[Paper Review] Voigt's transformations in the beginning of the relativistic era

Ricardo Heras|arXiv (Cornell University)|Nov 10, 2014

Relativity and Gravitational Theory14 references3 citations

TL;DR

This paper re-examines Voigt's 1887 derivation of spacetime transformations that preserve the wave equation and the invariance of light speed, predating Einstein’s special relativity by 18 years. It presents a novel derivation of Voigt's transformations, highlights their conceptual and historical significance, and clarifies their distinction from Lorentz transformations, positioning Voigt as a foundational figure in the relativistic era’s inception.

ABSTRACT

In 1887 W. Voigt published the paper: On Doppler's Principle, which inaugurated the beginning of the relativistic era in physics. In this paper Voigt demanded covariance to the homogeneous wave equation in inertial frames and assumed the invariance of the speed of light in these frames, obtaining a set of spacetime transformations different from the Lorentz transformations. Without explicitly mentioning, Voigt applied the postulates of special relativity to the wave equation 18 years before Einstein enunciated these postulates. 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 Voigt and Lorentz transformations and present a novel derivation of the former.

Motivation & Objective

• To re-express and analyze Voigt’s original 1887 derivation of spacetime transformations that preserve the wave equation in inertial frames.
• To clarify the conceptual and historical importance of Voigt’s work in the development of special relativity, despite its relative obscurity.
• To distinguish Voigt’s transformations from Lorentz transformations and establish their unique role in the relativistic framework.
• To provide a novel derivation of Voigt’s transformations using modern theoretical tools, reinforcing their validity and significance.

Proposed method

• Reconstructing Voigt’s original 1887 derivation from his paper 'On Doppler's Principle' using mathematical analysis of the homogeneous wave equation.
• Applying the condition of covariance of the wave equation under spacetime transformations between inertial frames.
• Imposing the invariance of the speed of light in all inertial frames as a fundamental postulate in Voigt’s derivation.
• Deriving the specific form of Voigt’s transformations through algebraic manipulation of the wave equation’s invariance condition.
• Comparing Voigt’s transformations with Lorentz transformations to highlight structural and conceptual differences.
• Using modern theoretical language to re-derive Voigt’s transformations independently, validating their consistency and physical meaning.

Experimental results

Research questions

• RQ1 How did Voigt derive his spacetime transformations in 1887, and what assumptions underpinned his derivation?
• RQ2 To what extent did Voigt’s work anticipate the postulates of special relativity before Einstein’s 1905 formulation?
• RQ3 What is the precise mathematical and conceptual distinction between Voigt’s and Lorentz’s transformations?
• RQ4 Why was Voigt’s contribution historically overlooked despite its foundational role in the relativistic era?
• RQ5 Can a novel, modern derivation of Voigt’s transformations reaffirm their physical and theoretical significance?

Key findings

• Voigt derived a set of spacetime transformations that preserve the form of the homogeneous wave equation across inertial frames, independently of Lorentz or Einstein.
• Voigt’s transformations inherently assume the invariance of the speed of light, a core postulate of special relativity, 18 years before Einstein’s 1905 paper.
• The derived transformations differ from Lorentz transformations, particularly in their scaling of time and space coordinates.
• Voigt’s work constitutes a foundational but underappreciated milestone in the emergence of special relativity, demonstrating early insight into relativistic invariance.
• The novel derivation presented in the paper confirms the mathematical consistency and physical coherence of Voigt’s transformations.
• Historically, Voigt’s contribution marks the true beginning of the relativistic era in physics, predating Einstein’s formalization.