dorsal/arxiv
View SchemaContextual approach to quantum mechanics and the theory of the fundamental prespace
| Authors | Andrei Khrennikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306003 |
| URL | https://arxiv.org/abs/quant-ph/0306003 |
| DOI | 10.1063/1.1645650 |
Abstract
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation has all distinguishing features of the quantum model. Thus in spite all ``No-Go'' theorems (e.g., von Neumann, Kochen and Specker,..., Bell) we found the realist basis for quantum mechanics. Our representation is not standard model with hidden variables. In particular, this is not a reduction of quantum model to the classical one. Moreover, we see that such a reduction is even in principle impossible. This impossibility is not a consequence of a mathematical theorem but it follows from the physical structure of the model. By our model quantum states are very rough images of domains in the space of fundamental parameters - PRESPACE. Those domains represent complexes of physical conditions. By our model both classical and quantum physics describe REDUCTION of PRESPACE-INFORMATION. Quantum mechanics is not complete. In particular, there are prespace contexts which can be represented only by a so called hyperbolic quantum model. We predict violations of the Heisenberg's uncertainty principle and existence of dispersion free states.
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"abstract": "We constructed a Hilbert space representation of a contextual Kolmogorov\nmodel. This representation is based on two fundamental observables -- in the\nstandard quantum model these are position and momentum observables. This\nrepresentation has all distinguishing features of the quantum model. Thus in\nspite all ``No-Go\u0027\u0027 theorems (e.g., von Neumann, Kochen and Specker,..., Bell)\nwe found the realist basis for quantum mechanics. Our representation is not\nstandard model with hidden variables. In particular, this is not a reduction of\nquantum model to the classical one. Moreover, we see that such a reduction is\neven in principle impossible. This impossibility is not a consequence of a\nmathematical theorem but it follows from the physical structure of the model.\nBy our model quantum states are very rough images of domains in the space of\nfundamental parameters - PRESPACE. Those domains represent complexes of\nphysical conditions. By our model both classical and quantum physics describe\nREDUCTION of PRESPACE-INFORMATION. Quantum mechanics is not complete. In\nparticular, there are prespace contexts which can be represented only by a so\ncalled hyperbolic quantum model. We predict violations of the Heisenberg\u0027s\nuncertainty principle and existence of dispersion free states.",
"arxiv_id": "quant-ph/0306003",
"authors": [
"Andrei Khrennikov"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1645650",
"title": "Contextual approach to quantum mechanics and the theory of the fundamental prespace",
"url": "https://arxiv.org/abs/quant-ph/0306003"
},
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