Consequently, as cs increases to c, the absolute speeds v_e and v_a of the emitter and absorber relative to the fixed medium merge into a single relative speed u between the emitter and absorber, independent of any reference to a fixed medium, and we arrive at the relativistic Doppler formula for waves propagating at c for an emitter and absorber with a relative velocity of u:

— 2.4  Doppler Shift for Sound and Light

— Reflections on Relativity

— mathpages

2010.12.21 Tuesday ACHK