A Non-local Phase Field Model of Bohm’s Quantum Potential

@article{Mauri2021ANP,
  title={A Non-local Phase Field Model of Bohm’s Quantum Potential},
  author={Roberto Mauri},
  journal={Foundations of Physics},
  year={2021},
  volume={51},
  pages={1-8}
}
  • R. Mauri
  • Published 4 March 2021
  • Physics
  • Foundations of Physics
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. 
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A covariant non-local phase field model of Bohm's potential

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.

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