# Photon

In physics, the photon (from Greek φοτος, meaning light) is a quantum of the electromagnetic field, for instance light. Photons were originally called "energy quanta".

File:Photon waves.png
The photon can be perceived as a wave or a particle, depending on how it is measured

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 some respects a photon acts as a particle, for instance when registered by the light sensitive device in a camera. In other respects, a photon acts like a wave, as when passing through the optics in a camera. According to the so-called wave-particle duality in 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 or brightness 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.

## Symbol

A photon is usually given the symbol $\displaystyle \gamma$ (gamma), although in high-energy physics this symbol refers to a very high-energy photon (a gamma ray).

## Properties

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. Photons are fundamental particles. They can be created and destroyed when interacting with other particles, but are not known to decay on their own.

Unlike most particles, photons have no detectable intrinsic mass, or "rest mass" (as opposed to relativistic mass). Photons are always moving at the speed of light (which varies according to the medium in which they travel) with respect to all observers. Despite their lack of mass, photons have momentum proportional to their frequency (or inversely proportional to their wavelength), and this momentum can be transfered when a photon collides with matter (like a moving billiard ball transfers momentum into another ball). This is known as radiation pressure, which may some day be used for propulsion with a solar sail.

Photons are deflected by a gravitational field twice as much as Newtonian mechanics predicts for a mass traveling at the speed of light with the same momentum as the photon. This observation is commonly cited as evidence supporting the general relativity, a very successful theory of gravity published in 1915 by Albert Einstein. In general relativity, photons always travel in a "straight" line, after taking into account the curvature of space-time. (In curved space, this is called a geodesic).

### Creation

Photons are produced by atoms when a bound electron moves from one orbital to another orbital with less (more negative) energy. Photons can also be emitted by an unstable nucleus when it undergoes some types of nuclear decay. Furthermore, photons are produced whenever charged particles are accelerated.

Atoms continuously emit photons due to their collisions with each other. The wavelength distribution of these photons thus are related to their absolute temperature (usually in Kelvin). The Maxwell-Boltzmann distribution provides the probability of a photon being a certain wavelength when emitted by a collection of atoms at a given temperature. The spectrum of such photons are normally found in the range between microwave and infrared, but hot objects will emit visible light as well. As temperature is further increased, some photons will reach even higher frequencies, such as ultraviolet and X-rays.

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. 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 stimulated emission. More energetic photons can be created by nuclear transitions, particle-antiparticle annihilation, and in high-energy particle collisions.

### Spin

Photons have spin 1 and they are therefore classified as 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 observable with three distinct spin projections (−1, 0 and 1). However, the zero projection would require a frame where the photon is at rest. Because the (rest) mass is zero, such a frame does not exist, according to the theory of relativity. So photons in empty space always travel at the nominal speed of light, and show only two spin projections, corresponding to two opposite circular polarizations. On account of the zero intrinsic mass, photons are therefore always transversely polarized, in the same way as electromagnetic waves are, in empty space.

### Quantum state

Visible light, from the Sun, or a lamp, is commonly a mixture of many photons of different wave-lengths. 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, which (in part) accounts for the appearance of comets as they travel close by the Sun.

On the other hand, an assembly of photons can also exist in much more well-organized states. For instance, in so-called coherent states, describing coherent light such as emitted by an ideal laser. The high degree of precision obtained with laser instruments is due to this organization.

The quantum state of a photon assembly, like that of other quantum particles, is the so-called Fock state denoted $\displaystyle |n\rangle$ , meaning $\displaystyle n$ 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:

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

Here $\displaystyle k_i$ denote the possible modes, and $\displaystyle n_{k_i}$ the number of photons in each mode

### Molecular absorption

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

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

## Photons in vacuo

In empty space, called a perfect vacuum, all photons move at the speed of light, c, defined as equal to 299,792,458 metres per second, or approximately 3×108 m s−1. The metre is defined as the distance traveled 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, which rely on the second being defined by means of a very accurate clock.

According to one principle in Einstein's special relativity, all observations of the speed of light in vacuo are 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.

## Photons in matter

When photons pass through matter, such as a prism, different frequencies will be transmitted at different speeds. This is called refraction and results in the 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, f, and wavelength, λ. Or, equivalently, between their energy, E, and momentum, p. It is simple in vacuo, since the speed of the wave, v, is given by

$\displaystyle v=\lambda f = c\,$

The photon quantum relations are:

$\displaystyle E=hf \,$ and $\displaystyle p=h/\lambda \,$

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

$\displaystyle E=pc \,$

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

The energy of a photon can be shown in another way:

$\displaystyle E=h/T \,$

where T = 1 ⁄ f is a period of a photon. In this form, it seems that Planck's constant h might be interpreted as the energy of a "standard" photon with T = 1 s (i.e., a photon lasting 1 second), and that photon has an EM wave with period inversely proportional to its energy.

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.