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shminux comments on A case study in fooling oneself - Less Wrong
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My best understanding of the MWI's take on the Born rule is that the ratio of the number of branches for each outcome to the total number of branches gives you the probability of each outcome. Both numbers must be finite for the division to make sense. If you cannot count branches, you cannot calculate probabilities, reducing the model into just a feel-good narrative (with the Born rule inserted by hand). Refusing to acknowledge this issue is similar to what Mark does in the story.
This is a relevant discussion of the issue.
No, the probabilities in MWI are not counting discrete worlds. A world with large amplitude is not multiple identical worlds but a single world that is more real. Leaving aside the actual interpretation, your suggestion is mathematically incoherent. You seem to be demanding that the probabilities in QM are rational numbers with bounded denominator. This is an extremely radical position. It would simplify the ontology a lot, but there is no reason to believe that quantum mechanics can be approximated by a system where the amplitudes are not infinitely divisible. More precisely, a large finite subgroup of the unitary group does not look like the unitary group, but like a torus.
Sorry, I did not get your point about the group and subgroups, or at least not its relevance to the question. I would expect that to derive Born probabilities one has to assign measures to different worlds (how else would you express mathematically that "A world with large amplitude is not multiple identical worlds but a single world that is more real."?) I agree that counting branches is not the only way to do it, just the most obvious one. Unfortunately, none of the ways of assigning "strength" to different branches seems to work any better than this naive one in deriving the Born rule (that is to say, they do not work at all).
This is not the way the Oxford Everettians understand the Born rule. See the Hilary Greaves paper I linked to for a discussion of their decision-theoretic approach to probabilities in the MWI. This approach has its problems, but they are problems that the Everettians acknowledge and attempt to address (not entirely successfully, in my opinion). That's very different from Mark's attitude.
Also, the Orzel post you linked to doesn't seem to support your contention. Where do you see him committing himself to the branch counting appproach you propose? (EDIT: Actually, I see that there is discussion of the issue in the comments to that post, which is probably what you meant.)
From the paper:
This must a bad wording, or something, otherwise why does a "rational" agent who does not believe "she lives in an Everettian multiverse" can still confirm the Born rule experimentally time after time?
The proof does not address rational agents who do not believe they are in an Everettian multiverse. They would have other reasons for using the Born rule.
Is that necessarily true?
If they are infinite, then there should at least be a well-defined way to take a limit (or one of its generalizations), which amounts to nearly the same thing, constructing a sequence of ratios of finite numbers and proving convergence.