dorsal/arxiv
View SchemaNon-orthogonal preferred projectors for modal interpretations of quantum mechanics
| Authors | R. W. Spekkens, J. E. Sipe |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0003092 |
| URL | https://arxiv.org/abs/quant-ph/0003092 |
Abstract
Modal interpretations constitute a particular approach to associating dynamical variables with physical systems in quantum mechanics. Given the `quantum logical' constraints that are typically adopted by such interpretations, only certain sets of variables can be taken to be simultaneously definite-valued, and only certain sets of values can be ascribed to these variables at a given time. Moreover, each allowable set of variables and values can be uniquely specified by a single `preferred' projector in the Hilbert space associated with the system. In general, the preferred projector can be one of several possibilities at a given time. In previous modal interpretations, the different possible preferred projectors have formed an orthogonal set. This paper investigates the consequences of adopting a non-orthogonal set. We present three contributions on this issue: (1) we provide an argument for such non-orthogonality, based on the assumption that perfectly predictable measurements reveal pre-existing values of variables, an assumption which has traditionally constituted a strong motivation for the modal approach; (2) we generalize the existing framework for modal interpretations to accommodate non-orthogonal preferred projectors; (3) we present a novel type of modal interpretation wherein the set of preferred projectors is fixed by a principle of entropy minimization, and we discuss some of the successes and shortcomings of this proposal.
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"abstract": "Modal interpretations constitute a particular approach to associating\ndynamical variables with physical systems in quantum mechanics. Given the\n`quantum logical\u0027 constraints that are typically adopted by such\ninterpretations, only certain sets of variables can be taken to be\nsimultaneously definite-valued, and only certain sets of values can be ascribed\nto these variables at a given time. Moreover, each allowable set of variables\nand values can be uniquely specified by a single `preferred\u0027 projector in the\nHilbert space associated with the system. In general, the preferred projector\ncan be one of several possibilities at a given time. In previous modal\ninterpretations, the different possible preferred projectors have formed an\northogonal set. This paper investigates the consequences of adopting a\nnon-orthogonal set. We present three contributions on this issue: (1) we\nprovide an argument for such non-orthogonality, based on the assumption that\nperfectly predictable measurements reveal pre-existing values of variables, an\nassumption which has traditionally constituted a strong motivation for the\nmodal approach; (2) we generalize the existing framework for modal\ninterpretations to accommodate non-orthogonal preferred projectors; (3) we\npresent a novel type of modal interpretation wherein the set of preferred\nprojectors is fixed by a principle of entropy minimization, and we discuss some\nof the successes and shortcomings of this proposal.",
"arxiv_id": "quant-ph/0003092",
"authors": [
"R. W. Spekkens",
"J. E. Sipe"
],
"categories": [
"quant-ph"
],
"title": "Non-orthogonal preferred projectors for modal interpretations of quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0003092"
},
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