Wave–particle duality exposes the deep paradox between the discrete emission of energy quanta and the continuous flow of time. Conventional quantum theory represents this duality through probabilistic wave functions but does not explain how discrete energy transitions can coexist with continuous temporal evolution. Within the framework of the Structural Unified Field (SUF), defined by the dimensionless equation , we propose a tension-geometric interpretation of quantum discreteness. In this model, energy quantization arises not from particle-like assumptions but as a geometric necessity of continuous tension fields constrained by finite boundaries, while the continuity of time follows from the differentiability of the field evolution . Introducing the tensional entropy function , we derive a coupling relation , representing an entropy–energy uncertainty principle that links geometric stability with energetic discreteness. Particle-like behavior corresponds to local minima of (structural stability states), whereas wave-like behavior corresponds to the propagation of its entropy gradient (continuous transmission of tension). This unified formulation reproduces the essential features of quantum mechanics while providing a geometric explanation for the coexistence of continuity and quantization. The framework predicts experimentally testable signatures—such as the modulation of spectral discreteness and smooth frequency shifts—in optical cavities and cold-atom systems. The results suggest that wave–particle duality is not a special property of the quantum domain but an inevitable projection of tension geometry across all continuous systems bounded by finite constraints.
This article proposes a unified theory framework encompassing a discrete topological interpretation of physical forces, wave functions, and the nature of space and time. It provides novel explanations for the collapse of wave functions, quantum entanglement, and offers insights into the origins of quantum probabilities. This article also explains the nature of mass, Higgs field, and suggests a path for unifying quantum mechanics and gravity. Elementary particles are represented as defects in discrete topological spaces. Entangled particles are directly connected to each other through a puncture in discrete space, separated by a distance of one Planck length. Wave functions are explained as mechanical stress waves within elastic discrete space. The results of the double-slit experiment are interpreted as wave functions maximizing the probability of rupture in high-stress areas of discrete space with obvious analogies to solid state mechanics. Wave-particle duality is explained as discrete topological defects causing extended distributed stress within space lattice.