Electromagnetism, Photon Dynamics, Gravitational Tensor Mapping, Quantum Dynamics, and Cosmological Expansion in the LOEANE Informational Framework

Abstract

This paper presents a complete derivation of fundamental physical phenomena from a discrete, self-updating informational substrate known as the Linearity of Existence and Non-Existence (LOEANE) framework. By replacing background continuous spacetime and externally imposed gauge groups with a relational architecture, the model demonstrates how standard macroscopic limits emerge naturally and cleanly. The core mathematics are driven by two primitive substrate fields: the scalar collapse-depth field \(\delta(x)\) and the internal periodic refresh-cycle phase \(\theta(x)\), which is governed by a fundamental four-stroke operator identity (\(F^4 = I\)). Key derivations detailed within this work include: Emergent Electrodynamics: Constructing the \(U(1)\) gauge group structure and Maxwellian field tensors directly from phase gradients coupled to collapse-depth variations. Photon Dynamics: Modeling a massless photon as a self-equilibrating, idempotent null cycle (\(P = ENEN\)) pinned to critical collapse-depth boundaries. Gravitational Tensor Mapping: Mapping second-order collapse-depth Hessians directly to the Einstein curvature tensor (\(G_{\mu \nu }\)) and deriving the emergent gravitational constant (\(G\)). Quantum Sector: Demonstrating how complexified collapse-depth oscillations simulate Schrödinger-like diffusion and relativistic Klein–Gordon wave dynamics. Expansion Cosmology: Deriving cosmological scale acceleration and vacuum energy limits from large-scale variations in the substrate network, offering an alternative origin for dark energy. Ultimately, these subsystems are tied together into a single total variational action, yielding a comprehensive set of unified LOEANE field equations that remain free from traditional ultraviolet divergences, singularities, and ontological incompatibilities.