Shor Oded, Benninger Felix, Khrennikov Andrei
Felsenstein Medical Research Center, Beilinson Hospital, Petach Tikva 4941492, Israel.
Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel.
Entropy (Basel). 2021 Jul 28;23(8):971. doi: 10.3390/e23080971.
This paper is devoted to the foundational problems of (DH theory). We used the ontic-epistemic (implicate-explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; it is zero-dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric spaces). Classical-quantum interrelations lose their sharpness; generally, simple dendrograms are "more quantum" than complex ones. We used the CHSH inequality as a measure of quantum-likeness. We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor a rejection of realism, but the nonergodicity of dendrogramic time series. Generally, the violation of ergodicity is one of the basic features of DH theory. The dendrogramic representation leads to the local realistic model that violates the CHSH inequality. We also considered DH theory for Minkowski geometry and monitored the dependence of CHSH violation and nonergodicity on geometry, as well as a Lorentz transformation of data.
本文致力于探讨（DH理论）的基础问题。我们采用了本体 - 认知（隐 - 显秩序）方法。认知方面基于用层次聚类算法构建的树状图对数据的表示。本体世界被描述为一个p进数树；它是零维的、完全不连通的、无序的且有界的（在p进数超度量空间中）。经典 - 量子相互关系失去了其明晰性；一般来说，简单的树状图比复杂的树状图“更具量子性”。我们使用CHSH不等式作为量子相似性的度量。我们证明，由树状图表示的经典实验数据可能违反该不等式。这种违反的根源既不是非局域性也不是对实在论的摒弃，而是树状图时间序列的非遍历性。一般来说，违反遍历性是DH理论的基本特征之一。树状图表示导致了违反CHSH不等式的局部实在模型。我们还考虑了闵可夫斯基几何下的DH理论，并监测了CHSH违反和非遍历性对几何的依赖性以及数据的洛伦兹变换。
