aetherIn the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
- Electromagnetic radiationElectromagnetic radiation
- Quantum opticsQuantum opticsQuantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...
- PhotonicsPhotonicsThe science of photonics includes the generation, emission, transmission, modulation, signal processing, switching, amplification, detection and sensing of light. The term photonics thereby emphasizes that photons are neither particles nor waves — they are different in that they have both particle...
- Phonons

- Photon polarizationPhoton polarizationPhoton polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized...
- Ballistic photonBallistic photonBallistic photons are the light photons that travel through a scattering medium in a straight line. Also known as ballistic light. If laser pulses are sent through a turbid medium such as fog or body tissue, most of the photons are either randomly scattered or absorbed. However, across short...
- MedipixMedipixMedipix is a family of photon counting pixel detector developed by an international collaboration, hosted by CERN.Detectors in the Medipix family include:* Medipix 1* Medipix 2* Medipix MXR* Timepix* Medipix 3.0 -Design:...
- PhotographyPhotographyPhotography is the art, science and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor or chemically by means of a light-sensitive material such as photographic film...
- LaserLaserA laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
- Advanced Photon SourceAdvanced Photon SourceThe Advanced Photon Source at Argonne National Laboratory is a national synchrotron-radiation light source research facility funded by the United States Department of Energy Office of Science...

at Argonne National Laboratory - Static forces and virtual-particle exchangeStatic forces and virtual-particle exchangeStatic force fields are fields, such as a simple electric, magnetic or gravitational fields, that exist without excitations. The most common approximation method that physicists use for scattering calculations can be interpreted as static forces arising from the interactions between two bodies...
- Two-photon physicsTwo-photon physicsTwo-photon physics, also called gamma-gamma physics, is a branch of particle physics for the interactions between two photons. If the energy in the center of mass system of the two photons is large enough, matter can be created.-Experiments:...