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A Covariant Non-Local Model of Bohm's Quantum Potential.
Roberto Mauri1, Massimiliano Giona2
1DICI, Department of Civil and Industrial Engineering, Università di Pisa, 56122 Pisa, Italy.
Entropy (Basel, Switzerland)
|June 28, 2023
Summary
This study offers a classical interpretation of quantum mechanics by linking gas energy to density. It introduces a covariant Madelung equation, demonstrating non-locality
Area of Science:
- Quantum Mechanics
- Classical Mechanics
- Statistical Mechanics
Background:
- The energy of a gas is assumed to depend non-locally on the logarithm of its mass density.
- This leads to density gradient terms in the equation of motion.
Purpose of the Study:
- To explore a classical interpretation of quantum mechanics based on non-locality.
- To generalize the Madelung equation with a finite speed of propagation for perturbations.
Main Methods:
- Non-local energy-density dependence.
- Truncation of density gradient terms.
- Imposition of a finite speed of perturbation propagation.
Main Results:
- Bohm's quantum potential and the Madelung equation are derived.
- A covariant formulation of the Madelung equation is determined.
Conclusions:
- Quantum mechanical hypotheses can admit a classical interpretation via non-locality.
- The covariant Madelung equation provides a generalized framework.
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