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Imagine I got 2 identical, perfectly synced and nigh indestructible clocks, then 1 clock starts to move in a really tight circle of 0.9c would it ticks slowly? I just want to test twin paradox says instead of 1 of the twin took off into space in a round trip at near speed of light the individual starts to run around in a really tight circle on the spot at 0.9c so would then this individual aged differently?

user6760
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  • If a clock spins on its axis the various parts of the clock would be moving at different speeds because the tangential speed is $v = r\omega$, so it's meaningless to says it spins at a speed of $0.9c$. Do you mean the clock is moving in a circle around some fixed point at $0.9c$? – John Rennie Feb 16 '22 at 08:17
  • @JohnRennie: oh I see then in that case the minimum speed is 0.9c, I'll reflect this in the question. – user6760 Feb 16 '22 at 08:21
  • The minimum speed cannot be $0.9c$ if the clock rotates on its axis because the speed of the points in the clock on the axis is zero. No matter what the angular velocity there will some value of $r$ for which $r\omega \lt 0.9c$. The only way your question makes sense is if the whole clock orbits some point in a circle and the orbital speed is $0.9c$. – John Rennie Feb 16 '22 at 08:22
  • Oh I will edit it. – user6760 Feb 16 '22 at 08:29
  • OK, now it's a duplicate of Can a ultracentrifuge be used to test general relativity? – John Rennie Feb 16 '22 at 08:32
  • It would have been interesting to see how the question would have been answered if the subject had been a clock spinning on its axis. – Marco Ocram Feb 16 '22 at 11:39

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Yes the clock going around in a circle registers less time, for each orbit, than a clock sitting at one point not accelerating. Indeed this is precisely what happens in a particle accelerator involving a ring, such as the one at CERN. Here the 'clocks' are particles moving around the ring. However for protons there is not much internal dynamics of the proton so they don't indicate their own elapsed time in a way easy for us to detect. But other storage rings use particles such as muons which can decay. This decay process is itself a type of clock: it has its own characteristic half-life, and the muons going around such a ring last very much longer than muons sitting still next to the ring. This is a perfectly good example of the twin paradox.

Andrew Steane
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