dorsal/arxiv
View SchemaNoncommutative analysis and quantum physics I. Quantities, ensembles and states
| Authors | Arnold Neumaier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001096 |
| URL | https://arxiv.org/abs/quant-ph/0001096 |
Abstract
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries no connotations of unlimited repeatability; hence it can be applied to unique systems such as the universe. Precise concepts and traditional results about complementarity, uncertainty and nonlocality follow with a minimum of technicalities. Probabilities are introduced in a generality supporting so-called effects (i.e., fuzzy events). States are defined as partial mappings that provide reference values for certain quantities. An analysis of sharpness properties yields well-known no-go theorems for hidden variables. By dropping the sharpness requirement, hidden variable theories such as Bohmian mechanics can be accommodated, but so-called ensemble states turn out to be a more natural realization of a realistic state concept. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.
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"abstract": "A unified conceptual foundation of classical and quantum physics is given,\nfree of undefined terms.\n Ensembles are defined by extending the `probability via expectation\u0027 approach\nof Whittle to noncommuting quantities. This approach carries no connotations of\nunlimited repeatability; hence it can be applied to unique systems such as the\nuniverse. Precise concepts and traditional results about complementarity,\nuncertainty and nonlocality follow with a minimum of technicalities.\nProbabilities are introduced in a generality supporting so-called effects\n(i.e., fuzzy events).\n States are defined as partial mappings that provide reference values for\ncertain quantities. An analysis of sharpness properties yields well-known no-go\ntheorems for hidden variables. By dropping the sharpness requirement, hidden\nvariable theories such as Bohmian mechanics can be accommodated, but so-called\nensemble states turn out to be a more natural realization of a realistic state\nconcept. The weak law of large numbers explains the emergence of classical\nproperties for macroscopic systems.",
"arxiv_id": "quant-ph/0001096",
"authors": [
"Arnold Neumaier"
],
"categories": [
"quant-ph"
],
"title": "Noncommutative analysis and quantum physics I. Quantities, ensembles and states",
"url": "https://arxiv.org/abs/quant-ph/0001096"
},
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