dorsal/arxiv
View SchemaNoncommutative analysis and quantum physics I. States and ensembles
| Authors | Arnold Neumaier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9909080 |
| URL | https://arxiv.org/abs/quant-ph/9909080 |
Abstract
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and ensembles, clarifies the logical relations and operations for them, and shows how they give rise to dynamics and probabilities. States are identified with maximal consistent sets of weak equalities in the algebra of observables (instead of, as usual, with the rays in a Hilbert space). This leads to a concise foundation of quantum mechanics, free of undefined terms, separating in a clear way the deterministic and the stochastic features of quantum physics. The traditional postulates of quantum mechanics are derived from well-motivated axiomatic assumptions. No special quantum logic is needed to handle the peculiarities of quantum mechanics. Foundational problems associated with the measurement process, such as the reduction of the state vector, disappear. The new interpretation of quantum mechanics contains `elements of physical reality' without the need to introduce a classical framework with hidden variables. In particular, one may talk about the state of the universe without the need of an external observer and without the need to assume the existence of multiple universes.
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"abstract": "In this sequence of papers, noncommutative analysis is used to give a\nconsistent axiomatic approach to a unified conceptual foundation of classical\nand quantum physics.\n The present Part I defines the concepts of observables, states and ensembles,\nclarifies the logical relations and operations for them, and shows how they\ngive rise to dynamics and probabilities.\n States are identified with maximal consistent sets of weak equalities in the\nalgebra of observables (instead of, as usual, with the rays in a Hilbert\nspace). This leads to a concise foundation of quantum mechanics, free of\nundefined terms, separating in a clear way the deterministic and the stochastic\nfeatures of quantum physics.\n The traditional postulates of quantum mechanics are derived from\nwell-motivated axiomatic assumptions. No special quantum logic is needed to\nhandle the peculiarities of quantum mechanics. Foundational problems associated\nwith the measurement process, such as the reduction of the state vector,\ndisappear.\n The new interpretation of quantum mechanics contains `elements of physical\nreality\u0027 without the need to introduce a classical framework with hidden\nvariables. In particular, one may talk about the state of the universe without\nthe need of an external observer and without the need to assume the existence\nof multiple universes.",
"arxiv_id": "quant-ph/9909080",
"authors": [
"Arnold Neumaier"
],
"categories": [
"quant-ph",
"gr-qc"
],
"title": "Noncommutative analysis and quantum physics I. States and ensembles",
"url": "https://arxiv.org/abs/quant-ph/9909080"
},
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