AI Article Synopsis
- The energy of a gas is influenced by the logarithm of its mass density, leading to a body force in motion equations that includes density gradient terms.
- By truncating the series after the second term, we derive Bohm's quantum potential and the Madelung equation, indicating that certain assumptions in quantum mechanics can have a classical interpretation through non-locality.
- This work further generalizes the approach by incorporating finite propagation speed of perturbations, resulting in a covariant form of the Madelung equation.
Article 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.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10297607 | PMC |
| http://dx.doi.org/10.3390/e25060915 | DOI Listing |
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