Passage from Einsteinian to Galilean Relativity and Clock Synchrony

Abstract

Abstract There is a general belief that under small velocity approximation. Special Relativity goes over into Galilean Relativity. Should this be interpreted exclusively in terms of the kinematical symmetry transformations (Lorentz vs. Galilei) a misconception could easily arise that would stem from overlooking the role of conventionality ingredients of Special Relativity Theory. It is observed that the small velocity approximation cannot alter the convention of distant simultaneity. In order to exemplify this point further, the Lorentz transformations are critically compared, under the same approximation, with two other space time transformations, one of which represents an Einstein world with Galilean synchrony whereas the other describes a Galilean world with Einsteinian synchrony