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I understand that an observer in an uniformly accelerating frame in "free space" cannot distinguish this condition from the presence of a gravitational field. Or, at least, this holds "locally", that is the observer is not measuring the field in different places and is not looking "outside". This is usually the case for astronauts sitting in a rocket in "free space" accelerating at $g$ who feel the same force as if they were "still" on earth.

What happens instead if my frame of reference is rotating? I think I read somewhere that the equivalence principle does not hold in this case. But I could measure the "force" I am experiencing in different points of my frame, getting a $0$ in the centre of rotation and more and more as I move away from the centre of rotation. Would this not be compatible with some gravitational field? How can I conclude in this case that I am rotating and not immersed in a gravitational field?

I am also thinking at astronauts at $0 g$ that use rotating cylindrical rooms for simulating gravity and doing jogging.

any idea?

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In a frame that is rotating with respect to distant stars, centrifugal and other velocity-dependent(Coriolis) and angular acceleration-dependent(Euler) forces have to be introduced. Such forces are similar to gravity forces in that they are linear function of body mass, so all bodies experience the same acceleration. Thus they can be described as due to curved spacetime, just like gravity forces. But this is just similarity in effect on the level of description; these forces are't due to "real" gravity, due to massive bodies.

These forces are sometimes called "fictitious" because they don't have any obvious physical source, they are due to rotation of the frame with respect to absolute space/distant stars only. The concept of energy conservation does not work well in these non-inertial frames, bodies arbitrarily far away can acquire or lose immense amount of kinetic energy when rotation of the frame is changed, without any actual physical process or physical body interacting with the distant bodies. All these effects would be extremely hard to explain as a result of real gravity forces due to massive bodies.

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  • $\begingroup$ Is it possible to construct a non-rotating frame of reference which would be equivalent to a rotating frame of reference? Let's compare just limited regions of the frames. Can these regions contain the rotational axis like for example the whole Earth? $\endgroup$
    – pabouk - Ukraine stay strong
    Commented Aug 15 at 18:22
  • $\begingroup$ @pabouk-Ukrainestaystrong What does it mean that a non-rotating frame is equivalent to a rotating frame? Usually they are not considered equivalent, because equations of motion look different in rotating and non-rotating frames; non-rotating frames are preferred. $\endgroup$
    – Ján Lalinský
    Commented Aug 16 at 0:05
  • $\begingroup$ Thank you. I just thought that something like that the OP wanted to hear (and me to). Some flat-earthers claim that Einstein said that on the Earth we cannot distinguish if the Earth is moving or stationary. :D $\endgroup$
    – pabouk - Ukraine stay strong
    Commented Aug 16 at 9:14

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