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Investigation of Realism through Reconsiderations of Interpretations of Quantum Mechanics.

通过重新考虑量子力学的解释来研究实在论。

基本信息

批准号：
11610001
负责人：
ISHIGAKI Toshio
金额：
$ 0.96万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

项目摘要

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

自从量子力学被发现以来，就一直伴随着关于如何描述它所处理的对象的争论。最著名的是爱因斯坦-玻尔的辩论。这些争论还没有达到目的，对量子力学的各种解释已经提出。我的研究旨在通过重新考虑这些解释来呈现量子力学世界的可能现实图像。Bub（1997）^* 表明量子力学的解释可以通过选择偏好的可观察量来表征，并断言量子力学概率可以解释为部分布尔代数上由偏好的可观察量确定的真值赋值集合上的经典概率。克利夫顿和迪克森同意后一种观点。然而，正如我们的研究所示，（可数）无限维希尔伯特空间中的内在情况对于σ-可加性变得明显。由于量子概率和经典概率是σ-可加的， ...更多信息 Hilbert空间的子空间格是（σ-）完备的，如何将σ-可加性和σ-完备性引入量子力学的解释中是一个非常重要的问题.本文研究了命题定真值意义下的定性，物理量定值意义下的定性，以及量子概率解释为经典概率的可能性，以及它们在σ-可加性和σ-完备性方面的相容性，证明了在没有ω-不相容性的情况下，不能把真值赋值与连续谱物理量的观测命题联系起来，并由此得出了一个很好的结论，即我们需要把观测命题替换成更经典的命题，以获得它们在物理量的情况下的兼容性，这些结果不一定有利于量子力学的现实解释，我将继续在更广泛的领域包括量子场论的研究。^* Bub，J. 1997年：《解读量子世界》剑桥大学出版社.少