Time Dilation vs. Doppler Effect: Similarities & Differences

[BadgerBadger92]

Does time dilation in Special Relativity relate to the Doppler effect? If you move near the speed of light you experience time differently and the sound is stretched. Are these similar phenomenon?

 

[Dale]

Sometimes time dilation is called the transverse Doppler shift, so they are related. But the relativistic Doppler is a different formula than the classical Doppler, and the difference is precisely the time dilation. In other words, classical physics predicts no transverse Doppler, but relativity does.

 

[vanhees71]

One has to distinguish two cases: (a) Doppler effect for em. waves in the vacuum and (b) Doppler effect of other waves like sound waves. Case (a) is special, because here the Doppler effect only depends on the relative velocity beween transmitter and receiver, while in case (b) there is a preferred reference frame, the (local) rest frame of the medium the wave propagates in (for sound waves, e.g., the air). In all cases time dilation is part of the Doppler effect. In case (a) the transverse Doppler effect, i.e., the observer measures light emitted perpendicularly to the velocity of the source, is purely due to time dilation. For details, see

https://itp.uni-frankfurt.de/~hees/pf-faq/rela-waves.pdf

 

[Janus]

"classical" Doppler effect is a result of the changing distance between observer and source (it also relies on a medium, so it makes a difference as to whether it is the source or observer which is moving relative to the medium.)
Relativistic Doppler effect also has a component which depends on the changing distance between observer and source. The difference is that with classical Doppler shift, if you factor out the effect caused by changing distance, you end up with no net time difference, but with Relativistic Doppler effect, when you factor the changing distance out, you are still left with a time difference, which is the time dilation.

 

[vanhees71]

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

https://itp.uni-frankfurt.de/~hees/pf-faq/rela-waves.pdf