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The four-frequency of a massless particle, such as a photon, is a four-vector defined by
where ν {\displaystyle \nu } is the photon's frequency and n ^ {\displaystyle {\hat {\mathbf {n} }}} 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 V b {\displaystyle V^{b}} will observe a frequency
Where η {\displaystyle \eta } is the Minkowski inner-product
Closely related to the four-frequency is the four-wavevector defined by
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