Due to some other threads going on I’m interested in improving my understanding of relativity as it works with rotating reference frames. Now I’m prepared to be told even my initial setup for discussion is flawed, but I’m hoping it isn’t.
Let’s say I build myself a large cylindrical spaceship/spacestation of length l and radius r and call it, just at random, Rama. I set up a sort of light clock along the central axis with lasers and reflectors. The time between each pulse is equal to the time it takes a pulse to traverse the cylinder and they’re synchronised, from a position on the cylinder wall, halfway from the circular ends, I see two flashes, the firing laser and the reflection of the incoming previous pulse, from the two ends arriving at the same time. This links the clock to the length of the cylinder and light speed. Change the length or change light speed and the synchronisation breaks.
Next I spin up the cylinder so I’m moving at some speed while I stand on the cylinder wall. For convenience I could make it so I experience 1G. Now one knee jerk, and I believe false, application of SR would be to say that I’m now moving at some speed, so time is slowed, and I observe the still synchronised pulses arriving at my location closer together, so light is either moving faster than light, or the cylinder is shorter.
But SR is about relative motion, and me and the cylinder center are not moving relative to each other, so I think using SR is wrong.
But I am accelerated which, I think, means GR says time slows down compared to inertial reference frames, so I am observing the “faster than light” change in my giant light clock. My understanding though is that there are two sensible ways to look at this situation. Either I ignore all the signs that I’m in a rotating cylinder and say that I’m in a gravity well and that the light lock is obviously not as deep in that well and should be ticking faster, or I say that I am in a rotating cylinder and this is just the gravity-like behaviour I should expect.
Am I horribly off on any points in this description?