Quantization in classical mechanics and reality of Bohm's psi-field

TL;DR

This paper links dissipative forces in classical mechanics to quantum potential via Chetaev's theorem, proposing a new interpretation of the wave function as a density of particle trajectories in Bohmian mechanics.

Contribution

It introduces a generalized stability condition for Hamilton systems using Chetaev's theorem, connecting dissipative energy to Bohm's quantum potential, and reinterprets the wave function in Bohmian mechanics.

Findings

Dissipative forces generate energy equal to Bohm's quantum potential.

Wave function amplitude corresponds to particle trajectory density.

Conditions for Bohm-Chetaev interpretation validity are discussed.

Abstract

Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of Hamilton systems in the form of the Schrodinger equation. It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with the Bohm "quantum" potential. Within the framework of Bohmian quantum mechanics supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave function in the Schrodinger equation is equivalent semantically and syntactically to the probability density function for the number of particle trajectories, relative to which the velocity and the position of the particle are not hidden parameters. The conditions for the correctness of the Bohm-Chetaev interpretation of quantum mechanics are discussed.