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A few questions regarding the bending of space

Eldad Eshel

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In general relativity space bends in a 4 dimensional space right ? Does it bend in a certain direction ? Or can bend in any direction ? Does the direction it bends change whether it causes attraction or repelling ?



I do wish popsci stopped offering this picture.


In order to bend in 4 dimensions, 3D space must be embedded in a 4D universe.

We have no evidence of the existence of this 4th dimension.


The 'bending effect' is due to mathematical transformations between the various points that are all in 3D space only.

The amount of 'bend', ie the values of the coefficients in the transformations, depends upon the amount of mass and energy and its distribution around the 3D points.

With no mass or energy present there is no bend, but when it is the distribution also controls the variation of the bend with direction, through the coefficients.

Edited by studiot
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In general relativity space bends in a 4 dimensional space right ?

Space-time 'bends', ie, has non-zero curvature, as a 4 dimensional Riemannian manifold.



We do not need to think of space-time as being embedded into a higher dimensional space (manifold), though we can always do that. Physically, there is no evidence that our space-time is embedded into something higher dimensional, but theories like string theory suggest this might be the case.



So it bends in different directions ?

I think this question is based on misunderstanding the notion of intrinsic curvature.




No matter the direction it always causes attraction and not repelling ?

You can, in the context of general relativity, have exotic situations in which gravity is repelling.

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