Demonstrating that Particles are Mutual Energy Flow, Not Self-Energy Flow, Based on the K-G Equation

Since proposing the electromagnetic mutual energy theorem and its inner product concept in 1987, and subsequently improving Huygens' principle (1989), the author formally established the mutual energy flow theorem in 2017, aiming to completely replace the traditional Poynting vector (self-energy flow) with mutual energy flow. He also proposed a process analogous to wave function collapse in quantum mechanics, namely the “reverse collapse” of self-energy flow back to its origin. In 2022, the author further clarified that since self-energy flow must be reactive power and does not transfer energy, the mutual energy flow theorem should be updated to the mutual energy flow law. Following the extension of this idea to the Schrödinger equation (by defining a “magnetic field” and correcting the phase to establish a particle-like mutual energy flow), this paper demonstrates the universality of this framework for the Klein-Gordon (K-G) equation. By constructing a magnetic field for the K-G equation and correcting its phase, the corresponding mutual energy flow law is derived. The research confirms that this mutual energy flow, formed by the coupling of retarded and advanced waves, is generated at the source and annihilated at the sink, perfectly unifying the wave and particle properties and providing a solid theoretical foundation for understanding wave-particle duality.