A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory
A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory
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DOI：
10.1063/1.2883742
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发表时间：
2007-03
影响因子：
1.3
通讯作者：
A. Döring;C. Isham
中科院分区：
文献类型：
--
作者：
A. Döring;C. Isham
本文是系列文章中的第二篇，其目标是发展一种构建物理学理论的全新方法。其动机来自于一种渴望，即解决在思考空间和时间的量子理论时出现的某些深层问题。我们的基本论点是，构建一个物理学理论等价于在一个附着于该系统的某种形式语言的主题中找到一个表示。当topos是集合的范畴时，经典物理学就产生了。其他类型的理论采用不同的主题。在本文中，我们深入研究了命题语言PL（S）在量子理论中的拓扑表示。在这样做的过程中，我们与早期将拓扑斯理论应用于量子物理的工作建立了直接的联系，并澄清了这些工作。关键的一步是一个我们称之为“daseinisation”的过程，通过这个过程，投影算子被映射到光谱前层的一个子对象经典状态空间的拓扑量子模拟。在论文的第二部分，我们改变齿轮...
This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we study in depth the topos representation of the propositional language, PL(S), for the case of quantum theory. In doing so, we make a direct link with, and clarify, the earlier work on applying topos theory to quantum physics. The key step is a process we term “daseinisation” by which a projection operator is mapped to a subobject of the spectral presheaf—the topos quantum analog of a classical state space. In the second part of the paper, we change gear ...