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General relativity tells us that there is no absolute frame of reference (actually, it tells us that all frames are relative, which is close but not the same as there is no absolute frame).

Special relativity demonstrates that there is an absolute: the speed of light.

Notwithstanding the impracticality of the issues, is it possible to determine an absolute frame of reference based on minuscule difference in the wave length of light (measured by doppler shift)?

In effect, can we measure our (Earth's) compound frame of reference by measuring the doppler shift / compression of light in our own frame of reference. Or would any relativistic compression be undetectable within that same frame of reference? Or would it be practically infeasible?

If practically impossible, is it theoretically possible; how would multiple frames of reference affect our ability to examine this question?

Here is another way of looking at it:
We know a moving sound source (such as a train) creates doppler shift, irrespective of whether or not anyone is in the "stationary" frame of reference. So, is it a reasonable conjecture to say that the Sun is creating doppler shift in light, irrespective of any specific observer or frame of reference? If so, that would seem to indicate that we could measure motion respective to an absolute frame of reference.

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  • $\begingroup$ Actually, you can do exactly this and do it with the cosmic microwave background. Someone offered that as an answer to a previous question I asked, I was rather surprised, but it makes sense. It can measure your velocity relative to the average velocity of matter when the big bang happened. $\endgroup$
    – Alan Rominger
    Commented Oct 19, 2011 at 21:11
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    $\begingroup$ @Zassounotsukushi: It's still not an absolute reference frame, though, just the rest frame of a particularly interesting object. Anyway, Robert: there are a couple of things I'm not clear on in your question. What do you mean by "compound frame of reference"? What physical phenomenon are you referring to as compression and elongation of light waves? $\endgroup$
    – David Z
    Commented Oct 19, 2011 at 21:50
  • $\begingroup$ @DavidZaslavsky In hindsight, "compound" frame of reference probably isn't very clear. What I meant by that was the sum of all of the motions that we are a part of, such as: universal expansion + galactic rotation + solar orbit (this probably not a complete enumeration, just an example). $\endgroup$
    – Robert Altman
    Commented Oct 19, 2011 at 22:32
  • $\begingroup$ OK, I kind of see what you mean. The thing is, all those motions are themselves relative. I'd guess that you're talking about something like measuring the Earth's motion relative to the universe as a whole. $\endgroup$
    – David Z
    Commented Oct 20, 2011 at 0:28
  • $\begingroup$ Here is another way of looking at it: we know a moving sound source (such as a train) creates doppler shift, irrespective of whether or not anyone is in the "stationary" frame of reference. So, is it a reasonable conjecture to say that the Sun is creating doppler shift in light, irrespective of any specific observer or frame of reference? If so, that would seem to indicate that we could measure motion respective to an absolute frame of reference. $\endgroup$
    – Robert Altman
    Commented Oct 20, 2011 at 1:31

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By compression of light you mean the Doppler shift?
Then yes you can measure your speed relative to the light source by comparing the Doppler shift in different directions.

It's been used for a number of different radio positioning systems - but it only gives you a motion relative to the light sources

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    $\begingroup$ Right. If at one end of a railroad car there is a horn of a known pitch, and a microphone at the other end, there will be no doppler shift at the microphone (even though the speed of sound between them is affected by the car's speed). $\endgroup$
    – Mike Dunlavey
    Commented Oct 20, 2011 at 2:01
  • $\begingroup$ @Martin Beckett - That's true. See edits above regarding the a moving sound source; the sound is being "compressed" (raised pitch) in front of it and elongated (lowered pitch) behind it. This is happening in the medium of the air, through which the sound is emanating; and while it won't be observed by someone in the same reference frame, it still exists independent of the observer. That is why I asked the question in terms of compression and elongation rather than doppler shift. The question is, does the same hold true for light, and, if so, is it theoretically possible to measure it? $\endgroup$
    – Robert Altman
    Commented Oct 20, 2011 at 19:38
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Technically, doppler shift for light happens due to relativistic time dilation, so it is subtly different than acoustic doppler shift. It cannot therefore be used to determine an absolute reference frame.

That doesn't mean there isn't one. Spacetime as we know it is formed by the big bang, so that might be an absolute reference frame if only we can figure out how to detect it. Unfortunately, we can't, and in a very real sense the Big Bang happened EVERYWHERE, since all of space was compressed to a tiny point.

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  • $\begingroup$ There is no time dilation in relativistic Doppler as is easily seen considering a star away, it could not know who the observer is and thus also not know the relative speed to the future observer. Invoking time dilation is a common error in intro books on relativity written by good educators but poor relativists.... $\endgroup$
    – JohannR
    Commented Jun 30, 2020 at 20:04

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