Research Project
Grant-in-Aid for Challenging Exploratory Research
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.
All 2014 2013 2012 Other
All Journal Article (19 results) (of which Peer Reviewed: 2 results, Open Access: 1 results, Acknowledgement Compliant: 1 results) Presentation (28 results) (of which Invited: 17 results) Book (1 results) Remarks (6 results)
Journal of Physics A: Mathematical and Theoretical
Volume: 47 Issue: 23 Pages: 235302-235302
10.1088/1751-8113/47/23/235302
Journal of Physics: Conference Series
Volume: 504 Pages: 012024-012024
10.1088/1742-6596/504/1/012024
量子集合論,数学セミナー
Volume: 53(3) Pages: 48-53
量子論理から量子集合論へ,数学セミナー
Volume: 53(2) Pages: 56-61
不確定性原理と相補性原理,数学セミナー
Volume: 53(1) Pages: 50-55
最新量子測定問題,数理科学
Volume: 52(1) Pages: 16-21
数理科学(2014年1月号,No.607,サイエンス社)
Volume: 52 Pages: 16-21
数学セミナー(2014年1月号,No. 627,日本評論社)
Volume: 52 Pages: 56-61
数学セミナー(2014年2月号,No. 628,日本評論社)
Volume: 53 Pages: 50-55
数学セミナー(2014年3月号,No. 629,日本評論社)
Volume: 53 Pages: 48-53
現代思想
Volume: 41(10) Pages: 154-180
数学セミナー
Volume: 52(4) Pages: 50-55
Volume: 52 Pages: 50-55
Volume: 52(1) Pages: 58-63
数理科学
Volume: 50(4) Pages: 26-27
科学
Volume: 82(7) Pages: 778-787
Volume: 50(9) Pages: 23-29
Volume: 51(11) Pages: 36-41
Volume: 51(12) Pages: 52-57
http://www.math.cm.is.nagoya-u.ac.jp/~ozawa/
http://researchmap.jp/ozawa/