Quantum entanglement, the deep correlation between spatially separated particles, poses conceptual challenges for reconciling quantum nonlocality with relativity. A promising route to a geometric reading is the ER = \(\mathcal {EPR}\) conjecture (Maldacena and Susskind), according to which an entangled pair may be connected by an Einstein–Rosen bridge (a wormhole), rendering entanglement a topological effect of spacetime. In the \(\mathcal{P}\mathcal{T}\) -symmetric wormhole framework considered here, two distinct spacetime sheets, denoted \(\mathcal {M}_+\) and \(\mathcal {M}_-\) , are identified at the throat \(r=\alpha \) through a \(\mathcal{P}\mathcal{T}\) symmetry combining time reversal \((\mathcal {T}: t \rightarrow -t)\) and spatial parity \((\mathcal {P}: \vec {x} \rightarrow -\vec {x})\) . We demonstrate that quantum entanglement can be understood as the geometric manifestation of a topological identification between a point \(P \in \mathcal {M}_+\) and its twin \(P' \in \mathcal {M}_-\) , thereby providing a natural realization of \(\mathcal {EPR}\) -type correlations within a causally consistent framework: relativistic causality is preserved (no superluminal signaling), while correlations violating Bell inequalities (Bell nonlocality) admit an interpretation as an inter-sheet geometric connection.
