Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics. Based on a semiclassical geometric approach, here we conjecture...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-07-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722003126 |
| _version_ | 1811249989435785216 |
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| author | Jaume Giné Giuseppe Gaetano Luciano |
| author_facet | Jaume Giné Giuseppe Gaetano Luciano |
| author_sort | Jaume Giné |
| collection | DOAJ |
| description | The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics. Based on a semiclassical geometric approach, here we conjecture an effective generalization of this principle, which is well-suited to be extended to general relativity scenarios as well. We apply our formalism to Schwarzschild and de Sitter spacetime, showing that the ensuing uncertainty relations can be mapped into well-known deformations of the HUP. We also infer the form of the perturbed metric that mimics the emergence of a discrete spacetime structure at Planck scale, consistently with the predictions of the Generalized Uncertainty Principle. Finally, we discuss our results in connection with other approaches recently appeared in the literature. |
| first_indexed | 2024-04-12T15:57:08Z |
| format | Article |
| id | doaj.art-681e87c679b143e79760e03673d17ca0 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-12T15:57:08Z |
| publishDate | 2022-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-681e87c679b143e79760e03673d17ca02022-12-22T03:26:20ZengElsevierResults in Physics2211-37972022-07-0138105594Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approachJaume Giné0Giuseppe Gaetano Luciano1Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Catalonia, Spain; Corresponding author.Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Catalonia, Spain; Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132 I-84084 Fisciano (SA), Italy; INFN, Sezione di Napoli, Gruppo collegato di Salerno, ItalyThe Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics. Based on a semiclassical geometric approach, here we conjecture an effective generalization of this principle, which is well-suited to be extended to general relativity scenarios as well. We apply our formalism to Schwarzschild and de Sitter spacetime, showing that the ensuing uncertainty relations can be mapped into well-known deformations of the HUP. We also infer the form of the perturbed metric that mimics the emergence of a discrete spacetime structure at Planck scale, consistently with the predictions of the Generalized Uncertainty Principle. Finally, we discuss our results in connection with other approaches recently appeared in the literature.http://www.sciencedirect.com/science/article/pii/S2211379722003126Uncertainty principle(s)Schwarzschild spacetimeDe sitter spacetimePlanck scale |
| spellingShingle | Jaume Giné Giuseppe Gaetano Luciano Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach Results in Physics Uncertainty principle(s) Schwarzschild spacetime De sitter spacetime Planck scale |
| title | Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach |
| title_full | Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach |
| title_fullStr | Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach |
| title_full_unstemmed | Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach |
| title_short | Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach |
| title_sort | gravitational effects on the heisenberg uncertainty principle a geometric approach |
| topic | Uncertainty principle(s) Schwarzschild spacetime De sitter spacetime Planck scale |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722003126 |
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