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Mitchell_Porter90

First let's be clear about what we're explaining: the Born rule as it appears in conventional observer-centric QM, which is best understood as an incomplete positivistic theory in which "measurements" of "observables" are reality and wavefunctions are just calculating devices.

Both Bohmian mechanics and objective collapse theories have a probabilistic axiom among their defining postulates. Bohmian mechanics is deterministic but it explains quantum-mechanical states as a particular probability distribution over Bohmian states. Objective collapse theories are nondeterministic and probability enters directly in the dynamical rule governing when and how the quantum state vector departs from Schrodinger evolution and makes a random jump.

What they have in common is that the ontologically incomplete framework of ordinary QM - in which "observables" are a fundamental concept - is explained in terms of a deeper theory which makes no reference to observers, measurements, consciousness, etc. The deeper theory is not much deeper in either case, but the subjective cast of QM has in both cases been replaced by a theory which just says how things are.

When we come to many worlds theories, and to retrocausal theories like the transactional interpretation, this condition is not met. Many worlds certainly has an objective-looking formalism - reality is just a wavefunction-of-the-universe, evolving according to a Schrodinger equation - but it does not have a derivation of the Born rule given this ontology. In other words, it potentially possesses objectivity, but presently falls short of actually explaining QM. Certainly various derivations have been claimed (David Deutsch) or proposed (Robin Hanson). But Deutsch's claim is (correctly) disputed, while Robin's proposal has a number of issues, and still lacks a precise formulation for quantum systems of any complexity or realism. The only sure way I see to get the Born rule from many worlds is to go to some form of quantum cosmology in which a set of distinct universes (e.g. the consistent histories of Gell-Mann and Hartle) or universe-moments (e.g. the time capsules of Julian Barbour) is enumerated, and to simply declare that each universe has a probability or a "degree of reality" equal to the squared modulus of its amplitude. But then you don't actually need the wavefunction any more, all that matters is the probability distribution on the set of universes. The price of making many worlds into a formally exact theory is that you abandon most of the concepts which define it informally.

As for the transactional interpretation, it has the complementary problem of not having an objective-looking formalism. It's a way of talking about the (conventional, subjectively flavored) QM formalism which sounds like it ought to be based on some sort of objective theory, but no such theory has been written down. You could count Feynman-Wheeler absorber theory as an attempt at an objective explanation of QM in the transactional spirit, but it falls short in the details. However, there are various other objective options which remain largely undeveloped.

By the way, I don't believe that any of the above is The Answer, but one or more of them might be a step towards the truth. The truth is going to come from a study of the most advanced theories, such as M-theory, and these existing paradigms of "how to explain QM" are at best ideas and inspirations for how to proceed regarding the real thing. The most advanced theories have numerous properties missing from nonrelativistic QM - for example, the holographic duality that appears in quantum gravity - and some of these new properties are probably essential to the ultimate explanation of QM. I would be unsurprised to learn that the final explanation of QM, whatever it is, is specific to M-theory, and that all lesser quantum theories are just echoes of M-theory in its present-day, obfuscated, QM-like form. (Needless to say, these are eccentric personal opinions, which is why I didn't start my reply with them.)

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BlazeOrangeDeer20

How is a "probabilistic axiom" different from an assumed Born rule? You seem to be penalizing the latter and calling it incomplete or inelegant but I don't see how the first is better.

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See in context
by MinibearRex
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Today's post, If Many-Worlds Had Come First was originally published on 10 May 2008. A summary (taken from the LW wiki):

 

If early physicists had never made the mistake, and thought immediately to apply the quantum laws at all levels to produce macroscopic decoherence, then "collapse postulates" would today seem like a completely crackpot theory. In addition to their other problems, like FTL, the collapse postulate would be the only physical law that was informally specified - often in dualistic (mentalistic) terms - because it was the only fundamental law adopted without precise evidence to nail it down. Here, we get a glimpse at that alternate Earth.


Discuss the post here (rather than in the comments to the original post).

This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Collapse Postulates, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.

Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.

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[-]Mitchell_Porter170

We should consider another counterfactual, "If The Transactional Interpretation Had Come First On Less Wrong".

Some "interpretations", like Bohmian mechanics and objective collapse theories, are recognizably physical theories in the sense of being perfectly explicit hypotheses about what exists and how it changes, which reduce to quantum mechanics in some limit.

Then there are interpretations which are still just at the stage of being a qualitative hypothesis about the nature of reality. These are the ones which can't derive the Born rule, for example. Many-worlds is one of these. There is no standard derivation of the Born rule within many worlds, just competing claims and ideas about how to do it. As things stand, to employ many-worlds as a predictive theory, your theory really needs to be "Many worlds + Born rule". Many-worlds is your metaphysics, your conception of reality, and the Born rule is a further assumption (about the frequencies of the worlds) that you have to make in order to calculate anything.

The transactional interpretation is another instance of this. I would prefer to regard it as just one representative of a long-running genre of quantum interpretation, in which quantum mechanics is explained as due to causality operating future-to-past as well as past-to-future. In such a world, there are no literal superpositions. The peculiar features of the quantum probability calculus, such as the destructive interference (existence of dark zones where the particle does not arrive) in the double-slit experiment, are attributed to the ordinary calculus of conditional probability being at work in both "directions": the presence of closed chains of probabilistic dependence that loop in time imposes consistency conditions on what can happen, conditions which appear anomalous or nonlocal.

So far as I can see, transactional interpretations are at least as plausible as many-world interpretations. The whole Quantum Physics Sequence could have been written around them, with no change in any Less Wrong epistemological doctrine. The only difference would be, that LW discussion of QM would proceed from the premise that basic physics is all about an interference between procausal and retrocausal chains, not about an ensemble of parallel worlds.

At least, I can't see any difference that substituting John Cramer for Hugh Everett would make. There is nothing here to cause one to judge LW principles any differently, just evidence that they weren't applied perfectly in this case. But perhaps someone more devoted to LW epistemology and methodology could check this for me. Does anything fundamental change (from the perspective of "refining human rationality") if it turns out that the central factual claim of this sequence is wrong?

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[-]BlazeOrangeDeer00

How do other theories get the born rule? Do any of them make less assumptions than MWI?

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[-]Mitchell_Porter90

First let's be clear about what we're explaining: the Born rule as it appears in conventional observer-centric QM, which is best understood as an incomplete positivistic theory in which "measurements" of "observables" are reality and wavefunctions are just calculating devices.

Both Bohmian mechanics and objective collapse theories have a probabilistic axiom among their defining postulates. Bohmian mechanics is deterministic but it explains quantum-mechanical states as a particular probability distribution over Bohmian states. Objective collapse theories are nondeterministic and probability enters directly in the dynamical rule governing when and how the quantum state vector departs from Schrodinger evolution and makes a random jump.

What they have in common is that the ontologically incomplete framework of ordinary QM - in which "observables" are a fundamental concept - is explained in terms of a deeper theory which makes no reference to observers, measurements, consciousness, etc. The deeper theory is not much deeper in either case, but the subjective cast of QM has in both cases been replaced by a theory which just says how things are.

When we come to many worlds theories, and to retrocausal theories like the transactional interpretation, this condition is not met. Many worlds certainly has an objective-looking formalism - reality is just a wavefunction-of-the-universe, evolving according to a Schrodinger equation - but it does not have a derivation of the Born rule given this ontology. In other words, it potentially possesses objectivity, but presently falls short of actually explaining QM. Certainly various derivations have been claimed (David Deutsch) or proposed (Robin Hanson). But Deutsch's claim is (correctly) disputed, while Robin's proposal has a number of issues, and still lacks a precise formulation for quantum systems of any complexity or realism. The only sure way I see to get the Born rule from many worlds is to go to some form of quantum cosmology in which a set of distinct universes (e.g. the consistent histories of Gell-Mann and Hartle) or universe-moments (e.g. the time capsules of Julian Barbour) is enumerated, and to simply declare that each universe has a probability or a "degree of reality" equal to the squared modulus of its amplitude. But then you don't actually need the wavefunction any more, all that matters is the probability distribution on the set of universes. The price of making many worlds into a formally exact theory is that you abandon most of the concepts which define it informally.

As for the transactional interpretation, it has the complementary problem of not having an objective-looking formalism. It's a way of talking about the (conventional, subjectively flavored) QM formalism which sounds like it ought to be based on some sort of objective theory, but no such theory has been written down. You could count Feynman-Wheeler absorber theory as an attempt at an objective explanation of QM in the transactional spirit, but it falls short in the details. However, there are various other objective options which remain largely undeveloped.

By the way, I don't believe that any of the above is The Answer, but one or more of them might be a step towards the truth. The truth is going to come from a study of the most advanced theories, such as M-theory, and these existing paradigms of "how to explain QM" are at best ideas and inspirations for how to proceed regarding the real thing. The most advanced theories have numerous properties missing from nonrelativistic QM - for example, the holographic duality that appears in quantum gravity - and some of these new properties are probably essential to the ultimate explanation of QM. I would be unsurprised to learn that the final explanation of QM, whatever it is, is specific to M-theory, and that all lesser quantum theories are just echoes of M-theory in its present-day, obfuscated, QM-like form. (Needless to say, these are eccentric personal opinions, which is why I didn't start my reply with them.)

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[-]BlazeOrangeDeer20

How is a "probabilistic axiom" different from an assumed Born rule? You seem to be penalizing the latter and calling it incomplete or inelegant but I don't see how the first is better.

Reply
[-]Mitchell_Porter120

Let's contrast the three options of: phenomenological QM (Copenhagen interpretation); an objective collapse theory; and many worlds.

Phenomenological QM assumes a Born rule, and makes no sense as a final objective theory (unless you're a solipsist). An objective collapse theory has an objective world-picture including a probabilistic axiom (the physical law of collapse) and you can logically prove that this implies the validity of a phenomenological Born rule for observers. Many worlds has an objective world-picture not including a probabilistic axiom, and cannot logically prove that this world-picture implies a phenomenological Born rule for observers.

What most many-worlds believers are doing, is assuming the truth of the many-worlds picture of reality, and also assuming the truth of the Born rule just as if they were doing ordinary subjectivist QM. But their picture of reality all by itself ought to determine what observers typically see; having opted for a specific objective theory - and one which supposedly has no probabilistic axioms - there shouldn't be room, logically speaking, to "assume" anything further about the truth of the Born rule. Either the phenomenological Born rule is a true implication of their theory, or their theory implies that observers see something different to reality.

This seems to be a subtle point. One analogy would be if there was a quantum "interpretation" which consisted of saying "I believe that reality is described by this enormous unsolvable differential equation, and I also believe that if you could solve it, it would look like reality as described by the Born rule." That's not much of a theory, because having decided that reality is described by the equation, the equation should imply how reality looks, not your further assumption.

Many worlds is a little like this, except that their equation is already part of QM; it's the part of QM they find acceptable, the Schrodinger equation. But the same critique still applies. If "wavefunction evolving according to the Schrodinger equation" is everything, then the Born rule must be an implication of this equation. And they cannot exhibit any such implication. All attempts to do so either involve a long chain of reasoning in which the Born rule is implicitly reintroduced at some point (this is what Deutsch does) or involve focusing on specific substructures in the wavefunction and saying "those are the worlds" (this is what Hanson does). The latter step is surely one that has to be performed anyway, just to make sense of the wavefunction - from the perspective of Hilbert space, even just by talking about configurations, you're preferring a particular basis - but a lot of many-worlds believers don't want to take this step. As a rule, how it works is that non-physicist MWI believers just assume that configurations are the preferred basis, because spatial configurations are the everyday reality they're already familiar with, and physicist MWI believers import whatever they need from Copenhagen QM in order to avoid having an ontologically preferred basis, even though a self-sufficient objective theory should have no logical room for such "imported" extra components.

Sorry for the complexity of this answer, but the facts about how people are thinking, and the logical relations, dissimilarities, etc between the various approaches, and the normative evaluation of the relative merits of the different approaches, are just not simple. Strictly phenomenological QM has a certain simplicity. A final objective theory which really does the job of explaining QM will have some form of simplicity. But the path from the first to the second - which is taking decades - passes through a great deal of confusion, not just because there are wildly dissimilar theoretical options to be considered, but because people lose sight of what "an objective theory that fully explains QM" actually requires, because there are preachers saying "turn back! Copenhagen positivism was already the final answer, this other way leads only into the desert of philosophy", and for many other meta reasons.

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[-]Shmi40

As a rule, how it works is that non-physicist MWI believers just assume that configurations are the preferred basis, because spatial configurations are the everyday reality they're already familiar with, and physicist MWI believers import whatever they need from Copenhagen QM in order to avoid having an ontologically preferred basis, even though a self-sufficient objective theory should have no logical room for such "imported" extra components.

How, do you think, does EY think about it? I could not find it stated clearly anywhere in the sequence, beyond "MWI is decoherence, decoherence is MWI", which is not overly helpful.

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[-]Mitchell_Porter60

Along with the emphasis on decoherence, he has expressed a liking for Robin Hanson's "mangled worlds" approach, for the position basis because of the importance of relativistic locality, and for the "time capsules" of Julian Barbour. These ideas are at odds with each other in various ways. The last two utilize the position basis, the first two do not; and Barbour's time-capsules are universe-wide configurations, so the spirit of relativity is lacking in his theory, putting it at odds with the other motivation for preferring the position basis. But I think you should regard this as a dynamic tension in Eliezer's thought, rather than as a complacent contradiction. He knows his preferred hypothesis, but he doesn't know the details, so various mutually contradictory refinements of the idea are playing a role in his thinking at the same time.

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[-]Shmi50

If early physicists had never made the mistake, and thought immediately to apply the quantum laws at all levels to produce macroscopic decoherence, then "collapse postulates" would today seem like a completely crackpot theory.

It would have been yet another interpretation, to be added to the wiki list and promptly forgotten, except by a few washed up physicists-turned-philosophers.

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