twofish-quant
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Old Smuggler said:However, to construct a theory of time-variable alpha
compatible with SR seems impossible, since this means that there would be a way to distinguish between inertial frames by doing local non-gravitational experiments, even in vacuum.
But you can already. Look at the doppler shift with respect to CMB. If the difference in alpha is due to some big-bang field that is weakening over time, then I don't see any problems that are worse than the fact that the CMB creates a preferred reference frame.
(In particular, there might be a "preferred" inertial frame where alpha varies only in time, not in space.)
Sure. The preferred reference frame of the CMB.
I'm still not seeing out a time shifting alpha is worse than dark energy. You could in principle measure the space time curvature that is caused by dark energy, and that is going to change over time.
I can see no obvious way to circumvent said argument, but maybe you do.
I still don't see how a time varying alpha field is worse than dark energy or anything else that is already in the standard model, and none of those is considered to break GR. One thing that should be pointed out is that in the 1960's these sorts of arguments were taken pretty seriously as reasons why the BB could not be correct. The BB creates a preferred reference frame.
For example, you can come up with a theory in which dark energy creates some sort of shielding effect on electric charge and as the universe expands, changes in dark energy causes observable effects in alpha.