That explanation seems like it would not line up with the mathematical reality of the situation. It seems like one of those handwave-y things that always confused me as a child. “Gravity is just massive objects deforming space like a weight deforming a sheet, and things fall into the well they make.” Ok but what would make something fall into the well, there is no gravity.
That is a very good point! Gravity is just such an ingrained intuition that people tend to be ok with saying things go into the spacetime wells, but it is a little tautological.
My understanding is that a more correct intuition is thinking of straight paths on the curved sheet. Say it's like a loosely woven tablecloth - objects in free fall will go along the threads of the weave, so if you stretch the fabric by placing a heavy object on it, the paths of smaller objects on the fabric will be stretched towards the heavy thing.
This metaphor falls apart for orbits though, as it requires "stretching" the fabric so much that the threads now somehow go in a circle around the mass heh. But the underlying principle is the same - an object in orbit is in free fall along a straight path in curved spacetime.
In my explanation, if the particles trajectory can change, you can see how gravity affects distortion of space. Its not really that the space is some sort of entity that is being distorted, its the concept of measuring what you define as distance gets influenced by how these particles fly about.
