dorsal/arxiv
View SchemaEnsembles and experiments in classical and quantum physics
| Authors | Arnold Neumaier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0303047 |
| URL | https://arxiv.org/abs/quant-ph/0303047 |
| DOI | 10.1142/S0217979203018338 |
Abstract
A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the `probability via expectation' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.
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"abstract": "A philosophically consistent axiomatic approach to classical and quantum\nmechanics is given. The approach realizes a strong formal implementation of\nBohr\u0027s correspondence principle. In all instances, classical and quantum\nconcepts are fully parallel: the same general theory has a classical\nrealization and a quantum realization.\n Extending the `probability via expectation\u0027 approach of Whittle to\nnoncommuting quantities, this paper defines quantities, ensembles, and\nexperiments as mathematical concepts and shows how to model complementarity,\nuncertainty, probability, nonlocality and dynamics in these terms. The approach\ncarries no connotation of unlimited repeatability; hence it can be applied to\nunique systems such as the universe.\n Consistent experiments provide an elegant solution to the reality problem,\nconfirming the insistence of the orthodox Copenhagen interpretation on that\nthere is nothing but ensembles, while avoiding its elusive reality picture. The\nweak law of large numbers explains the emergence of classical properties for\nmacroscopic systems.",
"arxiv_id": "quant-ph/0303047",
"authors": [
"Arnold Neumaier"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/S0217979203018338",
"title": "Ensembles and experiments in classical and quantum physics",
"url": "https://arxiv.org/abs/quant-ph/0303047"
},
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