On 11 Nov 2017, at 07:59, agrayson2...@gmail.com wrote:
On Friday, November 10, 2017 at 11:32:13 PM UTC-7,
agrays...@gmail.com wrote:
On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:
On 11/10/2017 10:01 PM, agrays...@gmail.com wrote:
On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote:
On 11/10/2017 1:01 PM, agrays...@gmail.com wrote:
On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote:
On 11/10/2017 4:06 AM, Alan Grayson wrote:
On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker
<meek...@verizon.net> wrote:
On 11/9/2017 9:15 PM, Alan Grayson wrote:
On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker
<meek...@verizon.net> wrote:
On 11/9/2017 8:55 PM, agrays...@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
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
Modification of De Sitter will be flat and therefore open. I find
the open universe model in contradiction to the finite age of the
universe. Is this unreasonable?
Well, if you have an infinite universe, and toward the past it is
scaled by a factor a, and a->0 does the universes size go to zero?
Why is the closed universe model less favored when it was
discovered that expansion is accelerating?
Because the De Sitter universe that can "tunnel from the vacuum"
automatically has a positive cosmological constant.
Brent
Unfortunately, my understanding of the scale factor and
cosmological constant as they relate to the various geometries is
insufficient to appreciate your comments. Maybe you could restate
your above comments with that in mind. TIA.
Didn't you read Vic's "Comprehensible Cosmos"? Why are you over
here on the everythinglist asking physics questions anyway, Alan?
You should try the stackechange or quora.
Brent
I wasn't aware of those sites. Since "everything" includes physics,
I thought this group would be appropriate. And I see some topics
here include physics. I don't see the harm.
Sometimes we discuss physics, but in general it is in or through
relations with fundamental problems, including the mind-body problem,
notably.
You might look at the Space-Times Series (it exists on YouTube, link
below). I just "understood" (as far as a mathematician can understand
physics of course) why the "tunneling from the vacuum" imposes a
positive cosmological constant to some of solution of Einstein's GR
equation, or others (probably the De Sitter one I guess).
https://www.youtube.com/watch?v=X5rAGfjPSWE&t=712s
(That is not the episode which makes me get what Brent said.
I haven't read "Comprehensible Cosmos", but have done other reading.
Vic had a way of glibly dismissing complex issues and it turned me
off. Nevertheless, I basically respect his work. However, I really
don't believe the Cosmos is Comprehensible. In fact, QM tells me the
opposite. Ultimately, it's IRREDUCIBLY RANDOM as I think Bohr
believed, and thus, IMO, INCOMPREHENSIBLE. God DOES play dice with
the Universe. (Opinions can differ.)
You seem to take for granted that Reality is the or a Physical
Reality. But where that Physical reality comes from, and what is
physical about it?
Theoretical computer science, and its arithmetization, entails that if
we assume the local finiteness of the observers, the observable
correctly inferable of almost all finite observers emerges from a
lattice of computations restrained by self-correctness self-
referential relations.
God get just asleep and lost itself innumerably in a labyrinth of
dreams. technically, this should (and seems already) reduce the laws
of the observable to arithmetical self-reference (unfortunately only
well known by logicians (self-reference is handled in the arithmetical
sense explained in Gödel 1931 paper.
The Universal machine of Turing has a theology (a science of its own
limitation toward truth if truth exists) which includes physics, so it
is testable/refutable/improvable.
All mystics said this: the Universe/Truth is in your head. So I
suggest we compare the Universe which is in the head of the Universal
(Turing) machine and what we infer from observations.
You are right, there is something irreducibly random, if only the
first person view of self-duplication i Arithmetic. But there are
enumerable pieces of computations with an extreme redundancy in
elementary Arithmetic (which is Turing complete). Physics is a first
person plural view of arithmetic, and there must be derivation of the
role of each pieces of its mathematics, like the group theory implied.
Then the theology separates the true from the rationally justifiable,
etc. The big discovery is the discovery of the universal machine (Emil
Post, Alan Turing, Stephen Kleene, ...). It lives already in the
diophantine polynomial equations.
Bruno
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