Correct me if I'm wrong please, but the 'curved space' strategy describes the velocity of two objects in a 2 body scenario, but it doesn't describe the behavior when the two objects have zero velocity relative to each other, right?
The 'two spheres in a box' experiment for testing the gravitational constant has no relative velocity at all, so how could 'curved space' describe the force between them?
As I understand it, even objects with no velocity in space still have velocity in time, and the curvature of spacetime shifts it from the time component into the spatial components. In other words an object's velocity is a 4 dimensional vector, and the curvature of spacetime causes the angle in 4d spacetime of that vector change, while still preserving total momentum, thereby accelerating the object in space while decelerating it in time. So as an object falls into a gravity well, it actually moves more slowly through time, transferring more and more of its total momentum from temporal motion and into spatial motion.
The 'two spheres in a box' experiment for testing the gravitational constant has no relative velocity at all, so how could 'curved space' describe the force between them?