2011 Fiscal Year Final Research Report
Quantum Set Theory Aiming at Realistic Interpretation of Quantum Theory
| Project/Area Number |
22654013
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
OZAWA Masanao 名古屋大学, 情報科学研究科, 教授 (40126313)
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| Project Period (FY) |
2010 – 2011
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| Keywords | 数学基礎論 / 量子情報 / 科学哲学 / 量子論理 / 量子集合論 / 量子測定理論 / 様相解釈 / 代数的場の量子論 |
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| Research Abstract |
The problem of realistic interpretation of quantum theory has produced several paradoxes and remains an important open problem in foundations of quantum theory. In this study we introduced methods of foundations of mathematics into this problem, and constructed quantum set theory, a challenging new approach, aiming at a realistic interpretation of quantum theory. We developed quantum set theory over a general orthomodular lattice, gave foundations of modal interpretation of quantum theory based on it, and clarified the notions of reality in Bohr's complementarity principle.
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Research Products
(21 results)
