Revisiting Boole Equation in the Quantum Context

Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics

We construct a non-contextual hidden variable model consistent with all the kinematic predictions of quantum mechanics (QM). The famous Bell-KS theorem shows that non-contextual models which satisfy a further reasonable restriction are inconsistent with QM. In our construction, we define a weaker variant of this restriction which captures its essence while still allowing a non-contextual description of QM. This is in contrast to the contextual hidden variable toy models, such as the one by Bell, and brings out an interesting alternate way of looking at QM. The results also relate to the Bohmia…

Revisiting Quantum Contextuality

The purpose of this note is to complete the interesting review on quantum contextuality [1] that appeared recently. In particular we will introduce and discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems, and also to shift the emphasis from the first to the second one. We will also argue that whereas Kochen-Specker's is essentially a negative result (a no-go theorem), Gleason's is a positive one since it provides a mathematical justification of Born's rule. The link between these issues is provided by a specific quantum fea…

重新审视量子力学的诠释：从FAPP解决方案到情境本体论

Revisiting the Interpretations of Quantum Mechanics: From FAPP Solutions to Contextual Ontologies

本文通过比较量子力学不同诠释，提出基于情境量化的CSM框架，提供非FAPP本体论以解释不可逆性与测量装置结构。

Revisiting Born's rule through Uhlhorn's and Gleason's theorems

In a previous article [1] we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach there is no "emergence", but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that are accessible to a quantum system, and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason's theorem was emphasized, with the argument that CSM provides a physical justification for Gleason's hypo…

在代数框架下重新审视量子语境性

Revisiting Quantum Contextuality in an Algebraic Framework

本文在代数框架下重新审视量子语境性，通过超语境性与超价性思想联系Kochen-Specker定理和Gleason定理，并借助无限张量积与扇区化机制，构建统一量子与经典物理的数学模型。

Revisiting Quantum Mysteries

In this article we argue that in quantum mechanics, and in opposition to classical physics, it is impossible to say that an isolated quantum system "owns" a physical property. Some properties of the system, its mass for example, belong to it in a sense close to that of classical physics; but most often a property must be attributed to the system within a context. We give simple motivations for adopting this point of view, and show that it clarifies many issues in quantum physics.