BurtJordaan on April 18th, 2017, 12:49 am wrote: Not quite. Although mental constructs, a Minkowski inertial frame is defined by a non-rotating, non-accelerated, non-expanding lattice of fictitious standard rods and synchronized clocks, somewhere in empty space. Observers can be either stationary in such a frame, or be moving relative to it. And such inertial frames can be in motion relative to each others. In cosmology, we normally set such inertial frames to be co-moving with the Hubble flow, meaning any observer static such a frame, will observe an isotropic cosmic background radiation (CMB), with the same average temperature in all directions.
Would you agree that “objects” are real? (Be they stars, galaxies, atoms or fundamental particles?).
Would you also agree that a “mental construct” is something fictitious? As is a fictitious, non-rotating, non-accelerated, non-expanding lattice, of fictitious standard rods, and (fictitious) synchronized clocks, somewhere in empty space?
Since we are doing mental visualisations, suppose some of these lattices, in empty space, have no body in it, how would you define the location of this lattice?
It is undoubtedly useful to construct such fictitious lattices to calculate the motion of bodies, (provided there are bodies in them), but it seems to me the fundamental thing here are the bodies themselves.
I could more fundamentally say, if I have a set of bodies that are not in relative motion with each other and observe the CMB the same in all directions, then they are comoving with the Hubble flow. I could then construct an imaginary lattice, with your fictitious rods and clocks, around them, so that this lattice is not in relative motion with them, and that would be the “mental construct” that you are talking about.
Unless you can convince me otherwise, I am quite clear in my mind that, in the ultimate analysis, bodies define the lattice and not the other way around.
BurtJordaan on April 18th, 2017, 12:49 am wrote: The math of GR can be formulated with a pre-choice of a time axis as part of its 4-D, or without that pre-choice being made. It makes no difference to the outcome. To a trained GR-specialist, it is perfectly clear how to get the time coordinate out of the Einstein field equations during the process of solving them. In the cosmological solution, a time coordinate falls out in a pretty obvious fashion.
I don’t quite understand what you are saying here. Are you saying that time disappears in the GR solutions?