Theoretical Analysis of Temporal Anomalies, 5D Spacetime Geometry, and Quantum Eraser Mechanics in Superluminal Metric Engineering

The theoretical pursuit of superluminal travel has historically been constrained by the causal boundaries of general relativity and chronological paradoxes. In this paper, we employ the non-linear ADM 3+1 formalism to rigorously model superluminal metric perturbations. By addressing causal entanglement, we propose a necessary topological extension into a 5D spacetime manifold, governed by quantum information mechanics, providing a mathematical failsafe to preserve thermodynamic and causal consistency. This paper investigates the theoretical consequences of superluminal spacetime metric engineering on causal structures and temporal progression. Utilizing the non-linear Arnowitt-Deser-Misner (ADM) 3+1 formalism and the Dual-Spherical Spacetime Drive framework, we model how superluminal shift vector fields induce localized metric perturbations that breach local light cone boundaries. To resolve macroscopic retrocausality paradoxes and the formation of Closed Timelike Curves (CTCs), we extend the spacetime manifold into a 5D bulk geometry. We demonstrate that causal paradoxes are non-destructive projections of continuous 5D worldlines, governed by delayed-choice quantum eraser mechanics. Finally, we propose an experimental architecture utilizing quantum optomechanical analog gravity to simulate these states in a laboratory setting. "Furthermore, the foundational principles of localized metric manipulation utilized in this macroscopic model build upon our prior theoretical analysis of quantum optical coherence and metric fluctuations within the framework of stochastic gravity [2]."