Field Depth as the Structural Basis of Electromagnetism and Matter

This preprint introduces field depth (w) as an intrinsic resonance parameter governing the degree to which field configurations are structurally anchored within an underlying field. Unlike a conventional spatial dimension, w does not represent an additional geometric axis, but encodes the depth-dependent stability of standing-wave structures within three-dimensional space. In this framework, the wavefunction is expressed as Ψ(x, y, z, w, t), where spatial coordinates describe observable position, while w characterizes the internal coherence structure responsible for persistence and localization. Stable particle-like states correspond to depth-anchored resonance nodes, while weakly anchored or unanchored configurations propagate as delocalized excitations. This formulation provides a unified geometric interpretation of several central features of quantum theory: • Wave–particle duality is understood as the relationship between extended resonance structures and their projection into three-dimensional space. • Spin emerges as a phase-consistency condition spanning both spatial and depth structure, naturally accounting for the observed 4π periodicity of spin-½ systems. • Quantum entanglement corresponds to shared depth-structured resonance configurations, explaining correlated outcomes without invoking superluminal signaling. The model preserves the standard mathematical structure of quantum mechanics, including the Schrödinger and Dirac equations, while supplying a geometric mechanism linking field structure, stability, and propagation. This Version 2 refines the conceptual framework by replacing earlier sequential formulations with a depth-based resonance description, and by explicitly distinguishing between depth-anchored stable structures and propagating excitations. It also establishes a clearer connection to a broader theoretical program, in which particle structure and electromagnetic interaction are developed as consequences of depth-dependent resonance geometry.