Hi Russ,
I try always to remember to say INFINITE loaf of bread, so no boundaries. At anyone moment the picture is just our old familiar Euclidean 3D space.
To me infinite 3D Euclidean space is as comfortable as an old pair of shoes. Europeans have been using it as a model for centuries without feeling the need to imagine boundaries. The old x,y,z coordinate system that generations of us have used.
It is really a relief that cosmologists have gotten back to picturing space (at anyone instant of time) that way. It is deeply rooted in our culture and in common sense. So the accepted picture agrees with conservative common sense in that way.
The 1916 equation of GR, unfortunately, has no stable solution unless that space is either expanding or contracting. But to me this is only a small matter. The Einstein equation is relatively simple and beautiful and fits observations out to many decimal places to most people's (not sub's!) satisfaction. I would not like to have to throw it out. And it says we must assume at least some very gradual expansion in order to get stability. In this one little detail there is disagreement with traditional common sense---which causes a lot of noise and ruckus (from certain people!) But personally this does not bother me.
I do not know any better model of gravity that one could use in place of 1916 GR, although there are strenuous efforts going on to construct alternative models they are as yet unfinished and untested. So I am content to stick with old 1916 GR which explains observed effects so well----even tho to get stability one must assume at least a very gradual expansion. (Dynamic things have a hard time keeping still and space is dynamic.)
And hey, by a weird coincidence, astronomers observe redshifts
that FIT with the model that has a bit of expansion in it. So I feel pretty comfortable about this as if it is common-sensical and in line with age-old traditional infinite x,y,z space-----only with the slight adjustment of a gradually growing scalefactor a(t).
But I think everyone else should go ahead and believe anything they want, even Astrology or Hindu Cosmology or Plasma Syrup with Angels Swimming thru the Aetherial Medium. As you say about the popular rejection of mathematical models, it is "self-delusion", but that is OK.
I share your pragmatic approach: to provisionally accept equation-based models at long as they appear WORK---even if some unintuitive or untraditional details are involved.
Inserted are a couple of comments marked with ***
Originally posted by russ_watters
Good luck getting it back to the original point - but I'll keep the ball rolling:
I am one of the people who initially fell into the trap of a finite universe. If I understand correctly now, you COULD say that SPACE is finite in one specific slice of time, but when you define the UNIVERSE it must include all time, therefore all space that will ever exist. Hence, infinite universe.
***infinite in anyone specific slice of time
Marcus, I still prefer the balloon analogy though - your loaf of bread analogy isn't bad for looking at a small piece of the universe (small part of the bread), but when you look at the whole thing, it implies boundaries, whereas the balloon analogy does not.
***infinite loaf of bread, no boundaries implied
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