Is the Linear Ehrenfest Paradox Accurate for Circular Motion?

[PeterDonis]

if lightning later strikes again simultaneously in S at the left side of the rectangle and the right side of the rectangle, the result will again be the same

Yes, but the strikes will be at different x coordinates in frame S, because the rectangle is moving in S.

the entire train will have 64 length in S, being 32 on side A (same as that train segment's proper length), and 32 on side B (contracted from a proper length of 68).

I think this way of putting it could be misleading. In S, the rectangle is moving to the left at 0.6c; one segment of the train is at rest; the other segment of the train is moving to the left at 0.88c. And which points on the train are the dividing points between the two segments changes from instant to instant in frame S. You can certainly set up lightning strikes at the two events which mark the dividing points on the train at a given instant in frame S, and we can always pick an observer on the train who is in the right location to be at rest in frame S and equidistant from the two strikes, so they both reach him at the same event and fulfill the Einstein simultaneity criterion. But to call this a measurement of the "length" of anything implies that the "thing" whose length is being measured does not change from instant to instant, whereas in fact it does.

Do you agree or disagree that the train always has length 64 in S?

I agree that the actual physical observables are as you have stated them. I'm not sure I agree that calling this a measurement of "the length of the train" is a good way of describing what is going on in ordinary language. Fortunately, however, we don't need to use that ordinary language; all observables and all physical predictions can be made without ever having to decide whether your choice of language here is good or bad. So I don't have to agree or disagree with you on this point because it's not a question of physics, it's a question of ordinary language terminology.

 

[JVNY]

I agree that the actual physical observables are as you have stated them.

OK, thanks.

If you instead consider a track across a whole closed cylindrical universe, you don't have any corners.

A.T., how is the cylindrical scenario modeled? Does it yield the same physical observables?

 

[A.T.]

A.T., how is the cylindrical scenario modeled? Does it yield the same physical observables?

If you google "twin paradox in closed universe", you should find some related analysis. Instead of two inertial twins you would have two large inertial objects (tracks & train) spanning the entire universe.

 

[JVNY]

Thanks.