Why Does Matter Fall to Center of a Mass? Explained

[Tomer Aman]

TL;DR

Why does all mater fall into the center of the mass and not down towards the curveture that the mass creates in spacetime?

Hi Guys.
I have a question about General Relativity.
If, according to GR, Mass curves Spacetime and gravity is simply matter falling into that curveture, why does all matter fall equally regardless to their spatial position on the mass. For example, why do people in let's say Australia fall into the center of the earth, and not down towards the curveture that Earth creates in 4d spacetime? Does it have something to do with the fact that its 4d and not 3d as the pictures show? Thanks

 

[PeroK]

What pictures are you looking at?

The "curvature" of spacetime is indeed in 4D, including "curvature" of the time dimension.

The important point is that the curvature near the Earth is spherically symmetric - so all around the Earth it looks the same.

And, the effect of the curvature is that the natural path for an object tends to be towards the centre of the Earth.

 

[phinds]

Does it have something to do with the fact that its 4d and not 3d as the pictures show?

It's not really possible to accurately show spacetime on a 2D piece of paper so you won't see ANY graphic representations that are actually correct. They are heuristics for discussions with beginners / lay people and are not to be taken seriously.

 

[timmdeeg]

Summary:: Why does all mater fall into the center of the mass and not down towards the curveture that the mass creates in spacetime?

Matter doesn't fall down towards the curvature. Instead spacetime curvature tells matter which path it falls and that is towards the center of mass.

 

[A.T.]

Does it have something to do with the fact that its 4d and not 3d as the pictures show?

The pictures you probably refer to are just showing 2d curved space and no time. This might help: