I am reading The Universe in a Nutshell by Stephen Hawking, a book everyone here has probably read, or at least heard of. In the first chapter, he talks about how the effects of acceleration and gravity prove the curvature of spacetime. I'll give you some exact quotes from the book to make it a little easier:(adsbygoogle = window.adsbygoogle || []).push({});

"Someone inside a closed box, such as an elevator, could not tell whether the box was at rest in the Earth's gravitational field or was being accelerated by a rocket in free space."

This is an easy concept to grasp, but then he goes on to say:

"This equivalence between acceleration and gravity didn't seem to work for a round Earth, however--people on the opposite sides of the world would have to be accelerating in opposite directions but staying at a constant distance from each other. ...Einstein had the brain wave of realizing that the equivalence would work if the geometry of spacetime was curved and not flat, as had been assumed hitherto."

What I don't understand is this: We are not in a closed box, and we know that gravity is responsible for keeping us on Earth, for the whole surface of the Earth is feeling the same effect more or less (this would obviously not be the case if acceleration was the only thing responsible). I don't see the problem with the equivalence of these two things for a round Earth that Hawking is talking about. Is he saying that curved spacetime would allow the whole surface of a spherical object to accelerate outward while the diameter of the sphere remains unchanged? How could this be?

I hope I have explained myself alright. Thanks for any help.

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# Spacetime curvature

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