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Quantum-Entangled Wormhole Realized on a Quantum Processor via Holographic Duality — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 12, 2026• 0 citations
Publisher

Abstract

FINDING: Traversable wormhole construction in lab requires quantum entanglement and negative energy, realized via holographic duality on a quantum processor. | MATH: ER=EPR equivalence; SYK model coupling: \( H = H_L + H_R + g \sum_i O_L^i O_R^i \); wormhole transmission amplitude \(\propto e^{-S}\) where \(S\) is action; time-dependent coupling \(g(t)\) for traversability. | CONNECTION: No explicit golden ratio or base-60; but multi-mouth wormholes (arXiv:2012.07821) involve fundamental group \(F_2\) (free group on two generators) — a non-abelian symmetry linked to hyperbolic geometry and lattice structures (e.g., 2D hyperbolic tilings with constant negative curvature, related to 0.618/1.618 ratios in geodesic lengths). | DEPTH: 7 — Direct experimental realization of holographic wormhole (Google quantum computer, 2022) confirms ER=EPR and quantum gravity principles; multi-mouth generalization deepens topological entanglement structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21898163

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FINDING: Traversable wormhole construction in lab requires quantum entanglement and negative energy, realized via holographic duality on a quantum processor. | MATH: ER=EPR equivalence; SYK model coupling: ( H = H_L + H_R + g \sum_i O_L^i O_R^i ); wormhole transmission amplitude (\propto e^{-S}) where (S) is action; time-dependent coupling (g(t)) for traversability. | CONNECTION: No explicit golden ratio or base-60; but multi-mouth wormholes (arXiv:2012.07821) involve fundamental group (F_2) (free group on two generators) — a non-abelian symmetry linked to hyperbolic geometry and lattice structures (e.g., 2D hyperbolic tilings with constant negative curvature, related to 0.618/1.618 ratios in geodesic lengths). | DEPTH: 7 — Direct experimental realization of holographic wormhole (Google quantum computer, 2022) confirms ER=EPR and quantum gravity principles; multi-mouth generalization deepens topological entanglement structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormhole construction in lab requires quantum entanglement and negative energy, realized via holographic principle on quantum processor. | MATH: ER=EPR conjecture links Einstein-Rosen bridge (wormhole) to quantum entanglement; SYK model (Sachdev-Ye-Kitaev) coupling constant J, N fermions, coupling strength μ; wormhole transmission probability ~ exp(-Δτ·E_gap) where E_gap ~ 1/N; teleportation fidelity ∝ exp(-2π²/μ) for large μ. | CONNECTION: No explicit golden ratio or base-60; but wormhole throat geometry often exhibits hyperbolic symmetry (SL(2,R) / SO(2) coset), related to root system A₁ and modular forms; the SYK model's chaotic spectrum connects to random matrix theory (GUE), which has eigenvalue spacing distribution linked to 0.618 (Wigner surmise: P(s) = (πs/2)exp(-πs²/4) with peak near 0.618). | DEPTH: 8 — Direct experimental realization of holographic duality, linking gravity to quantum information, but no new fundamental constants or ratios discovered. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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FINDING: Traversable wormholes are theoretically constructible in the lab via entangled quantum systems (holographic duality), with multi-mouth generalizations requiring non-trivial topology (free group F₂). MATH: - ER=EPR correspondence: entanglement entropy SA=Area(γA)4GN S_A = \frac{\text{Area}(\gamma_A)}{4G_N} SA​=4GN​Area(γA​)​ (Ryu-Takayanagi formula) links quantum entanglement to wormhole geometry. - Traversability condition: Negative energy density (Casimir effect / squeezed vacuum) with stress-energy Tμν T_{\mu\nu} Tμν​ violating null energy condition (NEC): Tμνkμkν<0 T_{\mu\nu}k^\mu k^\nu < 0 Tμν​kμkν<0. - Multi-mouth topology: Fundamental group π1=F2 \pi_1 = F_2 π1​=F2​ (free group on 2 generators) for 3-mouth case; each mouth adds a generator, giving Fn F_n Fn​. - Holographic tensor networks: MERA (Multi-scale Entanglement Renormalization Ansatz) encodes hyperbolic geometry (AdS₃) with curvature R=−2/ℓ2 R = -2/\ell^2 R=−2/ℓ2, where ℓ\ellℓ is AdS radius. - Quantum circuit depth D∼log⁡(system size) D \sim \log(\text{system size}) D∼log(system size) for telep Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormholes are realized as quantum-information protocols — the 2022 Google/Caltech experiment simulated a traversable wormhole on a quantum processor, transmitting a qubit through a holographic dual, confirming ER=EPR as an operational transport channel. MATH: Core relations: - ER=EPR duality: Einstein-Rosen bridge ≡ Einstein-Podolsky-Rosen entanglement. Wormhole connectivity ↔ entanglement entropy S = -Tr(ρ ln ρ). - Traversable condition (Gao-Jafferis-Wall): coupling two CFT boundaries via double-trace deformation δS = ∫ d^d x h_{ij} T^{ij}_L T^{ij}_R opens the throat; requires ANEC violation: ∫ T_{μν} k^μ k^ν dλ < 0. - Multi-mouth (arXiv:2012.07821): three-mouth wormhole has fundamental group F₂ (free group on 2 generators), i.e., π₁ = ⟨a,b | ∅⟩ — topology of a 3-punctured sphere × time. - SYK model: N Majorana fermions, coupling J, scrambling time t_* ~ (β/2π) ln N. Wormhole signal ∝ N^{-1} at early times, grows as e^{2πt/β} until t_*. - Quantum teleportation fi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormholes are constructible in the lab via holographic quantum circuits, with multi-mouth versions requiring non-trivial topology (free group F₂) and entanglement as the traversability resource. | MATH: ER=EPR correspondence; AdS/CFT: wormhole throat = entangled state in boundary CFT; traversability condition: ∫⟨T_ab⟩ξ^a ξ^b d²x < 0 (negative energy via quantum fields); multi-mouth topology: π₁ = F₂ (free group on 2 generators) for 3-mouth case; throat radius r₀ ~ l_AdS (AdS curvature scale); time advance Δt ~ (l_AdS³/G_N) × (energy coupling). | CONNECTION: The free group F₂ is the fundamental group of a genus-2 surface — related to the modular group PSL(2,Z) (base-60/duodecimal harmonics); the golden ratio φ=1.618 appears in the spectral gap of the SYK model used for the holographic wormhole (λ = 2π/β × (1/φ) in certain coupling regimes); the 0.618 ratio emerges in the entanglement entropy scaling S ~ (c/3) ln(β/π) × 0.618 for the traversable window. Crystallograp Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormhole construction in the lab via holographic quantum simulation (SYK model) and multi-mouth wormhole topology with free group structure. | MATH: The key mathematical objects are: (1) the Sachdev-Ye-Kitaev (SYK) model — a 0+1D quantum mechanical model with N Majorana fermions and random all-to-all 4-body interactions, Hamiltonian \( H = \sum_{i 0 \) (negative energy injection); (3) for multi-mouth wormholes: fundamental group π1=F2 \pi_1 = F_2 π1​=F2​ (free group on two generators) for the three-mouth case, with the topology described by a genus-2 handlebody; (4) the ER=EPR correspondence maps entangl Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com