Towards a Deterministic Interpretation of Quantum Mechanics: Insights from Dynamical Systems

TL;DR

This paper proposes a deterministic dynamical system with local interactions that mimics quantum behavior and offers an alternative to probabilistic interpretations, potentially explaining the quantum-classical transition.

Contribution

It develops a local, deterministic model that reproduces key quantum phenomena and provides insights into the quantum-to-classical transition, challenging existing nonlocal theories.

Findings

System trajectories resemble quantum particles under Schrödinger dynamics

Model reproduces double slit diffraction and superluminal traversal behaviors

System exhibits bifurcations into classical and quantum regimes

Abstract

Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical dependence, however it necessitates the existence of "ghost waves". This manuscript develops a deterministic dynamical system with local interactions. The aggregate behavior of the trajectories are reminiscent of a quantum particle evolving under the Schr\"{o}dinger equation and reminiscent of Feynman's path integral interpretation in three canonical examples: motion in free space, double slit diffraction, and superluminal barrier traversal. Moreover, the system bifurcates into various dynamical regimes including a classical limit. These results illustrate a deterministic alternative to probabilistic interpretations and aims to shed light on the transition from quantum to classical mechanics.