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. 2023 Jun 9;25(6):915.
doi: 10.3390/e25060915.

A Covariant Non-Local Model of Bohm's Quantum Potential

Roberto Mauri  1 , Massimiliano Giona  2
Affiliations

A Covariant Non-Local Model of Bohm's Quantum Potential

Roberto Mauri et al. Entropy (Basel). .

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 equation are obtained, showing explicitly that some of the hypotheses that led to the formulation 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.

Keywords: Bohm quantum potential; Madelung equation; non-local quantum mechanics.

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Conflict of interest statement

The authors declare no conflict of interest.

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