Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized through finite-mass systems that are subject to the laws of...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-08-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-08-29-1098/pdf/ |
| _version_ | 1797733490347737088 |
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| author | Viktor Zelezny |
| author_facet | Viktor Zelezny |
| author_sort | Viktor Zelezny |
| collection | DOAJ |
| description | In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized through finite-mass systems that are subject to the laws of quantum mechanics and must be included in the dynamical evolution. A fundamental physical theory should take this fact seriously. In this paper, we further develop a symmetry-inspired approach to describe physics from the perspective of quantum reference frames. We find a unifying framework allowing us to systematically derive a broad class of perspective dependent descriptions and the transformations between them. Working with a translational-invariant toy model of three free particles, we discover that the introduction of relative coordinates leads to a Hamiltonian structure with two non-commuting constraints. This structure can be said to contain all observer-perspectives at once, while the redundancies prevent an immediate operational interpretation. We show that the operationally meaningful perspective dependent descriptions are given by Darboux coordinates on the constraint surface and that reference frame transformations correspond to reparametrizations of the constraint surface. We conclude by constructing a quantum perspective neutral structure, via which we can derive and change perspective dependent descriptions without referring to the classical theory. In addition to the physical findings, this work illuminates the interrelation of first and second class constrained systems and their respective quantization procedures. |
| first_indexed | 2024-03-12T12:29:51Z |
| format | Article |
| id | doaj.art-9b19bbe5a8a147deb60ed12754ced6e3 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-12T12:29:51Z |
| publishDate | 2023-08-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-9b19bbe5a8a147deb60ed12754ced6e32023-08-29T15:36:14ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-08-017109810.22331/q-2023-08-29-109810.22331/q-2023-08-29-1098Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structureViktor ZeleznyIn standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized through finite-mass systems that are subject to the laws of quantum mechanics and must be included in the dynamical evolution. A fundamental physical theory should take this fact seriously. In this paper, we further develop a symmetry-inspired approach to describe physics from the perspective of quantum reference frames. We find a unifying framework allowing us to systematically derive a broad class of perspective dependent descriptions and the transformations between them. Working with a translational-invariant toy model of three free particles, we discover that the introduction of relative coordinates leads to a Hamiltonian structure with two non-commuting constraints. This structure can be said to contain all observer-perspectives at once, while the redundancies prevent an immediate operational interpretation. We show that the operationally meaningful perspective dependent descriptions are given by Darboux coordinates on the constraint surface and that reference frame transformations correspond to reparametrizations of the constraint surface. We conclude by constructing a quantum perspective neutral structure, via which we can derive and change perspective dependent descriptions without referring to the classical theory. In addition to the physical findings, this work illuminates the interrelation of first and second class constrained systems and their respective quantization procedures.https://quantum-journal.org/papers/q-2023-08-29-1098/pdf/ |
| spellingShingle | Viktor Zelezny Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure Quantum |
| title | Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure |
| title_full | Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure |
| title_fullStr | Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure |
| title_full_unstemmed | Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure |
| title_short | Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure |
| title_sort | quantum reference frames derivation of perspective dependent descriptions via a perspective neutral structure |
| url | https://quantum-journal.org/papers/q-2023-08-29-1098/pdf/ |
| work_keys_str_mv | AT viktorzelezny quantumreferenceframesderivationofperspectivedependentdescriptionsviaaperspectiveneutralstructure |