Equivalence Principle in muon experiment?

[Dale]

But already Einstein in his famous paper in 1905 has provided a physical way to provide the synchronization of the coordinate time via light signals.

But that synchronization remains only a convention. If it were more then simultaneity could not be relative.

 

[Ich]

I don't understand; zero two-way redshift relative to what observer? And what, exactly, do you mean by "two-way redshift"? Do you mean the net redshift of light doing a two-way round trip from A to somewhere else and then back to A? That's not what I've been talking about all this time; I've been talking about the redshift of A's light as observed by O, who is at infinity.

I was just arguing why I treat the redshift from A to O as purely gravitational time dilation, but not the redshift B to O. The difference is that A and O are static, so there's no contribution from a varying distance. B's redshift on the other hand does have such a contribution. I mentioned the two-way (round trip) redshift as a possible operational definition of "no changing distance", to be sure that this sentence is not frame-dependent.

 

[PeterDonis]

I mentioned the two-way (round trip) redshift as a possible operational definition of "no changing distance"

The usual operational definition of "no changing distance" is a constant round-trip travel time for light signals. I think this is equivalent to a zero round-trip redshift (i.e., redshift one way exactly canceled by blueshift the other way), but I haven't done a computation to prove it. You're right that either one is invariant and therefore not frame-dependent.