dorsal/arxiv
View SchemaSeven Principles of Quantum Mechanics
| Authors | Igor V. Volovich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212126 |
| URL | https://arxiv.org/abs/quant-ph/0212126 |
Abstract
The list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that such an approach is too general to be considered as the foundation of quantum mechanics. In particular in this approach any finite-dimensional Hilbert space describes a quantum system. Though such a treatment might be a convenient approximation it can not be considered as a fundamental description of a quantum system and moreover it leads to some paradoxes like Bell's theorem. I present a list from seven basic postulates of axiomatic quantum mechanics. In particular the list includes the axiom describing spatial properties of quantum system. These axioms do not admit a nontrivial realization in the finite-dimensional Hilbert space. One suggests that the axiomatic quantum mechanics is consistent with local realism.
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"abstract": "The list of basic axioms of quantum mechanics as it was formulated by von\nNeumann includes only the mathematical formalism of the Hilbert space and its\nstatistical interpretation. We point out that such an approach is too general\nto be considered as the foundation of quantum mechanics. In particular in this\napproach any finite-dimensional Hilbert space describes a quantum system.\nThough such a treatment might be a convenient approximation it can not be\nconsidered as a fundamental description of a quantum system and moreover it\nleads to some paradoxes like Bell\u0027s theorem.\n I present a list from seven basic postulates of axiomatic quantum mechanics.\nIn particular the list includes the axiom describing spatial properties of\nquantum system. These axioms do not admit a nontrivial realization in the\nfinite-dimensional Hilbert space. One suggests that the axiomatic quantum\nmechanics is consistent with local realism.",
"arxiv_id": "quant-ph/0212126",
"authors": [
"Igor V. Volovich"
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"title": "Seven Principles of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0212126"
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