# Re: The probability problem in Everettian quantum mechanics

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On 11 Oct 2013, at 13:09, Pierz wrote:```
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On Friday, October 11, 2013 12:25:45 PM UTC+11, Brent wrote:
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So there are infinitely many identical universes preceding a measurement. How are these universes distinct from one another?
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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.
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With comp too, it is best to see one consciousness differentiating than actual splitting of "universes".
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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?).
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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 (?).
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You have to take all the programs, and all computations. Your relative 1-indeterminacy bears on all computations going through your state.
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There is an uncountable set of such computations, as they dovetail on the reals. Just keep in mind that the UD is enough dumb to implement the infinite iterated self-duplication, which leads to uncountably many histories.
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(Having said that, there are many ways to put probability and measure on any set, finite, enumerable, non enumerable, etc. Sometimes people just relinquish the "sigma-additivity" condition, and still get something very close to a measure).
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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?
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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.
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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.
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That would have been nice to know. I really love the correspondence between Max Born and Albert Einstein. I think both would have accepted Everett, even if with some grimaces, like François Englert and many quantum cosmologists.
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I disagree with the idea that Everett propose a new interpretation of QM. Everett proposes a new theory, which is just Copenhagen without the collapse. Everett himself talk about a new formulation of QM, not a new interpretation. that is not so important, except when we begin to use logic, which forces to be precise on what is a theory, and what is an interpretation of a theory.
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And Everett QM obeys Occam in the sense that he used less hypotheses.

Bruno

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Brent

On 10/10/2013 6:11 PM, Pierz wrote:
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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?
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On Saturday, October 5, 2013 2:27:18 AM UTC+10, yanniru wrote:
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Foad Dizadji-Bahmani, 2013. The probability problem in Everettian quantum mechanics persists. British Jour. Philosophy of Science IN PRESS.
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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.
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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)
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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
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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.
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Richard
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