Study on data analysis for Ives-Stilwell-type experiments based on first principles

Ives-Stilwell experiment in 1938 is a historic experiment for confirming Einstein'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 Einstein's definition of the relativistic Doppler effect so that the Doppler effect and its associated time dilation have not actually been confirmed. 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, Ives-Stilwell data analysis method does not comply with the first principles, failing to find that the experimental data they provided actually does not support Einstein's Doppler effect. Robertson-Mansouri-Sexl test theory is widely used to test Lorentz invariance, but it does not adhere to the first principles either when employed to measure time dilation. Based on the first principles, we propose a justified data analysis and correctly confirm the Doppler effect and its associated time dilation in the Ives-Stilwell-type experiment.