发表机构
Ludwig-Maximilians University of München（慕尼黑路德维希-马克西米利安大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文论证量子力学中希尔伯特空间的物理性，提出物理性的层级观，区分本体论与操作主义解读，并用于解决量子场论中不等价表示带来的解释问题。
AI 中文摘要
在本文中，我探讨了量子力学中希尔伯特空间的物理性问题，这一话题因Carcassi等人的论文《希尔伯特空间的非物理性》而近期受到关注。我主张量子力学中的希尔伯特空间具有物理性，并证明若试图将物理态集合等同于其真子集，则不可避免地存在模糊性与任意性。此外，我将物理性的本体论与模态解读同实用主义与操作主义解读区分开来，进而发展出我所称的物理性的层级观。根据这一观点，物理性并非一个单一概念，而是分层的、允许有程度的。我展示了物理性概念与模态形而上学之间的联系，并最终解释了如何利用这一观点来应对由不等价表示的存在所引发的量子场论的解释问题。
英文摘要
In this paper, I address the problem regarding the physicality of Hilbert space in quantum mechanics, a topic brought into focus by Carcassi et al.'s paper "The unphysicality of Hilbert spaces" recently. I argue for the physicality of the Hilbert space in quantum mechanics, and demonstrate that there are inevitable ambiguity and arbitrariness if we want to identify the set of physical states with a proper subset of it. Moreover, I distinguish the ontological and modal reading of physicality from the pragmatic and operational reading of physicality, and then develop what I call the hierarchical view of physicality. According to this view, physicality is not a monolithic concept, but a layered one that admits degrees. I show the connection between the concept of physicality and modal metaphysics, and finally explain how it can be used to address the interpretational problem of quantum field theory brought by the existence of inequivalent representations.
