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Tricky one...

From an outside observer's perspective the train shrinks and can't possibly fit on the track. From the perspective of someone on the train, the track shrinks (in one dimension) and can't possibly hold the whole train. So what happens??

If the track is rigid (which I assume you are postulating), then this problem becomes that of the relativistic rigid rotating disk. Nasty problem; one needs a full general-relativistic treatment to tackle it. You can get a flavor of how complicated it is by reading the preceding link. Basically, rigidity and special relativity don't mix.

What would actually happen is that as relativistic effects started to become important, the shape of the train and the track would diverge enough that the train couldn't continue to accelerate -- the stresses between the different-sized circles would cause enough friction to slow down the train, and keep the paradox from occuring in the first place. The relativistic train simply wouldn't fit on the non-relativistic track.

If you let the track shrink along with the train, then the train can keep going, I suppose... How then to explain what things look like from the train's perspective, where now the track must look *way* too small to hold the train? The answer (as you can get from the link) is that there's no consistent way to look at the problem if you're riding the train. To quote from the link:

"The particles in a rotating disk (not assumed rigid) cannot agree on a global notion of simultaneity. For if you make a circuit around the edge, joining up the infinitesimal planes of simultaneity, when you return to your starting point, the planes no longer match up. This makes it problematical to talk about geometry "as seen by the particles" (or by observers standing on the disk)."

Think of it like 10,000 separate Barn and the Pole paradoxes... Just because the barn looks too big in one frame and too small in the other, doesn't mean there's not a consistent explanation in each frame. Same thing with each train. But this is still more complicated, because everything is now accelerating toward the middle of the circle, which complicates matters more than they are in the barn and the pole paradox...

Hope that was more enlightening than confusing!

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