In modern physics, the photon is the elementary particle responsible for electromagnetic interactions and light in particular. The energy and momentum of a photon depend only on its frequency (or, equivalently, its wavelength ) and Planck's constant . The prevailing Standard model of physics predicts that the photon is massless, which is consistent with experiment; hence, the photon moves at , the speed of light in empty space.

The word "photon" derives from the Greek word φως, "phōs" (meaning light) and was coined in 1926 by Gilbert N. Lewis. However, the concept of the photon was introduced earlier by Albert Einstein, who called it a "light quantum".

A photon is usually given the symbol γ, the Greek letter gamma, although in nuclear physics this symbol refers only to photons of the highest energy (a gamma ray). In chemistry, photons are sometimes symbolized by hν, which is the amount of energy of each photon.

The photon is one of the elementary particles. Based on the theory of quantum electrodynamics (QED) its interactions with electrons and atomic nuclei account for a great many of the physical properties of matter, such as the existence and stability of atoms, molecules, and solids.

In many circumstances, a photon acts as a particle, for instance when registered by the light-sensitive device in a camera. In other circumstances, a photon acts like a wave, as when passing through the optics in a camera. According to the wave-particle duality of quantum physics, it is natural for the photon to display either aspect of its natures, according to circumstances. Normally, a beam of light is composed of 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.

Photons are commonly associated with visible light, but this is actually only a very limited part of the electromagnetic spectrum. Based on quantum field theory, 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 each photon interacts with matter in discrete units individually or in groups. Photons appear to be fundamental particles. They can be created by dipole oscillations and destroyed (absorbed) after interacting with certain particles, but do not decay.

A photon of a definite frequency is described as a non-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 invariant mass ^[1] and zero electric charge, but they do carry energy, momentum and angular momentum. Although the photon is generally accepted to be massless, experiments can 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 the magnetohydrodynamics of the solar wind.^[2]

As massless particles, photons move at a speed of 2.998×10^8 m/s, which is represented by the symbol c (often called the speed of light in vacuum). Based on the theory 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 is partially or completely transferred when it interacts with matter. The force produced when photons interact with a surface is called radiation pressure, which can be used for propulsion in the vacuum of space as with a solar sail.

Experiments have shown that 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 on a geodesic which is the closest thing to a straight line that is possible due to the curvature of spacetime.

The source of the gravitational field is stress, momentum density, and energy density. Photons contribute to these so they produce gravity in spite of the fact that they are massless. Gravity acts on both the energy and momentum of a particle. These have the same magnitude for photons which is why the deflection is doubled (Newtonian theory would have it act only on energy).

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. (For creation of photons in the visible light range, see Balmer series) 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.

The annihilation of a particle and its antiparticle can produce photons that have a total energy, in the zero net momentum frame, of approximately the sum of the rest masses of the pair of particles that were annihilated (it will be slightly more if they were moving freely and slightly less if they were bound to each other). The end result of any annihilation must be consistent with the laws of conservation of energy, momentum, and angular momentum (including both orbital and spin angular momentum). This implies, for instance, that at least two photons must be created.

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. The production and absorption of photons during photon annihilation are constrained by energy and momentum conservation. Therefore, a single photon in vacuum can not annihilate and thus can propagate indefinitely. In some cases, photon annihilation (involving 2 or more high-energy photons, or a photon and another particle(s)) results in particle-antiparticle pair production in a process called matter creation. Most common and frequently observed in laboratory process of this kind is pair production of e- and e+ pair by a gamma-photon (which must have energy higher than the rest mass energy of an electron-positron pair E=1.04 MeV) passing near heavy nucleus. Pair production is main energy loss channel for high energy photons (E > 10 Mev) propagating in atomic matter.

Photons mediate the electromagnetic interaction; they are the gauge bosons of quantum electrodynamics (QED), which is a U(1) gauge theory. Photons have spin 1, and follow Bose-Einstein statistics, making them bosons. A massive (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. They have only two spin projections, or helicities, which correspond to the right- and left-handed circular polarizations of classical electromagnetic waves. Linear polarizations are produced by the 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, .

Emission is the reverse of this process.

"Relativistic mass" is simply but, in contemporary usage, "mass" means "invariant mass" (or, equivalently, "rest mass" if the invariant mass is non-zero). Hence a photon's "mass" is zero, since this refers to the invariant mass. Nonetheless, a composite system which includes photons, when viewed in the system's zero net momentum frame (if such a frame exists) will also include the photons' relativistic masses as part of the composite system's rest mass. Each component of the composite system, including the total composite system itself, and including massless components such as photons, obeys E=mc², where m is the relativistic mass, as long as m and E are both evaluated in the same frame, for example the system frame.

Therefore, even when considering the contempory usage of "mass" as "invariant mass", the mass of a system can increase due to photon energy. See Mass in special relativity for more details.

The theoretical proper (invariant) mass of the photon is generally believed to be exactly zero^[1] as mandated by QED. Since, due to measuring equipment limitations a zero can only be attained asymptotically, a series of experiments intended to constrain the photon mass have been undertaken. A limit on the photon mass can be obtained through satellite measurements of planetary magnetic fields. The Charge Composition Explorer spacecraft was used to derive a limit of 6x10^-16 eV with high certainty. This was slightly improved in 1998 by Roderic Lakes in a laborartory experiment which looked for anomalous forces on a Cavendish balance. The new limit is 6x10^-17 eV. This limit is about 17 orders of magnitude less than the equivalent energy mass of a visible light photon.

Studies of galactic magnetic fields suggest a much better limit of less than 3x10^-27 eV but there is some doubt about the validity of this method. Notwithstanding this, further efforts in order to tighten the error bars on the photon mass are to be expected.

References:

1. Eric Adelberger, Gia Dvali, Andrei Gruzinov, "Photon Mass Bound Destroyed by Vortices", arXig.org
2. Goldhaber, Alfred S., and Nieto, Michael Martin, "Terrestrial and Extraterrestrial Limits on The Photon Mass", Rev. Mod. Phys. vol.43 #3 pp.277–296, 1971 [1]
3. E. Fischbach et al., Physical Review Letters, 73,514-517 25 July 1994.
4. Official particle table http://pdg.lbl.gov/2005/tables/gxxx.pdf
5. L. Davis, A. S. Goldhaber, and M. M. Nieto, Phys. Rev. Lett. 35, 1402 (1975)
6. Roderic Lakes, "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential", Phys. Rev. Lett. 80, 1826 (1998) [2]
7. J. Luo et al., Phys. Rev. D 59, 042001 (1999)
8. B. E. Schaefer, Phys. Rev. Lett. 82, 4964 (1999)
9. J.Luo et al., Physical Review Letters, (28 February 2003)

In empty space (vacuum) all photons move at the speed of light, c, which is 299,792,458 metres per second, or approximately 3×10⁸m/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 universally 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, no proper time passes for them. The emission and absorption events form an interval of length zero in space-time.

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 a nonzero effective mass, which means that it cannot travel at c, the speed of light in a vacuum.

As is well known, quantum mechanics forbids the simultaneous measurement of the position and momentum of a particle in the same direction. Similarly, it forbids simultaneous measurement of the number of photons (see Fock state) in an electromagnetic wave and the phase (see Coherent state) of that wave.

• Electromagnetic radiation
• Photon polarization
• Particle physics
• Electromagnetic spectrum
• Photonics
• Optics
• Quantum mechanics
• Spectroscopy
• Photoelectric effect
• Compton scattering
• Bremsstrahlung
• Cherenkov radiation
• List of particles
• Photokinesis
• Creation and annihilation operators

• Pais A. (1982) Subtle is the Lord: The Science and the Life of Albert Einstein, Oxford University Press, pp. 364-388, 402-415.

• 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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