dorsal/arxiv
View SchemaQuantum Mechanics: Structures, Axioms and Paradoxes
| Authors | Diederik Aerts |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106132 |
| URL | https://arxiv.org/abs/quant-ph/0106132 |
Abstract
We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of `quantum structures research'. We concentrate mostly on the results of our group FUND at Brussels Free University. By means of a spin 1/2 model where the quantum probability is generated by the presence of fluctuations on the interactions between measuring apparatus and physical system, we show that the quantum structure can find its origin in the presence of these fluctuations. This appraoch, that we have called the 'hidden measurement approach', makes it possible to construct systems that are in between quantum and classical. We show that two of the traditional axioms of quantum axiomatics are not satisfied for these 'in between quantum and classical' situations, and how this structural shortcoming of standard quantum mechanics is at the origin of most of the quantum paradoxes. We show that in this approach the EPR paradox identifies a genuine incompleteness of standard quantum mechanics, however not an incompleteness that means the lacking of hidden variables, but an incompleteness pointing at the impossibility for standard quantum mechanics to describe separated quantum systems. We indicate in which way, by redefining the meaning of density states, standard quantum mechanics can be completed. We put forward in which way the axiomatic approach to quantum mechanics can be compared to the traditional axiomatic approach to relativity theory, and how this might lead to studying another road to unification of both theories.
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"abstract": "We present an analysis of quantum mechanics and its problems and paradoxes\ntaking into account the results that have been obtained during the last two\ndecades by investigations in the field of `quantum structures research\u0027. We\nconcentrate mostly on the results of our group FUND at Brussels Free\nUniversity. By means of a spin 1/2 model where the quantum probability is\ngenerated by the presence of fluctuations on the interactions between measuring\napparatus and physical system, we show that the quantum structure can find its\norigin in the presence of these fluctuations. This appraoch, that we have\ncalled the \u0027hidden measurement approach\u0027, makes it possible to construct\nsystems that are in between quantum and classical. We show that two of the\ntraditional axioms of quantum axiomatics are not satisfied for these \u0027in\nbetween quantum and classical\u0027 situations, and how this structural shortcoming\nof standard quantum mechanics is at the origin of most of the quantum\nparadoxes. We show that in this approach the EPR paradox identifies a genuine\nincompleteness of standard quantum mechanics, however not an incompleteness\nthat means the lacking of hidden variables, but an incompleteness pointing at\nthe impossibility for standard quantum mechanics to describe separated quantum\nsystems. We indicate in which way, by redefining the meaning of density states,\nstandard quantum mechanics can be completed. We put forward in which way the\naxiomatic approach to quantum mechanics can be compared to the traditional\naxiomatic approach to relativity theory, and how this might lead to studying\nanother road to unification of both theories.",
"arxiv_id": "quant-ph/0106132",
"authors": [
"Diederik Aerts"
],
"categories": [
"quant-ph"
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"title": "Quantum Mechanics: Structures, Axioms and Paradoxes",
"url": "https://arxiv.org/abs/quant-ph/0106132"
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