If gravity is the curvature of space and objects "fall" in to the gravity well because they are following a curved path, then, well, that can only happen if the object is moving, isn't it so? I understand there is still molecular and sub-atomic motion in matter and this would be the major contributing factor if this is true. But then escape velocities exist and I get really confused.

It's really simple provided you've read the original material by Einstein. A concentration of energy, usually in the guise of matter in the guise of a star, "conditions" the surrounding space, the effect of this diminishing with distance. See

Einstein's Leyden Address for that. Then imagine you could place optical clocks at various locations throughout an equatorial slice through the Earth and surrounding space. Clocks go slower when they're lower, so when you plot all your clock rates, what you get is a plot like this:

GNUFDL image by Johnstone, see Wikipedia That's a depiction of Riemann curvature. It's basically a picture of curved spacetime. Like Pmb said,

*space* isn't curved. See the

Baez website and note this:

*"not the curvature of space, but of spacetime"*. Curved spacetime isn't curvature of space and curvature of time. It's a curvature in your plot of measurements of motion

*through* space

*over* time. It's a curvature of "the metric", metric being to do with measurement. And note that the force of gravity depends on the slope of the plot at some location, not on the curvature. Like Pmb said, that's to do with the tidal force. Also note

this on the Baez website:

*"Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers."*Those clocks I referred to are optical clocks. And they go slower when they're lower because light goes slower when it's lower. See

this Shapiro quote:

*"The proposed experiment was designed to verify the prediction that the speed of propagation of a light ray decreases as it passes through a region of decreasing gravitational potential."*People refer to this speed of light as the "coordinate" speed of light. The locally-measured speed of light is the speed that's constant, because of a

tautology wherein we define the second and the metre using the motion of light. Anyway,

like Einstein said, light curves because the speed of light varies. There's a nice gif showing this on Ned Wright's

deflection and delay article where you can read this:

*"In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light."*Light doesn't curve because spacetime is curved. It curves because the speed of light is lower near the floor. It's a bit like the way a car veers when it encounters mud at the side of the road. Or like the way

sonar waves curve. Once you know that and you know about the wave nature of matter, and pair production and electron diffraction and magnetic moment and spinors, it's quite easy to work out why matter falls down. And it is because of that sub-atomic motion. Think of an electron as a wave going round and round, then simplify it to a wave going round a square path. Then imagine the horizontal sections curve down a little, like this:

The electron falls down. And just as general relativity predicts, light is deflected twice as much as matter because only the horizontal component of the matter wave curves downward. See

Albrecht Giese's description which is similar. There's things he says that I don't like, but I think the gist of his explanation is correct.