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Physics
Special and General Relativity
Time Dilation vs. Doppler Effect: Similarities & Differences
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[QUOTE="vanhees71, post: 6567831, member: 260864"] One should be aware that if there is a medium involved in both the Newtonian and the relativistic description the (local) restframe of the medium is in a sense a "preferred reference frame", i.e., the relativistic description of these kind of Doppler effects like sound waves in a general frame involves three four-velocities: that of the medium, that of the observer/receiver, and that of the source. The only additional effect in relativity in relation to the Doppler effect indeed is time dilation. An exception is of course the propagation of light in a vacuum. There you don't have any preferred frame of reference since the vacuum is Poincare invariant and thus does not provide any such preferred frame of reference. That's the modern way of the denial of an aether as a medium for free em. waves, and indeed in the only correct relativistic description of the Doppler effect in this case within a general reference frame there are only the four-velocities of source and receiver involved. The Doppler effect involves thus only the relative four-velocity of source and receiver and contains both the effect from this relative motion and the time dilation effect (leading to a "transverse Doppler effect", which is of 2nd order in ##v_{\text{rel}}/c##). For more details on both the "acoustic" and the "electromagnetic vacuum" Doppler effect, see [URL]https://itp.uni-frankfurt.de/~hees/pf-faq/rela-waves.pdf[/URL] [/QUOTE]
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Special and General Relativity
Time Dilation vs. Doppler Effect: Similarities & Differences
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