In quantum physics, the photon (from Greek φως, "phōs", meaning light) is the quantum of the electromagnetic field (light). That is to say, electromagnetic fields are made up of large numbers of photons, and the electromagnetic interaction is mediated by the exchange of virtual photons. The term photon was coined by Gilbert N. Lewis in 1926.

The photon is one of the elementary particles. Its interactions with electrons and atomic nuclei account for a great many of the features of matter, such as the existence and stability of atoms, molecules, and solids. These interactions are studied in quantum electrodynamics (QED), which is the oldest part of the Standard Model of particle physics.

In many circumstances, a photon acts as a classical particle, for instance when registered by the light-sensitive device in a camera. In other circumstances, a photon acts like a classical wave, as when passing through the optics in a camera. According to the so-called wave-particle duality of quantum physics, it is natural for the photon to display either aspect of its nature, according to the circumstances. Normally, light is formed from a large number of photons, with the intensity related to the number of them. At low intensity, it requires very sensitive instruments, used in astronomy or spectroscopy, for instance, to detect the individual photons.

Some say a photon "sometimes acts like a wave and sometimes acts like a particle". This is slightly misleading, because a photon always acts like both. For example, when shooting single photons through a slit, a detector can detect each photon when it hits—but over time, the detector will detect the same diffraction pattern as it would if the photons were given off all in one burst.

A photon is usually given the symbol γ, the Greek letter gamma, although in nuclear physics this symbol refers to a very high-energy photon (a gamma ray). In chemistry, photons are sometimes symbolized by hν, which is the amount of energy each photon represents (h = Planck's constant, ν the Greek letter nu symbolizing the photon frequency).

Photons are commonly associated with visible light, but this is actually only a very limited part of the electromagnetic spectrum. All electromagnetic radiation is quantized as photons: that is, the smallest amount of electromagnetic radiation that can exist is one photon, whatever its wavelength, frequency, energy, or momentum, and that light or fields interact with matter in discrete units of one or several photons. Photons are fundamental particles. They can be created and destroyed when interacting with other particles, but do not decay.

A photon of a definite frequency is not a localized particle. Photons thus exhibit a position-frequency uncertainty relation similar to that of matter particles and exactly analogous to the bandwidth theorem of classical optics. According to the quantum electrodynamics of the Standard Model, photons have zero rest mass and zero electric charge, but they do carry energy, momentum and angular momentum. Although the photon is generally accepted to be massless, experiments may only show that its mass is consistent with zero. A conservative upper limit for the mass of the photon, given by the Particle Data Group, is 6×10⁻¹⁷ eV, based on changes in magnetohydrodynamics which would contradict solar wind observations.

As massless particles, photons must always move at c (often called the speed of light in vacuum), which is approximately equal to 2.998×10^8 m/s. Because of special relativity, photons always move at a constant speed with respect to all observers, regardless of the observers' own velocities. The energy and momentum carried by a photon is proportional to its frequency (or inversely proportional to its wavelength) with a constant of proportionality equal to the Planck constant. The momentum carried by a photon can be transferred when it interacts with matter. The force due to photons interacting with a surface is called radiation pressure, which may be used for propulsion as with a solar sail.

Photons are deflected by a gravitational field twice as much as Newtonian mechanics predicts for a test mass traveling at the speed of light. This observation was a key piece of early evidence supporting Einstein's theory of gravitation, general relativity. In general relativity, photons (as well as any other object in a free fall) always travel in a "straight" line, taking into account the curvature of spacetime. (In curved space, such lines are called geodesics).

Photons are produced by changes in quantum state of a charged particle, from a state of higher energy to a state of lower energy, for example by atoms when a bound electron moves from one orbital to another orbital that has less energy or when a free electron becomes bound by an atom. Photons can also be emitted by an unstable nucleus when it undergoes some types of nuclear decay, producing gamma radiation. The frequency of an emitted photon is the result of a beat between the frequencies (energies) of the two stable states involved in the quantum transition, and the photon may be viewed as the electromagnetism of the moving charge involved in the mixture of states during the transition; the photon frequency or energy therefore represents the difference in energies of the states. If a mixture of two states does not result in an oscillation of the electric charge (mean probabilistic position), then the transition is said to be "disallowed" as there will be no coupling to radiation. Photons are also radiated whenever charged particles are accelerated, as in the production of bremsstrahlung, cyclotron or synchrotron radiation.

Atoms frequently emit photons due to their collisions and interactions with each other. The wavelength distribution of photons in thermal equilibrium with emitting atoms is related to their absolute temperature by the Planck distribution. The spectrum of such photons at a temperature T peaks around 2.9 mm/T, determined by Wien's law. For the Sun (5780 K) this is around 500 nm (visible light); for the Earth (~300 K), the peak is around 10 μm (infrared). As temperature is further increased, the photons will reach higher frequencies, such as ultraviolet, X-ray, gamma rays (though a system in equilibrium at a high enough temperature to emit in the gamma-ray spectrum probably does not exist).

Radio, television, radar and other types of transmitters used for telecommunication and remote sensing routinely create a wide variety of low-energy photons by the oscillation of electric fields in conductors. Particle-like properties are not detectable at such low frequencies. Magnetrons emit coherent photons used in household microwave ovens. Klystron tubes are used when microwave emissions must be more finely controlled. Masers and lasers create monochromatic photons by the same stimulated emission process. More energetic photons can be created by nuclear transitions, particle-antiparticle annihilation, and in high-energy particle collisions.

Since there is no conservation of photon number, photons may be annihilated. This process may occur as the time reversal of any way in which photons are created; for example, in absorption by atoms, nuclei or molecules. As long as total energy and momentum are conserved (say, by transfer to an optical medium), a photon may split into two photons, or two photons can combine into one.

In some cases, high-energy photons may be turned into particles which have rest mass, such as electrons and positrons. Such a case of pair production, requires a total energy of at least 1022 keV for one electron-positron pair. A single photon cannot turn into a particle-antiparticle pair without violating conservation of energy and momentum; however, such processes may occur by interaction with heavy nuclei, with other charged particles, or even (at a low rate) with other photons.

Photons have spin 1, and obey Bose-Einstein statistics, making them bosons. Photons mediate the electromagnetic interaction; they are the gauge bosons of quantum electrodynamics (QED), which is a U(1) gauge theory. A non-relativistic spin-1 particle has three possible spin states (−1, 0 and +1). However, in the framework of special relativity, this is not the case for massless spin-1 particles, such as the photons, which have only two spin projections, helicities, corresponding to the right- and left-handed circular polarizations of classical electromagnetic waves. The more familiar linear polarization is formed by a superposition of the two spin projections of a photon.

Visible light from ordinary sources (such as the Sun or a lamp) is a mixture of many photons of different wavelengths, phases and polarizations. One sees this in the frequency spectrum, for instance by passing the light through a prism. In so-called "mixed states", which these sources tend to produce, light can consist of photons in thermal equilibrium (so-called black-body radiation). Here they in many ways resemble a gas of particles. For example, they exert pressure, known as radiation pressure.

On the other hand, an assembly of photons of long (many wavelengths) wave function can also exist in much more coherent states, called Bose-Einstein condensate — such as in the light emitted by laser. The high degree of precision obtained with laser instruments is partially due to coherence laser photons.

The quantum state of a photon assembly, like that of other quantum particles, is the so-called Fock state denoted , meaning photons in one of the distinct "modes" of the electromagnetic field. If the field is multimode (involves several different wavelength photons), its quantum state is a tensor product of photon states, for example:

Here denote the possible modes, and the number of photons in each mode

A typical molecule, , has many different energy levels. When a molecule absorbs a photon, its energy is increased by an amount equal to the energy of the photon. The molecule then enters an excited state, .

Although a single photon has zero mass, multi-particle objects including photons may collectively have mass. For example, a mirrored box containing a gas of photons, or even a single photon, with total energy E will have greater mass (by Δm = E/c²) than if the box did not contain photon(s). [In the case of a single photon, the weight must be taken in the inertial frame in which the mass of the photon and box sum to zero, see mass of systems in mass in special relativity. However this will generally be close to the rest frame of the empty box.]

In empty space (vacuum) all photons move at the speed of light, c, defined as 299,792,458 metres per second, or approximately 3×10⁸ m/s. The metre is in fact defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second.

According to one principle of Einstein's special relativity, all observations of the speed of light in vacuo are the same in all directions to any observer in an inertial frame of reference. This principle is generally accepted in physics, since many practical consequences for high-energy particles in theoretical and experimental physics have been observed.

Since photons move at the speed of light, by relativist time dilation they do not take any time to get from their source to where they are finally absorbed; that is, they have zero lifetime but can travel arbitrarily far. The emission and absorption events are at zero space-time interval. From this point of view, first articulated by Gilbert N. Lewis in 1926, the photon's energy never exists in the vacuum, but transfers from the source to the absorber without delay.

When photons pass through matter, such as a prism, different frequencies will be transmitted at different speeds. This is called dispersion of colors, where photons of different frequencies exit at different angles. A similar phenomenon occurs in reflection where surfaces can reflect photons of various frequencies at different angles.

The associated dispersion relation for photons is a relation between frequency, , and wavelength, , or equivalently, between their energy, , and momentum, . It is simple in vacuo, since the speed of the wave, , is given by

The photon quantum relations are:

and

Here is Planck's constant. So one can also write the dispersion relation as

which is characteristic of a zero-mass particle. One sees that Planck's constant relates the wave and particle aspects.

In a material, photons couple to the excitations of the medium and behave differently. These excitations can often be described as quasi-particles (such as phonons and excitons); that is, as quantized wave- or particle-like entities propagating though the matter. "Coupling" means here that photons can transform into these excitations (that is, the photon gets absorbed and medium excited, involving the creation of a quasi-particle) and vice versa (the quasi-particle transforms back into a photon, or the medium relaxes by re-emitting the energy as a photon). However, as these transformations are only possibilities, they are not bound to happen and what actually propagates through the medium is a polariton; that is, a quantum-mechanical superposition of the energy quantum being a photon and of it being one of the quasi-particle matter excitations.

According to the rules of quantum mechanics, a measurement (here: just observing what happens to the polariton) breaks this superposition; that is, the quantum either gets absorbed in the medium and stays there (likely to happen in opaque media) or it re-emerges as photon from the surface into space (likely to happen in transparent media).

Matter excitations have a non-linear dispersion relation; that is, their momentum is not proportional to their energy. Hence, these particles propagate slower than the vacuum speed of light. (The propagation speed is the derivative of the dispersion relation with respect to momentum.) This is the formal reason why light is slower in media (such as glass) than in vacuum. (The reason for diffraction can be deduced from this by Huygens' principle.) Another way of phrasing it is to say that the photon, by being blended with the matter excitation to form a polariton, acquires an effective mass, which means that it cannot travel at c, the speed of light in a vacuum.

• Particle physics
• Electromagnetic spectrum
• Photonics
• Optics
• Quantum mechanics
• Spectroscopy
• Photoelectric effect
• Compton scattering
• Bremsstrahlung
• Cerenkov radiation
• List of particles
• Photokinesis

• Lewis, G.N. The conservation of photons. Nature 1926, 118, 874-875.

• The Nature of Light: What Is A Photon? OPN Trends, Oct 2003
• MISN-0-212 Characteristics of Photons (PDF file) by Peter Signell and Ken Gilbert for Project PHYSNET.
• Particle Data Group

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