While answering a question over on Worldbuilding.SE I found myself looking at a situation that I can't figure out:
You have a train track of length L that makes a very large circle. You have a train that fills the whole track and is moving down that track at such a speed that the Lorentz factor is 2.
The track is length L. When the train was sitting still it was also of length L. Now that it's up to speed it's length is L/2--yet it's still riding on a track of L. Since the train goes all the way around it has no way to change length, nor can any issue of the location of observers explain this.
How can this be resolved?
Edit: While I agree that an observer at one spot on the train won't see a circular track I don't see how this avoids the paradox. The observer will see the track shrunk in the direction the observer is currently moving but it will be just as far across. The whole track has a length of 2 pi * r, Lorentz isn't going to change the track in the direction that the observer isn't currently moving in. Since we are at Lorentz factor 2 the train length is only pi * r but even if you shrink it to zero in the direction the observer is moving you have a track of 4 r length. The train still doesn't fit.