Diffusion Scattering of Waves is a Model of Subquantum Level?

TL;DR

This paper explores mathematical models of wave diffusion scattering in phase space, linking them to quantum mechanics and suggesting they may serve as subquantum models with gauge invariance and potential deviations from quantum predictions.

Contribution

It introduces gauge-invariant models of wave diffusion scattering that relate classical processes to quantum mechanics and discusses their potential as subquantum models.

Findings

Models exhibit gauge invariance under Galileo transformations.

Quantum mechanics emerges as an asymptotic approximation in these models.

Deviations from quantum behavior may occur with rapidly changing potentials.

Abstract

In the paper, we discuss the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. In the previous works it is shown that in these models of classical scattering process of waves, the quantum mechanical description arises as the asymptotics after a small time. In this respect, the proposed models can be considered as examples in which the quantum descriptions arise as approximate ones for certain hypothetical reality. The deviation between the proposed models and the quantum ones can arise, for example, for processes with rapidly changing potential function. Under its action the diffusion scattering process of waves will go out from the states described by quantum mechanics. In the paper it is shown that the proposed models of diffusion scattering of waves possess the property of gauge invariance. This implies that they are described similarly in all inertial coordinate systems, i.e., they are invariant under the Galileo transformations. We propose a program of further research.