Geometric Realization of ER=EPR in Flat Spacetime via the Zhang Effective Metric

The ER=EPR conjecture posits that quantum entanglement is geometrically connected by Einstein-Rosen (ER) bridges. While extensively studied within the AdS/CFT correspondence, a dynamical realization in asymptotically flat spacetime remains an open challenge. In this paper, we propose a geometric realization of ER=EPR within the rotational-order geometric unification framework. Using the Zhang Effective Metric, we demonstrate that two entangled particles share a topological thread in the internal S³ fibre of the 15-dimensional manifold. When projected to 4D flat spacetime, this internal topological connection manifests as a non-singular, wormhole-like throat. We derive the two-point correlation function and show that the entanglement entropy scales with the cross-sectional area of the geometric throat, furnishing a flat-spacetime analogous relation inspired by the Ryu-Takayanagi formula. Crucially, this geometric connection does not permit classical superluminal signaling.