量子逻辑与非交换几何

组合非交换运算的反事实结果时的逻辑不一致性：解构GHZ-Bell定理

Logical inconsistency in combining counterfactual results from non-commutative operations: Deconstructing the GHZ-Bell theorems

格林伯格、霍恩、蔡林格（GHZ）定理对于考虑量子力学中隐变量的可能性至关重要。由于它依赖于对三个粒子的单组测量的预测，它消除了贝尔定理遇到的采样漏洞，需要大量的观测来获得少量有用的联合测量。在回避这个问题时，GHZ定理被认为证实了贝尔的历史性结论，即局部隐变量与量子力学的结果不一致。GHZ定理依赖于预测测量集合的结果，其中仅可以执行一个测量集合，即，反事实在本文中，这些未执行的测量序列的非交换方面进行了严格审查。三个经典的例子和两个变化的GHZ结构进行了分析，以证明非交换操作的组合反事实的结果是在一般逻辑上不一致的可执行的测量序列，考虑到非交换。因此，关于局部隐变量的否定结论并不像历史上那样从GHZ和Bell定理得出。

Black hole entropy from trace dynamics and non-commutative geometry

Spontaneous localisation is a falsifiable, phenomenological, mechanism for explaining the absence of macroscopic position superpositions, currently being tested for in the laboratory. The theory of trace dynamics provides a possible theoretical origin for spontaneous localisation. We have recently proposed how to employ non-commutative geometry to include gravity in trace dynamics, and suggested the emergence of classical space-time geometry via spontaneous localisation. In our theory, which we call non-commutative matter gravity, a black hole arises from the spontaneous localisation of an ent…

Let the Mathematics of Quantum Speak: Allowed and Unallowed Logic

Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to highlight some rather bold points about the `logic' aspect in quantum physics, necessarily restricting when and which logic may be admissible. And one may understand why that path is hardly followed in the literature. The mathematics/formalism of quantum, compared with classical, physics, may be fairly basically characterized by non-commutative algebras replac…

非交换几何的两种方法

Two Approaches to Non-Commutative Geometry

展望数学史，人们可以找到两种几何学的外部方法。第一个（代数）是由于笛卡尔和第二个（群论）-克莱因。我们将看到他们不是竞争对手，而是（伽罗瓦）并列。我们还研究了他们的现代生活的非交换几何哲学。讨论了不同对象之间的连接（参见关键字）。保留字：Heisenberg群，Weyl对易关系，Manin plain，量子群，SL（2，R），Hardy空间，Bergman空间，Segal-Bargmann空间，Szeg“o投影，Bergman投影，Clifford分析，Cauchy-Riemann-Dirac算子，Moebius变换，泛函演算，Weyl演算（量子化），Berezin量子化，Wick序，量子力学.