Four-frequency
The four-frequency of a massless particle, such as a photon, is a four-vector defined by
where is the photon's frequency and is a unit vector in the direction of the photon's motion. The four-frequency of a photon is always a future-pointing and null vector. An observer moving with four-velocity will observe a frequency
Where is the Minkowski inner-product
Closely related to the four-frequency is the four-wavevector defined by
where, is the speed of light and and is the wavelength of the photon. The four-wavevector is more often used in practice than the four-frequency, but the two vectors are related by
