FORMAL DERIVATION OF EMERGENT ELECTROMAGNETISM FROM INFORMATION SYMMETRIES

This document presents a comprehensive formal derivation of gauge forces from information-theoretic principles, with a specific focus on the emergence of electromagnetism from information symmetries and the relationship between quantum electrodynamics (QED) and classical electrodynamics (Maxwell’s equations). The derivations are grounded in the Quni-Gudzinas Framework for Scale-Invariant Information-Theoretic Physics, which posits that fundamental physical laws emerge from information-theoretic principles rather than being fundamental in themselves. The central thesis of this work is that gauge symmetries, traditionally viewed as fundamental principles in physics, actually emerge from conservation laws related to information currents. Specifically, we demonstrate how the U(1) gauge symmetry of electromagnetism arises from a symmetry transformation where the phase rotation of matter fields depends on a background scalar information field, $\kappa(x)$, representing the normalized information density of spacetime.