Resolution of Divergence in Energy Formulas——Based on the Orthogonal Projection Framework of World Quantum Theory

In classical physics and relativity, the energy formula E=γmc2 diverges as the velocity approaches the speed of light (γ→∞), while the photon energy formula E=pc cannot be applied when the object is at rest (p=0). This divergence and inapplicability have long been regarded as inherent features of physics. Based on the orthogonal decomposition postulate c2=v2+d2 and the linear energy allocation postulate of World Quantum Theory (WQT), this paper proposes that total energy can always be expressed as the projection onto two independent orthogonal channels—the mass channel and the momentum channel. When one channel closes (d=0 or v=0), the formula of the other channel naturally takes over, thus completely avoiding the divergence problem. This paper presents two complementary formulas and their limit behaviors, demonstrating that within the WQT framework, the divergence of energy formulas is not a physical essence but a limitation of using a single expression to cover all physical states. The correct approach is to retain two independent channel formulas and select the appropriate one according to the physical state. Keywords: Energy Formula; Divergence; World Quantum Theory; Orthogonal Projection; Mass Channel; Momentum Channel