>>10839981Always remember the "time" part of "spacetime". It's by far the most important one when it comes to the apparent "force" of gravity in GR. The curvature of space alone is much less significant for objects with mass moving at mundane speeds. This is something often lost on those 2D metaphors with sheets and balls. You might fairly ask: "Ok, fine, I get that it's curved, but why do I seem to start moving from nothing even when I'm stationary (relative to the source of the gravitational field)?"
The answer is that nothing is ever stationary in all four dimensions of spacetime.
In the framework of relativity, everything has a four-velocity (x,y,z,t) with a magnitude of c. Think of it like a 4D arrow of a constant fixed length. It can't get shorter or longer, it can only point in some direction. In your inertial reference frame something "stationary" relative to you (such as, well, you) has the four-velocity (0,0,0,c). In other words, its arrow points straight forward along the t axis. In a massive body's gravitational field, spacetime - including the t axis - is curved towards the body. So even if you have no motion through space, your ever present journey into the future still draws you closer together.
For a simplified example, imagine an otherwise flat and empty universe with just you and me in it. We are nearby, but we are not moving relative to each other. Our world lines (paths through spacetime) are parallel lines along the time axis. So far so good, in truly flat spacetime we would never meet. However, being massive, our very presence curves spacetime locally. Just as lines of longitude which are parallel at the equator will converge at the poles, so too will our parallel lines through spacetime converge at some point in the future. To us, this looks like an attractive force toward our shared center of mass. But it's not a magic force from nothing: it's the consequence of our motion through time.
