Comment on ’’Self-inverse form of the Lorentz transformation’’

Abstract

It has been shown that the kinematic relations between two iertial reference frames in relative motion can be made symmetric by an appropriate orientation of the coordinate axes of the two frames. It follows from this symmetry and the principle of relativity that the transformation matrix, A, from one frame to the other, and its inverse, A/sup -1/, are equal. This result, along with a limiting-velocity postulate, was used in a derivation of the Lorentz transformation. The present note points out that only two transformation laws are compatible with the symmetry condition A = A/sup -1/. One of these is the Lorentz transformation and the other violates causality. Thus, if the limiting-velocity postulate is replaced by the requirement that causality be satisfied in all inertial frames, one arrives at a derivation of the Lorentz transformation based entirely on concepts which were known and widely accepted long before the advent of special relativity: the homogeneity and isotropy of space in all inertial frames, the principle of relativity, and the principle of causality. (RWR)