Experiment and theory: the case of the Doppler effect for photons

TL;DR

This paper reviews the historical and theoretical development of the Doppler effect for photons, emphasizing the importance of Schrödinger's dynamical treatment often overlooked in experimental analyses, and discusses implications for special relativity.

Contribution

It highlights the significance of Schrödinger's energy-momentum conservation approach in understanding photon Doppler effects, contrasting it with traditional wave-based explanations and analyzing experimental neglect.

Findings

Schrödinger's dynamical treatment explains Doppler shifts via energy-momentum exchange.

Historical experiments often ignore Schrödinger's approach, relying on wave theory.

Modern experiments continue to test special relativity without fully considering quantum dynamics.

Abstract

In 1907, Einstein suggested an experiment with flying atoms for corroborating time dilation. In that paper, the flying atom was conceived as a flying clock: the reference to the Doppler effect was only indirect (the experiments by Stark to the first order of $v/c$). In 1922, Schr\"odinger showed that the emission of a light quantum by a (flying) atom is regulated by the conservation laws of energy and linear momentum. Therefore, the Doppler effect for photons is the consequence of the energy and momentum exchange between the atom and the photon: a central role is played by the quantum energy jump $\Delta E$ of the transition (a relativistic invariant). The first realization of the experiment devised by Einstein is due to Ives and Stilwell (1938). Since then till nowadays experiments of this kind have been repeated in search of better precision and/or a deviation from the predictions of special relativity. The striking feature is that all the papers dealing with these experiments completely neglect Schr\"odinger's dynamical treatment. The origins of this omission are of different kind: pragmatic (agreement between formulas, wherever coming from, and experiments), historical (deep rooting of the wave theory of light) and epistemological (neglect of basic epistemological rules).