You ask why it’s not even a possibility that finiteness is
required for high density. The answer is that GR and the FLRW
metric allow for infinite spatial extent at all times, even under
extreme density conditions. There’s no physical principle
preventing this, so the burden is on you to show why infinity at
high density would be impossible.
Although I posed it as impossible, but that's probably going too far.
I think It's possible that the entire universe is getting smaller as
we go back in time, and this accounts for its super high temperature
at or near the BB. AG
Quentin
Le mer. 12 févr. 2025, 19:41, Alan Grayson <agrays...@gmail.com> a
écrit :
On Wednesday, February 12, 2025 at 10:10:40 AM UTC-7 Quentin
Anciaux wrote:
Le mer. 12 févr. 2025, 17:55, Alan Grayson
<agrays...@gmail.com> a écrit :
On Wednesday, February 12, 2025 at 2:09:58 AM UTC-7
Quentin Anciaux wrote:
Le mer. 12 févr. 2025, 09:55, Alan Grayson
<agrays...@gmail.com> a écrit :
If the age of the universe is finite, which is
generally believed, then no matter how fast it
expands, it can never become spatially
infinite, So,*IF* it is spatially infinite,
this must have been its initial condition at
or around he time of the Big Bang (BB). But
this contradicts the assumption that it was at
a super high temperature at or around the time
of the BB.
AG, your assumption that a finite-age universe
must be spatially finite is flawed. If the
universe is infinite now, it was infinite at the
Big Bang,
That's what I wrote. AG
just in a much hotter and denser state everywhere.
The Big Bang wasn’t an explosion from a point
I didn't assume that. What it actually is, or was, we
don't know. But at that time it was hugely denser and
hotter than at present. AG
No, you initially framed it as a contradiction—"If it’s
infinite now, it must have been infinite at the Big Bang,
but that contradicts the high temperature assumption."
That’s what was wrong. There’s no contradiction between an
infinite universe and high density. If you now accept
that, great, but don’t pretend that was your original point.
I assumed that if the universe were infinite, it couldn't have
become so in finite time, so IF infinite that must have been
its initial condition. I later added, in summary, or that's
what I meant to do, that this is contradictory to a super high
temperature at the time of the BB. You claim this is
inconsistent with GR. Can you prove that? AG
Yet, your reasoning implicitly relies on treating the
universe as if it "shrinks" to a single location when run
backward. A spatially infinite universe was never
"smaller" in an absolute sense—just denser everywhere.
Well, that's what all the diagrams of the evolution of the
universe show, that it becomes smaller as we go back in time,
begins as a point, and what I've heard or read what some
cosmologists claim. AG
but a transition from an extremely dense, uniform
state, which applies whether the universe is
finite or infinite.
Eternal inflation suggests the universe was
already infinite before the Hot Big Bang phase.
Sure, provided eternal inflation is occurring, but
it's speculative, as is my conclusion. Most
cosmologists believe it was smaller in the past than
at present, as implied by present day expanson run in
reverse. AG
No, they believe the observable universe was smaller.
Why just the observable region? AG
That doesn’t mean the entire universe was ever finite.
The observable universe was once small and dense,
but the entire universe could have been infinite
at all times.
Yes, COULD HAVE BEEN. I assumed, for the sake of
argument, that it COULD NOT HAVE *BECOME* INFINITE IN
FINITE TIME, and THEN inferred what that implied;
namely, that it became infinite at the time of the BB.
Also, if you believe in the Cosmological Principle, if
the observable universe was finite, then so was the
entire universe.AG
Spatial flatness doesn’t imply finiteness
I didn't assume it does. In fact, I assumed the
reverse, as do cosmologists. I don't object to your
criticisms, but you seem to be reading me with a
jaundiced eye. AG
—flat, infinite universes expanding from a dense
state are fully consistent with general relativity.
Does my conjecture conflict with GR, or is it also
consistent? AG
Yes, if you’re implying an infinite universe can’t be
dense at early times or that it had to "become" infinite
I am assuming it couldn't become infinite in finite time, so,
IF it is infinite now, it had to BE infinite at the time of
the BB. AG
There’s no contradiction between a spatially
infinite universe and high density at early times.
The problem isn’t with cosmology—it’s with your
mistaken assumption that high density requires
finiteness.
My assumption isn't necessarily mistaken. Rather, it's
another possibility. AG
No, it’s mistaken. Assuming high density requires
finiteness is a misunderstanding of both GR and cosmology.
You claim it's not even a possibility. Why not? AG
Quentin
Quentin
IOW, if we run the clock backward, the
universe seems to get incredibly small, and
for *this reason* incredibly hot, roughly
analogous to a highly compressed gas.
Therefore, it cannot have a flat global
geometry, since such a geometry is infinite in
spatial extent. QED. AG
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