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What does a rotating hoop, with each point moving at a velocity close to the speed of light, appear like with respect from a stationary observers perspective. For example how does the shape of the hoop change? (Note, I'm not intending to ask about optical effects, but rather what physically happens, analogous to length contraction of a moving train.)

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Do you care about Doppler beaming of the emitted light, or do you count that as "optical effects"? –  kleingordon Oct 6 '12 at 5:18
I do consider that an optical effect. When I made my comment about optical effects however, I meant it so users don't get bogged down in optical effects, but of course it would be a nice optional extra. –  Mew Oct 6 '12 at 5:21
My main curiosity was on physical features of the disk such as apparent dimensions, and shape however, but how it actually looks would be a bonus though. –  Mew Oct 6 '12 at 5:22
This possibly brings up issues similar to those in the Ehrenfest paradox (, although I haven't thought carefully enough to say for sure how related these problems are. –  kleingordon Oct 6 '12 at 5:27
Thanks, at first glance it looks very similar to my question. –  Mew Oct 6 '12 at 5:28

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By symmetry, it'll look circular. Just look at it from above, along the axis. You can synchronize clocks along the rim by a signal from the center. Then have those rim clocks all emit signals simultaneously. In the rest frame, their signals will arrive at the same time as those of stationary clocks positioned around the "orbit".

Or imagine encasing the whole thing in a hollow toroidal container at rest. Like the proton bunches going around the LHC. No ambiguity about what the encasing torus looks like.

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