论文标题
遵循数学！：量子力学的数学作为线性隔板的数学，将其线性化为（Hilbert）向量空间
Follow the Math!: The mathematics of quantum mechanics as the mathematics of set partitions linearized to (Hilbert) vector spaces
论文作者
论文摘要
本文的目的是表明量子力学（QM）的数学是固定分区的数学（指定不确定性和确定性），该数学是线性化为向量空间的数学，尤其是在希尔伯特空间中。也就是说，QM的数学是数学的希尔伯特空间版本，它描述了客观的不确定性，即在设定的水平上是分区的数学。关键的分析概念是确定性与不确定性，区分与不明显的区别，以及可区分性与难以区分的性。从不确定到更明确的状态的关键机制是在量子级别预备的设定级别上的分区连接操作，以及由DIRAC的完整通勤操作员（CSCOS）组成的最大最大状态描述的形成。通过在集合水平和量子水平上的量子逻辑熵进行定量测量这种发展。这种跟进的方法支持了QM的字面解释 - 正如Abner Shimony等人所提倡的，这是客观无确定性的现实，这与现实的常识和经典观点截然不同，因为现实是“一直以来都是“确定的”。
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac's Complete Sets of Commuting Operators (CSCOs). This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM--as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being "definite all the way down."
