Relativity with or without light and Maxwell

TL;DR

This paper analyzes the relationship between Einstein's second postulate and Maxwell's electromagnetism, framing a pedagogical discussion around how special relativity can emerge from or be independent of electromagnetic theory. It presents a simple Ignatowski-inspired derivation showing Lorentz-like transformations can be obtained from purely kinematic assumptions (linearity, isotropy, reciprocity, causality) with a universal speed parameter $\Omega$, and identifies a derived limit speed $\overline c=1/\sqrt{\Omega}$. It then contrasts this with the traditional, Maxwell-influenced route where the constancy of the speed of light $c=(\epsilon_0\mu_0)^{-1/2}$ ties time to light propagation and yields Lorentz covariance of Maxwell's equations. The discussion highlights the pedagogical value of distinguishing between a purely kinematic relativistic framework and the physical postulate that links time, electromagnetism, and a universal speed, while situating the historical debate about Maxwellian relativity and the second postulate within the broader history of physics.

Abstract

The complex relationship between Einstein's second postulate and the Maxwell electromagnetic theory is elucidated. A simple deduction of the main results of the Ignatowski approach to the theory of relativity is given. The peculiar status of the principle of relativity among the Maxwellians is illustrated.