Doppler Effect

Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B).

Edit: I am adding a relativistic space-time diagram below this with lines of simultaneity drawn. I am also editing the description to be more relavent to the updated diagram.

Doppler revisited

The diagram shows the frame of a stationary observer B. A travels with velocity c/2. A emits flashes of light every second (according to the time of observer B - flashes of light are shown as dashed lines and are emitted where the lines of simultaneity meet the worldline of A and hence they are emitted every second in the time of B)

We see that in the frame of B, we begin to see the light one second after it is emitted. light is continuous and after the lag shown, light from a time delta t' (according to the time in frame B) is observed across time delta t (which is 2 x delta t').

This seems to indicate that what we OBSERVE in frame B seems to depend on only the slope of A. Is this indeed what we will see in B?

  • 1
    $\begingroup$ A big difference is that the Doppler shift for inertial frame A relative to inertial frame B is directly observable, whereas the time dilation is not. To observe time dilation, you have to separate and then reunite two clocks, which involves moving at least one of them noninertially (as in the Hafele-Keating experiment en.wikipedia.org/wiki/Hafele-Keating_experiment ). $\endgroup$
    – user4552
    Apr 8, 2013 at 1:46
  • $\begingroup$ I have added my answer as a document. Would appreciate your comments on it. I have used spacetime geometry and my analysis seems to point out that Relativistic Doppler shift is more than just a frequency shift, it's a visual shift of the whole of time. Of course, I could be wrong. $\endgroup$ May 10, 2013 at 18:08
  • $\begingroup$ @user4552 The only problem with Hafele–Keating experiment and similar is that plane moves relative to the air mass, which is in tune of Earth motion. Someone is making childish mistake here assuming that plane velocity is relative to the center of Earth rather than its surface... $\endgroup$
    – mip
    Sep 13, 2020 at 22:08

3 Answers 3


One significant difference is that the doppler effect is dependent on the direction of the velocity, while time dilation is only dependent on the speed. This is why the doppler effect changes when A passes B, while the time dilation would be the same before and after. For this reason there is also no doppler effect when something moves perependicularly to you, while there is still time dilation.

Another difference is that the doppler effect is "stronger" than the time dilation effect when something moves towards you or from you. The doppler effect gives a factor $(1\pm\frac{v}{c})$ while the time dilation gives a factor:

$$ \frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}} $$

Because of this, the combined effect, the relativistic doppler effect, is dominated by the doppler effect in these cases.

  • $\begingroup$ I agree with your Doppler factor. I have tried to do some analysis on my own using space time geometry to combine time dilation and doppler effect. The results are presented as my own answer. I would appreciate you views/comments on it. According to my analysis, its not just frequency that shifts but the whole of time. I could be very wrong about this and I have no source of validation. So, I would appreciate if you took some time to look at my answer and see if and where I might have made a mistake. Thanks! $\endgroup$ May 10, 2013 at 18:12
  • $\begingroup$ But there is a transverse Doppler effect. en.m.wikipedia.org/wiki/Relativistic_Doppler_effect - caused by time dilation. Semantics perhaps, but your statement risks confusion. $\endgroup$
    – ProfRob
    Feb 8, 2020 at 14:06

I have given this question much thought. I am providing a link to what I think is the answer, as putting the answer here would be too long.

Please note that I am new to physics so my thinking may be wrong. I would appreciate your comments on whether you think this idea is correct or not.


Link to analysis: https://www.dropbox.com/s/fibfs9uoxjn6lgl/Time%20dilation%20and%20contraction%20effects%20in%20waves%20-%20v48.pdf

  • $\begingroup$ "Time dilation" is a ridiculous term which sowed a havoc in physicists minds. If you look at history of Lorentz transformations you will see that they are derived from something similar to your concept (en.wikipedia.org/wiki/Relativity_of_simultaneity). "Time dilation" was boggling my mind too and even though I have no time to read your paper in depth (sorry), I think you are mostly correct. I don't know what makes people to think that it is time, which ticks slower/faster, rather than information being transmitted slower/faster. But it's the same story as withc "axial vectors" etc. $\endgroup$
    – mip
    Sep 13, 2020 at 16:52

Is important to realize time dilation and the Doppler effect are 2 frame-dependent parts of a single relativistic phenomenon: the constancy of the magnitude of four-velocity (which is always ||c||). Requiring that all inertial observers see a four-velocity with magnitude ||c|| leads to frame dependent observations of time dilation and Doppler effect.

For a Doppler radar, the relativistic Doppler effect can be derived by forcing the scattered radar's (read: photon's) four-acceleration to be orthogonal (in Minkowski space) to the targets 4-velocity, that is:

[(E, pc) - (E', p'c)]*(c, v) = 0.


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