Analysis of the Nature of Kinetic Energy and Potential Energy within the World Quantum Theory Framework

Within the World Quantum Theory (WQT) framework, starting from the total energy formula E = γm₀c² and the orthogonal decomposition c² = v² + d², this paper derives the expressions for kinetic energy T and potential energy V, and thereby reveals the physical nature of the Lagrangian L = T - V and the Hamiltonian H = T + V. We point out that: · The Hamiltonian H = T + V is an empirical formula summarized from macroscopic phenomena in traditional physics. It correctly adds the energy contributions of macro-rotation (tangential motion) and internal rotation (radial confinement) to obtain the total energy. · But traditional physics does not know that these two contributions correspond respectively to the energy projections along the two orthogonal directions of the particle's own existence—tangential (v) and radial (d). It only observes two energy contributions from the outside and adds them together. · The WQT geometric structural expression E² = E_p² + E_m² starts from the particle's own existence and reveals the orthogonal projection nature of energy, providing the physical picture that the traditional empirical formula lacks.