Re: Quantum mechanics without quantum logic

2004-04-27 Thread Bruno Marchal
At 17:28 17/04/04 +0200, I wrote:

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.


Well sorry, but von Neumann did invoke consciousness
in 1932. I was wrong, and it remains an open question for me
if von Neumann was hoping that his (modular) Quantum Logic
could give light on the conceptual problem of QM.
http://iridia.ulb.ac.be/~marchal/



Re: Quantum mechanics without quantum logic

2004-04-17 Thread Bruno Marchal
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/



Re: Quantum mechanics without quantum logic

2004-04-17 Thread Stephen Paul King
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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