This is really interesting kev. But here's the problem: although something like "contraction" should appear in Schwarzschild spacetime, it will be determined by the Schwarzschild metric, not by the Lorentz transformations.
The Lorentz transformations are rotations of Minkowski (flat) spacetime...
To the first part: I like this analogy, but don't see how it can work. We want to understand the laws of motion of a relativistic rolling ball. In particular, the transverse motion of a rolling ball is determined in part by the "spinning" -- or more precisely (at least in the classical case) by...
I agree kev, that due to its transverse motion, the ball must contract in this way -- this follows from the principle of relativity, as I said in the beginning. However, what I would still like to know is 1) why the laws of rotation at relativistic speeds imply this (independent of the principle...
I've seen a lot of nice suggestions so far (and some irrelevant stuff). Some people seem convinced that the ball take on a contracted form "like jello" or "like a grape with tank-treads." That was my original intuition, but I don't see how one knows that this is true. What still has not been...
You raise a very good point. Here's an attempt to pose the problem more clearly:
Imagine that a homogeneous spherical mass rolls without slipping, such that its center of mass has uniform velocity v in the horizontal direction. Now take the limit as v/c approaches 1. (Perhaps even this is not...
You were supposed to read that sentence as a reductio ad absurdum, Mentz114. Assume, *for the purpose of reductio*, that relativistic rolling balls wobble like grapes. Then absolute rest could be determined in the way in which I describe above. This contradicts the principle of relativiy...
A spherical ball rolls without slipping along a surface, with uniform velocity v/c (close to 1) with respect to the lab frame. It is thus seen to contract by a factor of \gamma, forming a grape-like shape.
Why doesn't it wobble as it rolls, like a rolling grape?
One can certainly argue...