Principled Unification: A Gauge-Theoretic Integration of Matter, Force, and Spacetime

Abstract This paper presents a rigorous, principle-driven unification of the four fundamental interactions—electromagnetism, weak and strong nuclear forces, and gravity—within a gauge-theoretic framework grounded entirely in established physics. Avoiding speculative constructs such as extra dimensions or undiscovered particles, the theory builds upon the Standard Model symmetries (U(1), SU(2), SU(3)), General Relativity, and Quantum Field Theory, deriving each interaction from first principles using covariant derivatives, field strength tensors, and Lagrangian formalism. Crucially, the framework incorporates information as a physically meaningful entity, linking entropy, energy, and curvature through the relation ΔE ∼ T ΔS. This energy-information equivalence allows thermodynamic and quantum principles to converge, embedding informational dynamics directly into the unified Lagrangian. Gravity is treated via canonical quantization of the Einstein-Hilbert action, leading to the Wheeler-DeWitt equation and a wavefunctional description of quantum geometry. The resulting theory integrates all known forces—including quantum gravity—into a single coherent structure that respects both quantum mechanics and relativistic invariance. This work offers a conservative yet ambitious pathway toward a theory of everything, emphasizing mathematical consistency, physical observability, and the ontological role of information as the connective tissue of spacetime, matter, and force.