>Several attempts following the realist approach have come close to deducing rules like the Born rule that we know work well experimentally, but I think without final success.
which is kind of the heart of things.
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.
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
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.
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.
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.
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!
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".
I don't think that's the only reason people are mystified. From what Weinberg says, and I've heard from other physicists, when you get to the root of the issue they just won't accept a multiverse theory.
It has profound philosophical consequences, so I guess they go looking for ways to make their understanding of QM fit their strongly held preconceptions. Some avoid this fact you just mentioned, but others fight the Born rule derivations or wrongly apply Occam's Razor or have more original objections.
They don't have to. But they do have to accept that entanglement and measurement are the same physical phenomenon.
But I am not saying they "have to" - I'm saying that is their reason for not accepting the bare formalism.
> But I am not saying they "have to" - I'm saying that is their reason for not accepting the bare formalism.
Well, OK, but then the burden is on them to come up with something better. QM is one of the most thoroughly tested scientific theories of all time. If you want to call yourself a scientist you can't legitimately reject it just because it doesn't make you feel warm and fuzzy inside.
The fact that we accept QM because it predicts the outcome of experiments is philosophy. So I could theoretically imagine someone holding the belief in our universe being what it seems higher than mathematical sense.
Yet my primary point is physicists are just human and have all the same irrational tendencies as the rest of us. You can't ignore their feelings if you hope to convince them of something.
Likewise, you are constantly bombarded with overwhelming evidence that you are a classical physical entity living in a classical universe. But that is not true either. It's a very good approximation to the truth, good enough for most day-to-day purposes, but it is not the truth.
You can choose to accept these facts, or you can choose to bury your head in the sand. But you cannot legitimately say that there is a "problem with quantum mechanics" when in fact what is going on is that you have chosen to bury your head in the sand. There is no more a "problem" with quantum mechanics than there is a "problem" with relativity, evolution, or the Copernican theory. There is no intractable mystery here, only people who choose not to accept what the math is telling them.
I don't think Ron Garret even touched on the Born rule, Everett of many worlds just hand waves and assumes it. The attempts I've seen are basically of the form that if the rule was different from the probability equaling the absolute amplitude squared then reality wouldn't come out as we find, so it must be so, which is not much of an explanation in my book.
It's true that I don't talk about the Born rule or multiple worlds in the paper, but I do talk about multiple worlds in the video (at the end, during the Q&A) and in the blog posts I linked to above.
As for the Born rule, what kind of an explanation are you hoping for? Some things can't be explained beyond, "That's just how it is." For example, why do the fundamental physical constants have the values that they have?
Maybe this will help:
In fact, I would even go so far as to say that if you are going to merely "enforce" the Born rule without justification, then you are no longer proposing an Everettian interpretation. The whole point of these interpretations is that simply "unitary quantum mechanics" describes the whole universe.
Everett himself however seems to basically "enforce" the Born rule without justification so I guess that would be Everettian.
See https://www-tc.pbs.org/wgbh/nova/manyworlds/pdf/dissertation... page 34
>we define a square-amplitude distribution, Pi...
Probability is a funny thing to deal with. Say you have an experiment where you push a button and a red light or green comes on based on some quantum effect but the green light is 1000x more likely. In many worlds you'd end up with different worlds with an observer seeing one or another but it's tricky to see how the 1000x thing comes in.