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From a 1D completed scattering and double slit diffraction to the quantum-classical problem for isolated systems. (English) Zbl 1236.81007

Summary: It follows by probability theory that the probability space underlying the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us, this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density, and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering and double slit diffraction, we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the concept of real contexts (complexes of physical conditions) presented by A. Khrennikov [Found. Phys. 35, No. 10, 1655–1693 (2005; Zbl 1102.81008)] to determine uniquely the properties of quantum ensembles. Namely, we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows for a correct statistical interpretation and becomes compatible with classical physics.

MSC:

81P05 General and philosophical questions in quantum theory
81R30 Coherent states

Citations:

Zbl 1102.81008
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References:

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