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Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from quantum logic. I think in quantum logic, some physical phenomena, like collapse of state, have been transformed to some requirements of the structure. Quantum Bayesianism, as an interpretation, may want to interpret some phenomena like collapse of state, then they should not borrow the results from quantum logic. If they borrow some results,which come from some requirements , to derive some other results related to these requirements, then it can't be a logical theory.

By the way, is it possible to build a logical theory based on quantum logic? Or is any promising way to make quantum mechanic more logical?

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closed as unclear what you're asking by CuriousOne, ACuriousMind♦, MAFIA36790, honeste_vivere, unsym Jun 10 '16 at 19:13

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@CuriousOne What's the reason that quantum logic fails? – Nicky Jun 10 '16 at 1:08
    
I have been watching quantum logic for like 30 years now and I am not aware that its proponents could even find a set of rules that has physical significance, let alone that it can correctly predict the behavior of physical systems. We do, by the way, not expect conventional logic to do the same for classical Hamiltonian systems, either. We do not even expect there to be a possible framework in which a set of finite algebraic operations can possibly predict system behavior because we have known since the late 19th century that not even an infinite set can do this. – CuriousOne Jun 10 '16 at 1:12
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Regarding quantum Bayesianism (qbism as it's called), Mermin has also written lots about it that you might find interesting, e.g., along with Fuchs arxiv.org/abs/1311.5253 Re your second question, (re)constructing "a logical [quantum] theory based on quantum logic" (quoting you above), that's separate. It's typically called "the coordinatiztion problem", i.e., constructing a Hilbert space from the lattice of propositions. A short discussion is Section 4.3.2 of arxiv.org/abs/1211.5627 but the most complete is Chapter 21 of ebooks.cambridge.org/ebook.jsf?bid=CBO9781107340725 – John Forkosh Jun 10 '16 at 3:02
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I recommend the reading of Quantum Bayesianism: A Study (Timpson, 2007) for a thorough study of QBism and its ontology and issues. – Stéphane Rollandin Jun 10 '16 at 7:56
    
The comments by @CuriousOne is again misleading. The user doesn't understand the modern forms of Quantum Information Theory, but only (as he says himself) 30year old, outdated theories. QBism, epistemic interpretations vs. ontic versions has been developed in a very active field over recent years, see: nature.com/nphys/journal/v8/n6/abs/nphys2309.html nature.com/nphys/journal/v11/n3/full/nphys3233.html and so on. I would suggest that the user will be blocked from topics involving quantum theory, or at least quantum information theory. How to formally request that? – NiceDean Jun 12 '16 at 11:45
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Bayesian probability is based on the classical logic of plausible reasoning, as described by Jaynes, Probability Theory: The Logic of Science. One can and should try to find a Bayesian interpretation of the wave function. Here I can recommend Caticha's "entropic dynamics" as one possible approach.

But I don't think "quantum logic" will be helpful here. Classical logic is something one cannot and should not weaken. Every weakening is a misinterpretation. The use of misleading denotations - like "measurement" for some interaction which gives a result which possibly depends on the "observer" too - can, of course, lead to a necessity to weaken the rules of logic to avoid contradictions.

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"The use of misleading denotations - like "measurement" for some interaction which gives a result which possibly depends on the "observer"" - every experimentalist in the world calls that "a measurement error" and we deal with it accordingly. One has to be completely out of ones mind to think that one can learn anything about quantum mechanics from analyzing ones own false assumptions about a system, and many of the quantum mystics are, I am afraid. As for classical logic... that's overvalued, too, as a short look at non-integrable system dynamics will prove beyond any doubt. – CuriousOne Jun 9 '16 at 20:13
    
To understanding my remark, I recommend to read Bell's "Against Measurement": "When it is said that something is 'measured' it is difficult not to think of the result as referring to some preexisting property of the object in question. This is to disregard Bohr's insistence that in quantum phenomena the apparatus as well as the system is essentially involved. ... When one forgets the role of the apparatus, as the word 'measurement' makes all too likely, one despairs of ordinary logic - hence 'quantum logic'. When one remembers the role of the apparatus, ordinary logic is just fine." – Schmelzer Jun 9 '16 at 20:52
    
That's not the core problem of quantum logic, though. The core problem is that no algebraic theory can express the complexity of an analytic one. Quantum logic, from the perspective of a mathematical logician, is a foolish undertaking of children who didn't listen when they were explained this in an introductory class on mathematical logic. – CuriousOne Jun 10 '16 at 1:15

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