Doppler effect:
The Doppler effect is all about medium, wave length, and rate of propagation. The pitch of the ambulance siren does not enter the equation except as a constant.
To register the effect, you must let the ambulance pass. If it hits you, the pitch gives you no knowledge of its speed.
You cannot get information about photons that pass, only about the ones that hit you.
Photons need no medium for their propagation, hence there is no wave, no wavelength, no Doppler effect. ‘Relativistic Doppler Effect’, real or not, is a misnomer. It states that the frequency of the photon, - the payload-, depends on the the motion of the source.
Both hypotheses (Ritz vs Einstein) generate the same value for the momentum of the arriving photon. The spectrometer, having no information about the motion of the source, translates this value into a frequency reading.
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