dorsal/arxiv
View SchemaQuantum systems as classical systems
| Authors | Antonio Cassa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0111070 |
| URL | https://arxiv.org/abs/quant-ph/0111070 |
| DOI | 10.1063/1.1402957 |
Abstract
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in a random way with a statistical character. What kind of statistical theory is obtainable in this way? It is possible, for example, to obtain exactly the statistical previsions of quantum mechanics? Or, in other words, can a physical system showing a classical behaviour appear to be a quantum system to a confusing observer? We show that from a mathematical viewpoint it is not difficult to produce a theory with hidden variables having this property. We don't even try to justify in physical terms the artificial construction we propose; what we do is to give a general and rigorous argument showing how the interplay between the classical and quantum mechanics we offer is interpretable as the difference between an imaginary very expert observer and another nonexpert observer. This proves also that besides the well known theorems concerning the impossibility of hidden variables (cfr. Von Neumann [Neu] and Jauch-Piron [J-P]) there is also room for a result in favor of the possibility.
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"abstract": "A characteristical property of a classical physical theory is that the\nobservables are real functions taking an exact outcome on every (pure) state;\nin a quantum theory, at the contrary, a given observable on a given state can\ntake several values with only a predictable probability. However, even in the\nclassical case, when an observer is intrinsically unable to distinguish between\nsome distinct states he can convince himself that the measure of its\n\u0027\u0027observables\u0027\u0027 can have several values in a random way with a statistical\ncharacter. What kind of statistical theory is obtainable in this way? It is\npossible, for example, to obtain exactly the statistical previsions of quantum\nmechanics? Or, in other words, can a physical system showing a classical\nbehaviour appear to be a quantum system to a confusing observer? We show that\nfrom a mathematical viewpoint it is not difficult to produce a theory with\nhidden variables having this property. We don\u0027t even try to justify in physical\nterms the artificial construction we propose; what we do is to give a general\nand rigorous argument showing how the interplay between the classical and\nquantum mechanics we offer is interpretable as the difference between an\nimaginary very expert observer and another nonexpert observer. This proves also\nthat besides the well known theorems concerning the impossibility of hidden\nvariables (cfr. Von Neumann [Neu] and Jauch-Piron [J-P]) there is also room for\na result in favor of the possibility.",
"arxiv_id": "quant-ph/0111070",
"authors": [
"Antonio Cassa"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1402957",
"title": "Quantum systems as classical systems",
"url": "https://arxiv.org/abs/quant-ph/0111070"
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