On Friday, October 11, 2013 12:25:45 PM UTC+11, Brent wrote: > > So there are infinitely many identical universes preceding a > measurement. How are these universes distinct from one another? > They aren't 'distinct'. The hypothesis is that every universe branch contains an *uncountable* infinity of fungible (identical and interchangeable) universes. While this seems extravagant, it actually kind of makes more sense than the idea of a universe "splitting" into two (where did the second universe come from?). Instead, uncountable infinities of universes are differentiated from one another. Quantum interference patterns arise because of the possibility of universes merging back into one another again.
> Do they divide into two infinite subsets on a binary measurement, or do > infinitely many come into existence in order that some branch-counting > measure produces the right proportion? Do you not see any problems with > assigning a measure to infinite countable subsets (are there more even > numbers that square numbers?). > > The former. Deutsch goes into the problem of infinite countable sets in great detail and shows how this is *not* a problem for these uncountable infinities (as Russell points out)), whereas it may be a problem for Bruno's computations - a point I've tried to argue with Bruno, but he bamboozles my sophomoric maths with his replies. To me it seems you can't count computations that go through a state, because for every function f that computes a certain function, there is also some function f1 that also computes f such that f1 = f + 1 - 1. But maybe that can be solved by counting only the functions with the least number of steps (?). > And why should we prefer this model to simply saying the Born rule derives > from a Bayesian epistemic view of QM as argued by, for example, Chris Fuchs? > > I don't know about Chris Fuchs, although isn't that just Copenhagen? It's clear that one would need strong reasons to favour MWI with its crazy proliferation of entities, which at first blush seems to run against Occam's razor. However Deutsch makes a damn good fist of explaining why we in fact have those reasons. For instance, when a quantum computer calculates a function based on a superposition of states, MWI can explain where these calculations are occurring - in other universes. The computer is exploiting the possibility of massive parallelism inherent in that infinity of universes. It is entirely unclear how these calculations occur in the standard interpretation. MWI also solves the problem of what happens to non-realized measurement states once a system decoheres. And of course it gets around the intractable difficulties of non-computable wave "collapse". So it's a case of choose your poison: infinite universes or conceptual incoherence. I'll take the former, even though in some ways I'd "like" the universe (or the multiverse) better if it wasn't that way. Max Born was my great grandfather. I wonder what he would have made of Everett if he'd been a bit younger. When he died in 1970, it was still probably too out there for him to have seriously considered. > Brent > > On 10/10/2013 6:11 PM, Pierz wrote: > > I'm puzzled by the controversy over this issue - although given that I'm > not a physicist and my understanding comes from popular renditions of MWI > by Deutsch and others, it may be me who's missing the point. But in my > understanding of Deutsch's version of MWI, the reason for Born > probabilities lies in the fact that there is no such thing as a "single > branch". Every branch of the multiverse contains an infinity of identical, > fungible universes. When a quantum event occurs, that set of infinite > universes divides proportionally according to Schroedinger's equation. The > appearance of probability arises, as in Bruno's comp, from multiplication > of the observer in those infinite branches. Why is this problematic? > > On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote: >> >> Foad Dizadji-Bahmani, 2013. The probability problem in Everettian quantum >> mechanics persists. British Jour. Philosophy of Science IN PRESS. >> >> ABSTRACT. Everettian quantum mechanics (EQM) results in ‘multiple, >> emergent, branching quasi-classical realities’ (Wallace [2012]). The >> possible outcomes of measurement as per ‘orthodox’ quantum mechanics are, >> in EQM, all instantiated. Given this metaphysics, Everettians face the >> ‘probability problem’—how to make sense of probabilities, and recover the >> Born Rule. To solve the probability problem, Wallace, following Deutsch >> ([1999]), has derived a quantum representation theorem. I argue that >> Wallace’s solution to the probability problem is unsuccessful, as follows. >> First, I examine one of the axioms of rationality used to derive the >> theorem, Branching Indifference (BI). I argue that Wallace is not >> successful in showing that BI is rational. While I think it is correct to >> put the burden of proof on Wallace to motivate BI as an axiom of >> rationality, it does not follow from his failing to do so that BI is not >> rational. Thus, second, I show that there is an alternative strategy for >> setting one’s credences in the face of branching which is rational, and >> which violates BI. This is Branch Counting (BC). Wallace is aware of BC, >> and has proffered various arguments against it. However, third, I argue >> that Wallace’s arguments against BC are unpersuasive. I conclude that the >> probability problem in EQM persists. >> >> http://www.foaddb.com/FDBCV.pdf >> Publications (a Ph.D. in Philosophy, London School of Economics, May >> 2012) >> ‘The Probability Problem in Everettian Quantum Mechanics Persists’, >> British Journal for Philosophy of Science, forthcoming >> ‘The Aharanov Approach to Equilibrium’, Philosophy of Science, 2011 >> 78(5): 976-988 >> ‘Who is Afraid of Nagelian Reduction?’, Erkenntnis, 2010 73: 393-412, >> (with R. Frigg and S. Hartmann) >> ‘Confirmation and Reduction: A Bayesian Account’, Synthese, 2011 179(2): >> 321-338, (with R. Frigg and S. Hartmann) >> >> His paper may be an interesting read once it comes out. Also available >> in: >> ‘Why I am not an Everettian’, in D. Dieks and V. Karakostas (eds): >> Recent Progress in Philosophy of Science: Perspectives and Foundational >> Problems, 2013, (The Third European Philosophy of Science Association >> Proceedings), Dordrecht: Springer >> >> I think this list needs another discussion of the possible MWI >> probability problem although it has been covered here and elsewhere by >> members of this list. Previous discussions have not been personally >> convincing. >> >> Richard >> > -- > 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] <javascript:>. > To post to this group, send email to [email protected]<javascript:> > . > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > > No virus found in this message. > Checked by AVG - www.avg.com > Version: 2014.0.4158 / Virus Database: 3609/6739 - Release Date: 10/10/13 > > > -- 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 post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. 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