From a 1D completed scattering and double slit diffraction to the quantum-classical problem: A new approach

TL;DR

This paper introduces a new approach to the quantum-classical problem by modeling quantum phenomena as compound processes with alternative subprocesses, resolving paradoxes like the Hartman effect and providing clearer interpretations of quantum superpositions.

Contribution

It develops models treating quantum superpositions as compound processes with alternative subprocesses, offering a new perspective on the quantum-classical transition.

Findings

Quantum superpositions can be modeled as compound processes with alternative subprocesses.

The approach resolves paradoxes such as the Hartman effect.

Observable data are incompatible with the entire superposition ensemble.

Abstract

We present a new approach to the quantum-classical problem, which treats it as the problem of modelling the quantum phenomenon described by a coherent superposition of microscopically distinct substates (CSMDS) as a compound one consisting of alternative subprocesses creating unremovable contexts for each other, or as that of reducing a non-Kolmogorovian quantum probability space to underlie a CSMDS to the sum of Kolmogorovian ones. We develop such models for a 1D completed scattering and double slit diffraction. The quantum-classical problem disappears when, in quantum theory with its integral superposition principle, CSMDSs obey the "either-or" rule to guide alternative random events. There is no observable which could be associated with the whole ensemble of statistical data described by a CSMDS, because such data are incompatible -- in the case of a CSMDS, any observable splits into noncommuting observables associated with the substates. To calculate the average value of any observable as well as to introduce characteristic times is meaningful only for the substates of a CSMDS. Ignoring this feature in the conventional description of CSMDSs just leads to paradoxical results (e.g., to the Hartman effect and passing a particle through two slits in the screen simultaneously).