>>12504530The best way to understand curved space-time is Einstein's way in 1907. Imagine all of space is filled with clocks which are held in place, but they need tick at different rates in order to stay simultaneous with each other. Near a massive object, the clocks tick slowly, away from masses, they tick faster.
Particles travel through space so that they locally take the path of maximum time between fixed endpoints, so that between endpoints which are close to a massive object, their path curves out a little, meaning that they are bent toward the massive object.
This is a statement of the Einstein 1907 theory of gravity, which he knew then would be the weak field, slow velocity approximation to Genera Relativity. It is counterintuitive for a few reasons:
1. In geometry, straight line paths are minimum distance. In relativity the path is a local maximum. This is a consequence of the minus sign in the Pythagorean theorem in relativity. In relativity, unlike in geometry, the sum of the length of two legs of a triangle (when these are not imaginary) is always less than the third, so that straight lines maximize proper time.
2. There is only one function which describes the curving of space time, and this is the clock rate. The curvature is determined by this clock rate, but it is purely a time curvature. Space is not curved at all.
3. The geodesic motion is not trivial to see from the clock-rate description. You might naively think that to maximize the proper time you need to move away from massive objects, because time ticks slower near them. But the maximization is holding the endpoints fixed. To give an equation of motion without the concept of maximum proper time, you can just say that objects feel a force of attraction towards regions of slower clock-tick, and leave it at that. But this doesn't look like a geometrical condition (although it is).
I don't believe that there are two pictures of a phenomenon, one for laymen and a separate one for physicists.
