dorsal/arxiv
View SchemaQuantum theory without Hilbert spaces
| Authors | Charis Anastopoulos |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0008126 |
| URL | https://arxiv.org/abs/quant-ph/0008126 |
| DOI | 10.1023/A:1012690715414 |
| Journal | Found.Phys. 31 (2001) 1545 |
Abstract
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum theory, liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen- Specker's theorem (it has distributive "logic"). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Kopenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems.
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"abstract": "Quantum theory does not only predict probabilities, but also relative phases\nfor any experiment, that involves measurements of an ensemble of systems at\ndifferent moments of time. We argue, that any operational formulation of\nquantum theory needs an algebra of observables and an object that incorporates\nthe information about relative phases and probabilities. The latter is the\n(de)coherence functional, introduced by the consistent histories approach to\nquantum theory. The acceptance of relative phases as a primitive ingredient of\nany quantum theory, liberates us from the need to use a Hilbert space and\nnon-commutative observables. It is shown, that quantum phenomena are adequately\ndescribed by a theory of relative phases and non-additive probabilities on the\nclassical phase space. The only difference lies on the type of observables that\ncorrespond to sharp measurements. This class of theories does not suffer from\nthe consequences of Bell\u0027s theorem (it is not a theory of Kolmogorov\nprobabilities) and Kochen- Specker\u0027s theorem (it has distributive \"logic\"). We\ndiscuss its predictability properties, the meaning of the classical limit and\nattempt to see if it can be experimentally distinguished from standard quantum\ntheory. Our construction is operational and statistical, in the spirit of\nKopenhagen, but makes plausible the existence of a realist, geometric theory\nfor individual quantum systems.",
"arxiv_id": "quant-ph/0008126",
"authors": [
"Charis Anastopoulos"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1023/A:1012690715414",
"journal_ref": "Found.Phys. 31 (2001) 1545",
"title": "Quantum theory without Hilbert spaces",
"url": "https://arxiv.org/abs/quant-ph/0008126"
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