Investigation of Realism through Reconsiderations of Interpretations of Quantum Mechanics.

自从量子力学被发现以来，关于如何给出它所处理的物体的图像的争论一直伴随着它。最著名的是爱因斯坦和玻尔的辩论。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可能的量子力学世界的现实图景。Bub(1997)^*证明了量子力学的解释可以通过选择首选观测来表征，并断言量子力学概率可以解释为由首选观测确定的部分布尔代数上的真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，正如我们的研究所表明的那样，关于σ可加性，无限维希尔伯特空间中的内蕴情形变得明显。由于量子概率和经典概率是σ可加的和…的而且希尔伯特空间的子空间格是(σ-)完备的，如何将σ可加性和σ完备性融入到量子力学的解释中是一个非常重要的问题.我研究了命题的确定真值意义上的确定性，物理量确定值意义上的确定性，量子概率解释为经典概率的可能性，以及它们与σ可加性和σ完备性的兼容性.证明了在没有ω不相容的情况下，不能将物理量的观测命题的真值估计与连续谱联系起来，并由此得出一个很好的结论，即在物理量具有连续谱的情况下，我们需要将观测命题替换为更经典的命题，以获得它们的兼容性。这些结果不一定有利于对量子力学的现实解释，我将继续在更广泛的领域进行研究，包括量子场论。^*Bub，J.(1997)-解释量子世界。剑桥大学出版社。较少

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