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Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity
Beilinson Med Ctr, Israel;Tel Aviv Univ, Israel.
Beilinson Med Ctr, Israel;Tel Aviv Univ, Israel;Rabin Med Ctr, Israel.
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2021 (English)In: Entropy, E-ISSN 1099-4300, Vol. 23, no 8, article id 971Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
MDPI, 2021. Vol. 23, no 8, article id 971
Keywords [en]
ontic, epistemic, dendrograms, dendrogramic holographic theory, clustering algorithms, quantumness, CHSH inequality, nonergodicity
National Category
Mathematics Physical Sciences
Research subject
Natural Science, Physics; Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-106877DOI: 10.3390/e23080971ISI: 000690548500001PubMedID: 34441111Scopus ID: 2-s2.0-85112415706Local ID: 2021OAI: oai:DiVA.org:lnu-106877DiVA, id: diva2:1592861
Available from: 2021-09-09 Created: 2021-09-09 Last updated: 2023-03-28Bibliographically approved

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Khrennikov, Andrei

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