On Wednesday, February 26, 2025 at 8:44:11 PM UTC-7 Brent Meeker wrote:
On 2/26/2025 2:24 AM, Alan Grayson wrote:
On Wednesday, February 26, 2025 at 1:22:21 AM UTC-7 Alan Grayson wrote:
On Tuesday, February 25, 2025 at 10:07:41 PM UTC-7 Brent Meeker wrote:
On 2/25/2025 7:59 PM, Alan Grayson wrote:
On Tuesday, February 25, 2025 at 6:40:35 PM UTC-7 Brent Meeker wrote:
On 2/25/2025 3:48 PM, Alan Grayson wrote:
On Tuesday, February 25, 2025 at 12:46:46 PM UTC-7 Brent Meeker wrote:
I think all cosmologist, like Hartle, recognize that *the observable
universe* was much smaller in the past. Which is perfectly compatible with
*the
universe* be spacially flat and infinite.
Brent
I fully anticipated that response. But why would the observable universe
behave radically different from the entire principle, particularly in light
of the Cosmological Principle? AG
It's not radically different. It's different in exactly the way that
finite subsets of infinite sets behave.
Brent
But if the observable universe contracts to zero volume, the entire
universe has a singularity, which is inherently contradictory. So, the
model is, to say the least, inconsistent. AG
It's not contradictory or inconsistent, it's unphysical, i.e. it can't be
physically realized; which just means the theory of general relativity
doesn't work there. This is not a surprise since GR is not a quantum
theory and if you're concerned with a subatomic scale region you'll
probably need a quantum theory.
Brent
My conjecture is that there's a fifth force, repulsive in Nature, that
prevents the mass of a high mass collapsing star to reach zero volume. AG
I don't imagine a quantum theory. More important, I can't grasp the idea of
the observable universe contracting to zero or near zero volume as we go
backward in time, while the unobservable universe remains infinite in
spatial extent. Can you grasp it? Can you explain it? AG
Yes and yes. If the universe is infinite then the ratio of its size to
that of any finite subset is infinite, no matter how large or small the
subset is. Imagine the infinite set of the integers. Consider the finite
subset {0,1,2,3,4,5,6,7,8,9,10,...,1e12}. It's size is obviously 1e12.
Now shrink the universe by striking every tenth number. Your subset is now
{0,1,2,3,4,5,6,7,8,9,11,...,1e12-1} and it's size is 1e12-1. But the
universe is still infinite.
Brentc
I know enough about set theory to have easily generated what you write
above. But math isn't physics. If the finite observable universe converges
to a singularity, we have a hypothetical universe which is not physically
possible, whether finite or infinite. So I am not sure how we can
distingush between an infinite and finite universe. Set theory does not
help. AG
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