So there are infinitely many identical universes preceding a measurement. How are these universes distinct from one another? 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?).

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?


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 <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

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