If the force of gravity can be thought of as masses leaving dents on a sheet of spacetime, what is holding up that sheet?
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$\begingroup$ tension? Anyway it does not matter. Such intuitive pictures are to be taken with huge grain of salt. The point of the sheet analogy is to make layman believe that curved spacetime can indeed cause gravity and that is it. You cannot extract any of the "hows" though, because it is really bad analogy. If you want to understand more, you must look for better explanations/analogies. $\endgroup$– UmaxoCommented Oct 18, 2019 at 12:01
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1$\begingroup$ Related if not duplicates: physics.stackexchange.com/q/7781 , physics.stackexchange.com/q/3009 , physics.stackexchange.com/q/90592 , $\endgroup$– BioPhysicistCommented Oct 18, 2019 at 12:21
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4$\begingroup$ Possible duplicate of How exactly does curved space-time describe the force of gravity?. It's not the same question exactly, but the answers there look just like the ones being posted here. Therefore, this question has essentially already been answered on this site. $\endgroup$– BioPhysicistCommented Oct 18, 2019 at 12:23
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$\begingroup$ Possible duplicates: physics.stackexchange.com/a/13839/2451 , physics.stackexchange.com/q/7781/2451 , physics.stackexchange.com/q/51198/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Oct 19, 2019 at 13:06
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2 Answers
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The visual is a bit misleading. There is no “up” in spacetime and there is no need for an additional force pulling down. More importantly, the visual neglects any curvature along the time direction, which is essential for understanding gravity.
Step back from the visual for a moment. Consider an ant walking slowly on the surface of a ball. Let’s say that this ant never turns but goes straight forward every step. Even though the ant walks straight it will eventually wind up back where it started and will have traveled along a great circle.
This is the meaning of curved spacetime. It isn’t about some force outside of spacetime pulling things down, like in the sheet analogy. Instead, it is about the fact that if you always travel straight ahead on a curved surface your path can do weird things like loop around or otherwise curve from a different perspective.
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$\begingroup$ Let us continue this discussion in chat. $\endgroup$– DaleCommented Oct 18, 2019 at 19:18
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Nothing. There is no sheet. It's just a metaphor to help you visualise the bending of three-dimensional space. Metaphors always break down if you push them too far...
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2$\begingroup$ Space-time is four not three dimensional in general relativity. $\endgroup$– hof_aCommented Oct 18, 2019 at 12:43
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$\begingroup$ @hof_a Whoops! (You know what I mean...) $\endgroup$ Commented Oct 19, 2019 at 13:03