Einstein’s time dilation and the relativistic Doppler shift: avoiding the pitfalls

Abstract

Abstract Introductory textbooks for the theory of special relativity discuss the time dilation effect after introducing the Lorentz transformations. Reading the dictum ‘moving clocks run slow’ a student is likely to have the impression that this is a measured effect. On the other hand, after considering the relativistic Doppler effect the same student might be puzzled that this effect depends on the relative emitter-observer direction, contrary to Einstein’s time dilation. Simple thought experiments are presented here where the inferred time dilation and the observed relativistic Doppler effect give quite opposite answers. Before solving the puzzle, we show how easily one can get confused and obtain apparently contradictory results.