Someone noted that the famous muon half-life experiment, supporting time dilation in SRT, seems to violate the equivalence principle of GRT. The very large radial acceleration in the experiment does not appear to cause any additional slowing. The acceleration does not seem to have an equivalent effect on slowing the clock rate as a very strong gravitational field should have. I went searching for the answer in your FAQ and came upon the "clock hypothesis" - that accelerations do not affect clock rates, only velocities do. And then you address that very question of why or how the equivalence principle can still be valid. But it seemed to me that your defense was a sort of bait and switch. You describe a pair of observers in an accelerating rocket passing signals fore and aft, and noting the red and blue shifts respectively, just like they would occur in a gravitational field. The signal from the aft sender, for example, appears red-shifted to the front observer. Isn’t the critical word in that sentence "appears", i.e., the aft clock is not really running slower, it only appears to be running slower? It must also appear to run faster to any observers even further aft. I was under the impression that varying clock rates in SRT and GRT were real. I came to that conclusion by re-reading Einstein’s original paper wherein he describes the situation of two stationary synchronized clocks A and B. Should clock A be moved to clock B’s location, it will have lost some time. Isn’t that unambiguous? Different clock rates due to motion in SRT (and acceleration / gravity in GRT) are real? Your defense seems to be dealing with situations of clock rate appearances only and not real clock rates. The muon experiment seems to be a situation with real clock rates. And it sure seems like that experiment does violate the equivalence principle, as I think everyone agrees that stronger gravity does slow down clocks, as in the GPS clocks, etc. But apparently the very large acceleration in that experiment does not slow down the muon’s clocks even further than that due to the velocity as per SRT. I hope someone can clarify this for me. Thanks.