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Quantum Teleportation Wormholes: Lab Construction via SYK Model and F₂ Topology — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 19, 2026• 0 citations
Publisher

Abstract

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

DOI
10.5281/zenodo.23465240

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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
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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 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 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 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 realizable in the lab via holographic quantum circuits (SYK model) and multi-mouth constructions in 4D spacetime; the 2022 quantum computer experiment (Google Sycamore) demonstrated a "holographic wormhole" teleportation signal. | MATH: The SYK model (Sachdev-Ye-Kitaev) has coupling JJJ and NNN Majorana fermions; the traversable wormhole requires a negative-energy shockwave with coupling μ\muμ (or ggg in Maldacena-Qi). The teleportation fidelity is governed by the out-of-time-order correlator (OTOC) F(t)=⟨V(0)W(t)V(0)W(t)⟩F(t) = \langle V(0) W(t) V(0) W(t) \rangleF(t)=⟨V(0)W(t)V(0)W(t)⟩, which decays as e−λLte^{-\lambda_L t}e−λL​t with Lyapunov exponent λL=2πkBT/ℏ\lambda_L = 2\pi k_B T/\hbarλL​=2πkB​T/ℏ (maximal chaos). The multi-mouth wormhole (arXiv:2012.07821) uses the free group F2F_2F2​ as its fundamental group, with each mouth corresponding to a generator; the Einstein-Rosen bridge length is L∼log⁡SL \sim \log SL∼logS (entropy). | CONNECTION: The free group F2F_2F2​ is the fundamental group of a genus-2 surface — Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com