Complex Field Theory of Dark Matter and Dark Energy: Novel Atomic and Nuclear Models and a Unified Framework for the Four Fundamental Forces

Abstract

Complex Field Theory (CFT) describes Dark Matter (DM) and Dark Energy (DE) as complex fields composed of positively and negatively charged complex mass, respectively. These complex fields permeate the entire universe and play fundamental roles in governing the physical characteristics of everything in it. Several aspects of the theory have been discussed in earlier publications. In this paper, we investigate whether the forces associated with DM and DE at the atomic and nuclear scales share the same fundamental origin as the gravitational force at cosmic scales. Within the CFT framework, we derived a positive Yukawa force that balances the attractive Coulomb force acting on ground-state atomic electrons. We also derived an atomic radiation sink that prevents atomic electrons from radiating electromagnetic energy externally, thereby providing a mechanism for atomic stability. The paper concludes that the forces underlying both Bohr’s atomic model and the quantum mechanical model are rooted in the same complex nature as the complex charges of DM- and DE, responsible for gravity. Consequently, these forces are interpreted as different manifestations of a single unified origin rather than as distinct physical sources. Bohr’s model (1913) was the first successful theory to quantize atomic energy levels and provided a theoretical foundation for Rydberg’s empirical formula. However, it incorrectly attributed the stability of ground-state electrons to a balance between the attractive Coulomb force and the centrifugal force of the orbital electrons. Furthermore, it did not provide a physical explanation for the atomic radiationless nature. The quantum mechanical (QM) model, developed by de Broglie, Schr?dinger, and Max Born, describes ground-state electrons by a three-dimensional stationary wave function governed by Schr?dinger’s equation. Within this framework, atomic stability is attributed to the combined effects of the attractive Coulomb force and the uncertainty principle, which prevents the electron from collapsing into the nucleus. In addition, the stationary nature of the bound-state wave function implies the absence of a time-varying electric dipole moment in the electron probability distribution, thereby preventing external electromagnetic radiation. In this paper, the concepts of CFT, together with the path-integral formulation of Quantum Field Theory, are used to develop a framework for deriving both the ground-state stability and the radiationless nature of atomic electrons. Furthermore, a repulsive Yukawa force is derived to balance the attractive Coulomb force in the ground state. CFT also concluded an alternative model to Yukawa strong nuclear force model and validated it with experimental data. The analysis identifies a common factor of complex nature that unifies the Yukawa force with the energy and momentum associated with the uncertainty principle.