Classical mechanics as nonlinear quantum mechanics

TL;DR

This paper demonstrates that classical mechanics can be derived from a nonlinear Schrödinger equation with a real, positive wave function, challenging traditional quantum interpretations and suggesting new perspectives on nonlinear quantum theories.

Contribution

It shows that classical physics emerges from a nonlinear quantum framework where the wave function is real and positive, offering a novel interpretation of classical and nonlinear quantum mechanics.

Findings

Classical mechanics can be reproduced from a nonlinear Schrödinger equation.

A real, positive wave function is key to classical behavior.

Implications for Bohmian and nonlinear quantum interpretations.

Abstract

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.