Study on data analysis for Ives-Stilwell-type experiments

Abstract: Ives-Stilwell experiment in 1938 was a historic experiment for confirming Einstein's special relativity, and various modern types have been repeated by use of laser technology. In this paper, we reveal and solve a long-lasting unrecognized fundamental issue that the data analysis for all those experiments was not consistent with Einstein's definition of the relativistic Doppler effect so that the Doppler effect was not actually confirmed. For example, in the Letter [Phys. Rev. Lett. 113, 120405 (2014)] the definition of the measurement accuracy of Doppler effect, given by $\varepsilon=\sqrt{\nu_a\nu_p/(\nu_1\nu_2)}-1$, is not physical because Einstein's Doppler formula cannot be confirmed even when $\varepsilon = 0$ holds. Based on existing data, we propose a justified data analysis and correctly confirm the Doppler effect in the Ives-Stilwell-type experiment, thus resulting in a great advance in the experimental verification of Lorentz invariance via the Doppler effect. The proposed data analysis in the paper is quite straightforward, but it is the result of the correct way of thinking based on first principles: (i) Einstein's Doppler effect refers to the same photon (laser beam) exhibiting different frequencies observed in two inertial frames of relative motion, and (ii) the quantity (measurement accuracy) used as a measure to confirm the effect must be able to confirm Einstein's Doppler formula itself. However, the way of thinking set up in the 1938 Ives-Stilwell experiment was incorrect because it was not consistent with the first principles, although it had been followed by quite a few generations of physicists. Even Einstein seemed unaware of this subtle problem with such a far-reaching impact, which highlights the significance of the way of thinking provided in the present paper for analyzing and confirming Einstein's Doppler effect.