On the Quantization Procedure in Classical Mechanics and Problem of Hidden Variables in Bohmian Mechanics

TL;DR

This paper derives a generalized stability condition for Hamiltonian systems using Chetaev's theorem, revealing that the quantum potential in Bohmian mechanics arises from dissipative forces, and argues that this framework excludes hidden variables.

Contribution

It introduces a generalized stability condition linking Chetaev's theorem to the Schrödinger equation, providing a new perspective on the nature of hidden variables in Bohmian mechanics.

Findings

The quantum potential corresponds to dissipative forces in the system.

Bohmian mechanics with Chetaev's theorem excludes hidden variables.

The stability condition reproduces the Schrödinger equation.

Abstract

Basing on the Chetaev's theorem on stable trajectories in dynamics in the presence of dissipative forces we obtain a generalized stability condition for Hamiltonian systems that has the form of the Schrodinger equation. We show that the energy of the dissipative forces generating generalized Chetaev's stability condition exactly coincides with Bohm's "quantum" potential. Using the principle of least action of perturbation we prove that the Bohmian quantum mechanics complemented with the Chetaev's generalized theorem does not have hidden variables.