Dear Collegues!
I use the opportunity given by Andrei to add a little bit of information.
This summer, in several discussions, I referred to the book I was
writing (my PhD thesis in Computing and Philosophy):
Investigations into Information Semantics and Ethics of Computing, that
now is published under:
http://www.diva-portal.org/diva/getDocument?urn_nbn_se_mdh_diva-153-2__fulltext.pdf
( abstract: http://www.diva-portal.org/mdh/abstract.xsql?dbid=153
)
You will find many reflections of FIS exchanges in it.
I am thankful for your comments, opinions, criticism, etc.
Best regards,
Gordana
__________________________________
Gordana Dodig-Crnkovic
Senior Lecturer
M�lardalen University,
Department of Computer Science and Electronics
http://www.idt.mdh.se/personal/gdc/
Andrei Khrennikov wrote:
> Dear Collegues!
>
> During summer holidays we were involved in interesting debates on
> Quantum and Classical Information Theories (which were tarnsformed
> finally into a deep discussion on meaning of informartion and its
reality).
>
> I would like to present some concluding remarks. After this I propose
> that everybody who is interested can send his own concluding remarks and
> after that (may be in one--two weeks) session will be closed. I recall
> my viewpoint:
>
> We all work with models of reality. We cannot <<understand
reality>>,
> but only describe it by using this or that model. The most advanced way
> of modeling of reality is mathematical modeling. Sometimes reality is
> even identified with a mathematical model. This happened with the modern
> picture of space-time reality which is based on using of real continuum.
> I pointed out that there were attempts to propose alternative models of
> reality even for space-time, e.g., p-adic models.
>
>
> There are two main mathematical models of information:
>
>
> a). Classical thermodynamical model in that information is defined from
> entropy and the latter is based on the Kolmogorov measure-theoretic
> definition of probability.
>
> b). Quantum information model in that information is defined by using
> linear algebra (operator theory).
>
>
> Mathematical structures of models are different. In particular, QI is
> noncommutative theory. The natural question arises:
>
> <<Is it just difference in mathematical models, in mathematical
> descriptions, so just different mathematical representations of the same
> kind of reality or one should consider two extremely different types of
> physical phenomena, classical and quantum?>>
>
>
> The conventional point of view is that there are two extremely different
> domains of physics, quantum and classical. The first one is about
> microworld and the second is about macroworld. This is the Copenhagen
> viewpoint: there are microscopic systems and macroscopic observers.
> It induces many problems and paradoxes, but nevertheless it is
> convenient in applications and it dominates in physics. One of the main
> problems is the boundary between the quantum and classical domains.
>
> In the quantum domain a system can be in a superposition of a few
> different states. This is precisely why quantum computers should work
> quicker than classical ones. In classical it could not. For example, as
> was pointed by Roger Penrose, a single neuron could not be at the same
> time in the superposition of two states: firing and nonfiring.
>
> The famous Schrodinger cat was created by Schrrodinger to show
> absurdness of Copenhagen interpretation. This example was proposed in
> his letter to Einstein and it was a modification of an example from one
> of Einsteins letters about pistolet and bomb. The main idea was that if
> one assumes superposition of states for microscopic systems one would be
> always able to lift this superposition to macroscopic systems.
>
>
> My point was that two information theories are based on two probability
> theories: classical Kolmogorov measure-theoretic probability and quantum
> von Neumann Hilbert space probability. In the second case we operate not
> directly with probabilities but with complex probability amplitudes.
>
> Some people think that quantum probability is more complicated than the
> classical one. I do not think so. Theory of Lebesgues integral is
> essentially deeper and more complicated from the mathematical viewpoint
> than linear algebra, especially in finite dimensional spaces which are
> used in quantum information theory.
>
>
> I am trying to sell the idea that the whole quantum enterprise is about
> simplification of description of extremely complex physical phenomena.
> I developed models in that the quantum probabilistic model appears as a
> projection of more complex classical statistical model.
>
> Then I proceed: Wau! In such a case it seems that quantum probability
> theory and quantum information could be used everywhere where we could
> not provide the complete description of phenomena and we just try to
> create a simplified representation in complex Hilbert space.
>
> So one can apply quantum information theory everywhere, from financial
> mathematics to genetics.
>
> Finally, about the last part of discussion about reality of information.
> I understood that my rather restricted philosophic basis was not
> sufficient to debate this problem on the same level as opponents of
> non--reality of information. But I stay on my position: information is
> not less real than mass or charge.
>
>
> I agree with Søren Brier that the main problem is that in modern science
> information is always reduced to probability:
> <<Thus information as a basic quality in the world is something
entirely
> different from the present information theory that is based on
> thermodynamics ensemble theory. That information concept is then more
> basic than quantum theory.>>
>
> There should be done something cardinally new...
>
> I would like to thank all participants of out discussion.
>
>
>
> References:
>
> Khrennikov A.Yu. ,p-adic valued distributions and their applications to
> the mathematical physics, Kluwer, Dordreht, 1994.
>
> Khrennikov A.Yu., Information dynamics in cognitive,
> psychological, social, and anomalous phenomena.Kluwer, Dordreht,2004.
>
> Proceedings of Conference Quantum Theory: Reconsideration of
> Foundations-3, American Institute of Physics, Ser. Conference
> Proceedings, Melville, NY, 2006.
>
> A. Yu. Khrennikov, The principle of supplementarity: A
> contextual probabilistic viewpoint to complementarity, the
> interference of probabilities, and the incompatibility of variables
> in quantum mechanics.Foundations of Physics, 35, N.
> 10, 1655 - 1693 (2005).
>
> A. Yu. Khrennikov, Interference in the classical probabilistic
> model and its representation in complex Hilbert space. Physica, E 29,
> 226-236 (2005).
>
> A. A. Ezhov, A. Yu. Khrennikov, Agents with left and right
> dominant hemispheres and quantum statistics. Phys. Rev. E (3)
> 71 , N. 1, 016138-1 -8 (2005).
>
> A. Yu. Khrennikov, Quantum-like brain: Intereference of
> minds. BioSystems, 84, 225-241 (2005).
>
> With Best Regards,
>
> Andrei Khrennikov
>
> Director of International Center for Mathematical Modeling in Physics,
> Engineering, Economy and Cognitive Sc.,
> University of Vaxjo, Sweden
>
>
>
>
>
>
>
>
>
>
>
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Received on Tue Sep 12 08:34:26 2006
