Emergent Forces Between Soliton Solutions of the Rotor Field Equation

In the Rotor Dynamics Framework the vacuum is modeled as a four-dimensional rotor manifold whose dynamics are governed by the nonlinear Rotor Field Equation. Previous papers in this series demonstrated that localized soliton solutions of the Rotor Curvature Field correspond to particle structures, including the electron as a vortex soliton, the proton as a closed rotor soliton, and the neutron as a composite core–sheath soliton. In the present work the interaction between such soliton solutions is analyzed. When multiple solitons are embedded within the same curvature field, their curvature disturbances overlap and modify the total curvature energy of the field configuration. The resulting dependence of the curvature energy on soliton separation defines an interaction energy and an associated force between the soliton structures. At large separations the interaction arises from the overlap of weak far-field curvature disturbances, producing long-range curvature-mediated forces. At short separations nonlinear coupling between the soliton cores dominates the interaction and may produce strong attraction, repulsion, or the formation of composite rotor structures. These results show that particle forces emerge naturally from the nonlinear dynamics of the Rotor Curvature Field, providing a geometric origin for particle interactions within the rotor framework.