In all the ones I've seen, it appears to curve toward the object, which appears to be inconsistent with 2D visualizations.
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$\begingroup$ unclear to me what you mean, could you elaborate further? $\endgroup$– user126422Commented Apr 9, 2017 at 1:11
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$\begingroup$ Related: physics.stackexchange.com/a/13839/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Apr 9, 2017 at 3:07
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By 2D visualizations, I presume you mean this:
- As you can see in the picture, spacetime is bending down toward the object, Earth. This way, if there is an object near Earth, they will travel toward each other, similar to two objects on a stretched blanket. In contrast, if spacetime bent up and away from the objects, they would be pushed apart. See this video for a visualization. You may find it interesting.
- The reason for why spacetime curves toward objects and not away is because if it curved "away", the objects would be pushed apart. In the 2D model, spacetime curves toward the object. In a 3D model, spacetime also curves toward the object.
There is far more to this answer if you look into Einstein's Theory of General Relativity, but my knowledge of physics is not adequate enough to explain it all in one answer. I hope this helped!
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$\begingroup$ Well that is the only way mass/energy and space inter-act. Einstein said - "Mass tells space how to curve and space tells mass how to move". Physicists do not bother about actual physical mechanism of curving, they only go by the quantitative formulation which till date, is given most accurately by GR. $\endgroup$– kpvCommented Apr 9, 2017 at 3:27
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$\begingroup$ Why would the mass probe fall? are you assuming an extradimensional (perpendicular to the plane) gravity force pointing downwards? the rubber sheet analogy is not really good $\endgroup$– user126422Commented Apr 9, 2017 at 15:49
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$\begingroup$ The rubber sheet analogy seems like the most common, simplistic, and understandable analogy for general relativity regardless of its practicality. Since the question implies such a visualization, I just continued using this analogy. But both of you are correct, and I agree that the rubber sheet analogy is not very good. $\endgroup$– SkyminerCommented Apr 10, 2017 at 19:07