On Thursday, March 20, 2025 at 2:12:29 AM UTC-6 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 <agrays...@gmail.com> 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, 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 The entire universe can be covered with a countable set of 4 dimensional balls, each centered at integer clock readings, with unit radii, each ball includes its boundary. No need in this model for applying the Axiom of Choice. Each ball is infinite in the number of events it contains, and each is closed since it contains its boundary, so we can consider each ball as a finite region of spacetime. As time runs backward, each ball shrinks as close to zero as desired, and ISTM that the entire universe shrinks with it. How can the universe remain infinite in spatial extent in this situation? 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/e506485b-8375-4025-be5f-a771b9c422c2n%40googlegroups.com.
