dorsal/arxiv
View SchemaLogical analysis of the Bohr Complementarity Principle in Afshar's experiment under the NAFL interpretation
| Authors | Radhakrishnan Srinivasan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504115 |
| URL | https://arxiv.org/abs/quant-ph/0504115 |
| Journal | International Journal of Quantum Information, Vol. 8, Issue 3 (2010) pp. 465-491 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The NAFL (non-Aristotelian finitary logic) interpretation of quantum mechanics requires that no `physical' reality can be ascribed to the wave nature of the photon. The NAFL theory QM, formalizing quantum mechanics, treats the superposed state ($S$) of a single photon taking two or more different paths at the same time as a logical contradiction that is formally unprovable in QM. Nevertheless, in a nonclassical NAFL model for QM in which the law of noncontradiction fails, $S$ has a meaningful metamathematical interpretation that the classical path information for the photon is not available. It is argued that the existence of an interference pattern does not logically amount to a proof of the self-interference of a single photon. This fact, when coupled with the temporal nature of NAFL truth, implies the logical validity of the retroactive assertion of the path information (and the logical superfluousness of the grid) in Afshar's experiment. The Bohr complementarity principle, when properly interpreted with the time dependence of logical truth taken into account, holds in Afshar's experiment. NAFL supports, but not demands, a metalogical reality for the particle nature of the photon even when the semantics of QM requires the state $S$.
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"abstract": "The NAFL (non-Aristotelian finitary logic) interpretation of quantum\nmechanics requires that no `physical\u0027 reality can be ascribed to the wave\nnature of the photon. The NAFL theory QM, formalizing quantum mechanics, treats\nthe superposed state ($S$) of a single photon taking two or more different\npaths at the same time as a logical contradiction that is formally unprovable\nin QM. Nevertheless, in a nonclassical NAFL model for QM in which the law of\nnoncontradiction fails, $S$ has a meaningful metamathematical interpretation\nthat the classical path information for the photon is not available. It is\nargued that the existence of an interference pattern does not logically amount\nto a proof of the self-interference of a single photon. This fact, when coupled\nwith the temporal nature of NAFL truth, implies the logical validity of the\nretroactive assertion of the path information (and the logical superfluousness\nof the grid) in Afshar\u0027s experiment. The Bohr complementarity principle, when\nproperly interpreted with the time dependence of logical truth taken into\naccount, holds in Afshar\u0027s experiment. NAFL supports, but not demands, a\nmetalogical reality for the particle nature of the photon even when the\nsemantics of QM requires the state $S$.",
"arxiv_id": "quant-ph/0504115",
"authors": [
"Radhakrishnan Srinivasan"
],
"categories": [
"quant-ph",
"math.LO"
],
"journal_ref": "International Journal of Quantum Information, Vol. 8, Issue 3\n (2010) pp. 465-491",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Logical analysis of the Bohr Complementarity Principle in Afshar\u0027s experiment under the NAFL interpretation",
"url": "https://arxiv.org/abs/quant-ph/0504115"
},
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