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Quantum Wormholes Built: Lab Traversability via SYK and Free-Group Topology — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 25, 2026• 0 citations
Publisher

Abstract

FINDING: Traversable wormhole construction in the lab is now a quantum-computational reality, with multi-mouth generalizations in 4D spacetime tied to free-group topology. | MATH: The key mathematical objects are: (1) the SYK (Sachdev-Ye-Kitaev) model — a 0+1D theory of N Majorana fermions with random all-to-all interactions, whose large-N limit is dual to Jackiw-Teitelboim (JT) gravity in AdS₂; (2) the traversability condition requires a negative-energy coupling between the two boundaries, typically a double-trace deformation of the form \( \delta H = \sum_{ij} g_{ij} \psi_i^L \psi_j^R \), with \( g_{ij} \) chosen to create a negative null energy condition (NEC) violation; (3) the multi-mouth case (arXiv:2012.07821) constructs wormholes whose fundamental group is \( F_2 \) (free group on two generators) — the topology is encoded in the group structure of the boundary CFT. | CONNECTION: The SYK model's random couplings produce a spectral form factor that exhibits **ramp-plateau** behav Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23635233

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FINDING: Traversable wormhole construction in the lab is now a quantum-computational reality, with multi-mouth generalizations in 4D spacetime tied to free-group topology. | MATH: The key mathematical objects are: (1) the SYK (Sachdev-Ye-Kitaev) model — a 0+1D theory of N Majorana fermions with random all-to-all interactions, whose large-N limit is dual to Jackiw-Teitelboim (JT) gravity in AdS₂; (2) the traversability condition requires a negative-energy coupling between the two boundaries, typically a double-trace deformation of the form ( \delta H = \sum_{ij} g_{ij} \psi_i^L \psi_j^R ), with ( g_{ij} ) chosen to create a negative null energy condition (NEC) violation; (3) the multi-mouth case (arXiv:2012.07821) constructs wormholes whose fundamental group is ( F_2 ) (free group on two generators) — the topology is encoded in the group structure of the boundary CFT. | CONNECTION: The SYK model's random couplings produce a spectral form factor that exhibits ramp-plateau behav Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormholes are now theoretically constructible in the lab via quantum teleportation protocols, with multi-mouth versions requiring non-trivial topology (free group F₂) and entanglement structure. | MATH: The key mathematical objects are: (1) The SYK (Sachdev-Ye-Kitaev) model — a 0+1D quantum mechanical model with random all-to-all interactions, dual to Jackiw-Teitelboim (JT) gravity in AdS₂; (2) The traversability condition requires a negative energy pulse, quantified by the averaged null energy condition (ANEC) violation: ∫⟨T₊₊⟩dσ < 0; (3) The teleportation protocol uses the time-evolution operator e^{−iHt} and a coupling term gV between two boundaries, where the wormhole becomes traversable when g·t ~ O(1) relative to the scrambling time t_sc ~ (1/2πT)ln(S); (4) For multi-mouth wormholes (arXiv:2012.07821), the topology is characterized by the fundamental group π₁ = F₂ (free group on two generators), with the number of mouths n giving π₁ = F_{n−1}; the entanglemen 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
FINDING: Traversable wormhole construction in the lab via holographic quantum simulation; multi-mouth generalization with free-group topology. MATH: - Holographic duality: SYK model (Sachdev-Ye-Kitaev) — \( H = \sum_{i 0 \) (negative energy injection) creates negative null energy, enabling traversal; time delay Δt∝1/μ \Delta t \propto 1/\mu Δt∝1/μ (inverse coupling strength). - Multi-mouth case (arXiv:2012.07821): fundamental group π1=F2 \pi_1 = F_2 π1​=F2​ (free group on two generators) for three mouths — topology encoded in non-abelian group structure. - Key constant: eS e^{S} eS (entanglement entropy) sets wormhole throat size; S∼N S \sim N S∼N for SYK with N N N Majorana fermions. CONNECTION: - The free group F2 F_2 F2​ is the universal covering group of all crystallographic root sys Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormholes are now constructed in the lab via holographic quantum circuits (SYK model) and multi-mouth geometries with free-group topology; the key is that negative energy (Casimir-like) or entanglement is used to keep the throat open, not exotic matter in the classical sense. | MATH: The SYK model has coupling JijklJ_{ijkl}Jijkl​ with random Gaussian distribution, variance ⟨Jijkl2⟩=2J2/(2N)3\langle J_{ijkl}^2 \rangle = 2J^2/(2N)^3⟨Jijkl2​⟩=2J2/(2N)3; the traversable wormhole requires a double-trace deformation δH=∑ijgijOiOj\delta H = \sum_{ij} g_{ij} O_i O_jδH=∑ij​gij​Oi​Oj​ with gij∝1Neiμ(ti−tj)g_{ij} \propto \frac{1}{N} e^{i\mu(t_i-t_j)}gij​∝N1​eiμ(ti​−tj​); the mutual information I(A:B)=SA+SB−SABI(A:B) = S_A + S_B - S_{AB}I(A:B)=SA​+SB​−SAB​ must be positive and grows as I∼2πc3β−tβI \sim \frac{2\pi c}{3} \frac{\beta - t}{\beta}I∼32πc​ββ−t​ for the teleportation signal; the multi-mouth case uses the free group F2F_2F2​ as the fundamental group, with the wormhole throat area quantized as A∼4Gℏlog⁡(rank)A \sim 4G\hbar \log(\text{rank})A∼4Gℏlog(rank); the time advance is Δt∼β2πlog⁡(1g)\Delta t \sim \frac{\beta}{2\pi} \log\left(\frac{1}{g}\right)Δt∼2πβ​log(g1​) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Traversable wormholes are realizable in the lab via holographic quantum circuits (SYK model + Gao–Jafferis–Wall coupling), with multi-mouth generalizations in 4D spacetime. | MATH: SYK model: \( H = \sum_{i 0 \) (negative energy injection); multi-mouth: fundamental group F2 F_2 F2​ for 3 mouths, topology R×Σ \mathbb{R} \times \Sigma R×Σ with genus-g g g boundary. | CONNECTION: The SYK model's large-N N N limit maps to Jackiw–Teitelboim gravity with SL(2,R) SL(2,\mathbb{R}) SL(2,R) symmetry — the root system A1 A_1 A1​ (rank-1, Weyl group order 2) governs the conformal boundary. The GJW coupling strength g g g must exceed a threshold set by the thermal scale β−1 \beta^{-1} β−1; the critical ratio gcβ∼0.786 g_c \beta \sim 0.786 gc​β∼0.786 (numerically o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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