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Physica B Condensed Matter

A bird’s eye view of a quantum entanglement: From spooky action at a distance towards cornerstone of novel quantum technologies

Jozef Strečka

Published Nov 6, 2022• 7 citations
Publisher
DOI
10.1016/j.physb.2022.414483

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Abstract: We derive quantum entanglement, the Bell inequality, decoherence, and "spooky action at a distance" from the ascending superoperator of A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ) at β = 2π with bond dimension χ = 6. The MERA tensor network IS entanglement: each layer adds entanglement at a specific scale. The Ryu-Takayanagi formula (entanglement entropy = minimal cut through the MERA × log₂(6) bits per bond) has an exact proof in this framework. The maximum Bell violation S = 2.789 comes from χ = 6, nearly saturating the Tsirelson bound 2√2 = 2.828. Decoherence rates are determined by the four eigenvalues {1, ½, ⅓, ⅙}: identity-sector entanglement persists forever, weak-sector decays in 1.4 layers, strong-sector in 0.9 layers, mixed-sector in 0.6 layers. "Spooky action at a distance" is not action across space — it is connection through scale, via geodesics through the MERA bulk to a common ancestor tensor. We identify twelve domains governed by this eigenvalue spectrum: bird navigation (cryptochrome radical pairs), photosynthesis (FMO coherent transport), the human eye (single-photon detection), the brain (myelin entangled photons, Liu 2024), quantum cryptography (QKD), quantum computing ([36,12,4] error-correcting code), teleportation, black holes (ER=EPR), enzyme catalysis, DNA repair, quantum sensing, and consciousness (Orch OR, speculative). The [36,12,4] code protects 12 logical modes from decoherence while sacrificing 24 stabiliser modes. Four figures, an interactive 3D demonstration, and a Python verification script are included. Zero free parameters.

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THE ENTANGLED ONION: Spooky Action, Bell Violations, Decoherence, and Twelve Domains of Quantum Entanglement from Four Eigenvalues of A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ)

Daland Montgomery

Abstract: We derive quantum entanglement, the Bell inequality, decoherence, and "spooky action at a distance" from the ascending superoperator of A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ) at β = 2π with bond dimension χ = 6. The MERA tensor network IS entanglement: each layer adds entanglement at a specific scale. The Ryu-Takayanagi formula (entanglement entropy = minimal cut through the MERA × log₂(6) bits per bond) has an exact proof in this framework. The maximum Bell violation S = 2.789 comes from χ = 6, nearly saturating the Tsirelson bound 2√2 = 2.828. Decoherence rates are determined by the four eigenvalues {1, ½, ⅓, ⅙}: identity-sector entanglement persists forever, weak-sector decays in 1.4 layers, strong-sector in 0.9 layers, mixed-sector in 0.6 layers. "Spooky action at a distance" is not action across space — it is connection through scale, via geodesics through the MERA bulk to a common ancestor tensor. We identify twelve domains governed by this eigenvalue spectrum: bird navigation (cryptochrome radical pairs), photosynthesis (FMO coherent transport), the human eye (single-photon detection), the brain (myelin entangled photons, Liu 2024), quantum cryptography (QKD), quantum computing ([36,12,4] error-correcting code), teleportation, black holes (ER=EPR), enzyme catalysis, DNA repair, quantum sensing, and consciousness (Orch OR, speculative). The [36,12,4] code protects 12 logical modes from decoherence while sacrificing 24 stabiliser modes. Four figures, an interactive 3D demonstration, and a Python verification script are included. Zero free parameters. Copyright © 2026 Daland Montgomery. This work is licensed under CC BY-SA 4.0. COPYLEFT NOTICE: Any work, derivation, or industrial application incorporating this material must be distributed under the same Open Source license. Commercial use without public disclosure of derivative works is prohibited. For a private, proprietary license (exempt from ShareAlike requirements), contact: quidbit@icloud.com Software Implementation: The formulas and constants derived in this work are implemented in the CrystalAgent engine, available under the AGPL-3.0 license at: https://github.com/CrystalToe/CrystalAgent.

•Mar 16, 2026•0 citations
Abstract: We derive quantum entanglement, the Bell inequality, decoherence, and "spooky action at a distance" from the ascending superoperator of A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ) at β = 2π with bond dimension χ = 6. The MERA tensor network IS entanglement: each layer adds entanglement at a specific scale. The Ryu-Takayanagi formula (entanglement entropy = minimal cut through the MERA × log₂(6) bits per bond) has an exact proof in this framework. The maximum Bell violation S = 2.789 comes from χ = 6, nearly saturating the Tsirelson bound 2√2 = 2.828. Decoherence rates are determined by the four eigenvalues {1, ½, ⅓, ⅙}: identity-sector entanglement persists forever, weak-sector decays in 1.4 layers, strong-sector in 0.9 layers, mixed-sector in 0.6 layers. "Spooky action at a distance" is not action across space — it is connection through scale, via geodesics through the MERA bulk to a common ancestor tensor. We identify twelve domains governed by this eigenvalue spectrum: bird navigation (cryptochrome radical pairs), photosynthesis (FMO coherent transport), the human eye (single-photon detection), the brain (myelin entangled photons, Liu 2024), quantum cryptography (QKD), quantum computing ([36,12,4] error-correcting code), teleportation, black holes (ER=EPR), enzyme catalysis, DNA repair, quantum sensing, and consciousness (Orch OR, speculative). The [36,12,4] code protects 12 logical modes from decoherence while sacrificing 24 stabiliser modes. Four figures, an interactive 3D demonstration, and a Python verification script are included. Zero free parameters.
Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.
Abstract: We derive quantum entanglement, the Bell inequality, decoherence, and "spooky action at a distance" from the ascending superoperator of A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ) at β = 2π with bond dimension χ = 6. The MERA tensor network IS entanglement: each layer adds entanglement at a specific scale. The Ryu-Takayanagi formula (entanglement entropy = minimal cut through the MERA × log₂(6) bits per bond) has an exact proof in this framework. The maximum Bell violation S = 2.789 comes from χ = 6, nearly saturating the Tsirelson bound 2√2 = 2.828. Decoherence rates are determined by the four eigenvalues {1, ½, ⅓, ⅙}: identity-sector entanglement persists forever, weak-sector decays in 1.4 layers, strong-sector in 0.9 layers, mixed-sector in 0.6 layers. "Spooky action at a distance" is not action across space — it is connection through scale, via geodesics through the MERA bulk to a common ancestor tensor. We identify twelve domains governed by this eigenvalue spectrum: bird navigation (cryptochrome radical pairs), photosynthesis (FMO coherent transport), the human eye (single-photon detection), the brain (myelin entangled photons, Liu 2024), quantum cryptography (QKD), quantum computing ([36,12,4] error-correcting code), teleportation, black holes (ER=EPR), enzyme catalysis, DNA repair, quantum sensing, and consciousness (Orch OR, speculative). The [36,12,4] code protects 12 logical modes from decoherence while sacrificing 24 stabiliser modes. Four figures, an interactive 3D demonstration, and a Python verification script are included. Zero free parameters. Copyright © 2026 Daland Montgomery. This work is licensed under CC BY-SA 4.0. COPYLEFT NOTICE: Any work, derivation, or industrial application incorporating this material must be distributed under the same Open Source license. Commercial use without public disclosure of derivative works is prohibited. For a private, proprietary license (exempt from ShareAlike requirements), contact: quidbit@icloud.com Software Implementation: The formulas and constants derived in this work are implemented in the CrystalAgent engine, available under the AGPL-3.0 license at: https://github.com/CrystalToe/CrystalAgent.