Dear Friends,

    I found the seventh paragraph on page 9 to be telling:

"The conditions of the Kochen-Specker theorem are not carried out in the
approach described in present paper. ..."

    This might be the locus upon which the fallacy of the paper turns.

Stephen

----- Original Message ----- 
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Saturday, April 17, 2004 11:28 AM
Subject: Re: Quantum mechanics without quantum logic


> At 11:42 15/04/04 +0200, Saibal Mitra wrote:
>
>
>
> >http://arxiv.org/abs/quant-ph/0404045
> >
> >
> >Quantum mechanics without quantum logic
> >Authors: D.A. Slavnov
> >Comments: 24 pages, no figures, Latex
> >
> >We describe a scheme of quantum mechanics in which the Hilbert space and
> >linear operators are only secondary structures of the theory. As primary
> >structures we consider observables, elements of noncommutative algebra,
> >and the physical states, the nonlinear functionals on this algebra, which
> >associate with results of single measurement. We show that in such scheme
> >the mathematical apparatus of the standard quantum mechanics does not
> >contradict a hypothesis on existence of an objective local reality, a
> >principle of a causality and Kolmogorovian probability theory.
>
>
>
>
> To talk frankly it seems to me that Slavnov is a little bit unfair
> about Quantum Logic (QL), confusing it with some Hilbert Space idolatry.
> It looks still more unfair when you remember that, in the process of
> writing the QL founding 1936 paper (ref in my thesis), von Neumann
> wrote to Birkhoff  and said:
>
> "I would like to make a confession which may seem immoral: I do not
> believe absolutely in Hilbert space any more." (quoted at length in the
> formidable book by Miklos Redei : Quantum Logic in Algebraic
> Approach , Kluwer, 1998).
>
> And so we can say that QL has been literally born from a first skeptical
> move with respect to the Hilbert space worship. And as far as I
> understand Slavnov his move seems similar to von Neumann's one.
> Which I think is not a bad move at all. The reason why von Neumann
> has abandonned the "obvious" orthomodular lattice of the closed linear
> subspaces of an (infinite dimensional) Hilbert space was that he
> wanted to keep *modularity* which is closer to the distributivity (of
> the 'and' and the 'or') axioms of a Boolean Algebra, ... so close that
> it makes it possible to define the unique
> probabilities from the "probability one" logic, that is from Quantum
> Logic (there would be some universal density operator).
>
> I do believe this has no bearing at all with any magical trick capable
> of making vanishing the other relative worlds, histories, minds,
> maximal consistent extensions, possibilities ... That seems to me
> the most preposterous part of Slavnov paper.
> In 1939 von Neumann still  invokes a "magical"
> role of consciousness in his singling out a "collapsed" reality.
>
> That Quantum logic *can* be a formidable tools is exemplified in
> my thesis where I show that if we are turing-emulable then
> physics (as a science of correct prediction) is necessarily
> redefined as a measure on all the "computational histories"
> going through our relatively actual states.
> The "all" is managed by explicit appeal to Church thesis.
> And then, translating this in the language of a sound
> universal (lobian) machine I extract the logic of the
> probability one (from and on all the maximal consistent
> extensions) and got an (arithmetical) quantum logic (AQL*)
> Is it modular, orthomodular?  Open problems!
>
> Of course modularity would help for the sequel (the derivation
> of physics from arithmetics/machine 'psychology'). You can
> look at the last pages of the following document for the
> precise definition of the arithmetical quantum logic which I
> call AQL* now but is named QuelQL* in the following document:
> http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume1CC/4Recapitulation.pdf
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
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