A Relativistic Treatment of Space-Time Rays and the Doppler Effect in General Media

Abstract

For waves in plasmas and similar media, space-time rays with a 4-vector formulation are used to obtain an approximate expression for the rapidly varying part of the wave, on the assumption that the plasma properties vary slowly in space and time. It is shown that the phase function associated with the rapid variations is invariant with respect to Lorentz transformation and that the ray equations may be written in vector form. These results are used to obtain expressions for the Doppler shift that are consistent with special relativity. The possibility that the medium is moving and time-varying is allowed for, and a variety of possible sources are considered.