A non local phase field model of Bohm's quantum potential

TL;DR

This paper presents a non-local phase field model that derives Bohm's quantum potential from classical non-locality assumptions, providing a new perspective on quantum mechanics.

Contribution

It introduces a classical non-local phase field model that reproduces Bohm's quantum potential and the Madelung equation, linking quantum phenomena to non-local classical effects.

Findings

Derivation of Bohm's quantum potential from a non-local classical model

Reproduction of the Madelung equation within a classical framework

Demonstration of classical non-locality as a basis for quantum hypotheses

Abstract

Assuming that the free energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term, Bohm's quantum potential and the Madelung equation are identically obtained, showing explicitly that some of the hypotheses that led to the formulation of quantum mechanics admit a classical interpretation based on non-locality.