Einstein refuted in a single sentence:
University of Texas: "Thus, the moving observer sees a wave possessing the same wavelength (...) but a different frequency (...) to that seen by the stationary observer. This phenomenon is known as the Doppler effect."
For the moving observer the formula:
(frequency) = (speed of the light wave)/(wavelength)
is valid, and since "the moving observer sees a wave possessing the same wavelength", the shift in frequency can only be due to a shift in the speed of the light wave relative to the observer. That is, as the observer starts moving towards the light source with (small) speed v, the frequency shifts from f=c/L to f'=(c+v)/L (L is the wavelength), which obviously implies that the speed of the light relative to the observer shifts from c to c'=c+v, in violation of special relativity.
Pentcho Valev