A covariant non-local phase field model of Bohm's potential

TL;DR

This paper develops a covariant, non-local phase field model of Bohm's potential, linking quantum mechanics to classical non-locality and finite propagation speed, providing a new perspective on quantum equations.

Contribution

It introduces a covariant, finite-speed non-local phase field model of Bohm's potential, extending classical interpretations of quantum mechanics.

Findings

Derivation of a covariant Madelung equation with finite propagation speed

Connection between non-local energy dependence and quantum potential

Classical interpretation of quantum hypotheses through non-locality

Abstract

Assuming that the 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 equations are obtained, showing explicitly that some of the hypotheses that led to the formulationb of quantum mechanics do admit a classical interpretation based on non-locality. Here, we generalize this approach imposing a finite speed of propagation of any perturbation, thus determining a covariant formulation of the Madelung equation.