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).


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

As it bends 4D space while you’re a 3D being it’s quite hard to visualize. This is exactly the reason why people use the other, albeit wrong, visualisation.

Just look at a simple 4D cube, one of the basic 4D shapes, it’s quite hard to wrap one’s head around as no matter what we will always only see at best a 3D projection of that space.

Basically you could imagine a 4D “grid”, that we obviously don’t see, and mass deforming the entire grid around a body. Bodies then still move on that grid, but as it is deformed their paths are different.

But then again you’ll hardly be able to visualize a 4D grid in the first place, let alone a deformed one.

The visualization is just an abstraction, as gravity exists across more than 3 dimensions. The visualization is mostly good at conveying the principal that gravitational force gets stronger along a similar curvature to the ball in the trampoline curvature.

If you imagine a 3D grid around a massive object, it will distort and bunch together toward the massive body.

Any arbitrary 2D slice of this 3D grid (taken through the center of the massive body) will look the same, and appear as if you were looking straight down on the 2D sheet visualization.

In 3D the “gravity well” is the same as in the 2D visualization, except “downhill” is “toward the center” instead. It’s omnidirectional.

Yes, it’s only an analogy and doesn’t capture the full complexity, but it’s still a good analogy.

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.

Might not actually help you visualise 4 dimensions from your 3 dimensional worldview, but no 10 minutes listening to Carl Sagan is wasted.