Reconstruction of Electromagnetic Self-force Based on Spacetime Energy Balance and the Mutual Energy Flow Theorem

Abstract This study proposes a novel framework to address the century-old unresolved problem in classical electrodynamics—the self-force and its resulting runaway solutions. Unlike traditional theories that view the self-force as the local coupling of a charge with its self-generated field, this paper, based on the physical axiom that “radiation does not leak out of the universe,” utilizes the spacetime energy balance equation to reconstruct electromagnetic interaction as a mutual energy flow process between the source and the cosmic absorber. The research demonstrates: Mathematical Innovation: By introducing a phase operator j correction to the electromagnetic field (i.e., H\sim\pm jE), the imaginary work representing local energy loss is transformed into real energy exchange on a spacetime scale, fundamentally eliminating radiation divergence. Simplified Logical Derivation: Using the composite time-translation logic of retarded and advanced waves, the standard term of radiation reaction force, \tau\dot{\mathbf{a}}, is directly derived without the need for integration by parts. This derivation proves that the self-force is essentially the global feedback force exerted by the entire cosmic absorber on the source, rather than the charge doing work on itself. Termination of Pathological Solutions: Quantitative calculations demonstrate that the energy scale required for runaway solutions (approximately 105 MeV) far exceeds the valid domain of classical physics, ruling out its physicality within the classical regime on physical grounds. This theory proves that under the closed-loop constraint of spacetime, runaway solutions cannot physically exist because their initial conditions violate energy conservation, while naturally circumventing the cumbersome renormalization requirements of modern field theory. This work not only provides a self-consistent classical explanation for the self-force problem but also offers a new physical picture based on “full reciprocity” for the interpretation of quantum mechanics and the construction of unified field theories.