First principles for analysis and confirmation of relativistic Doppler effect

Ives-Stilwell experiment in 1938 is a historic experiment for confirming Ein-stein’s special relativity, and various modern types have been repeated by use of laser technology. However in this paper, we reveal and solve a fundamental issue that the data analysis for all those experiments is not consistent with Ein-stein’s definition of the relativistic Doppler effect so that the Doppler effect has not actually been confirmed. For example, in the Letter [Phys. Rev. Lett. 113, 120405 (2014)] the definition of the measurement accuracy of Doppler effect, given by ε = sqrt[ νaνp /(ν1ν2) ]− 1, is not physical because Einstein’s Doppler formula cannot be confirmed even when ε = 0 holds (see Appendix A). We argue that there are two first principles for analyzing and confirming Einstein’s Doppler effect, stating: (i) Einstein’s Doppler effect refers to the same photon (or laser beam) exhibiting different frequencies observed in different inertial frames, and (ii) the quantity (or measurement accuracy) used as a measure to confirm the effect must be able to confirm Einstein’s Doppler formula itself. Unfortunately , the data analysis for the 1938 Ives-Stilwell experiment does not comply with the first principles, so it fails to confirm the relativistic effect (see Appendix B), although this data analysis has been mimicked by quite a few generations of physicists. Based on the first principles, 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.