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Have you aware of Adrian Kent's critiques of (many of) these attempts?

https://arxiv.org/abs/0905.0624




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


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.


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.


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.


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.


> If that can be mathematically derived it probably requires some axioms of probability.

I have no problem with axioms of probability being used. I just think you need to be explicit about what the fundamental postulates of the theory are and what is being derived. Clearly, in order to make predictions in line with experiment, a physical meaning must be assigned to the norm-squared of the wave-function. Most modern accounts don't make this a fundamental postulate, so it needs to be derived in a coherent manner.

> it's not a valid objection because the situation is much better than any other theory of probability

Beside the point. If our best theory of nature is flawed then we need to be honest about it.

> like frequentism!

OK- what about Quantum Bayesianism? That's a coherent and consistent account of quantum probabilities. It just lacks in what one can really say about the underlying reality.

> it's clear how that would work classically and how it's analogous to the WMI with equal branch weights.

I think its a false analogy. There aren't actually two copies of you in MWI, just a superposition of two different states. I need an explicit process by which classical probabilities emerge, not an intuitive allusion to how it's kind of like some classical process. A superposition is not classical; that's the whole issue!


We are not being dishonest here. Even if Born's rule was postulated, WMI would still have the most technical merit. Physics can never have a proof anyway.

And the Born rule is just assigning probability to the norm-squared of the wave function, so I'm not sure why you think it's assumed in a derivation of the Born rule itself. That would make the proof a tautology. The assumptions are laid out explicitly for the various proofs throughout the series of papers and critiques.

QBism is all about belief of agents and if you think that's a valid approach than the decision theoretic proof from Deutsch and Wallace shouldn't be hard to accept. Actually a derivation of the Born rule in QBism must take the same form.

A superposition of two different states is two copies after decoherence. They occupy different parts of the wave function and they share nothing, so can't interact. In configuration space (not classical space) they are separated "wave packets".




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