dorsal/arxiv
View SchemaLorentz-covariant quantum mechanics and preferred frame
| Authors | Pawel Caban, Jakub Rembieliński |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9808013 |
| URL | https://arxiv.org/abs/quant-ph/9808013 |
| DOI | 10.1103/PhysRevA.59.4187 |
| Journal | Phys.Rev. A59 (1999) 4187-4196 |
Abstract
In this paper the relativistic quantum mechanics is considered in the framework of the nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincar{\'e} covariance but (at least formally) distinguishes an inertial frame. This enables to avoid the problem of a noncausal transmision of information related to breaking of the Bell's inequalities in QM. Our analysis has been focused mainly on the problem of existence of a proper position operator for massive particles. We have proved that in our framework such an operator exists for particles with arbitrary spin. It fulfills all the requirements: it is Hermitean and covariant, it has commuting components and moreover its eigenvectors (localised states) are also covariant. We have found the explicit form of the position operator and have demonstrated that in the preferred frame our operator coincides with the Newton--Wigner one. We have also defined a covariant spin operator and have constructed an invariant spin square operator. Moreover, full algebra of observables consisting of position operators, fourmomentum operators and spin operators is manifestly Poincar\'e covariant in this framework. Our results support expectations of other authors (Bell, Eberhard) that a consistent formulation of quantum mechanics demands existence of a preferred frame.
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"abstract": "In this paper the relativistic quantum mechanics is considered in the\nframework of the nonstandard synchronization scheme for clocks. Such a\nsynchronization preserves Poincar{\\\u0027e} covariance but (at least formally)\ndistinguishes an inertial frame. This enables to avoid the problem of a\nnoncausal transmision of information related to breaking of the Bell\u0027s\ninequalities in QM. Our analysis has been focused mainly on the problem of\nexistence of a proper position operator for massive particles. We have proved\nthat in our framework such an operator exists for particles with arbitrary\nspin. It fulfills all the requirements: it is Hermitean and covariant, it has\ncommuting components and moreover its eigenvectors (localised states) are also\ncovariant. We have found the explicit form of the position operator and have\ndemonstrated that in the preferred frame our operator coincides with the\nNewton--Wigner one. We have also defined a covariant spin operator and have\nconstructed an invariant spin square operator. Moreover, full algebra of\nobservables consisting of position operators, fourmomentum operators and spin\noperators is manifestly Poincar\\\u0027e covariant in this framework. Our results\nsupport expectations of other authors (Bell, Eberhard) that a consistent\nformulation of quantum mechanics demands existence of a preferred frame.",
"arxiv_id": "quant-ph/9808013",
"authors": [
"Pawel Caban",
"Jakub Rembieli\u0144ski"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.59.4187",
"journal_ref": "Phys.Rev. A59 (1999) 4187-4196",
"title": "Lorentz-covariant quantum mechanics and preferred frame",
"url": "https://arxiv.org/abs/quant-ph/9808013"
},
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