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Does the curvature of spacetime theory assume gravity?
Since I read Cosmos long ago, I see the same analogy about the balls rolling on a rubber sheet used to explain how gravity works. But a ball rolls on a surface because gravity is pulling it down. In space it will follow a straight line and go over any hole on the surface.
So, in the analogy we all know, where the curvature of the rubber sheet is gravity, what is pulling the ball down? If space is curved, what keeps an object attached to that "surface" of space?
Answer
This is one of the problems with analogies (when not treated as analogies). Obviously, spacetime is not a sheet and masses are not rolling on it. You encounter these kinds of problems whenever you take an analogy too far or out of its context.
For example, you get in the same mess when you try to describe (attractive) electromagnetic forces as rubberbands between particles. Because what's going on inside the rubberbands? That's electromagnetic forces at work! So, as with your question, this analogy gets you into trouble if you ask about the nature of the elements in the analogy.
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