Velocity reciprocity and the relativity principle

Abstract

Velocity reciprocity means that the velocity of an inertial frame S with respect to another inertial reference frame S′ is the opposite of the velocity of S′ with respect to S. While velocity reciprocity holds true for both the Lorentz and Galilean transformations, it need not be true in general, and it is a widely held misconception that velocity reciprocity is a sole consequence of the relativity of motion principle. The situation is, in fact, much more complicated, and it is the purpose of this paper to call attention to and hopefully help to rectify the matter regarding the misconception. We show that if we ascribe universal and unrestricted validity to the relativity of motion principle, then velocity reciprocity cannot possibly follow only from the relativity principle, and we detail the additional assumptions that must be made in order for velocity reciprocity to hold.