THE FUNDAMENTAL DILEMMA IN EINSTEIN'S RELATIVITY

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."

If v is small, the relativistic corrections are negligible and f'=(c+v)/lambda is a virtually exact formula for light waves, in both the non-relativistic and relativistic interpretations.

So the frequency shifts from f=c/lambda to f'=(c+v)/lambda, the speed of the light (relative to the observer) from c to c', the wavelength from lambda to lambda'. Given the formula:

(frequency) = (speed of light)/(wavelength)

two combinations are conceivable:

(A) c' = c+v ; lambda' = lambda

(B) c' = c ; lambda' = c(lambda)/(c+v)

A is reasonable (all waves obey its equations) but fatal for Einstein's relativity. B is totally unreasonable (the change of the speed of the observer cannot change the wavelength of the incoming light) but it saves relativity.

Pentcho Valev

http://rockpile.phys.virginia.edu/mod04/mod34.pdf
Paul Fendley: "Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) (it goes up heading toward you, down away from you). There are relativistic corrections, but these are negligible here."

Premises from which this frequency shift is rigorously deduced in the case when the observer starts moving towards the light source with (small) speed v:

(A) (frequency) = (speed of light)/(wavelength)

(B) The speed of the light relative to the observer shifts from c to c'=c+v (in violation of special relativity)

(C) The change in the speed of the observer cannot alter the wavelength of the incoming light

There is no other reasonable set of premises from which the frequency shift from f to f'=f(1+v/c) can be deduced.

Pentcho Valev