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I've seen the preferred basis problem referred to in many places, but have not seen a clear explanation of what the problem is. For example, this question asks whether the problem has been solved, but I wasn't able to glean anything from the discussion on what the problem was. Zurek 2001 gives the following:

the original MWI does not address the "preferred basis question" posed by Einstein

with a footnote quoting Einstein as saying this:

When the system is a macrosystem and when ψ1 and ψ2 are 'narrow' with respect to the macrocoordinates, then in by far the greater number of cases this is no longer true for ψ = ψ1 + ψ2. Narrowness with respect to macrocoordinates is not only independent of the principles of quantum mechanics, but, moreover, incompatible with them.

The first sentence seems obvious to me. I'm baffled by the second sentence. Some states are narrow and some are not. What's the problem, and what does this have to do with a basis or a preferred basis?

Zurek, "Decoherence, einselection, and the quantum origins of the classical," http://arxiv.org/abs/quant-ph/0105127

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Narrowness is precisely the essence of the preferred basis problem.

Consider: some states are narrow, some are not. Given that some are narrow and some are not, why should 'narrowness' come about as a meaningful concept at all? Why should this quality be an interesting one?

Consider the position of a pointer. We don't interpret non-narrowly pointed states of the pointer as physical, basically by the very definition of what we mean by "a pointer" (after all, we take for granted that some systems can only occupy narrow states, and these are called pointer states in common terminology). In quantum mechanics, the non-narrow states of the pointer are perfectly valid. Then how does the pointer come in practice to inhabit the narrow states?

The answer is that the pointer has a preferred basis (or something which is almost but not quite an orthonormal basis, in the case of literal pointers having different positions): a basis in which its environment tends preferentially to interact, so that the information about the state of the pointer which is encoded in that basis gets copied in other systems, and is therefore strongly correlated. (This is the notion of quantum Darwinism: the information best suited to be reproduced elsewhere, comes to spread faster than it could be stopped, giving rise in practise to decoherence in the basis in which that information is represented.) The question then arises: how does one determine that basis, and why should this basis be priviledged in our experience of the world? For instance, whatever the superposition to which we supposedly belong, according to the MWI, we percieve a strong tendancy for objects to be spatially localised. Why? How does one explain the way in which the myriad potential microscopic worlds merge into distinguishable macroscopic worlds? Why should a superposition state seem, from the inside, like a decomposition with respect to any particular basis?

That is the preferred basis problem, in a nutshell.

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    $\begingroup$ Is it a fair summary to say that the problem is "how does classical physics come out of all this" $\endgroup$ – sudo rm -rf slash Nov 24 '17 at 14:10
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    $\begingroup$ @sudorm-rfslash: That is one, very curt, way of summarising the problem, yes. Only because that question is one which can be applied more generally to all of quantum mechanics, it is not a very precise way of summarising the problem. A more precise way of summarising the problem would be: "how precisely does the phenomenon of measurement as we understand it come out of all of this?" $\endgroup$ – Niel de Beaudrap Nov 30 '17 at 19:00
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Stapp's paper has a series of misunderstandings on how MWI collapse dynamics should be formulated (In his benefit I can say that even Everett was not at all clear at the time either)

The main misunderstanding is that in MWI "There is no collapse". What happens is more subtler than that: Collapse does not dissappear, it is replaced by multipart system entanglement arising from regular Hamiltonian wavefunction dynamics. Or put more succinctly, collapse is nothing but entanglement from the perspective of one of the systems being entangled, when it can be described macroscopically as an observer or a measurement apparatus

The second, more nuanced misunderstanding is overestating the need for a "natural basis" to arise. Basis are naturally sampled depending on how the multiple parts interact and become entangled: if the observer system has a steep magnetic gradient, then the natural basis of interaction with spin-1/2 particles will be the Stern-Gerlach basis. If the observer system has just a large but constant magnetic field, then the natural basis will be those of different linear momenta

Let me know if that clarifies the issue

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I just read Stapp's paper on the basis problem, and I have to say I find these arguments compelling - so compelling that the whole Many Worlds interpretation seems thoroughly undermined to me. And yet you have major scientists like Sean Carroll more or less swear by the MWI. Do people like Carroll have effective arguments that buttress the interpretation up? Honestly to the extent I've paid attention to Carroll's arguments they seem to be along the lines of "MWI must be true because it contains no mechanisms that we have no theory for." I.e., we don't understand collapse, so a theory that sets collapse aside is to be preferred. That's well and good, but I'd ask that the theory also WORK and not have manifest problems of the type that Stapp refers to.

A major concern I have here is that the MWI camp has ulterior motives. The traditional interpretations seem to at least threaten to introduce observers, or observer's minds, or something in that neighborhood, as non-physical entities (i.e., entities not governed exclusively by Schrodinger's equation). I think many in the MWI camp are adamantly, violently opposed to admitting any such thing, as a matter of philosophy, and furthermore are committed to bringing about as much community agreement with that position as they possibly can. I think for some of them this quest for public mind share has become more important that the quest for truth, so they have lost their objectivity. I don't mean to criticize the character/integrity of these people - the whole thing may be thoroughly subconscious.

You see a similar effect on both sides of the climate change debate - it seems clear to me that both sides of that issue care more about influencing public opinion than they do about getting at the cold hard truth. It seem that in some ways science "loses its way" when the "stakes are high." That's a very disappointing thing to me, but perhaps it's nearly impossible to avoid - we are human after all.

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  • $\begingroup$ "it seems clear to me that both sides of [the climate change debate] care more about influencing public opinion than they do about getting at the cold hard truth." - Care to explain what convinced you of this? $\endgroup$ – probably_someone Dec 12 '18 at 12:16
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    $\begingroup$ I fail to see how this answer actually addresses the question. You say that you find the preffered basis problem compelling, but the closest you seem to get to explaining what the problem actually is is a hint at a reference in your first sentence and from there your answer moves further and further away from the topic at hand. $\endgroup$ – By Symmetry Dec 12 '18 at 13:27

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