On Wednesday, February 26, 2025 at 9:41:35 PM UTC-7 Alan Grayson wrote:

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 


If we assume an infinite universe and run the clock backward, is it 
reasonable to conclude that the singularity we imagine forming in the 
observable region, is identically the same singularity for the entire 
universe? Secondly, why do we imagine the hypothetical singularlty 
indicates the GR fails in this situation? After all, if the expanding 
universe is determined by measurements, and the average distances between 
galaxies decreases as the clock runs backward is also determined by 
measurements, what has this to do with GR, since it's all measurement 
determined? TY, AG 

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