To: fis@listas.unizar.es
Subj: [Fis] QI and probabilities
Dear Andrei,
I cannot understand how the rule of addition of probabilities is violated.
Does it mean that when A and B are events of void intersection, the equality
P (A U B) = P(A) + P(B)
could be violated ? Or what else ?
In classical probability that may be false when the events are not defined on
the same probability space, in which case the quantity P(A)+P(B) has normally
no sense.
Are QI probabilities falling in this situation ?
The probabilities computed from two different quantum experiments should
correspond to events in a common probability space before being added
and telling that the addition lead to an unacceptable result.
What may be this common probability space here ?
Detailing your example with slits would be nice (defining the
probability space, writing the events, their probabilities,
the sum, etc..).
If such a space exists, and if the formula is violated, thus I would not
speak about a probability space in this context. And if so, what could be
the << probability >> rules indeed working in the quantum context ?
Best regards,
Michel,
Michel Petitjean, 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: Andrei Khrennikov <Andrei.Khrennikov@vxu.se>
>
> 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
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Received on Sat May 27 22:00:03 2006
