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Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity.

Oded Shor1,2, Felix Benninger1,2,3, Andrei Khrennikov4

  • 1Felsenstein Medical Research Center, Beilinson Hospital, Petach Tikva 4941492, Israel.

Entropy (Basel, Switzerland)
|August 27, 2021
PubMed
Summary
This summary is machine-generated.

Dendrogramic holographic theory explains quantum-like behavior in classical data. Nonergodicity in dendrogramic time series leads to violations of the CHSH inequality, challenging local realism.

Keywords:
CHSH inequalityclustering algorithmsdendrogramic holographic theorydendrogramsepistemicnonergodicityonticquantumness

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Area of Science:

  • Theoretical Physics
  • Quantum Information Theory
  • Complex Systems

Background:

  • Explores foundational problems in dendrogramic holographic theory (DH theory).
  • Utilizes the ontic-epistemic (implicate-explicate order) methodology.
  • Investigates classical-quantum interrelations and their blurring.

Purpose of the Study:

  • To represent data using dendrograms from hierarchical clustering.
  • To describe the ontic universe as a bounded, zero-dimensional p-adic tree.
  • To analyze the quantum-likeness of dendrograms using the CHSH inequality.

Main Methods:

  • Hierarchical clustering algorithms for dendrogram construction.
  • P-adic ultrametric spaces for describing the ontic universe.
  • Utilizing the CHSH inequality to measure quantum-likeness.

Main Results:

  • Demonstrates violation of the CHSH inequality by classical experimental data represented by dendrograms.
  • Identifies nonergodicity of dendrogramic time series as the cause of CHSH violation, not nonlocality or rejection of realism.
  • Shows that simpler dendrograms exhibit more quantum-like properties.

Conclusions:

  • Dendrogramic holographic theory provides a local realistic model that violates the CHSH inequality.
  • Nonergodicity is a fundamental feature of DH theory.
  • Analyzes the impact of Minkowski geometry and Lorentz transformations on CHSH violation and nonergodicity.