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It is known that a spacetime variation of the dimensionless gauge coupling constants of the standard models would lead to a violation of the Einstein equivalence principle (EEP). This point is discussed for example in Uzan 2011 or Will 2018. Hence an measurement of the variation of the couplings would be in direct contradiction with general relativity and metric theories of gravity.

However, we also know for a fact that the values of the coupling constants are running with energy in QFT, such that their measured value will be dependent on the energy scale at which they are measured. Does anyone has some references on the possible link between these two points as well as possible estimations of the violation of the EEP induced by running couplings within GR+QFT and its consequences for quantum gravity?

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    $\begingroup$ I am not sure I understand some of the arguments in Uzan. He lists the electron and proton mass as "constants", but the absolute masses (as measured at low energy) are unit dependent. At most the ratio is a relevant constant. That ratio can vary with energy scale because a proton is a compound system. It's completely meaningless to talk about "a proton" at 3TeV. There is no such thing. At 3TeV the excitations of the physical vacuum are many things, but they are not pure protons. The electron seems a little more fundamental, but it, too, is not an absolute. It is only well defined at T=0. $\endgroup$ Jan 26 at 21:34
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    $\begingroup$ Agreed. I guess that the Yukawa couplings should be considered instead. This is why I limited my question to the gauge couplings, as masses are a bit more intricate to think about. But whether we talk about masses or not, the whole problem lies in the huge difference between the energy scales at which GR and QFT are tested. $\endgroup$ Jan 26 at 21:46
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    $\begingroup$ However, note that Uzan is specifying that the question of "varying constants" is meaningful only for dimensionless parameters (i.e. mass ratios here). This point can be traced back to several other authors, as Duff (2002) $\endgroup$ Jan 26 at 21:47
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    $\begingroup$ I would agree there is a relevant question there. We don't know if the equivalence principle holds at high energies. The only tests we have that I am aware of are at room temperature and at the density of solid state matter. Would a piece of neutron star fall as fast as a feather? That's for a future physicist to find out. We are, of course, testing this at CERN, right now. They are doing antimatter fall experiments, even if they aren't very precise, yet. $\endgroup$ Jan 26 at 21:49
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    $\begingroup$ Would it be fair to say that the equivalence principle only puts a mild constraint on microscopic constants? The mass-energy in a given volume has to fall as fast as the mass-energy in any other volume. How it satisfies that constraint internally with a non-trivial set of running coupling is not fully specified? Just riffing here. $\endgroup$ Jan 26 at 22:24

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