形式化量子力学不必使用量子逻辑

Formalizing Quantum Mechanics without Quantum Logic

一般认为,标准量子力学需要使用一套它自己的逻辑系统,即量子逻辑。量子逻辑采用与一般逻辑系统不同的语义规则,因此和古典逻辑无法兼容。此篇文章将呈现一套量子力学的严格形式基础,它是对古典二值逻辑之保守扩充;保守扩充意指比原先之逻辑系统强,但较强的原因为它有较多之词汇。此套逻辑为三值逻辑。古典逻辑中为真的句子仍然为真。古典逻辑中为假的句子将被区分为强性假与中性。第三个真值一中性一考虑了非本征态情况中之观察句。本文详列了物理的公理并显示它们具有一个模型。此提案的可行性说明了量子逻辑是不必要的,并且存在一个共同的逻辑架构可提供给数学、非量子物理及量子力学使用。

A strict formal base of standard quantum mechanics is found in a three-valued logic which is a conservative extension of classical bivalent logic. A third truth value, neutral, takes account of observation sentences in the case of non-eigenstates. The feasibility of the present proposal demonstrates that quantum logic is not necessary and that a common logical framework is available for mathematics, non-quantum physics and quantum mechanics.