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.
Henrik Nilsson (Mon,) studied this question.