Is the classical doopler effect for light shift equal to $1-v/c$ exact or an approximation of a classical formula? I know that it is an approximation of the relativistic formula, but what was the corresponding classical formula? I ask this because in Einstein's On the Electrodynamics of moving bodies he derives $\sqrt\frac{1-v/c}{1+v/c}$ and notes that it is different from the classical case. I'm not exactly sure what formula he is comparing it to.
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He is comparing $\sqrt{1-v\over 1+v}$ to the classical Doppler shift $(1-v)$ (where v is the velocity divided by c, since I use units where c=1). The formula you give $1-v\over 1+v$ doesn't have a classical interpretation, and Einstein reduces to Doppler's at slow speeds. |
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