http://www.hep.man.ac.uk/u/roger/PHY.../lecture18.pdf
Roger Barlow, Professor of Particle Physics: "The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. (...) Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/lambda waves pass a fixed point. A moving point adds another vt/lambda. So f'=(c+v)/lambda. (...) Relativistic Doppler Effect: These results depend on the absolute velocities of the source and observer, not just on the relative velocity of the two. That seems odd, but is allowable as sound waves are waves in a medium, and motion relative to the medium may legitimately matter. But for light (or EM radiation in general) there is no medium, and this must be wrong. This needs relativity. (...) If the source is regarded as fixed and the observer is moving, then the observer's clock runs slow. They will measure time intervals as being shorter than they are in the rest frame of the source, and so they will measure frequencies as being higher, again by a gamma factor: f'=(1+v/c)(gamma)f..."
In the non-relativistic case (v is small and gamma is virtually unity), as the observer starts moving towards the light source with speed v, the speed of the light waves relative to him shifts from c to c'=c+v, and this causes the frequency he measures to shift from f=c/(lambda) to f'=c'/(lambda)=(c+v)/(lambda)=(1+v/c)f. Special relativity is violated - the speed of light relative to the observer varies with the speed of the observer.
In the relativistic case (v is great and accordingly Einsteinians take into account time dilation), as the observer starts moving towards the light source with speed v, the speed of the light waves relative to him shifts from c to c'=(c+v)(gamma), and this causes the frequency he measures to shift from f=c/(lambda) to f'=c'/(lambda)=(c+v)(gamma)/(lambda)=(1+v/c)(gamma)f. Special relativity is violated again.
If v is small enough, in both the non-relativistic and relativistic case we have c'=c+v, which means that the speed of light relative to the observer varies with the speed of the observer as predicted by Newton's emission theory of light and in violation of special relativity.
Pentcho Valev