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

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).

💡 Research Summary

The paper revisits the Doppler effect for photons from both historical and theoretical perspectives, tracing its development from Einstein’s 1907 proposal of a “moving atomic clock” to the modern high‑precision experiments that test special relativity. In the early 20th century, Stark’s observation of a first‑order (v/c) Doppler shift in light emitted by fast hydrogen atoms was interpreted by Einstein as an indirect verification of time dilation: the atom was treated as a clock whose ticking rate would appear slower to a stationary observer. This interpretation relied on a classical picture of the atom as a periodic system (harmonic electron vibrations or Bohr orbits), an assumption that became untenable after the advent of quantum mechanics.

In 1922 Erwin Schrödinger offered a fundamentally different description. Assuming that a photon carries energy ℏω and momentum ℏω/c, he wrote down the conservation of energy and linear momentum for the emission (or absorption) of a light quantum by a moving atom. His equations (5)–(7) relate the atom’s rest energies before and after the transition (E₁, E₂), the corresponding Lorentz factors (γ₁, γ₂), the atom’s velocities (v₁, v₂) and the photon’s direction (θ₁, θ₂). From these relations he derived an expression for the photon energy

Eₚ = ΔE ·