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It is known that space behaves like a 3D rubber sheet, when mass is present, and bends. Gravity can be explained by the curvature of this bending.

Water forms a highly flat surface that also behave like a rubber sheet due to surface tension, be it in 2D. Water striders use the elastic property to propel themselves. The crystal-like aligning of the water molecules at the surface does not go too far to the inside, and soon gives way to the random motion. Thus the skin depth of water is only a few molecules thick.

If this similarity could be taken further, what would be the skin depth of space?

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    $\begingroup$ You've taken an analogy used as an illustration way beyond it's level of fidelity to the thing that it's trying to illustrate. $\endgroup$ – Brick Aug 1 at 14:31
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/a/13839/2451 and links therein. $\endgroup$ – Qmechanic Aug 1 at 16:11
  • $\begingroup$ Also related. $\endgroup$ – rob Aug 1 at 18:29
  • $\begingroup$ With the 2D rubber sheet analogy, you should mostly ignore the 3rd dimension as a misleading artifact of the model. Just focus on what happens to the curvature: imagine a grid on the sheet and pay attention to how that grid gets distorted. There's a nice answer somewhere on the site that looks at the distorted grid from the POV of ants crawling on the sheet. $\endgroup$ – PM 2Ring Aug 2 at 5:26
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Space doesn't behave like a 3D rubber sheet and gravity cannot be explained by the bending. The rubber sheet is a common metaphor for spacetime curvature but it is not the way general relativity describes the curvature. There are lots of questions on this topic already. See for example Better explanation of the common general relativity illustration (stretched sheet of fabric)

So spacetime isn't a surface curved in some higher dimension, and consequently there is nothing analogous to the skin depth of a water surface.

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The "rubber sheet" explanation is about if we thought of the space as 2d, and the "curvature" would be on the z-axis. However, we live in a 3-dimensional space, and similarly to what we thought of the 2d "rubber sheet" explanation, the gravitational "curvature" would need another dimension to explain. However, We only observe 3 axes of space, so we cannot observe, and therefore cannot measure the "skin depth" of water. You'll eventually learn how general relativity works at some point, so just think of it as "Gravity works like this" for now.

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