Quantum Analytical Mechanics: Quantum Mechanics with Hidden Variables

TL;DR

Quantum analytical mechanics extends standard quantum mechanics by introducing stochastic trajectories in configuration space, providing a dynamical description of measurement processes without replacing the traditional formalism.

Contribution

It presents a mathematical completion of quantum mechanics using hidden variables as stochastic trajectories, enriching the description of quantum phenomena.

Findings

Derives equations of motion for stochastic trajectories in configuration space

Provides a dynamical framework for understanding measurement processes

Complements Hilbert space quantum mechanics without replacing it

Abstract

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of standard quantum mechanics based on the concept of stochastic trajectories in the configuration space of a quantum system. For particle systems, configuration space is made up out of their coordinates and, if relevant, their orientation. Quantum analytical mechanics derives equations of motion for these variables which allow a description of the measurement process as a dynamical physical process. After all, it is exactly these variables experiments are designed to interact with. The theory is not a replacement of Hilbert space quantum mechanics but a mathematical completion enriching our toolset for the description of quantum phenomena.