In
physicsPhysics 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 particleIn 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
quantumIn 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
lightLight 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 radiationElectromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
. It is also the
force carrierIn 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
forceIn 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
interactionIn 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 mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particlelike and wavelike behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
and will exhibit
wave–particle dualityWave–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 quantumscale objects...
, exhibiting properties of both
waveIn 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
refractedRefraction 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
lensA 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 momentumIn 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 EinsteinAlbert Einstein was a Germanborn 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 modelThe electromagnetic wave equation is a secondorder 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
matterMatter 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
radiationElectromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
to be in
thermal equilibriumThermal 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 PlanckMax 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 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
quantizedIn 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
quantaIn 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 ModelThe 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 physicsParticle 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
symmetryIn 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
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being threedimensional 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
chargeElectric 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...
,
massThe 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
spinIn 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 symmetryIn 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 lightThe neutrino theory of light is the proposal that the photon is a composite particle formed of a neutrinoantineutrino pair. It is based on the idea that emission and absorption of a photon corresponds to the creation and annihilation of a particleantiparticle 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
laserA 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 theoryQuantum 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 manybody systems. It is the natural and quantitative language of particle physics and...
, and the
probabilistic interpretationIn 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
photochemistryPhotochemistry, a subdiscipline 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...
,
highresolution microscopyTwophoton 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 redshifted excitation light which can also excite...
, and
measurements of molecular distancesFörster 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 computerA 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 communicationOptical 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 cryptographyQuantum 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 blackbody 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 is one of the oldest physics journals worldwide. The journal publishes original, peerreviewed papers in the areas of experimental, theoretical, applied and mathematical physics and related areas...
he called these packets "energy elements". The word
quantaIn 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
quantum) was used even before 1900 to mean particles or amounts of different
quantitiesQuantity 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
electricityThe 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 EinsteinAlbert Einstein was a Germanborn 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 wavepackets. He called such a
waveIn 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 is an independent branch of the IndoEuropean family of languages. Native to the southern Balkans, it has the longest documented history of any IndoEuropean 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 coined
[Although the 1967 Elsevier translation of Planck's Nobel Lecture interprets Planck's Lichtquant as "photon", the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein The origin and development of the quantum theory, The Clarendon Press, 1922 (here http://www.readanybook.com/ebook/theoriginanddevelopmentofthequantumtheory48217#downloadable) uses "lightquantum". 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 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 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 ComptonArthur 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 letterThe 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...
gammaGamma 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 rayGamma radiation, also known as gamma rays or hyphenated as gammarays 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 VillardPaul Ulrich Villard was a French chemist and physicist, born in SaintGermainauMontd'Or, Rhône, 28 September 1860...
, named by
Ernest RutherfordErnest Rutherford, 1st Baron Rutherford of Nelson OM, FRS was a New Zealandborn British chemist and physicist who became known as the father of nuclear physics...
in 1903, and shown to be a form of
electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
in 1914 by Rutherford and
Edward AndradeEdward 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
chemistryChemistry 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 engineeringOptical 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 letterThe 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 , is the 13th letter of the Greek alphabet. In the system of Greek numerals it has a value of 50...
) is the photon's
frequencyFrequency 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 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 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 spontaneouslyParticle 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
polarizationPhoton 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 vectorIn 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 bosonIn 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
electromagnetismElectromagnetism 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 numberIn 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 nonleptonic particles 0...
,
baryon number, and flavour quantum numbers) are zero.
Photons are emitted in many natural processes. For example, when a charge is
acceleratedIn 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 radiationThe 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
molecularA 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...
,
atomThe 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
nuclearThe 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 levelA 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 rayGamma radiation, also known as gamma rays or hyphenated as gammarays 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
antiparticleCorresponding 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
annihilatedAnnihilation 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,
electronpositron annihilationElectron–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 lightThe 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
energyIn 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
momentumIn 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
magnitudeThe 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
frequencyFrequency 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
wavelengthIn 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 vectorIn 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 frequencyIn 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 constantThe 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 is
The photon also carries
spin angular momentumIn 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 righthanded and lefthanded, correspond to the two possible
circular polarizationIn 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 massIn 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...
frameA 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 momentumIn 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 fourmomentumIn 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 productionPair 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 highenergy photons such as
gamma rayGamma radiation, also known as gamma rays or hyphenated as gammarays 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 radiationElectromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
can be reexpressed in terms of photon events. For example, the
pressure of electromagnetic radiationRadiation 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
momentumIn 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 socalled 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 spacetime. Thus, it would still be the speed of spacetime ripples (gravitational waves and
gravitonIn 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 lawCoulomb's law or Coulomb's inversesquare 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 fieldIn physics, an electric field surrounds electrically charged particles and timevarying 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 potentialThe 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 fieldA 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 nonobservation 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 mechanismIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire nonvanishing masses through absorption of NambuGoldstone 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 shortrange inside superconductors.
Historical development
In most theories up to the eighteenth century, light was pictured as being made up of particles. Since
particleIn 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
refractionRefraction 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...
,
diffractionDiffraction 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
birefringenceBirefringence, 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 DescartesRené 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 HookeRobert 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 NewtonSir 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 YoungThomas Young was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphics before JeanFrançois Champollion eventually expanded on his work...
and
August FresnelAugustinJean 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 MaxwellJames 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
predictionMaxwell'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 wavesRadio 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 theoryThe electromagnetic wave equation is a secondorder 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
intensityIn 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
frequencyFrequency 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 reactionsPhotochemistry, a subdiscipline 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 effectIn 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 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 energyIn strong field laser physics, the term Ponderomotive Energy refers to the cycle averaged quiver energy of a free electron in an Efield 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 PlanckMax 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 was a Germanborn 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 is a form of energy that exhibits wavelike behavior as it travels through space...
; for this explanation of the
photoelectric effectIn 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 PrizeThe 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 pointlike 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 blackbody radiation is accepted, the energy quanta must also carry
momentumIn classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
p=h/λ, making them fullfledged
particlesIn 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 ComptonArthur 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 PrizeThe 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 EinsteinAlbert Einstein was a Germanborn 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 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...
and its successor, the
Standard ModelThe 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 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 experimentIn physics, Compton scattering is a type of scattering that Xrays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an Xray or gamma ray photon, called the Compton effect...
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 wavelike behavior as it travels through space...
itself might be particulate. (See, for example, the Nobel lectures of
WienWilhelm 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...
,
PlanckMax 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 scatteringIn physics, Compton scattering is a type of scattering that Xrays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an Xray 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 BohrNiels 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 KramersHendrik Anthony "Hans" Kramers was a Dutch physicist.Background and education:...
and
John SlaterJohn 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 socalled
BKS modelThe BohrKramersSlater theory was perhaps the final attempt at understanding the interaction of matter and electromagnetic radiation on the basis of the socalled 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 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...
s are merely emissions inducedIn 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 energymomentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in
Compton scatteringIn physics, Compton scattering is a type of scattering that Xrays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an Xray or gamma ray photon, called the Compton effect...
obey causality to within 10
psA 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 coworkers gave their model "as honorable a funeral as possible". Nevertheless, the failures of the BKS model inspired
Werner HeisenbergWerner 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 mechanicsMatrix 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 radiationElectromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
is not quantized, but matter appears to obey the laws 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 particlelike and wavelike 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 photoncorrelation 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 process]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 inequalityIn 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 antibunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photonanticorrelation 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 wavelike and particlelike properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wavelike phenomena such as
diffractionDiffraction 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
doubleslit experimentThe doubleslit 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 distributionIn 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 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...
. 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 splitterA 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 pointlike 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 pointlike
electronThe 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 pointlike particle whose trajectory is shaped probabilistically by the
electromagnetic fieldAn 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
EinsteinAlbert Einstein was a Germanborn 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 photoncorrelation 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 theoryQuantum 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 manybody 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 mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particlelike and wavelike behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
is
Heisenberg'sWerner 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 principleIn 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 experimentA 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 powerAngular resolution, or spatial resolution, describes the ability of any imageforming 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
opticsOptics 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 angleThe 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 principleIn 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 stateA Fock state , in quantum mechanics, is any element of a Fock space with a welldefined 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 stateIn 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
doubleslit experimentThe doubleslit 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 waveThe electromagnetic wave equation is a secondorder 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 equationThe 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 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
complexA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the onedimensional number line to the twodimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
fieldIn 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
realIn 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
probabilityIn 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 secondquantized theory of photons described below,
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...
, in which photons are quantized excitations of electromagnetic modes.
Bose–Einstein model of a photon gas
In 1924,
Satyendra Nath BoseSatyendra 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 blackbody radiation without using any electromagnetism, but rather a modification of coarsegrained counting of
phase spaceIn 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 nonlocal interaction", now understood as the requirement for a
symmetric quantum mechanical stateIdentical 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 stateIn 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 (
bosonIn 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 condensationA 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,
bosonIn 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
fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s with halfinteger spin). By the
spinstatistics theoremIn quantum mechanics, the spinstatistics 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
FermiDirac statisticsFermi–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 semiclassical, 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 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 radiationElectromagnetic radiation is a form of energy that exhibits wavelike 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 densityIn physics, astronomy, and chemistry, number density is an intensive quantity used to describe the degree of concentration of countable objects in the threedimensional 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 lowerenergy 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 spontaneouslySpontaneous 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 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...
). 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
degeneracyIn 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
temperatureTemperature 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 DiracPaul 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 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 manybody 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 lightparticle motion was first considered by
NewtonSir 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
birefringenceBirefringence, 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 BornMax Born was a Germanborn physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solidstate physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...
's
probabilistic interpretationIn 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 Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.Early life:...
derived Planck's law of blackbody radiation from a relatively simple assumption. He correctly decomposed the electromagnetic field in a cavity into its
Fourier modesIn 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 blackbody 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,
BornMax Born was a Germanborn physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solidstate physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...
,
HeisenbergWerner 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
reinterpreted Debye's concept in a key way. As may be shown classically, the
Fourier modesIn 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 fieldThe electromagnetic fourpotential 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 spacetime fourvector. 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.
DiracPaul 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 radiationIn 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 secondorder
perturbation theoryIn 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 photonsIn 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
electricCoulomb's law or Coulomb's inversesquare 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
magneticMagnetism 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 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 manybody 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
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
gaugeIn 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 secondorder and higherorder perturbation calculations can give apparently
infiniteInfinity 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
renormalizationIn quantum field theory, the statistical mechanics of fields, and the theory of selfsimilar 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
electronThe 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...

positronThe 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...
pairsPair 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 photonphoton scattering, as well as electronphoton scattering, is meant to be one of the modes of operations of the planned particle accelerator, the
International Linear ColliderThe 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 stateA Fock state , in quantum mechanics, is any element of a Fock space with a welldefined number of particles . These states are named after the Soviet physicist, V. A. Fock.Definition:...
, a
tensor productIn 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
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being threedimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
. For the
electromagnetic fieldAn 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
AbelianIn 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) symmetryIn 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 numberA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the onedimensional number line to the twodimensional 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
phaseIn 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 functionsIn 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
energyIn 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
LagrangianThe 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 fieldIn 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 chargeElectric 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
spinIn 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
righthanded and lefthanded circularly polarizedIn 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 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...
may also adopt unphysical polarization states.
In the prevailing
Standard ModelThe 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 interactionIn 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 threeThe 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 , 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
massThe 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
mechanismIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire nonvanishing masses through absorption of NambuGoldstone bosons arising in spontaneous symmetry breaking....
that breaks their
SU(2) gauge symmetryThe 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 SalamMohammad 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 WeinbergSteven 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 PrizeThe 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 theoriesThe term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at highenergy, 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
gluonGluons 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 chromodynamicsIn 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 colorcharged fermions...
; however, key predictions of these theories, such as
proton decayIn 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 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
renormalizationIn quantum field theory, the statistical mechanics of fields, and the theory of selfsimilar 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 momentIn 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
leptonA 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 structureThe 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
muoniumMuonium 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
positroniumPositronium is a system consisting of an electron and its antiparticle, 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
stressenergy tensorThe 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 nongravitational force fields...
, they exert a gravitational attraction on other objects, according to the theory of
general relativityGeneral 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
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being threedimensional 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 loweredIn 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 potentialIn 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
PoundRebka experimentThe 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 wavesElectromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
.
Photons in matter
Light that travels through transparent matter does so at a lower speed than
c, the speed of light in a vacuum. Xrays, on the other hand, usually have a phase velocity above c, as evidenced by
total external reflectionTotal 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
scatteringScattering 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 nonuniformities in the medium through which they pass. In conventional use, this also includes deviation of...
and
absorptionIn 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
coreThe 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 indexIn 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 (quasiparticles such as
phononIn 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
excitonAn 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
polaritonIn physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipolecarrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also known as the anticrossing 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 speedsThe 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
dispersionIn 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 lightSlow 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 quasiparticles may be observed directly in
Raman scatteringRaman 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 scatteringBrillouin 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
absorbedIn 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 levelA 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
retinalRetinal, 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 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
biochemistBiochemistry, 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 WaldGeorge 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 coworkers. The absorption provokes a cistrans 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
photodissociationPhotodissociation, 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
chlorineChlorine 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
photochemistryPhotochemistry, a subdiscipline 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
photodisintegrationPhotodisintegration 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 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...
.
Individual photons can be detected by several methods. The classic
photomultiplierPhotomultiplier tubes , members of the class of vacuum tubes, and more specifically phototubes, are extremely sensitive detectors of light in the ultraviolet, visible, and nearinfrared ranges of the electromagnetic spectrum...
tube exploits the
photoelectric effectIn 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 everamplifying avalanche of electrons.
Chargecoupled deviceA chargecoupled 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
semiconductorA 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
capacitorA capacitor is a passive twoterminal 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 counterA 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 lowpressure 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 spectrumThe 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 bulbA fluorescent lamp or fluorescent tube is a gasdischarge lamp that uses electricity to excite mercury vapor. The excited mercury atoms produce shortwave 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
twophoton excitation microscopyTwophoton 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 redshifted 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 reemits a photon of a different frequency. This is the basis of
fluorescence resonance energy transferFörster 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 biologyMolecular 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
proteinProteins 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 generatorIn 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 lowlevel, 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 beamsplitter. 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 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 wellsuited to be elements of an extremely fast
quantum computerA 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 entanglementQuantum 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 processesNonlinear 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
twophoton absorptionTwophoton 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...
,
selfphase modulationSelfphase modulation is a nonlinear optical effect of lightmatter 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 instabilityIn 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 spectralsidebands and the eventual breakup of the waveform into a train of pulses.Initial instability and...
and
optical parametric oscillatorAn 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 downconversion 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 singlephoton states. Finally, photons are essential in some aspects of
optical communicationOptical 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 cryptographyQuantum 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...
.
[Introductorylevel material on the various subfields of quantum optics can be found in ]
See also
 Doppler shift
 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...
 Luminiferous aether
In the late 19th century, luminiferous aether or ether, meaning lightbearing aether, was the term used to describe a medium for the propagation of light....
 Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
 Quantum 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 :...
 Photonics
The 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 polarization
Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized...
 Ballistic photon
Ballistic 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...
 Medipix
Medipix 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:...
 Photography
Photography 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 lightsensitive material such as photographic film...
 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...
 Advanced Photon Source
The Advanced Photon Source at Argonne National Laboratory is a national synchrotronradiation light source research facility funded by the United States Department of Energy Office of Science...
at Argonne National Laboratory
 Static forces and virtualparticle exchange
Static 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...
 Twophoton physics
Twophoton physics, also called gammagamma 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:...