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Indeed it's not that solved. A big problem is as Weinberg puts it

>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.

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.

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


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".

Just because Steven Weinberg is unaware of or does not accept the solution does not mean that the problem is not in fact solved.

If you are religiously convinced that the QIT interpretation is the only true one that doesn't make it true. For me it is just one of the many interpretations and I think that it is wrong on par with all the others that I'm aware of. If this wasn't the case then the measurement problem and the unification with the relativity theory (or with a theory that supersedes the relativity) would be already solved today. I'm really not in the field, but I don't think that anyone that actively works on QM is debating on solved problems.

I am absolutely not religiously convinced that QIT is the only true explanation. In fact, I explicitly say at the end of my talk that it is not, that multiple-worlds is equally valid, and which you choose is a matter of personal preference. But if want to argue that no solution exists (and this is Weinberg's claim) then you have to consider all of the solutions on the table, and Weinberg does not. He deliberately ignores the fundamental (and IMHO ultimately clarifying) fact that entanglement and measurement are intimately related (and are in fact the same physical phenomenon). It is entirely unsurprising that anyone who ignores this fact ends up believing that there is a big mystery. But in fact there is no big mystery. There are only people who are mystified because they are ignoring (or ignorant of) this crucial fact.

> There are only people who are mystified because they are ignoring (or ignorant of) this crucial fact.

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 just won't accept a multiverse theory

They don't have to. But they do have to accept that entanglement and measurement are the same physical phenomenon.

These things are not unrelated :) If you accept that there is only the wave function as in the bare formalism, either an infinity of worlds or zero worlds, like in QIT, are the logical outcomes.

But I am not saying they "have to" - I'm saying that is their reason for not accepting the bare formalism.

> These things are not unrelated :) If you accept that there is only the wave function as in the bare formalism, either an infinity of worlds or zero worlds, like in QIT, are the logical outcomes.


> 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.

Maybe I agree with you, but science is built on philosophy, which is not rigorous - but based on fuzzy feelings of what is right.

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.

In your everyday experience, you are constantly bombarded with overwhelming evidence that space and time are two completely different things, that matter and energy are two completely different things, that life is much too complex and well adapted to its environment to have arisen without an intelligent designer, and that the sun revolves around the earth. And yet, none of these things are true.

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 that's been solved either or most physicists for that matter. I've read some of the attempts and they are not terrible good.

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.

FYI, I am Ron Garret.

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:



Two of the appealing arguments for many worlds type interpretations are that the number of required assumptions is small, and that it gives a reasonable physical intuition for why measurement outcomes occur as they do. Having to bolt on the Born rule weakens both of these.

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.

I agree that bolting on the Born rule seems a weakness of the many world view. It would be nice if you could say everything follows the Schrodinger equation and hence the probabilities naturally come out the way they do but it doesn't seem to work that way very easily.

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.

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