Lorentz, Poincaré, and Einstein: Rethinking Doppler, Aberration, and the Fresnel Drag

TL;DR

The paper analyzes historical trajectories for Doppler, aberration, and Fresnel drag, contrasting Lorentz's ether-based, first-order constructions with Einstein's 1905–1907 relativity-based kinematics. It demonstrates a formal similarity in phase handling between Lorentz and Einstein, but a fundamental shift in premises: Einstein replaces the ether with the relativity principle and uses exact Lorentz transformations to derive the relativistic Doppler and aberration laws, as well as the exact velocity addition $u = \frac{u' + v}{1 + \frac{u'v}{c^{2}}}$, of which Fresnel drag is the low-velocity limit. Lorentz’s approach relies on local time and yields Fresnel dragging only at first order, while Einstein's framework yields unbounded behavior as $v \to \pm c$, reflecting genuine relativistic kinematics. The work also clarifies why Poincaré’s dynamics did not yield the relativistic Doppler/aberration laws, tying the development to a broader shift from constructive to principle theories in modern physics.

Abstract

This paper examines Lorentz's 1895 derivations of the classical Doppler formula and Fresnel drag, Einstein's 1905 derivation of the relativistic Doppler effect and aberration, and Einstein's 1907 kinematical route to the exact velocity composition law from which Fresnel drag is obtained as a low-velocity limit. Einstein acknowledged that he had read Lorentz's "Versuch" well before 1905. In 1907, Einstein identified Lorentz's "Versuch" as a crucial precursor to relativity. In that work, Lorentz had already invoked local time to derive Fresnel's drag coefficient from Maxwell's equations. There is a genuine "family resemblance" between Lorentz's and Einstein's treatments in that both preserve the phase of a plane wave under transformation. Yet I demonstrate that this resemblance is only formal. I also discuss the absence of the relativistic Doppler and aberration laws in Poincaré's Dynamics of the Electron.