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/ > > > > > ------------------------ Yahoo! Groups Sponsor ---------------------~--> > Buy Ink Cartridges or Refill Kits for your HP, Epson, Canon or Lexmark > Printer at MyInks.com. Free s/h on orders $50 or more to the US & Canada. > http://www.c1tracking.com/l.asp?cid=5511 > http://us.click.yahoo.com/mOAaAA/3exGAA/qnsNAA/pyIolB/TM > ---------------------------------------------------------------------~-> > > > Yahoo! Groups Links > > <*> To visit your group on the web, go to: > http://groups.yahoo.com/group/Fabric-of-Reality/ > > <*> To unsubscribe from this group, send an email to: > [EMAIL PROTECTED] > > <*> Your use of Yahoo! Groups is subject to: > http://docs.yahoo.com/info/terms/ > > >