On Thursday, March 20, 2025 at 6:11:01 AM UTC-6 Quentin Anciaux wrote:
AG, your reasoning assumes that because each countable 4D ball shrinks arbitrarily close to zero, the entire universe must shrink as well. This misinterprets how infinity works in both set theory and general relativity. Shrinking finite regions doesn’t imply a finite universe. Each of your 4D balls represents a finite spacetime region, but an infinite number of shrinking finite regions does not make the total universe finite. Even if every individual region shrinks, an infinite set of them still covers all of space, preserving its infinite extent. The universe can remain infinite despite local contraction. Imagine an infinite 1D line divided into shrinking segments. Each segment gets smaller, but since there are infinitely many, the total length remains infinite. The same applies in higher dimensions: even as each 4D ball shrinks, the universe as a whole remains infinite because there is no bound on the number of shrinking regions. General relativity allows an infinite universe to contract everywhere without requiring a finite total volume. This is why an infinite universe can undergo a Big Bang—density increases everywhere without demanding a global contraction. Your argument assumes a globally shrinking boundary, implying that these 4D balls define the total size of the universe. *Their union does define the total size of the universe if they cover it, which they do. Your general argument is likely correct, but to be sure we have to deal with the convergence value of this union as the balls shrink in volume. AG* But in an infinite universe, no such global boundary exists. There is no edge where "shrinking" causes the entire structure to collapse into a finite size. An infinite universe remains infinite while every finite region contracts. Your logic would only apply if the universe were globally finite from the start. Since an infinite universe has no fixed size to contract, space simply becomes denser everywhere as you go back in time. Quentin -- 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 [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/4dada6f1-c186-4e99-a408-1e2640f968c4n%40googlegroups.com.
