Relativistic Doppler Effect and the Principle of Relativity

The frequency shifts predicted by the ‘relativistic’ Doppler effect are derived in the photon picture of light. It turns out that, in general, the results do not depend exclusively on the relative velocity between observer and light source. In this respect, the relativistic Doppler effect is not distinct from the classical one, where the shifts are also different depending on whether the source or the observer moves. The ‘relativistic’ formulae for these two cases have been confirmed by experiment and are described in many textbooks. It was, however, not recognized that they are at variance with Einstein’s relativity principle extended to electromagnetic waves.