Einstein in his "On the electrodynamics of moving bodies" (1905) starts the derivation of the Doppler shift formula by stating: In the system K,(adsbygoogle = window.adsbygoogle || []).push({}); very farfrom the origin of coordinates let there be a sourcce of electromagnetic waves..." . Taking into account his advise "never stop thinking" we could ask if the Doppler shift formula he derives holds in the case of scenarios which do not fulfil the "very large source-receiver" assumption.

Consider a scenario proposed by A.P.French,Special Relativity" (Nelson 1968) pp 141-143that involves a satellite (plane) that moves at a constant altitude emitting light signals at constant time intervals which are received by a stationary observer located on Earth. In order to recover Einstein's formula, French makes the assumption: ' The satellite travels avery small distance during one cycle of its transmitter signalwhich is equivalent with Einstein's assmption or with the assumption thatthe period at which the successive liht signals are emitted is very small (the frequency is very high). Take into account that we can emit successive light signals at lowmechanical frequencies.

My question is: Before using a ready derived formula following a given scenario, should we investigate if the assumtions made deriving it fit in the case of the scenario we follow.

My oppinion is that we should, deriving shift formulas in accordance with the scenario we follow showing how flexible special relativity theory is. What is your oppinion?

Sine ira et studio

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# Doppler shift formula and the assumptions behind it

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