Quantum Entanglement and Gravity in Discrete Geometric Physics: Geometric Derivation of ER = EPR from the 26 Vertex Cubic Lattice
Year: 2026
Type: article
Abstract: This work presents a complete geometric derivation of quantum entanglement and its equivalence to gravity (ER = EPR) from the 26‑vertex cubic lattice within Discrete Geometric Physics (DGP). Entanglement is defined as a common spiral contour passing through two particles, and the correlation function is derived from the lattice geometry. The key results are: (i) the correlation function has the form ⟨σ_A σ_B⟩ = cosθ · (w_k/Σw) · e^(−d/λ_coh) with a coherence length λ_coh = 9.3968 m (corrected from 7.5 m using the exact integer level N=113); (ii) Bell inequalities are modified and violation decays on scales beyond ~15 m, providing a testable experimental threshold; (iii) the ER = EPR theorem is proved rigorously — entanglement (common contour) generates gravitational interaction and vice versa; (iv) gravity is derived from the entanglement gradient; (v) entanglement entropy matches the Bekenstein‑Hawking formula; (vi) dark matter and dark energy affect the coherence length and phase; (vii) bounce creates an entanglement echo with testable gravitational wave signals; (viii) cosmological anomalies (Axis of Evil, CMB peaks, BAO) are explained as manifestations of the common contour geometry. All results are derived from the topological invariants Σw=14, θ=arcsin(1/√3), φ=(1+√5)/2, and variational minimisation on the lattice, without empirical fitting. This corrected version uses the precise coherence length λ_coh = 9.3968 m (a(113)=0.1678 m) and clarifies the gravitational basis N=116 (a(116)=1.343 m). The work includes full derivations, numerical tests, Python code, and experimental protocols.
Author: Ivan Davidenko
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166319733