The wave-particle duality of light and matter remains a cornerstone of quantum mechanics.The Standard Model of particle physics defines both the photon and the electron as strictly elementary, indivisible point particles. In this paper, we propose a composite model of quanta wherein these purported elementary particles are composed of multiple, underlying vibratory entities. We introduce a topological wave-packet framework and examine how this sub-structural hypothesis can naturally recover wave-particle duality by explaining the wave and the particle phenomena of light simultaneously without changing models, address theoretical singularities, and propose potential testable predictions. We also consider the physical reason and origin of the relativity of mass and energy, and the physical meaning of Planck's constant within this framework.