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# Photon

In physics, the photon (from Greek φοτος, meaning light) is a quantum of excitation of the quantised electromagnetic field and is one of the elementary particles studied by quantum electrodynamics (QED) which is the oldest part of the Standard Model of particle physics.

In layman's terms, photons are the building blocks of electromagnetic radiation: that is, a photon is a "particle" of light, although, according to quantum mechanics, all particles, including the photon, also have some of the properties of a wave.

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## Symbol

A photon is usually given the symbol γ (gamma), although in high energy physics this refers to a high energy photon (a gamma ray; a photon of the immediately lower energy range is denoted X, an X-ray).

## Properties

All electromagnetic radiation, from radio waves to gamma rays, is quantised as photons: that is, the smallest amount of electromagnetic radiation that can exist is one photon whatever its wavelength, frequency, energy, or momentum. Photons are fundamental particles. Their lifetime is infinite, although they can be created and destroyed. Photons are commonly associated with visible light, which is actually only a very limited part of the electromagnetic spectrum. Photons have zero invariant mass but a definite finite energy. Because they have energy, the theory of general relativity states that they are affected by gravity, and this is confirmed by observation.

### Creation

Photons can be produced in a variety of ways, including emission from electrons as they change energy states or orbitals. Photons can be created by nuclear transitions, particle-antiparticle annihilation, or any fluctuations in an electromagnetic field. Special devices like masers and lasers can create coherent low energy photon radiation.

### Spin

Photons have spin 1 and they are therefore bosons. Photons mediate the electromagnetic field (that is, they are the particles that enable other particles to interact with each other electromagnetically and with the electromagnetic field), so they are gauge bosons. In general, a boson with spin 1 should be observed in three spin projections (−1, 0 and 1). The zero projection would require a frame where the photon is at rest, but, since photons travel at the speed of light, such a frame does not exist according to the theory of relativity, and so photons have only two spin projections. Individual photons are circularly polarized on account of their unit spin.

### Quantum state

Even visible light is commonly encountered in quantum states which are not "pure" photons but combinations (technically, superpositions) of large numbers of photons — either coherent superpositions (so-called coherent states, describing coherent light such as emitted by an ideal laser) or mixtures (so-called thermal states ), describing light in thermal equilibrium (black-body radiation).

The associated quantum state is the Fock state denoted $|n\rangle$, meaning n photons in the electromagnetic field mode understood. If the field is multimode, its quantum state is a tensor product of photon states, for example:

$|n_{k_0}\rangle\otimes|n_{k_1}\rangle\otimes\dots\otimes|n_{k_n}\rangle\dots$

with ki the possible momenta of the modes and $n_{k_i}$ the number of photons in this mode.

### Molecular absorption

A typical molecule, M, 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, $M^* \,$.

$M + \gamma \to M^* \,$

## State in a vacuum

In a vacuum, all photons move at the speed of light, c, defined as equal to 299,792,458 metres per second (the metre is defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second, so the speed of light does not suffer any experimental uncertainty, unlike the metre or the second), or approximately 3×108 m s−1.

The dispersion relation of photons (that is, the ratio between their angular velocity and group velocity, or, equivalently, the ratio between their momentum and energy) is linear and the constant of proportionality is Planck's constant, h. Briefly considering the wave-like properties of a photon, it is also worth remembering that the speed of a wave, v, is given by the equation:

$v=\lambda f \,$

where

$\lambda \,$ (lambda) is the wavelength

f is the frequency (the symbol $\nu \,$ (nu) is often used instead, but f is used here to avoid ambiguity with v).

This yields two useful relations for kinematic studies:

1. The energy of a photon, E, is given by the equation $E=hf \,$ (or equivalently $E=hc/\lambda \,$)
2. The momentum of a photon, p, is given by the equation $p=h/\lambda \,$ (or equivalently, $p=hf/c \,$).

## State in media

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.