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Thomas comments on What are your contrarian views? - Less Wrong
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The spinning set of particles is a toroidal with let say 1 million light years across - the big R. and with the small r of just 1 centimetre. It is painted red and white, differently each metre.
The whole composition starts to slowly rotate on the signal from the centre. And slowly, very slowly accelerate to reach the speed of 0.1 c in a several million years.
Now, do we see any Lorentzian contraction due to the SR, or not due to the GR?
(Small rockets powered by radioactive decay are more than enough to compensate for the acceleration and for the centrifugal force. Both incredibly small. This is the reason why we have choose such a big scale.)
I'm going to assume mass is small enough not to take GR into effect.
From the point of view of a particle on the toroid, the band it's in will extend to about 1.005 meters long. Due to Lorentz contraction, from the point of reference of someone in the center, it will appear one meter long.
The question is ONLY for the central observer. At first he sees 1 m long stripes, but when the whole thing reaches the speed of 0.1 c, how long is each stripe?
One meter.
I just want to clarify. I'm assuming the particles are not connected, or are elastic enough that stretching them by a factor of 1.005 isn't a huge deal. If you tried that with solid glass, it would probably shatter.
Come to think of it, this looks like a more complicated form of Bell's spaceship paradox.
I think you're right, but you're interpreting “sees” literally I'm not 100% sure of that, because of light aberration (the Terrell-Penrose effect).
I wasn't interpreting "sees" literally, but it wouldn't make much of a difference. Since the observer is in the center of the circle, the light lag is the same everywhere. The only difference is that the circles bordering the bands will look slightly slanted, and the colors will be slightly blue-shifted.