The four-frequency of a photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

 is defined by


where is the photon's frequency

Frequency

Frequency 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...

 and is a unit vector in the direction of the photon's motion. The four-frequency is always a future-pointing and null vector. An observer moving with four-velocity

Four-velocity

In physics, in particular in special relativity and general relativity, the four-velocity of an object is a four-vector that replaces classicalvelocity...

  will observe a frequency


Where is the Minkowski inner-product (+---)

Closely related to the four-frequency is the wave four-vector defined by


where , is the speed of light and and is the wavelength

Wavelength

In 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...

of the photon. The wave four-vector is more often used in practice than the four-frequency, but the two vectors are related (using ) by