A Quantum Electrogravitic Coupled Gauge Theory

We present a quantum electrogravitics (QEG) theory in which gravity emerges as a $U\left(1\right)$ gauge interaction fully analogous to electromagnetism. Starting from the relativistic velocity dependence of gravitational mass, we derive a Lorentz-like gravitational force, an implied field-strength tensor $G_{\mu \nu }$ , and a complete set of gravitomagnetic Maxwell equations. Quantization yields both uncoupled and coupled $U\left(1\right)\times U\left(1\right)$ theories whose tree-level potentials recover Coulomb’s and Newton’s laws. The coupled version naturally produces an $E^2$ interaction term that matches the functional form observed in the Biefeld-Brown effect. The graviton appears as a massless spin-1 vector boson, and the entire framework remains fully calculable and renormalizable. This approach offers a concrete, experimentally testable unification of the long-range forces within a single quantum field-theoretic structure.