On 11 Nov 2017, at 21:50, [email protected] wrote:
On Saturday, November 11, 2017 at 12:40:45 PM UTC-7, Bruno Marchal
wrote:
On 11 Nov 2017, at 07:59, [email protected] wrote:
On Friday, November 10, 2017 at 11:32:13 PM UTC-7,
[email protected] wrote:
On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:
On 11/10/2017 10:01 PM, [email protected] wrote:
On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote:
On 11/10/2017 1:01 PM, [email protected] 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
<[email protected]> wrote:
On 11/9/2017 9:15 PM, Alan Grayson wrote:
On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker
<[email protected]> wrote:
On 11/9/2017 8:55 PM, [email protected] 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'll watch it. TY. I could be mistaken, but I thought the CC is (a
possibly IMPOSED) positive for an expanding universe. Before it was
discovered that the expansion is accelerating, cosmologists
preferred a closed, finite geometry; presumably a huge expanding
hypersphere. But Brent wrote that the open, flat, infinite model
became preferable after that discovery, presumably because
"tunneling from the vacuum" automatically IMPOSES a positive
cosmological constant. Is it the automatic imposition of a positive
CC that makes the open, flat, infinite model preferable?
That is my feeling, from what I can understand. I work on "physics"
from the other side (the possible observable of the universal turing
machine): that explains the bottom symmetries, the quantum logic and
alternate dream, and "duration", but it will take many generations of
mathematics to derive particles, spaces and (physical) times (if those
things exist). I suspect that mechanism could imply a infinite
physical past, making the "block space time" infinite. The physical is
the whole border of the "mind of the universal turing machine", but
that does not make it infinite automatically, due to many group
equivalence class.
This is really a huge change in perspective (and FWIW, not one I am
happy with).
Already with the very weak Robinson Arithmetic, shit happens.
With Peano arithmetic, shit happens, but also the guilt, and the
questions.
If you don't like something, expect it to be true or plausible.
Beware, perhaps, wishful thinking for the fundamental questions.
(although even that is an open problem, and by some token, the
"fundamental equation" of the mind, of the arithmetically sound
universal machine looks like a sort of wishful thinking formula (Löb's
formula, B(Bp -> p) -> Bp). If you convince Peano-Arithmetic that if
ever proving the existence of Santa Klaus entails the existence of
Santa Klaus, then Peano Arithmetic will prove the existence of Santa
Klaus!
I wonder; does the imposition of a positive CC ALSO automatically
imply open, flat, and infinite? TIA, AG
I don't know.
I don't know if there is an well definite answer for all solutions of
Einstein's equation, and I am not sure of the numerical approximations
made.
I content myself to contemplate the spectacle as a lazy layman. I
admire the field, but it misses (for methodological simplification)
what I think is the main ingredient, if interested in the very
fundamental question including consciousness, which is the notion of
"finite observer", which leads to the invariance of both theology and
physics, for the base theory. Of course, using this is not useful to
make direct prediction, only to make sense of the big picture.
No doubt that there is a physical reality, but when we assume
mechanism, we can no more invoke it to justify the experience of the
mind, we need to extract the appearances of the observable from number
self-reference. It fits up to now (at place where many have expected
the collapse of the theory).
Bruno
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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