"Given how many times we have debated this, your mind much have an edit function bordering on amnesia. Especially with inconvenient observations."
Projecting, are we John?
"Space presumably expands, but since the speed of light in a vacuum is constant and since those distant galaxies presumably are moving away in terms of how long the light takes to reach us, the vacuum must then be a constant."
You have an amazing facility for jumping to conclusions. Correlation is not causation -- the fact that the speed of light is constant does not imply that "the vacuum is a constant," whatever that means.
"So how is it that space expands, yet the vacuum remains constant?"
Beats me, since that makes no sense.
"Wouldn't the constant presumably be the denominator, thus the expansion, being the numerator, is only an increasing number of these stable units, otherwise known as increasing distance?"
As near as I can make out, you are saying that n/m grows larger if m is constant. True, but irrelevant. The universe is actually accelerating in its expansion.
"Which puts the whole situation in normal, three dimensional space and thus either means we are at the center of the universe, or that redshift is an optical effect of extreme distance, possibly due to dilation of the photon, beyond the point sufficient light can register relatively instantly."
I'll probably never understand how you arrive at this false dichotomy. Relativity however, explains the "center of the universe" problem.
"'How does Olber's paradox explain background radiation?'
"Olber's paradox is as to why the sky is not completely lit up by the light of ever distant sources, given an infinite universe. Background radiation is 'first light' from the very edge of the universe. If light is redshifted by extreme distance and it is an infinite universe, then the light that has been shifted completely off the visible spectrum would be just such a black body radiation, from the visible edge of the universe and it would have anisotropies to it, because while it is still no longer on the visible spectrum, it would have had definite sources and we would be seeing the vestiges of their form in this light. So we are 'seeing' the sky lit up by ever distant sources, just shifted off the visible spectrum."
*Or* -- siince we associate the background radiation with big bang theory, Olber's paradox is a superfluous explanation.
"'Einstein and Minkowski should have been delighted with the many worlds hypothesis.'
Einstein didn't even like the idea of 'God playing dice.' I'm sure he would have been thrilled that God had to create multiple realities in order to prevent the collapse of the wavefunction."
Um ... if the wave function doesn't collapse, there is no dice playing involved.
"'What would the shadow of spacetime look like?' It's not the patterns in the shadows that are physically real.'
Shadows are as real as any image."
Oh? So if I appear to you as a hologram and you shoot me through the heart, I will die. Thanks for the heads up.
"Spacetime is a set of measurements, a map and maps are real."
I thought you claimed spacetime isn't real. Change your mind?
"What cast those measurements? Is it the 'fabric of spacetime?' Or is it that measures of duration and distance can vary under different conditions?"
Will the false dichotomies never cease?
"When you assign agency to the pattern, ie. those measurements directly correlate to some physical property and are not derived from more complex interactions, you have essentially made the same conceptual leap of faith which assumed epicycles must be due to giant cosmic gear wheels."
The measurement of celestial epicycles doesn't require a leap of faith -- just a lot more calculating. Mathematicians are notoriously lazy.
"That these patterns are the reality, not a shadow of some other relationship at work."
Beg your pardon -- whether calculated by heliocentric or geocentric methods, the relationships among the bodies do not change.
"Remember math is only about discovering order. Religion is about assigning agency to it."
I'll remember that when you prove your first theorem.
Best,
Tom