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Representation of the Universe as a Dendrogramic Hologram Endowed with Relational Interpretation
 
 
Article

Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity

1
Felsenstein Medical Research Center, Beilinson Hospital, Petach Tikva 4941492, Israel
2
Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel
3
Department of Neurology, Rabin Medical Center, Petach Tikva 4941492, Israel
4
Department of Mathematics, Faculty of Technology, Linnaeus University, 35195 Växjö, Sweden
*
Author to whom correspondence should be addressed.
Academic Editors: Rosario Lo Franco, Arkady Plotnitsky and Gregg Jaeger
Entropy 2021, 23(8), 971; https://doi.org/10.3390/e23080971
Received: 13 June 2021 / Revised: 21 July 2021 / Accepted: 23 July 2021 / Published: 28 July 2021
(This article belongs to the Special Issue The Philosophy of Quantum Physics)
This paper is devoted to the foundational problems of dendrogramic holographic theory (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. View Full-Text
Keywords: ontic; epistemic; dendrograms; dendrogramic holographic theory; clustering algorithms; quantumness; CHSH inequality; nonergodicity ontic; epistemic; dendrograms; dendrogramic holographic theory; clustering algorithms; quantumness; CHSH inequality; nonergodicity
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MDPI and ACS Style

Shor, O.; Benninger, F.; Khrennikov, A. Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity. Entropy 2021, 23, 971. https://doi.org/10.3390/e23080971

AMA Style

Shor O, Benninger F, Khrennikov A. Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity. Entropy. 2021; 23(8):971. https://doi.org/10.3390/e23080971

Chicago/Turabian Style

Shor, Oded, Felix Benninger, and Andrei Khrennikov. 2021. "Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity" Entropy 23, no. 8: 971. https://doi.org/10.3390/e23080971

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