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Einstein's equivalence principle is often illustrated by pointing out that a person trapped in an elevator has no way of telling whether they are on the surface of the earth or in deep space in a rocket ship accelerating at 9.8 m/s2.
A third alternative is that the elevator is at the end of a very large centrifuge arm with $\omega$2r = 9.8 m/s2. But this case could be settled easily by setting up a gyroscope and watching to see if its axis rotates. Unfortunately, there is no gyroscope available. But there is a very sensitive gravimeter available.
The question is: how does a person determine just from gravimetric measurements whether or not they are in a centrifuge and which way the centrifuge is rotating? It's easy to say that it must come from the curl of the field, but it eludes me as to exactly what set of measurements to take or why the measurements would show non-zero curl.
There is a related post here but it doesn't offer the insight I was hoping for.

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The simplest thing is to test for the Coriolis force. One does not need a gravimeter, which is a sophisticated form of accelerometer, since an accelerometer will do. There will be a sideways force on a uniformly moving object. Or, if one prefers, one may simply observe the sideways acceleration of a moving inertial object. Depending on the rate of rotation of the centrifuge, this may be visible even without sophisticated equipment.

If you restrict measurements to static objects using gravimeters, then as far as I can see, you only have tidal forces to go on. For a gravitational field you may be able to detect that the gravitational forces converge toward the centre of the gravitating object. For centrifugal force they diverge.

I am not well versed in the practicality of measuring this with gravimeters, but I understand that gravimeters are accurate enough to measure tidal forces. All I can say is that it is possible in principle to detect a difference.

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  • $\begingroup$ @ Charles Francis Agreed - good point - just drop an object from the ceiling! But there is still something about the characteristics of the field inside the elevator that I'm not quite grasping. Is there a way of expressing this only in terms of field measurements? $\endgroup$
    – Roger Wood
    Nov 11 '20 at 21:25
  • $\begingroup$ @ Charles Francis As I think you're suggesting, the direction of the gravitational field gradient compared with the gravitational field itself will give a good indication of what's going on. But it is possible to create similar fields with a suitable mass distribution, eg. in the hole in a donut. What is distinctive, perhaps, is that gravitational fields in vacuum have zero divergence by definition. As far as I can tell, the field inside a rotating elevator has positive divergence, so it's not gravity. But the curl seems to be zero, so it doesn't show rotation direction - puzzled :-( $\endgroup$
    – Roger Wood
    Nov 13 '20 at 5:22

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