is space where it was?

In My Humble Opinion
1

Given all the distortion that spacetime experiences on account of stuff, can we assume that here will always be here, or could here eventually end up over there?

I mean, we are accustomed to the grid-and-rubber-sheet analogy with balls putting dents in it as a simple way to envision the bending of spacetime by gravity, but the rubber sheet always bounces back when the big ball is removed. Granted, I have never actually seen it bounce back, they never show that part; and there is no known state of “flat” spacetime anywhere in the observable universe, there is always some measure of gravitational gradient.

And we have theories of “dark energy”, or vacuum energy density, which seems to be causing spacetime itself to expand. So why would we assume that point A will always be at point A? Spacetime does not appear to be a static medium, why would it not also be moving in relation to everything else?

Could the very movement of spacetime itself be modeled to account for what we infer to be dark matter? And can we come up with some sort of sensible mechanism to explain the displacement of place?

2

This goes WAY back! Einstein and Mach disagreed on whether space had an intrinsic “metric.” (I’m damned if I can remember which held which view.)

Take a planet in an otherwise empty cosmos. Dead empty, just one world.

Does it spin? If so…what is it spinning relative to?

One view is that, yes, it can spin, and will produce an equatorial bulge. (This can equally well be seen as the cosmos spinning around the world, “pulling” the bulge out from the planet’s equator.)

The other view is, no, it can’t spin, since there isn’t any matter out there to use as a guide. If there were another planet, then you could meaningfully talk about one or both of them having some kind of spin, but not with only one planet.

I don’t know what the current state of GR mathematics is, and whether the equations have been solved to anyone’s satisfaction.