Law of inertia, clock synchronization, speed limit and Lorentz transformations

Abstract

In his first 1905 article on special relativity, clock synchronization by means of light rays was used by Einstein to derive the Lorentz transformations (Ann. Phys., Lpz. 322 891–921). However, the same goal can be achieved by using bodies in free motion to synchronize clocks. To this end, one has to accept the principle of relativity, the law of inertia and the existence of a limit value for the speed of massive bodies with no appeal to electromagnetic phenomena until the very last step of the derivation, when the limit speed must be identified with that of light in vacuum. (In the absence of this speed limit one recovers the Galilean transformations.)

Comment on ‘Maxwell’s equations and Lorentz transformations’

“…In the introduction of [1], the authors state that their proposed 'method of obtaining the Lorentz transformations could be an alternative way of introducing special relativity and has to be compared with a previous method [9] where we obtained the transformations without reference to any electromagnetic phenomena'. It should be specified, however, that the method presented in [9] via 'inertia-time', like any other 'relativity without light' approach, yields only Lorentz-like transformations, where c is the unknown limit speed of massive particles. To recover the actual Lorentz transformations, Aguirregabiria et al in [9] identify c with the speed of light in vacuum (which appears to be the simplest path to the Lorentz transformations), and light is an electromagnetic phenomenon 3 .…”

“…It should be specified, however, that the method presented in [9] via 'inertia-time', like any other 'relativity without light' approach, yields only Lorentz-like transformations, where c is the unknown limit speed of massive particles. To recover the actual Lorentz transformations, Aguirregabiria et al in [9] identify c with the speed of light in vacuum (which appears to be the simplest path to the Lorentz transformations), and light is an electromagnetic phenomenon 3 .…”

Reply to Maxwell’s equations and Lorentz transformations revisited

“…At the end of section 2, in the last remark, concerning a discussion of our previous paper [1], (Redzic's reference [8]), it is mentioned that 'to recover the actual Lorentz transformations' we identify the velocity limit c with the speed of light and, therefore, we are making use of an electromagnetic phenomenon. In that paper we make no mention to any electromagnetic phenomenon and the unreachable velocity for massive bodies c can be determined experimentally.…”

Maxwell’s equations and Lorentz transformations

“…The analysis of the loss of simultaneity among equivalent observers as well as other consequences in mechanics and other fields of physics may be analysed once the Lorentz transformations are obtained. This method of obtaining the Lorentz transformations could be an alternative way of introducing special relativity and has to be compared with a previous method [9] where we obtained the transformations without reference to any electromagnetic phenomena.…”