I am interested in the correspondence between reality and the mathematics of spacetime and wonder if that is an issue with anyone else? How is the question of correspondence handled in teaching students about General Relativity? I characterized the issue of correspondence as follows and wonder if I understand it correctly: Is it correct to say: General Relativity says that space and time are physically coupled into geometry of spacetime where points in time are events and spacetime connects mass, energy, time events and space into a physical geometry of all points in the universe where each point is fixed in the geometry of spacetime. Then at any given time, mass occupies its current point in spacetime and the EFEs describe how that mass will move, i.e. which point it will move to next. Given that geometry and motion as reality then as the universe expands it increases in volume and there is new space added as expansion proceeds because there are new points in spacetime that correspond to that expansion. That is the way the universe occupies all available space and why spacetime at this point, given accelerating expansion, would be considered open and finite and potentially infinite, i.e. able and likely to expand infinitely. Is that a proper characterization of what spacetime is? Can it properly be referred to as a lattice of spacetime points that began with the onset of spacetime from a Big Bang type event and within which the universe is causally connected to the Big Bang event? If so is it valid to wonder if there is a perfect correspondence between spacetime and reality i.e. is spacetime a reality or is it the best mathematical representation of the effect of gravity but not reality itself?