Formal Derivation: Maxwell's Equations from Information Dynamics

We present a novel derivation of Maxwell's electromagnetic equations from first principles of information dynamics in the Pentagonal Quantum Information Substrate (PQIS) framework. Rather than treating electric and magnetic fields as fundamental entities, we demonstrate how they emerge naturally as specific patterns in the organization and flow of quantum phase information. Starting with core postulates of D₅ symmetry and golden ratio relationships, we systematically derive all four Maxwell equations: Gauss's law for electricity emerges as phase rotation generators creating divergent phase gradients; Gauss's law for magnetism represents the topological constraint on phase circulation; Faraday's law reflects phase coherence maintenance during changes in circulation; and Ampère's law expresses balance between phase circulation, flow, and gradient changes. Additionally, we derive the precise values of electromagnetic constants (ε₀, μ₀, c) and the fine structure constant (α_EM ≈ 1/137.036) directly from PQIS parameters. This approach unifies classical and quantum electromagnetism within a single mathematical framework, providing deeper conceptual understanding and making novel, testable predictions, including specific modifications to electromagnetic behavior at short distances. Our derivation suggests that information, not fields or matter, may be the ultimate substrate of physical reality, with Maxwell's equations representing emergent patterns of information coherence.