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I'll try to be clear: example: If you send the ISS far enough for it not to undergo the Earth's gravity anymore, then you turn it and the—sleeping—astronauts in it upside down, when they wake up, will they know/feel that they're not the right way up? How?

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You don't even need to move the ISS away from Earth to do this experiment, unless the astronauts have some instrument which can sense the tiny tidal effect of the Earth's gravity. –  nibot Sep 1 '11 at 0:16
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You cannot move far enough to not undergo Earth's gravity. It's everywhere. –  Anixx Sep 1 '11 at 1:57
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No they will not. Space is intrinsically isotropic, so assuming they are not aware of any specific reference points, and they are far enough away from a massive body as to experience an insignificant amount of gravity, there would be no way of knowing their orientation. Gravity essentially provides observers with a force field that the body can utilise to establish orientation etc.

Hope this helps.

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This question is closely related to the conservation of angular momentum. In both classical and quantum mechanics, angular momentum is conserved when all the dynamics of a system are invariant with respect to infinitesimal rotations. Therefore, as long as we trust that our theories of mechanics are correct, we can test the isotropy of space by doing some experiments and seeing whether angular momentum is conserved. If angular momentum is not conserved in our experiments, then we are in a situation where we can detect rotations.

For example, on the surface of the earth, you can drop a ball and its angular momentum increases as it falls (relative to some axis to the side of the ball's trajectory). This indicates that the system (you + ball) can tell if you've been rotated. However, if we include the Earth itself in the system, angular momentum is again conserved because the Earth (theoretically) picks up equal and opposite angular momentum to the ball as it falls. When we rotate the Earth, you, and the ball all through the same angle, you won't be able to tell. The astronauts will probably find that unless their experiments are extraordinarily sensitive, angular momentum is conserved for the system (astronaut+ship+its fuel+everything in it), so no, the astronauts will not be able to tell they've been rotated. Finally, note that rotating a system through an angle does not refer to giving it an angular velocity. You can tell if you're actively spinning or not. You just can't tell your orientation relative to distant stars.

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Quick comment: the Earth doesn't pick up any angular momentum from the ball. The ball's angular momentum will be conserved as observed by an inertial observer outside the Earth. –  Emilio Pisanty Feb 6 '13 at 10:19
    
That makes no sense as an absolute statement. It depends on the axis about which you calculate the angular momentum. –  Mark Eichenlaub Feb 6 '13 at 14:09
    
Yes. But there is no interaction that transfers angular momentum between the ball and the Earth. Since Earth's motion around the sun can be neglected, its COM frame can be considered inertial. The non-conserved angular momentum in the fall of a ball we observe if we're careful is only due to our frame of reference rotating, and goes away in the Earth's COM frame. –  Emilio Pisanty Feb 6 '13 at 17:03
    
It depends on the axis you choose. I'm not making a statement about reference frames. You can see angular momentum changing in an inertial frame, depending on the axis you choose. –  Mark Eichenlaub Feb 6 '13 at 20:43
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There technically isn't an 'up' or 'down' - even with the concept of gravity. 'Up' and 'down' are subjective terms that really describe either moving toward or away from a centre of gravity and are dependent on the relative position of the observer.

At the moment, I'm wondering if gravity truely exists in it's own right, or if (as gravity has been described as the warping of space/time), gravity is actually the absence of 'normal' space/time behaviour...

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