arXiv quant-ph/06031722006-03-20quant-ph

关于经典力学和量子力学中的命题概念

On the Notion of Proposition in Classical and Quantum Mechanics

Claudio Garola, Sandro Sozzo

备注：: 22 pages. To appear in "The Foundations of Quantum Mechanics: Historical Analysis and Open Questions-Cesena 2004", C. Garola, A. Rossi and S. Sozzo Eds., World Scientific, Singapore, 2006

摘要：

在量子力学（QM）中，命题这个术语通常表示（标准）量子逻辑（QL）的一个元素。在QM的正统解释中，QL的命题不能与陈述物理系统的单个样本的性质的语言的句子相关联，因为性质在QM中是非客观的。这使得命题的解释成问题。通过采用其中一位作者提出的对质量管理的客观解释（语义实在论，或SR解释），可以消除这一困难。在这种情况下，可以对QM和经典力学（CM）采用统一的视角，并且可以构造具有塔斯基语义的简单一阶谓词演算L（x），使得可以将物理命题（即，一组物理状态）与L（x）的每个句子。所有物理命题的集合$P^{f}$是偏序的，并且包含可测试物理命题的子集$P^{f}_{T}$，其序结构取决于由物理理论建立的可测试性准则。特别地，$P^{f}_{T}$在CM中被证明是布尔格，而在QM中它可以被标识为QL。因此，QL的命题可以与L（x）的句子相关联，或者也可以与合适的量子语言$L_{TQ}(x)$的句子相关联，并且QL的结构表征了QM中的可测性概念。然后，我们可以证明，在这个视角下，量子真理的概念与经典真理的概念并不冲突。此外，这里提出的QL的解释被证明是等价于以前的语用解释的作者之一，并可以体现在一个更一般的角度，认为国家作为一个更广泛的语言与克里普金语义的一阶谓词。

英文摘要：

The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpretation of propositions problematical. The difficulty can be removed by adopting the objective interpretation of QM proposed by one of the authors (semantic realism, or SR, interpretation). In this case, a unified perspective can be adopted for QM and classical mechanics (CM), and a simple first order predicate calculus L(x) with Tarskian semantics can be constructed such that one can associate a physical proposition (i.e., a set of physical states) with every sentence of L(x). The set $P^{f}$ of all physical propositions is partially ordered and contains a subset $P^{f}_{T}$ of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, $P^{f}_{T}$ turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language $L_{TQ}(x)$, and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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