A review of Voigt's transformations in the framework of special relativity

TL;DR

This paper reviews Voigt's transformations within special relativity, highlighting their historical significance, derivation from wave equation covariance, and relation to Lorentz transformations.

Contribution

It provides a detailed analysis of Voigt's original derivation and explores the conceptual links between Voigt and Lorentz transformations.

Findings

Voigt's transformations derive from conformal covariance of the wave equation.

They are historically significant in the development of special relativity.

Voigt's transformations differ from Lorentz transformations but are related.

Abstract

In 1887 Woldemar Voigt published the paper "On Doppler's Principle," in which he demanded covariance to the homogeneous wave equation in inertial reference frames, assumed the invariance of the speed of light in these frames, and obtained a set of spacetime transformations different from the Lorentz transformations. Without explicitly mentioning so, Voigt applied the postulates of special relativity to the wave equation. Here, we review the original derivation of Voigt's transformations and comment on their conceptual and historical importance in the context of special relativity. We discuss the relation between the Voigt and Lorentz transformations and derive the former from the conformal covariance of the wave equation.