On Tue, Sep 16, 2025 at 1:05 AM Brent Meeker <[email protected]> wrote:
> * > John correctly observes that he hasn't proposed branch counting, but > requires that the Born rule attach probability weights to branches. But > he's wrong that nobody ever proposed branch counting. Even Sean Carroll, > an Everettian, discusses differential branching as a way to realize the > Born rule.* > *I've read Sean Carroll's books and he does indeed discuss branch counting, but then he goes on to explain why it WILL NOT WORK. See for yourself in a paper that he wrote with Charles T. Sebens:* *Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics <https://arxiv.org/pdf/1405.7577>* *Right there in the abstract they say "it is tempting to regard each branch as equiprobable, but we give new reasons why that would be inadvisable".* *And on page 14 of the article they say: * *"It is tempting to think that the number of copies of Alice cannot change without her physical state changing—this is the way things work in classical physics. But, in Everettian quantum mechanics, changes that purely affect her environment can change the number of copies of Alice in existence"* *And on page 17 they say: * *"In this section we will derive the Born rule probabilities as the rational assignment of credences post-measurement pre-observation. We will first derive the rule in a case with two branches that have equal amplitudes, then use similar techniques to treat a case with two branches of unequal amplitude. It is straightforward to extend these methods to more general cases **(see appendix C)"* *And finally, although they have two words in common, "differential branch counting" is very different from naïve "branch counting". Instead of discrete branches, in* *differential branch counting the wave function of the Multiverse splits in a way that is similar to a continuum. If it really is a continuum then it's impossible to count them because there is literally an uncountable number of universes. However you can group similar universes together in a countable, and possibly finite, number of sets; in a previous post I made the analogy of cutting a rope, which contains an infinite number of points, into a finite number of pieces of rope of various lengths, putting the pieces into a hat and then picking one out of that hat at random. If you knew the number of cuts that were made and their length then you could assign a probability of picking any particular piece out of that hat. * *If you want something that is never negative and always adds up to exactly 1, and is* *additive (if you group together multiple branches then the total weight is the sum of the individual weights) **then ∣ψ∣^2 is the only way to obtain a probability. **Gleason’s theorem proves that in any dimension greater than or equal to 3, the only probability measure that is compatible with the structure of Hilbert space is the Born rule.* *You can thus assign a measure over the branches, where the density of branches corresponds to ∣ψ∣^2, you weigh them according to their “thickness” or “differential weight” in Hilbert space. As I've mentioned before, when I see a map of branching universes drawn on a 2D surface, I imagine the line having a thickness determined by ∣ψ∣^2 because that is the natural measure of Hilbert space; it's what makes Hilbert space be Hilbert space. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* hsb -- 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/CAJPayv14o%3DDrQVJrchkwtjKggeeVUqj0Jk8wjawPSFr6mase%2BQ%40mail.gmail.com.
