Kassir, Radwan M.
January 8, 2015
Special Relativity, Einstein 1905, Relativistic Doppler shift.
Analysis of the Einstein’s general formula for the relativistic Doppler shift, derived in his 1905 paper On the Electrodynamics of Moving Bodies, revealed for the case of relative circular motions a critical contradiction with the relativistic time dilation prediction obtained in the same paper for reference frames in a relative rectilinear, uniform motion (i.e., relatively moving inertial frames). The time dilation under consideration was obtained for the traveling frame motion over an extremely small fraction (to the order of one light wavelength) of the circular path, so as the respective relative motion could be approximated with a rectilinear one.