Here's something that I recently thought about: If we assume a Doppler shifted EM wave retains the amplitude of the unshifted wave, then we must be creating/annihilating photons. This seems consistent with the conservation of energy; the removal of several photons removes energy from the system but this energy is conserved by the increase in energy of the remaining photons, as would be the case of a blue shift. Does this seam reasonable? I realize that number conservation of photons is never a requirement, but it originally bothered me that photons can just come in and out of existence in the manner described above. My explanation for this is that during a Doppler shift, a single photon is either joining with several others or splitting into several others in a manner that conserves energy. Does this seem reasonable?