Instructive derivation of basic relativistic time-space consequences without using Lorentz transformation and Doppler formulas for a plane wave and a spherical wave

Einstein's Doppler formula is not applicable when a moving point light source is close enough to the observer; for example, it may break down or cannot specify a determinate value when the point source and the observer overlap. In this paper, Doppler effect for a moving point light source is analyzed, and it is found that the principle of relativity allows the existence of intrinsic Lorentz violation. A conceptual scheme to experimentally test the point-source Doppler effect is proposed, and such a test could lead to an unexpected result that the frequency of a photon may change during propagation, which questions the constancy of Planck constant since the energy conservation in Einstein's light-quantum hypothesis must hold.