eli5 does space only curve in one direction?

Question

graphics about black holes or planets’ influence on gravity, etc., always show these bodies “sitting” on a flat surface and then bending that surface below them. is this a literal representation – ie is there a definitive “down” direction that always dips under the objects’ mass? or does it happen in multiple directions somehow? (or am i misunderstanding something fundamental about this curving?)

In: Physics

Answer 1

The heavy ball sitting on a stretched sheet causing a depression in the sheet causing objects to “fall down” the depression illustration only gets you so far, and you see its limitations.

The illustration itself relies on assuming gravity pulls things down in the first place, since otherwise objects have no reason to tend to fall down a depression in the sheet. To really understand GR, you have to understand two things.

One is that there are not just three spatial dimensions, but a fourth dimension, orthogonal to the the three spatial ones, and that’s time. Together they form spacetime.

The second is the idea of a geodesic, which is the shortest path between two points in a curved geometry. Objects take the shortest path through spacetime (not just through space, and not just through time, but through *spacetime*).

These two taken together give you the reason behind the phenomenon of gravitational attraction. Everything is moving with a constant “velocity” through space time. In the 2d curved sheet analogy, take an object, and then draw a straight line extending out to infinity. That’s how the object will travel absent any other forces. It will follow that straight line. But now when you start curving the sheet, suddenly that straight line is bent so it intersects with say a planet.

The reason you fall down to earth is because you’re moving through spacetime, and the earth is in your future. The reason it’s in your future is your future “worldline” (the line you take through spacetime) is a straight line through spacetime, but because the earth curves the region of spacetime around it your straight worldline intersects the earth.