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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/9134e606-3a1c-4f51-a78e-de1e98ca9aecn%40googlegroups.com.