Study of Quantum Set Theory Aiming at an Interpretation of Elements of Reality in Quantum Theory
Project/Area Number |
24654021
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Single-year Grants |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Nagoya University |
Principal Investigator |
OZAWA Masanao 名古屋大学, 情報科学研究科, 教授 (40126313)
|
Project Period (FY) |
2012-04-01 – 2014-03-31
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Project Status |
Completed (Fiscal Year 2013)
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Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 量子集合論 / 数学基礎論 / 数理物理学 / 科学哲学 / 様相解釈 / 量子力学 / 代数的場の量子論 / 量子測定 / 量子解釈 / 哲学 / 数理物理 |
Research Abstract |
It is one of long-standing open problems in the field across physics and philosophy to give a realistic interpretation for values of quantum observables. In this research we proposed a new approach to this problem based on quantum set theory. We studied the relationship between quantum set theory and modal interpretation of quantum theory, and we showed the equivalence between the condition for a von Neumann algebra to be a beable algebra for a given state and the condition for a subuniverse of quantum set theory to satisfy all the theorems of ZFC set theory in that state. We also extended the conventional no collapse interpretation for projective measurements to a no collapse interpretation for arbitrary generalized measurements by using the equivalence between quantum perfect correlation for two observables and the quantum-set-theoretical equality for two real numbers in quantum set theory.
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Report
(3 results)
Research Products
(54 results)