Can Lorentz transformations be determined by the null Michelson-Morley result?

J A S Lima,Fernando D Sasse

doi:10.1590/1806-9126-rbef-2016-0273

Abstract

The so-called principle of relativity is able to fix a general coordinate transformation which differs from the standard Lorentzian form only by an unknown speed which cannot in principle be identified with the light speed. Based on a reanalysis of the Michelson-Morley experiment using this extended transformation we show that such unknown speed is analytically determined regardless of the Maxwell equations and conceptual issues related to synchronization procedures, time and causality definitions. Such a result demonstrates in a pedagogical manner that the constancy of the speed of light does not need to be assumed as a basic postulate of the special relativity theory since it can be directly deduced from an optical experiment in combination with the principle of relativity. The approach presented here provides a simple and insightful derivation of the Lorentz transformations appropriated for an introductory special relativity theory course.

Highlights

In the standard lore of special relativity theory (SRT), the pillars of the theory rest on two postulates originally introduced by Einstein [1], namely: (i) the principle of relativity, and (ii) the principle that states that the speed of light is independent of the velocity of the source
It is worth mentioning that the above transformations are a particular case of the more general set assumed by Robertson [37], from which he concluded that the three second-order optical experiments taken together, namely: Michelson-Morley [36] (1887), Kennedy-Thorndike [38] (1932), and Ives-Stilwell [39, 40] (1938, 1941) are sufficient to single out the Lorentz transformations
Standard derivations of the generalized Lorentz transformations given by equations (1-5) show that the unique free-parameter to be determined is an invariant maximum speed, σ

Summary

Introduction

In the standard lore of special relativity theory (SRT), the pillars of the theory rest on two postulates originally introduced by Einstein [1], namely: (i) the principle of relativity, and (ii) the principle that states that the speed of light is independent of the velocity of the source The first attempt was made by Ignatowski [3] in 1910 He replaced the second Einstein postulate by the assumption of isotropy and homogeneity of space, which implies linearity of the transformation equations and Copyright by Sociedade Brasileira de Fısica. An additional list of references regarding derivations of this kind is given by Sonego and Pin [28] All these derivations arrive at formulas for the Lorentz transformations containing an unknown and invariant (constant) limiting speed. We show how the identification of this constant speed with the speed of light could have been made in the early years of the theory of special relativity, by applying the derived general transformations to the null results obtained in the Michelson-Morley experiment [36]. The approach discussed here establishes the speed of light as the limiting speed to be used at Lorentz transformations and shows explicitly that the hypothesis of the existence of a luminiferous aether does not interfere with the result since it becomes irrelevant as a consequence of the null Michelson-Morley experiment

Lorentz transformations without the second postulate

Michelson-Morley experiment and the limiting invariant speed

Conclusions