system
Given the following post, respond as if you're commenting on Reddit:
human
If gravity is caused by the bending of space, why doesn't that mean there is a fourth dimension (or something similar) for space to bend into?

In every video I have seen about space-time, they always explain gravity by the "bowling ball on a sheet analogy" where space is a huge sheet and placing a massive object on it causes space to bend and other objects to be attracted. There is a similar analogy when explaining wormholes - a sheet bends so much that two points are touching.

What I don't understand is how the 3d spacial dimensions can bend and remain three dimensional. Doesn't bending imply that there is another dimension that is being bent into so to speak? (If you bend a 2d sheet, you are entering a third dimension)

My guess is that this comes down to a misconception of space-time, but this has still been on my mind a lot recently.

Thanks for any input!
gpt
>Doesn't bending imply that there is another dimension that is being bent into so to speak?

Nope. At least, not necessarily. The mathematical framework we use to describe curvature is perfectly capable of doing so *without* assuming that there is a larger space in which the "object of interest" is "being curved". It's just that all of our *experience* with curvature comes from curved two-dimensional surfaces of three-dimensional objects; that's all we ever encounter in our day-to-day lives, and that's the sort of thing that our brain has evolved to "visualize". But there's no reason *in principle* that there must be such a larger space; specifically, the geometric description of spacetime curvature given by the general theory of relativity works perfectly fine without assuming such a larger space exists.

[edit]

I want to add that if you *do* want to insist that the curvature be "in" another dimension, probably so that it "looks" like what we're familiar with, then in a lot of cases you'll need significantly more than just one extra dimension.