the nature of gravity in the sense of how it works in a 3D universe

Question

I need help with an analogy here because I simply don’t know/can’t visualise the true physics here.

Many people use an analogy for gravity acting on space-time as a sheet of material stretched across a plane and a heavy object in its center acting as a celestial body.
This is great for envisioning orbits, the curvature of spacetime and so on.

Now this is a “2D” sheet/plane that deforms “downward” in the 3rd dimension, I get it… But how does it translate to the actual universe? The universe is always 3D in all directions, isn’t it?

I’m stuck here guys, science help me!

In: 81

Answer 1

So a counterintuitive fact is that a curved, two dimensional surface is still only two dimensional. When we see a sphere, we understand it as a three dimensional shape with volume, but the *surface* of the sphere is still only two dimensions. That is, we can represent every point in the surface of a sphere just using two measurements (such as latitude and longitude, which we use to define points on Earth’s surface).

From the perspective of a hypothetical, two-dimensional being on the surface of a sphere, they would only be able to move in two dimensions: east-west and north-south. They would have no concept of depth or the volume of their sphere. But they would be able to tell that their world was curved, based on how their geometry works. If they went in one direction in a straight line, they would eventually end up where they started, for example. The angles of a triangle drawn on the surface of their sphere would total more than 180 degrees, and two straight lines would converge or diverge rather than remain parallel.

General relativity posits the same is true for us, but in three dimensions. Space is still three dimensional — we can only move through it along forward-backwards, left-right, and up-down axes. But it is possible for there to be a curvature such that straight lines don’t remain parallel around massive objects.