2000 Fiscal Year Final Research Report Summary
Investigation of Realism through Reconsiderations of Interpretations of Quantum Mechanics.
| Project/Area Number |
11610001
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Philosophy
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
ISHIGAKI Toshio HOKKAIDO UNIVERSITY Graduate School of Science. Professor., 大学院・理学研究科, 教授 (40089363)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Quantum Mechanics / Interpretation / Reality / Boolean Lattice / Determinate Values / Classical Probability / Ignorance Interpretation / Continuous Spectrum |
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| Research Abstract |
Quantum mechanics has, since its discovery, been accompanied by debates on how to give the picture of objects it deals with. The most famous was Einstein-Bohr debate. These debates have not yet reached the goal, and various interpretations of quantum mechanics have been presented. My research aims to present possible realistic pictures of the quantum mechanical world through reconsiderations of these interpretations. Bub (1997) ^* showed that interpretations of quantum mechanics can be characterized by choices of preferred observables, and asserted that quantum mechanical probabilities are interpretable as classical probabilities on the set of truth-valuations over partial Boolean algebras determined by preferred observables. Clifton and Dickson share the latter opinion. As our research has shown, however, the intrinsic situations in (denumerably) infinite dimensional Hilbert space become evident with respect to σ-additivity. Since quantum and classical probabilities are σ-additive and
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the lattice of subspaces of Hilbert space is (σ-) complete, it is a very important problem how to incorporate σ-additivity and σ-completeness into the interpretations of quantum mechanics.
I have studied the definiteness in the sense of definite truth-values of propositions, the definiteness in the sense of definite values of physical quantities, and the possibility of interpreting quantum probability as classical one, and their compatibility in relation to σ-additivity and σ-completeness, and proved that we cannot associate truth-valuations to observational propositions of physical quantity with continuous spectrum without ω-inconsistency, and hence reached fine conclusion that we need to replace the observational propositions to more classical ones to get their compatibility in the case of physical quantity with continuous spectrum.
These results are not necessarily favorable to realistic interpretations of quantum mechanics, and I will continue the research in the broader area including quantum field theory.
^*Bub, J.(1997)-Interpreting the Quantum World. Cambridge University Press. Less
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