how the “bending space-time” visualization of gravity works/looks like in 3D space? (i.e. gravity is often visualized with a picture of a flat sheet-like plane, with a round object sitting on that plane and bending it so that objects roll towards the object).

Question

Obviously gravity isn’t acting on a 2D plane or objects would gravitate to the “bottoms” of other objects. I’m curious about whether there is a way to visualize how this model works in 3D.

In: Physics

Answer 1

Analogies are like cars; if you use them too much they start to break down.

The “bending spacetime” or “weight-on-a-rubber-sheet” analogy is a neat way of thinking about things, but relies on a bunch of stuff we’d rather not have to rely on when explaining gravity (such as gravity itself).

If you want a way of thinking about it in 4d (or 1+3d), think of gravity as stuff with mass (or energy) squishing spacetime together. Near a massive object there is more space-per-space and less time-per-time than there should be when viewed from the outside.

So you might have a path near a massive object, and from the outside think that it is 10,000km across, so moving at a known speed will take you a certain amount of time to travel along. But when you go along the path you find it is actually 11,000km long. There is a bunch of extra space in there, because it has been squished up by gravity; more space-per-space.

Similarly, even when you account for that extra space, you find that it took you a certain amount of time to get from one side to the other, but on the outside more time has passed; time was also squished up near the massive object (less time-per-time).

“Squishing” spacetime works a bit better than “bending” spacetime as an analogy, as you don’t need an extra dimension to do the bending in.