Posted: Jan 16, 2022 7:10 pm
by hackenslash
OK, so two odd things. The first is that, for some reason, I've never encountered this before. The second is the paradox itself. been scratching my head all afternoon on it, and I've made so much headway the spot I'm standing on is substantially rutted (though no females involved this time).

For those who haven't encountered it, it's a paradox that arises when special relativity meets rudimentary geometry in a very specific but extremely simple circumstance. We're to picture a rotating disc. It's probably helpful to think of this disc as being sufficiently large and rotating sufficiently quickly for relativistic effects to be significant. Fairly straightforward, right?

The paradox arises because, in order to maintain the constancy of c for all observers, Lorentz contraction applies in the direction of rotation, but only in that direction. The result is, of course, that this results in contraction of the circumference and, because C=2πr, the radius needs to contract, but the radius is orthogonal to the direction of travel, which basically means that you have to shrink a circle without shrinking a circle.

Anybody got any ideas?