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If there are two astronauts facing each other along a common axis that goes through both of their centres of gravity, and one is spinning about that axis, which one is stationary and which one is moving?

It seems to me that one of them will be experiencing more blood in their extremities, and that if they make themselves into a ball they will spin faster vs. the other astronaut will not experience any such effect, but will observe that the astronaut which is actually spinning does go faster when they make themselves into a ball. This seems to be true to me even if you remove the entire universe apart from the astronauts (which is how I heard this question couched). However I have heard it said that as all motion is relative, neither astronaut can tell which one is spinning. It will appear to both that they are stationary and the other astronaut is spinning and there is no way to resolve this. Surely space itself even though empty is some kind of absolute background here and the one which is stationary is stationary in space and the spinning one, since they are rotating in space will feel the effects of the rotation? Or have I got it completely wrong?

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    $\begingroup$ Both astronauts pull a wrench out of their pockets, stretch out their arm and let it go. Problem solved. The one who's wrench flies away was spinning. No universe needed. $\endgroup$ Oct 25, 2022 at 7:32
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    $\begingroup$ General reading for this: Mach's principle. $\endgroup$ Oct 25, 2022 at 11:16
  • $\begingroup$ @EmilioPisanty that's very interesting, and surprising that I haven't heard of it before given that it was so highly regarded by Einstein and seemed to him a key part of the principles underpinning relativity. However, it seems to me that the above question has been answered very capably both by FlatterMann in the comments and Agnius as a formal answer, without the need for it. $\endgroup$
    – Raffles
    Oct 26, 2022 at 7:25

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Only inertial reference frames can't be distinguished each from other. However, one of your system's is rotating, hence is a non-inertial one because it will have centrifugal inner forces acting inside system. So problem boils down about distinguishing some inertial system from a non-inertial one, which relatively easily can be done with several methods.

For example, one solution you proposed already is based on conservation of angular momentum $$ \vec L = I \vec {\omega} = \text {const} ,$$

While astronaut (let's call it tester) is decreasing moment of inertia, - by drawing in his arms and legs,- and increasing it back gain, by expanding arms/legs,- he should notice that other astronaut is periodically spinning at faster and slower rates. If, such observation is confirmed- then tester is spinning. Otherwise, if no such outcome is observed, (i.e. other astronaut spins at constant rate independent on tester arms/legs contraction)- then other astronaut is truly spinning and tester is at rest.

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  • $\begingroup$ Thanks. For anyone else arriving here, in a similar vein I found the following answer to a different question very helpful: physics.stackexchange.com/q/556763 (thanks to @EmilioPisanty for starting me looking into Mach's principle, which led me to looking into Newton's bucket. Who would guess, it turns out there's a physicist sitting in the bottom of it)! $\endgroup$
    – Raffles
    Oct 26, 2022 at 7:52

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