On the mystery of quantum probabilistic rule: trigonometric and hyperbolic probabilistic behaviours

摘要

We demonstrate the quantum probabilistic rule (which differ from classicalBayes' formula by the cosinus factor) can be obtained on purely classical basisas a consequence of the perturbation effect of preparation procedures. In anycase the interference can be easily simulated for macrosystems. Moreover, weobtain the classification of all possible transformations of probablities whichcan arise via perturbation effects. There are two main transformation classes:with trigonometric and hyperbolic ("interference") perturbations of classicalBayes' formula. Quantum probabilistic rule is just a particular case oftrigonometric probablistic behaviour. Hyperbolic probablistic behaviour can beeasily simulated. However, the question of its observation for "real physicalphenomena" is open.