Reconstruction of quantum theory on the basis of the formula of total probability

Details Reconstruction of quantum theory on the basis of the formula of total probability Reconstruction of quantum theory on the basis of the formula of total probability

2003-02-27

arxiv.org/abs/quant-ph/0302194v4

Proceedings of Conference Foundations of Probability and Physics-3, American Institute of Physics, Ser. Conference Proceedings

Physics

Quantum Physics

Scientific paper

10.1063/1.1874572

The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: ``first context and then probability.'' We start with the conventional formula of total probability for contextual (conditional) probabilities and then we rewrite it by eliminating combinations of incompatible contexts from consideration. In this way we obtain interference of probabilities without to appeal to the Hilbert space formalism or wave mechanics. However, we did not just reconstruct the probabilistic formalism of conventional quantum mechanics. Our contextual probabilistic model is essentially more general and, besides the projection to the complex Hilbert space, it has other projections. The most important new prediction is the possibility (at least theoretical) of appearance of hyperbolic interference.

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