Unified Gauge Theory across Fundamental Interactions and Superluminal Spacecraft

Abstract

This paper develops a Generalized Gauge Equation (GGE) framework within the principal bundle P ( M , G L ( n , ℂ ) ) to achieve geometric unification of fundamental interactions. The core innovation lies in establishing precise transformation mechanisms between gauge fields, particularly demonstrating how electromagnetic interactions can be geometrically mapped onto gravitational configurations through well-defined gauge transformations. The mathematical foundation integrates connections, curvature, and gauge transformations into a unified description where different interactions emerge as projections of underlying spacetime geometry. Crucially, we derive the Weyl-electromagnetic relation C μ ν ρ σ = κ ( F μ ρ F ν σ − F μ σ F ν ρ ) from first principles, with the conversion coefficient κ = 8 π α determined through variational analysis of the coupled Lagrangian ℒ ⊃ α R μ ν F μ σ F σ ν , rather than dimensional arguments alone. We demonstrate that two optical solitons transform into gravitational solitons via rotational gauge transformation, corresponding to photon-graviton conversion in weak-field limits. These gravitational solitons form localized curvature structures capable of superluminal propulsion, with derived effective velocities reaching 3 c . The geometric framework naturally supports Closed Timelike Curves, enabling feasible interstellar travel distances. This work extends established gauge theory without speculative assumptions, providing experimentally testable predictions for unified field theory and advanced propulsion concepts.