A moving wave surface in special relativity may be regarded as a hypersurface (a 3D subspace) in spacetime, formed by all the events passed by the wave surface. A wavetrain (denoted by some variable ) can be regarded as a one-parameter family of such hypersurfaces in spacetime. This variable is a scalar function of position in spacetime. The derivative of this scalar is a vector that characterizes the wave, the four-wavevector.

The four-wavevector is a wave four-vector that is defined, in Minkowski coordinates,