Four-frequency explained

The four-frequency of a massless particle, such as a photon, is a four-vector defined by

N ^{a} = \left( \nu, \nu \hat{ n } \right)

where

\nu is the photon's frequency and \hat{ 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} will observe a frequency(1)/(c) η \left(N ^{a,} V ^{b\right)} = (1)/(c) η _{ab} N ^{aV} ^{b}

Where

η is the Minkowski inner-product (+−−−) with covariant components η _{ab} .

Closely related to the four-frequency is the four-wavevector defined by

K ^{a} = \left( (\omega)/(c) , k \right)

where

\omega = 2 \pi \nu , c is the speed of light and $\backslash mathbf\; =\; \backslash frac\backslash hat$ and λ 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 (using c = \nu λ ) byK ^{a} = (2 \pi)/(c) N ^{a}

See also

• Four-vector
• Wave vector

References

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