A covariant nonlocal phase field model of Bohm's potential
Abstract
Assuming that the energy of a gas depends nonlocally 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 nonlocality. Here, we generalize this approach imposing a finite speed of propagation of any perturbation, thus determining a covariant formulation of the Madelung equation.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 arXiv:
 arXiv:2202.01533
 Bibcode:
 2022arXiv220201533M
 Keywords:

 Quantum Physics
 EPrint:
 9 pages