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

TL;DR

This paper demonstrates that the Lorentz transformations can be derived from the Michelson-Morley experiment without assuming the constancy of light speed, highlighting a pedagogical approach to special relativity.

Contribution

It shows that the unknown speed in generalized coordinate transformations can be determined solely from optical experiments and the principle of relativity, without Maxwell's equations.

Findings

The unknown speed in extended transformations is analytically determined.

The constancy of light speed can be deduced from optical experiments and relativity principles.

Provides a simple derivation of Lorentz transformations for educational purposes.

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.