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The visualization of gravity as shown by this video is pretty good at explaining how massive objects bend space, and such bending causes objects around it to fall towards it (a.k.a: gravity).

However, here's what I do not understand. The reason why the experiment in the video works in the first place, is because real gravity -the one in that room- is acting on the marvels and causing those marvels to bend the sheet. In the real world, there must be a force that causes massive objects to bend space in the first place. What is that force?

To put my question in a simple set of equations:

Experiment: Marvel + Sheet + Real Gravity = Sheet Bending (Fake Gravity).

Real World: Planet + Space + (?) = Space Bending (Real Gravity).

There are other questions about this on StackExchange, but they don't seem to address the missing variable in the equations above.

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The analogy between how a massive object bends a rubber sheet and how sources of mass-energy-momentum bend spacetime is a poor one. It's essentially comparing the mechanical deformation of a two dimensional sheet in space to the curvature of four dimensional (3+1) spacetime, which have a mathematical similarity, but not a physical one. In Newton's theory of universal gravitation, gravity is a force which acts pairwise between massive objects. In General Relativity, it is no longer a force, but rather a geometric affect of energetic objects on spacetime. That is, things with energy are the source of curvature in four-dimensional spacetime (3 spatial, 1 temporal). Because gravity is no longer a force, objects in curved spacetime that experience no net force still travel in what are called geodesics (paths of the shortest distance on a curved surface).

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