Flow of time during energy measurements and the resulting time-energy uncertainty relations
Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations, even though time is not an operator in standard quantum mech...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2022-04-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2022-04-07-683/pdf/ |
| _version_ | 1818394472923267072 |
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| author | Ismael L. Paiva Augusto C. Lobo Eliahu Cohen |
| author_facet | Ismael L. Paiva Augusto C. Lobo Eliahu Cohen |
| author_sort | Ismael L. Paiva |
| collection | DOAJ |
| description | Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations, even though time is not an operator in standard quantum mechanics. However, in these cases, different approaches are associated with different meanings and interpretations for these relations. The one of interest here revolves around the idea of whether quantum mechanics inherently imposes a fundamental minimum duration for energy measurements with a certain precision. In our study, we investigate within the Page and Wootters timeless framework how energy measurements modify the relative "flow of time'' between internal and external clocks. This provides a unified framework for discussing the subject, allowing us to recover previous results and derive new ones. In particular, we show that the duration of an energy measurement carried out by an external system cannot be performed arbitrarily fast from the perspective of the internal clock. Moreover, we show that during any energy measurement the evolution given by the internal clock is non-unitary. |
| first_indexed | 2024-12-14T06:01:45Z |
| format | Article |
| id | doaj.art-e8974d05399942318520be52b30593a7 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-14T06:01:45Z |
| publishDate | 2022-04-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-e8974d05399942318520be52b30593a72022-12-21T23:14:26ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2022-04-01668310.22331/q-2022-04-07-68310.22331/q-2022-04-07-683Flow of time during energy measurements and the resulting time-energy uncertainty relationsIsmael L. PaivaAugusto C. LoboEliahu CohenUncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations, even though time is not an operator in standard quantum mechanics. However, in these cases, different approaches are associated with different meanings and interpretations for these relations. The one of interest here revolves around the idea of whether quantum mechanics inherently imposes a fundamental minimum duration for energy measurements with a certain precision. In our study, we investigate within the Page and Wootters timeless framework how energy measurements modify the relative "flow of time'' between internal and external clocks. This provides a unified framework for discussing the subject, allowing us to recover previous results and derive new ones. In particular, we show that the duration of an energy measurement carried out by an external system cannot be performed arbitrarily fast from the perspective of the internal clock. Moreover, we show that during any energy measurement the evolution given by the internal clock is non-unitary.https://quantum-journal.org/papers/q-2022-04-07-683/pdf/ |
| spellingShingle | Ismael L. Paiva Augusto C. Lobo Eliahu Cohen Flow of time during energy measurements and the resulting time-energy uncertainty relations Quantum |
| title | Flow of time during energy measurements and the resulting time-energy uncertainty relations |
| title_full | Flow of time during energy measurements and the resulting time-energy uncertainty relations |
| title_fullStr | Flow of time during energy measurements and the resulting time-energy uncertainty relations |
| title_full_unstemmed | Flow of time during energy measurements and the resulting time-energy uncertainty relations |
| title_short | Flow of time during energy measurements and the resulting time-energy uncertainty relations |
| title_sort | flow of time during energy measurements and the resulting time energy uncertainty relations |
| url | https://quantum-journal.org/papers/q-2022-04-07-683/pdf/ |
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