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2000 Fiscal Year Final Research Report Summary

Investigation of Realism through Reconsiderations of Interpretations of Quantum Mechanics.

Research Project

Project/Area Number 11610001
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Philosophy
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

ISHIGAKI Toshio  HOKKAIDO UNIVERSITY Graduate School of Science. Professor., 大学院・理学研究科, 教授 (40089363)

Project Period (FY) 1999 – 2000
KeywordsQuantum Mechanics / Interpretation / Reality / Boolean Lattice / Determinate Values / Classical Probability / Ignorance Interpretation / Continuous Spectrum
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 … More 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

  • Research Products

    (4 results)

All Other

All Publications (4 results)

  • [Publications] 石垣壽郎: "量子力学の確率概念について"科学基礎論研究. 27・1. 39-44 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 石垣壽郎: "量子力学におけるブール束"科学基礎論研究. 28・1. 1-7 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] ISHIGAKE,Toshio: "Probability in Quantum Mechanics (in Japanese)"Journal of the Japan Association for Philosophy of Science. 27(1). 39-44 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] ISHIGAKI,Toshio: "Boolean Lattices in Quantum Mechanics (in Japanese)"Journal of the Japan Association for Philosophy of Science. 28(1). 1-7 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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