four-frequency

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

:$N^a = \left( \nu, \nu \hat \right)$

where $\nu$ is the photon's frequency and $\hat$ 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

:$\frac\eta\left(N^a, V^b\right) = \frac\eta_N^aV^b$

Where $\eta$ is the Minkowski inner-product (+−−−) with covariant components $\eta_$.

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

:$K^a = \left(\frac, \mathbf\right)$

where $\omega = 2 \pi \nu$, $c$ is the speed of light and $\mathbf = \frac\hat$ and $\lambda$ 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 $c = \nu \lambda$) by

:$K^a = \frac N^a$

See also

* Four-vector
* Wave vector

References

*

Four-vectors
Frequency

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