A Covariant Non-Local Model of Bohm’s Quantum 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. Truncating this series after the second term, Bohm’s quantum potential and the Madelung equation are obtained,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/6/915 |
| _version_ | 1797594977180581888 |
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| author | Roberto Mauri Massimiliano Giona |
| author_facet | Roberto Mauri Massimiliano Giona |
| author_sort | Roberto Mauri |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T02:30:20Z |
| format | Article |
| id | doaj.art-fee4c633c6034ee497de9fdfd77d5ef8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T02:30:20Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-fee4c633c6034ee497de9fdfd77d5ef82023-11-18T10:18:11ZengMDPI AGEntropy1099-43002023-06-0125691510.3390/e25060915A Covariant Non-Local Model of Bohm’s Quantum PotentialRoberto Mauri0Massimiliano Giona1DICI, Department of Civil and Industrial Engineering, Università di Pisa, 56122 Pisa, ItalyDICMA, Department of Industrial Engineering, Università di Roma La Sapienza, 00184 Roma, ItalyAssuming 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.https://www.mdpi.com/1099-4300/25/6/915non-local quantum mechanicsBohm quantum potentialMadelung equation |
| spellingShingle | Roberto Mauri Massimiliano Giona A Covariant Non-Local Model of Bohm’s Quantum Potential Entropy non-local quantum mechanics Bohm quantum potential Madelung equation |
| title | A Covariant Non-Local Model of Bohm’s Quantum Potential |
| title_full | A Covariant Non-Local Model of Bohm’s Quantum Potential |
| title_fullStr | A Covariant Non-Local Model of Bohm’s Quantum Potential |
| title_full_unstemmed | A Covariant Non-Local Model of Bohm’s Quantum Potential |
| title_short | A Covariant Non-Local Model of Bohm’s Quantum Potential |
| title_sort | covariant non local model of bohm s quantum potential |
| topic | non-local quantum mechanics Bohm quantum potential Madelung equation |
| url | https://www.mdpi.com/1099-4300/25/6/915 |
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