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? AGIt'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. AGIt'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. AGI 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.
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