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.