The four-frequency of a massless particle, such as a photon, is a four-vector defined by where
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
is the Minkowski inner-product (+−−−) with covariant components
Closely related to the four-frequency is the four-wavevector defined by where
ω = 2 π ν
The four-wavevector is more often used in practice than the four-frequency, but the two vectors are related (using