概念变量、量子理论和统计推断理论
Conceptual variables, quantum theory, and statistical inference theory
摘要：
本文提出了一种不同的量子理论方法。基础被认为是概念变量，物理变量，可能是可访问的或不可访问的，即，可能或不可能将数值分配给它们。在认知过程中，可接近的变量只是行动者或一些交流行动者观察到的理想观察。群作用定义在这些变量上，使用群表示理论，这是发展希尔伯特空间形式主义的基础。对应于可访问的概念变量的运营商派生的形式主义的结果，并在离散的情况下，它认为，可能的物理值是这些运营商的本征值。玻恩公式是在特定的假设下推导出来的。这里的全部讨论是对作者书的补充[1]。这种方法所隐含的对量子态（或本征向量空间）的解释是对自然的聚焦问题以及对这些问题的尖锐回答。如果同一性的解决方案与问题本身相联系;在玻尔定义的意义上，这些解决方案可能是互补的。这种解释可以称为量子理论的一般认识解释。它类似于Zwirn最近的Convival Solipsism，也类似于QBism，更一般地说，可以被视为Rovelli关系量子力学的具体实现。然而，本文件的重点不仅在于解释，也在于基础。但一些所谓的量子悖论的认识解释的简单后果进行了讨论。连接到统计推断理论进行了初步讨论，通过一个例子，并通过简要讨论量子测量理论。
英文摘要：
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical values to them. In an epistemic process, the accessible variables are just ideal observations as observed by an actor or by some communicating actors. Group actions are defined on these variables, and using group representation theory this is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible conceptual variables are derived as a result of the formalism, and in the discrete case it is argued that the possible physical values are the eigenvalues of these operators. The Born formula is derived under specific assumptions. The whole discussion here is a supplement to the author's book [1]. The interpretation of quantum states (or eigenvector spaces) implied by this approach is as focused questions to nature together with sharp answers to those questions. Resolutions if the identity are then connected to the questions themselves; these may be complementary in the sense defined by Bohr. This interpretation may be called a general epistemic interpretation of quantum theory. It is similar to Zwirn's recent Convival Solipsism, and also to QBism, and more generally, can be seen as a concrete implementation of Rovelli's Relational Quantum Mechanics. The focus in the present paper is, however, as much on foundation as on interpretation. But the simple consequences of an epistemic interpretation for some so called quantum paradoxes are discussed. Connections to statistical inference theory are discussed in a preliminary way, both through an example and through a brief discussion of quantum measurement theory.
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