Can anyone answer my relativity question about Ehrenfest's Paradox?

Question

I've been trying to teach myself relativity, but I'm stuck on a conceptual question involving Ehrenfest's Paradox. If you don't remember...the paradox involves a spinning disk. Presumably, the disk is Lorentz contracted along the direction of its motion but not along its radius. In other words, its circumference shrinks when it spins but its radius stays the same because its perpendicular to the disk's motion. Doesn't that mean that the ratio of the circumference of the disk to it's diameter will be greater than pi? How can the disk shrink while it's radius stays the same? How can that be? How is this paradox resolved? No comprendo Professor...que paso?

Answer 1

This is exactly why Einstein knew he had to generalize the theory of special relativity. Special relativity does not and cannot handle accelerated frames, it breaks down at that point. A spinning disk is an accelerated frame, so special relativity doesn't have an answer for this paradox. In general relativity, it does. Spacetime is warped, and it works, and the paradox is resolved.

Answer 2

The shrinking of the circumferance is actually a distortion of space and time. Remember that if you are riding on the disk you do not percieve this distortion. The disk stays the same, to you. Only to the outside observere does it appear to shrink. Also remember that the disks mass goes up toward infinity at the outer rings which further distort space.
If you figure the rest out, let me know LOL

Answer 3

well it is a paradox which means that it can not be resolved.