3 ms·

I know of 3 modern ways to derive the Born rule for WMI and all have various reasonable (yet not airtight) assumptions. In physics you can never really prove a

I know of 3 modern ways to derive the Born rule for WMI and all have various reasonable (yet not airtight) assumptions. In physics you can never really prove anything, but there is no serious technical issues here. Actually probability (the Born rule) is much better defined in WMI then in any other interpretation or even classically. A related beautiful thing about WMI is that is creates genuine subjective probability inside a deterministic system (the wave function). One thing QM shows us is that we experience real random events, which cannot just come from lack of knowledge. Yet, if you are a computer expert you should know that it's impossible to create real randomness without an outside source. And the universe has no outside sources at all, by definition. Also, it's clear that the basis of Weinberg's objection to WMI is philosophical if you don't selectively quote him so much. If he was concerned about deriving the Born rule we would talk about the specific assumptions he disagrees with.

n4r9 10y ago
Have you aware of Adrian Kent's critiques of (many of) these attempts? https://arxiv.org/abs/0905.0624 https://arxiv.org/abs/0905.0624
- akvadrako 10y ago
  I have read lots of critiques about the Born rule derivations but I've missed this one. Thanks for the pointer. He is only attacking one attempt, the decision-theoretic one. I have trouble finding his point in this paper because it's so rambling but he seems to be saying: > It seems prima facie surprising to claim that mathematical analysis could show that Born-weight mean utilitarianism, or any other strategy, is the unique rational way of optimizing the welfare of one’s own, and other people’s, many future selves in a multiverse. Okay, sure - but it's also just as ridiculous to say that you can prove with no assumptions how a rational agent should act in a classical world. Actually there is no explanation of probability in the classical world that's as clear as that in a multiverse, where you have actual proportions of outcomes. All you really need is to assume that branches of equal magnitude have an equal chance of occurring and the Born rule becomes obvious. That seems like a safe assumption to me but you can't prove it beyond all doubt without some axioms of probability. EDIT: I found a critique of his paper you might also want to read: https://arxiv.org/pdf/1111.2563.pdf https://arxiv.org/pdf/1111.2563.pdf
  - n4r9 10y ago
    I'm not sure what you mean by "safe". My understanding of Kent's objection is that there's no explanation for why the norm-squared magnitude is related to probability in the first place.
    - akvadrako 10y ago
      The simplest way to derive the Born rule is to assume "branches" of equal magnitude have equal chances of happening. This isn't controversial because it's a very basic part of QM that is demonstrated by experiments and it seems quite natural too. Yet even that assumption above can be weakened - that's what the derivations are trying to show to the critics because they find WMI so hard to accept for unrelated reasons. This is in contrast to the situation in collapse interpretations where the Born rule itself is simply postulated. And in classical mechanics, we need to resort to frequentist explanations which are pretty weak. So we have already gone quite far beyond the best explanations of probability in any other system.
      - n4r9 10y ago
        It is kinda controversial. At least in relation to MWI; the validity and meaning of that assumption forms the basis of much of the criticism of MWI. If there were a rigorous derivation of the Born rule as a logical consequence of a global state undergoing unitary evolution, then I and many others would be much more convinced. The other part of the problem is how/why observational outcomes occur in a probabilistic fashion in the first place. You keep saying that one or other branch "occurs" or "happens", but in MWI they're all happening. For some reason the observer only experiences one particular strand of their own superposition, and with a somewhat arbitrary probability to boot. It's not like that's the strand they're "actually in" but ignorant of. This is very different from subjective knowledge of a deterministic universe.
        akvadrako 10y ago
        What's not controversial is that empirically the equal branches are equally likely. If that can be mathematically derived it probably requires some axioms of probability. But still, it's not a valid objection because the situation is much better than any other theory of probability, like frequentism! The second problem is easy to see with the classical cloning analogy. Say, someone creates two clones of you and kills the original. Your experience will split, one version for each clone. I think it's clear how that would work classically and how it's analogous to the WMI with equal branch weights.
- deleted 10y ago
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n4r9 10y ago

Have you aware of Adrian Kent's critiques of (many of) these attempts? https://arxiv.org/abs/0905.0624 https://arxiv.org/abs/0905.0624

akvadrako 10y ago
I have read lots of critiques about the Born rule derivations but I've missed this one. Thanks for the pointer. He is only attacking one attempt, the decision-theoretic one. I have trouble finding his point in this paper because it's so rambling but he seems to be saying: > It seems prima facie surprising to claim that mathematical analysis could show that Born-weight mean utilitarianism, or any other strategy, is the unique rational way of optimizing the welfare of one’s own, and other people’s, many future selves in a multiverse. Okay, sure - but it's also just as ridiculous to say that you can prove with no assumptions how a rational agent should act in a classical world. Actually there is no explanation of probability in the classical world that's as clear as that in a multiverse, where you have actual proportions of outcomes. All you really need is to assume that branches of equal magnitude have an equal chance of occurring and the Born rule becomes obvious. That seems like a safe assumption to me but you can't prove it beyond all doubt without some axioms of probability. EDIT: I found a critique of his paper you might also want to read: https://arxiv.org/pdf/1111.2563.pdf https://arxiv.org/pdf/1111.2563.pdf
- n4r9 10y ago
  I'm not sure what you mean by "safe". My understanding of Kent's objection is that there's no explanation for why the norm-squared magnitude is related to probability in the first place.
  - akvadrako 10y ago
    The simplest way to derive the Born rule is to assume "branches" of equal magnitude have equal chances of happening. This isn't controversial because it's a very basic part of QM that is demonstrated by experiments and it seems quite natural too. Yet even that assumption above can be weakened - that's what the derivations are trying to show to the critics because they find WMI so hard to accept for unrelated reasons. This is in contrast to the situation in collapse interpretations where the Born rule itself is simply postulated. And in classical mechanics, we need to resort to frequentist explanations which are pretty weak. So we have already gone quite far beyond the best explanations of probability in any other system.
    - n4r9 10y ago
      It is kinda controversial. At least in relation to MWI; the validity and meaning of that assumption forms the basis of much of the criticism of MWI. If there were a rigorous derivation of the Born rule as a logical consequence of a global state undergoing unitary evolution, then I and many others would be much more convinced. The other part of the problem is how/why observational outcomes occur in a probabilistic fashion in the first place. You keep saying that one or other branch "occurs" or "happens", but in MWI they're all happening. For some reason the observer only experiences one particular strand of their own superposition, and with a somewhat arbitrary probability to boot. It's not like that's the strand they're "actually in" but ignorant of. This is very different from subjective knowledge of a deterministic universe.
      - akvadrako 10y ago
        What's not controversial is that empirically the equal branches are equally likely. If that can be mathematically derived it probably requires some axioms of probability. But still, it's not a valid objection because the situation is much better than any other theory of probability, like frequentism! The second problem is easy to see with the classical cloning analogy. Say, someone creates two clones of you and kills the original. Your experience will split, one version for each clone. I think it's clear how that would work classically and how it's analogous to the WMI with equal branch weights.
deleted 10y ago
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