Faster-than-light group velocities and causality violation

The classical analysis of Brillouin and Sommerfeld has shown that the appearance, in some frequency range, of group velocities in excess of the speed of light does not imply causality violation. The group velocity is not always identical with the velocity of signal propagation. We show that a necessary condition for causality violation is that the infinite- frequency limit of the phase velocity shall exceed the speed of light. Application of the theorem leads to the conclusions (a) that all Lorentz-invariant wave equations (and in particular the Feinberg ‘tachyon’) are causal, and (b) that the quasi-acoustic branch of the Bludman-Ruderman model is causal.