Investigation of Realism through Reconsiderations of Interpretations of Quantum Mechanics.

自从量子力学被发现以来，一直伴随着关于如何给出它所处理的物体的图像的争论。其中最著名的是爱因斯坦与玻尔的辩论。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的现实画面。Bub(1997) ^*表明量子力学的解释可以通过优选可观测物的选择来表征，并断言量子力学概率可以解释为由优选可观测物决定的部分布尔代数上的真值集上的经典概率。克利夫顿和迪克森同意后者的观点。然而，正如我们的研究表明的那样，在（可数的）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-可加性和σ-完备性的，并且Hilbert空间的子空间格是σ-完备性的，因此如何将σ-可加性和σ-完备性引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，物理量的确定值意义上的确定性，以及将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-完备性的相容性，证明了我们不能将具有连续谱的物理量的观测命题的真值与ω-不一致联系起来。因此得出了一个很好的结论我们需要用更经典的命题来代替观测命题来获得它们在物理量和连续谱的情况下的相容性。这些结果并不一定有利于量子力学的现实解释，我将继续在包括量子场论在内的更广泛的领域进行研究。^*Bub， J.(1997)-解释量子世界。剑桥大学出版社。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