Dear Michael,
The question on the difference between classical and quantum
probabilities is really fundamental for QI. The situation is not so
simple as it was described in the Email below. Yes, I agree that if we
consider one fixed experimental arrangement then we obtain the usual
classical probability. Statistical data follows the law of large numbers
and the relative frequencies give us approximations of probability. But,
as it was already emphasized in my previous Email, if we try to combine
statistical data obtained from a few different experiments then it would
be observed the evident deviation from the rules for classical
Kolmogorov probability. One of such deviations we see in the two slit
experiment: we collect data for three different complexes of
experimental physical conditions (contexts): two slits are open, the
first is open and the second is closed and, finally, vice versa. The
well know formula of total probability is evidently violated (Richard
Feynman wrote about teh violation of the rule of addition of
probabilities). The same behaviour is demonstrated by statistical data
for the EPR-Bohm experiment. I recall that there is also combined data
for at least three (and the real experiments four) experimental
arrangements.
Then one could ask: Is this difference fundamental? So that one could
not in principle reduce the quantum probability to the classical one.
The answer of von Neumann and majority of quantum community is: yes, the
difference is fundamental. Quantum randomness is IRREDICIBLE. Therefore
we should develop special quantum probability and even special quantum
logic.
Aa I pointed out, nevertheless, it is possible to find classical
probabilistic models which reproduce quantum probabilistic behaviour
EVEN FOR DATA COLLECTED IN DIFFERENT EXPERIMENTS. For example, Bohmian
mechanics: here quantum randomness is reduced to randomness of initial
conditions; stochastic electrodynamics: here quantum randomness is
reduced to randomness of vacuum fluctuations; Nelson\'s stochastic
mechanics -- the same as in SED. In the series of papers that I
mentioned in previous Emails I developed so called CONTEXTUAL CLASSICAL
PROBABILISTIC calculus that also reproduces quantum probabilistic behaviour.
Andrei
> Dear Michael,
>
> Except minor differences such that real valued / non real valued or
> discrete / continuous, the probabilities computed for the roll of a
> die
> and those computed for a quantum system are not fundamentally
> different:
> they all obey to the rules in vigor in a probability space.
> In this sense, the probabilities computed for a quantum system are
> classical, despite that the calculation involves the modulus of the
> wave function: it is an additional property which does not preclude
> the validity of the properties of ordinary probabilities.
>
> Best regards,
>
> , Email:
> petitjean@itodys.jussieu.fr
> ITODYS (CNRS, UMR 7086) ptitjean@ccr.jussieu.fr
> 1 rue Guy de la Brosse Phone: +33 (0)1 44 27 48 57
> 75005 Paris, France. FAX : +33 (0)1 44 27 68 14
> http://petitjeanmichel.free.fr/itoweb.petitjean.html
>
> From: Michael Devereux <dbar_x@cybermesa.com>
> > Dear Jonathan, Andrei, and colleagues,
> > ...
> > And we know that these probabilities for quantum objects are
> calculated
> > from the complex value of each eigenvector (the probability
> amplitude)
> > but not, as is done classically, by determining the real-valued
> > probabilities associated with, for example, each roll of a die.
> (Again,
> > ...
>
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Received on Sat May 27 15:39:37 2006
