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This is a slight modification to the Einstein's relativity thought experiment that I have not been able to find a discussion on.

Suppose that you are in a spaceship with no windows. Is there any experiment that you can run to determine if you are in orbit around a massive object (alternatively in free fall and really far away) or if you are in an empty universe with no external gravitational potential?

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A possible experiment is to place several small objects randomically at different points, floating inside the ship.

Without a gravitational field, any small initial speed from the instant of releasing any of them, continues until it kicks a wall. It bounces and follows another direction. The randominess of the positions of the objects at any instant tends to be the same.

Inside a gravitational field, and because that field is always non uniform, each object follows its own geodesic, that is different from the geodesic of the centre of gravitation of the ship.

For example, their average speed is the same of the ship, due to the randominess hypothesis. That ones floating in the half closer to the star or planet tends to become even closer, because the average speed is below what is required for orbiting. The opposite happens to the other half.

They are, we can say, expelled from the middle, and concentrates closer to the opposite walls, one closer and the other more distant from the gravity source.

Of course it takes time to that effect becomes noticeable, so it doesn't contradicts the equivalence principle.

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  • $\begingroup$ Interesting, so this experiment would exploit the tidal forces caused by a gradient in the gravitational potential. This is similar to the question brought up in a comment to the OP. Would it be possible to create a constant gravitational field? Something akin to the electric field inside of a capacitor? $\endgroup$ – Alex Shmakov Apr 6 at 1:07
  • $\begingroup$ @AlexShmakov "Would it be possible to create a constant gravitational field?" - It is pretty constant inside your living room. $\endgroup$ – safesphere Apr 6 at 3:58
  • $\begingroup$ @AlexShmakov What do you consider to be constant gravitational field in GR? It seems to me you think in constant gravitational field there should be no tidal forces. But no tidal forces mean the curvature of spacetime is zero which is equivalent to flat spacetime which is equivalent to no gravitational field at all. $\endgroup$ – Umaxo Apr 6 at 5:49
  • $\begingroup$ @AlexShmakov seems to mean the uniform gravitational field created by a infinite flat plate of matter. As this field is constant parallel to this plane one obtains Minkowski space after coordinate transformation. So no tidal forces. $\endgroup$ – timm Apr 6 at 8:20

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