On 11/10/2017 4:06 AM, Alan Grayson wrote:
On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:
On 11/9/2017 9:15 PM, Alan Grayson wrote:
On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker
<meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:
On 11/9/2017 8:55 PM, agrayson2...@gmail.com
<mailto:agrayson2...@gmail.com> wrote:
On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:
On 11/9/2017 6:23 PM, Alan Grayson wrote:
The difference between spatially flat and
asymptotically flat for a huge universe would be
virtually impossible to distinguish by measuring the
sum of angles in a triangle. Moreover, I don't see how
spatially flat can have nothing to do with extent,
since in applying Euclidean geometry we surely seem to
be dealing with an infinitely extended plane. TIA.
Not necessarily. You could have periodic boundary
conditions. But most cosmologists do assume the universe
is infinite in spatial extent. Of course the flatness
isn't measured by triangulation. It's measured by
comparing the spatial spectrum of the CMB variations to
model predictions with different mass densities.
https://arxiv.org/pdf/astro-ph/0004404
<https://arxiv.org/pdf/astro-ph/0004404>
Brent
However flatness is measured, the criterion still seems
Euclidean and hence infinite in extent if one believes the
triangle measured has combined angles of 180 degrees. And I
don't see how this is distinguishable from asymptotically
flat for a huge but finite universe.
It's not.
That's my point. No way of distinguishing flat from
asymptotically flat for a huge universe, so the assumption of
infinite spatial extent by cosmologists seems unwarranted. But as
you note below, the universe could have begun with infinite
spatial extent. But ours didn't AFAIK. It began as astronomically
tiny and expanded via inflation.
But you don't know that. According to Einstein's equations the
visible part of the universe started at /*zero*/ size. Of course
no one takes that entirely seriously since at very small distances
quantum mechanics must invalidate Einstein's equations.
Brent
If you're invoking QM, aren't you conceding it started out very small,
if not exactly zero size? So it seems more plausible to assume it
started out very small, surely not infinite. But according to your
previous statements and those that I have read by cosmologists, the
assumption of infinite spatial extent is generally accepted and IMO
unwarranted.
If it's flat or has negative curvature then the equations imply it's
infinite or perhaps periodic (no matter what the scale factor is). If
the curvature is positive then it's finite and closed and the scale
factor can be taken to be the radius, so it indeed starts small in the
absolute sense. Atkatz and Pagels showed that only FRW universes that
are closed (positive curvature) or De Sitter (flat with a positive
cosmological constant) can "tunnel out of nothing".
http://www.quantum-gravitation.de/media/99f63994b9064eb6ffff8004fffffff2.pdf
So most cosmologists liked the closed universe model, until it was found
that expansion is accelerating. So now more of them look to some
modification of the De Sitter space universe.
Brent
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