Measurement events relative to temporal quantum reference frames
The Page-Wootters formalism is a proposal for reconciling the background-dependent, quantum-mechanical notion of time with the background independence of general relativity. However, the physical meaning of this framework remains debated. In this work, we compare two consistent approaches to the Pag...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-01-01
|
| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-01-30-1616/pdf/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832577750830940160 |
|---|---|
| author | Ladina Hausmann Alexander Schmidhuber Esteban Castro-Ruiz |
| author_facet | Ladina Hausmann Alexander Schmidhuber Esteban Castro-Ruiz |
| author_sort | Ladina Hausmann |
| collection | DOAJ |
| description | The Page-Wootters formalism is a proposal for reconciling the background-dependent, quantum-mechanical notion of time with the background independence of general relativity. However, the physical meaning of this framework remains debated. In this work, we compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements with respect to a temporal quantum reference frame. The so-called "twirled observable" approach implements measurements as operators that are invariant with respect to the Hamiltonian constraint. The "purified measurement" approach instead models measurements dynamically by modifying the constraint itself. While both approaches agree in the limit of ideal clocks, a natural generalization of the purified measurement approach to the case of non-ideal, finite-resource clocks yields a radically different picture. We discuss the physical origin of this discrepancy and argue that these approaches describe operationally distinct situations. Moreover, we show that, for non-ideal clocks, the purified measurement approach yields a time non-local evolution equation, which can lead to non-unitary evolution. Moreover, it implies a fundamental limitation to the operational definition of the temporal order of events. Nevertheless, unitarity and definite temporal order can be restored if we assume that time is discrete. |
| format | Article |
| id | doaj-art-817d2339c4f44ed1aa5ac7e3e45278d7 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-817d2339c4f44ed1aa5ac7e3e45278d72025-01-30T15:49:11ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-01-019161610.22331/q-2025-01-30-161610.22331/q-2025-01-30-1616Measurement events relative to temporal quantum reference framesLadina HausmannAlexander SchmidhuberEsteban Castro-RuizThe Page-Wootters formalism is a proposal for reconciling the background-dependent, quantum-mechanical notion of time with the background independence of general relativity. However, the physical meaning of this framework remains debated. In this work, we compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements with respect to a temporal quantum reference frame. The so-called "twirled observable" approach implements measurements as operators that are invariant with respect to the Hamiltonian constraint. The "purified measurement" approach instead models measurements dynamically by modifying the constraint itself. While both approaches agree in the limit of ideal clocks, a natural generalization of the purified measurement approach to the case of non-ideal, finite-resource clocks yields a radically different picture. We discuss the physical origin of this discrepancy and argue that these approaches describe operationally distinct situations. Moreover, we show that, for non-ideal clocks, the purified measurement approach yields a time non-local evolution equation, which can lead to non-unitary evolution. Moreover, it implies a fundamental limitation to the operational definition of the temporal order of events. Nevertheless, unitarity and definite temporal order can be restored if we assume that time is discrete.https://quantum-journal.org/papers/q-2025-01-30-1616/pdf/ |
| spellingShingle | Ladina Hausmann Alexander Schmidhuber Esteban Castro-Ruiz Measurement events relative to temporal quantum reference frames Quantum |
| title | Measurement events relative to temporal quantum reference frames |
| title_full | Measurement events relative to temporal quantum reference frames |
| title_fullStr | Measurement events relative to temporal quantum reference frames |
| title_full_unstemmed | Measurement events relative to temporal quantum reference frames |
| title_short | Measurement events relative to temporal quantum reference frames |
| title_sort | measurement events relative to temporal quantum reference frames |
| url | https://quantum-journal.org/papers/q-2025-01-30-1616/pdf/ |
| work_keys_str_mv | AT ladinahausmann measurementeventsrelativetotemporalquantumreferenceframes AT alexanderschmidhuber measurementeventsrelativetotemporalquantumreferenceframes AT estebancastroruiz measurementeventsrelativetotemporalquantumreferenceframes |