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I was debating a variation of this Phys.SE question with a friend. The original question is:

"If you had your eyes closed, could you distinguish between standing still on earth and being in a spaceship which is constantly accelerated at 1g?"

Yes. When you are "standing still" on earth, you actually have velocity due to the fact that the earth is spinning. If gravity suddenly disappeared, you would fly off into space in a straight line, according to your velocity. Since you remain on the surface, there must be a gravitational force constantly pulling you down, constantly changing the direction of your velocity (velocity has both magnitude and direction). Acceleration is defined as the change of velocity, so as you are "standing still", you are actually being constantly accelerated. Now the question has been reduced to "does being accelerated in space feel the same as being accelerated on earth?"

What if the earth and all other objects in space were standing still? You could still feel the earth's gravitational pull. Would it feel different than being accelerated in space?

I imagine being accelerated feels different than not being accelerated. I also imagine you can feel a gravitational pull of a planet even if it is not spinning. This is about all I could muster.

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This is actually a famous theorem known as the Einstein Equivalence Postulate (sometimes Equivalence Principle). It's true that since Earth is spinning, acceleration in a spacecraft isn't quite the same situation we experience daily, but in general, yes, gravity is indistinguishable from uniform acceleration. Specifically, if you are in a box with no windows sitting on an infinite, massive plane, it would be impossible to tell if you were in fact stationary on a massive plane or accelerating through space, because the Postulate states that the two are actually one and the same. To get into specifics, you'll need to brush up on General Relativity. Of course, in practice, planets are not infinite planes, so since gravity pulls radially, its strength would vary between ends of a flat floor being somehow held statically above the planet's surface, so if the spaceship is sufficiently wide, and you are sufficiently far away from the gravitational source, you can easily tell the difference (these variations in gravity are called "tidal forces").

The short answer is that yes, being accelerated in space "feels" (can be measured to be) different than gravitational acceleration on a non-flat, finite, non-stationary mass. However, it's incorrect in this case to say that this is because

... being accelerated feels different than not being accelerated.

because a gravitational field is a uniform acceleration, this is a fundamental principle of General Relativity, so in both cases you are still accelerated.

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  • $\begingroup$ Did I understand correctly: whether the earth spins or not has no bearing on how we experience gravity? $\endgroup$ – Atte Juvonen Apr 21 '16 at 18:39
  • $\begingroup$ That depends what you mean. Whether the earth is spinning or not, when gravity stops you will continue traveling with whatever velocity you had, but if earth isn't spinning this is just zero. This is a very non-relativistic way to think of it, and technically, the spinning earth creates what is known as "frame dragging" which influences gravity somewhat in a very complex way. In short, no that's not what I meant. $\endgroup$ – ocket8888 Apr 21 '16 at 19:15
  • $\begingroup$ I re-read your question, and now I think that your comment didn't mean what I thought it did, so I clarified something. Please let me know if you still feel that this answer is incomplete. $\endgroup$ – ocket8888 Apr 21 '16 at 19:41
  • $\begingroup$ +1 but I disagree with your statement that "it's incorrect to say that '... being accelerated feels different than not being accelerated.'" Surely the latter is correct in and of itself; its application in this case was incorrect. No? $\endgroup$ – Mike Apr 21 '16 at 19:45
  • $\begingroup$ Yeah, that's correct. Inertial reference frames and all that. I'll clarify that a bit. $\endgroup$ – ocket8888 Apr 21 '16 at 19:49
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Gravity and uniform acceleration ar not the same. and with sensitive equipment the man in a box can tell the difference.

imaging he has two plum bobs, on strings. if he measures the difference between the top of the strings and the bottoms, he will notice in uniform acceleration the strings are parallel, But in Gravity the strings point to the center of mass. so the bottoms are slightly closer together.

Also in rotational acceleration the strings point away from the center of rotation.

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