Quantum-Entangled Wormholes: Lab-Built Free-Group Topologies — E8 Intelligence Research

Abstract

FINDING: Traversable wormholes are now theoretically constructible in the lab via quantum entanglement, with multi-mouth versions forming free-group topologies. | MATH: Key structures: (1) ER=EPR correspondence (Einstein-Rosen bridge = Einstein-Podolsky-Rosen entangled pair); (2) Multi-mouth wormhole fundamental group \(F_2\) (free group on two generators) for 3-mouth case — implying non-abelian topology; (3) Traversability requires negative energy density (Casimir effect, squeezed vacuum states) — energy condition violation quantified by \(\langle T_{\mu\nu}\rangle k^\mu k^\nu < 0\); (4) Maldacena's construction uses SYK model (Sachdev-Ye-Kitaev) with coupling \(\mu\) between two boundaries, giving traversability when \(\mu > \mu_c\) (critical coupling); (5) Eternal black hole geometry: \(ds^2 = -f(r)dt^2 + f(r)^{-1}dr^2 + r^2 d\Omega^2\) with two asymptotic regions connected by throat. | CONNECTION: The free group \(F_2\) on three mouths is a **hyperbolic group** — its Cayley graph i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com