Holographic Wormholes in the Lab via SYK Quantum Simulation — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 7, 2026• 0 citations

Abstract

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 $ \pi_1 = F_2 $ (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

DOI: 10.5281/zenodo.22633074

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Holographic Wormholes in the Lab via SYK Quantum Simulation — E8 Intelligence Research

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Publisher

Abstract

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 ( \pi_1 = F_2 ) (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

DOI: 10.5281/zenodo.22633074

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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 $\Delta t \propto 1/\mu$ (inverse coupling strength). - Multi-mouth case (arXiv:2012.07821): fundamental group $\pi_1 = F_2$ (free group on two generators) for three mouths — topology encoded in non-abelian group structure. - Key constant: $e^{S}$ (entanglement entropy) sets wormhole throat size; $S \sim N$ for SYK with $N$ Majorana fermions. CONNECTION: - The free group $F_2$ 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.comFINDING: 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 $ \Delta t \propto 1/\mu $ (inverse coupling strength). - Multi-mouth case (arXiv:2012.07821): fundamental group $ \pi_1 = F_2 $ (free group on two generators) for three mouths — topology encoded in non-abelian group structure. - Key constant: $ e^{S} $ (entanglement entropy) sets wormhole throat size; $ S \sim N $ for SYK with $ N $ Majorana fermions. CONNECTION: - The free group $ F_2 $ 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

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\Delta t \propto 1/\mu

(inverse coupling strength). - Multi-mouth case (arXiv:2012.07821): fundamental group

\pi_1 = F_2

(free group on two generators) for three mouths — topology encoded in non-abelian group structure. - Key constant:

e^{S}

(entanglement entropy) sets wormhole throat size;

S \sim N

for SYK with

N

Majorana fermions. CONNECTION: - The free group

F_2

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

\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

J_{ijkl}

with random Gaussian distribution, variance

\langle J_{ijkl}^2 \rangle = 2J^2/(2N)^3

; the traversable wormhole requires a double-trace deformation

\delta H = \sum_{ij} g_{ij} O_i O_j

with

g_{ij} \propto \frac{1}{N} e^{i\mu(t_i-t_j)}

; the mutual information

I(A:B) = S_A + S_B - S_{AB}

must be positive and grows as

I \sim \frac{2\pi c}{3} \frac{\beta - t}{\beta}

for the teleportation signal; the multi-mouth case uses the free group

F_2

as the fundamental group, with the wormhole throat area quantized as

A \sim 4G\hbar \log(\text{rank})

; the time advance is

\Delta t \sim \frac{\beta}{2\pi} \log\left(\frac{1}{g}\right)

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

J

and

N

Majorana fermions; the traversable wormhole requires a negative-energy shockwave with coupling

\mu

(or

g

in Maldacena-Qi). The teleportation fidelity is governed by the out-of-time-order correlator (OTOC)

F(t) = \langle V(0) W(t) V(0) W(t) \rangle

, which decays as

e^{-\lambda_L t}

with Lyapunov exponent

\lambda_L = 2\pi k_B T/\hbar

(maximal chaos). The multi-mouth wormhole (arXiv:2012.07821) uses the free group

F_2

as its fundamental group, with each mouth corresponding to a generator; the Einstein-Rosen bridge length is

L \sim \log S

(entropy). | CONNECTION: The free group

F_2

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