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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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Classical mechanics is the approximation of relativistic mechanics when the speed involved is small compared to that of light. – Siyuan Ren May 28 '12 at 2:41
Doppler, not doopler... – WIMP May 28 '12 at 7:14
up vote 1 down vote accepted

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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Thanks. I thought there was another, more exact, classical formula. – MadScientist May 31 '12 at 4:07
@BarryBarrett: What would it be? You can do a weird transformation of space and time in 1+1d space with right-moving light which keeps distances unstretched and keeps the speed of right-moving light constant, but this is just a mathematical trick, it has no physical significance. – Ron Maimon Jun 1 '12 at 6:12

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