From a 1D completed scattering and double slit diffraction to the quantum-classical problem for isolated systems

TL;DR

This paper introduces a new quantum-mechanical framework that decomposes non-Kolmogorovian probability spaces into Kolmogorovian parts, enabling correct statistical interpretation of quantum phenomena like double slit diffraction.

Contribution

It develops a novel approach to quantum superpositions by decomposing probability spaces into classical parts, resolving interpretational issues in quantum mechanics.

Findings

Decomposition of probability space into Kolmogorovian components.

Application to 1D scattering and double slit diffraction.

Quantum mechanics becomes compatible with classical physics.

Abstract

By probability theory the probability space to underlie 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 presented by Khrennikov ({\it Found. of Phys., 35, No. 10, p.1655 (2005)}) concept of real contexts (complexes of physical conditions) 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 a correct statistical interpretation and becomes compatible with classical physics.