  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.
