On 3/20/2025 1:12 AM, Alan Grayson wrote:
On Wednesday, March 19, 2025 at 11:49:50 PM UTC-6 Brent Meeker wrote:
On 3/19/2025 10:09 PM, Alan Grayson wrote:
On Wednesday, March 19, 2025 at 10:50:41 PM UTC-6 Brent Meeker wrote:
On 3/19/2025 9:14 PM, Alan Grayson wrote:
On Wednesday, March 19, 2025 at 3:28:40 PM UTC-6 Brent
Meeker wrote:
On 3/19/2025 4:56 AM, Alan Grayson wrote:
On Wednesday, March 19, 2025 at 5:40:48 AM UTC-6 John
Clark wrote:
On Wed, Mar 19, 2025 at 4:30 AM Alan Grayson
<[email protected]> wrote:
/> If the universe is infinite in spatial
extent, and we run the clock backward, is all
the mass/energy of the observable region
confined to a tiny or zero volume?/
*The short answer is nobody knows what will happen
if you run the clock back to zero, and the mystery
remains regardless of if the universe is finite or
infinite. Nobody knows what will happen when things
get super small because our two best physical
theories, Quantum Mechanics and General Relativity,
disagree with each other. Most believe that
something will prevent a zero volume from ever
occurring, but nobody knows what that "something" is. *
*
*
***John K Clark See what's on my new list at
Extropolis <https://groups.google.com/g/extropolis>*
Maybe it's a 5th force. What I'd like to know is this;
assuming an infinite spatial universe and that it gets
very very small as we run the clock backward, the
observable regions shrinks, but what happens to the
unobservable region? Quentin claimed to have an answer,
but I can't recall what it was. AG
All theories treat the unobservable regions as being
similar to the observable (what else could you
justify?). So every finite region, observable or not
shrinks to zero.
Brent
*But if every finite subset of an infinite set strinks to
zero, in the case the assumed infinite set is the spatial
extent of the universe, won't the infinite spatial set of
the universe also shrink to zero (which is what Quentin
denies)? AG*
*No.
Brent*
But, as I've shown, this contradicts basic set theory. AG
Basic set theory has no metric. Shrink to zero in meaningless for
a set.
Brent
"No" isn't an argument. It's just a claim. My argument is based on set
theory and topology. If an infinite set can be contained in a
countable set of finite sets,
But that's not the case. The number for finite sets is, hypothetically,
infinite. Space is a continuum, an order alpha1 infinity.
We should get back to what is actually shown by the FLRW model. It
assumes the universe isotropic and so can be characterized by a scale
factor, a. So the only variables are a and time t. Parameters are
pressure and mass/energy density which depend on a. Our present state is
taken to be the boundary condition at a=1. The the solution can be
propagated into the future and into the past. In the past a goes to
zero. In the future it can expand toward and asymptotic limit, expand
without limit, or contract to zero. All this is calculus, so it's
assuming a continuum of spacetime. The set theory measure of every
piece of spacetime is the same alpha1 infinity.
Brent
and if they represent spacetime, and each shrinks to zero, then so
will the original infinite set. But maybe the infinite set of
spacetime points cannot be contained in a countable set, in which case
we'd have to use the Axiom of Choice. But I'm not sure if the infinite
set of spacetime points can be covered or contained in an uncountable
set created by applying the Axiom of Choice. In any event, you need an
argument to establish your claim. AG
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