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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 wave four-vector defined by

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

See also[edit]


  • Woodhouse, N.M.J. (2003). Special Relativity. London: Springer-Verlag. ISBN 1-85233-426-6.