Maxwell Equations derived from (Coulomb’ Law + velocity), Maxwell-type Gravity derived from (Newton’s Law + velocity), Spin-Electromagnetics derived from (Coulomb’ Law + spin), Spin-Gravity derived from (Newton’s Law + spin) — Duality, Symmetry, and Uni - Peng, Hui (European Journal of Applied Sciences, 2025)
The Universal Mathematical Field Theory (UMFT) is established, which states that the combination of inverse square laws and either a vector field or an axial vector field create the curl of an axial vector field. Utilizing UMFT, we mathematically: (1) derive the Maxwell electromagnetics (Maxwell-EM) and the Lorentz force from Coulomb’s law and the velocity of an electric source; (2) establish Maxwell-type gravity (Gravito-EM) and Lorentz-type gravitational force from Newton’s law and the velocity of a gravitational source; (3) establish Spin Electromagnetics (Spin-EM) from the Coulomb’s law and the spin of the electric source; (4) establish Spin gravity (Spin-gravity) from the Newton’s law and the spin of the mass (such as neutron); (5) predicate the spin related Lorentz-type force. The so-derived Maxwell-EM justifies UMFT and shows that the experiments-based Maxwell equations have mathematical origin. UMFT shows that mathematical identities lead to physical dualities, such as the duality between Maxwell-EM, Gravito-EM, Spin-EM and Spin-gravity. Therefore, the concepts, effects and phenomena of Maxwell-EM may be directly converted to that of gravity and Spin. The Gravito-EM can be quantized, along the line of quantizing Maxwell-EM, and unified with Maxwell-EM force. Spin-EM predicts several new effects, the Spin-Lorentz-type force, and Lagrangian-Lorentz-type force. If experimentally proved, the Spin-related force may be the New Force. Spin-EM can be utilized to describe the new interaction between protons, while Spin-gravity can be utilized to describe the new interaction between neutrons. The Maxwell-EM, Gravito-EM, Spin-EM, and Spin-gravity are all derived from UMFT and thus, they are dual to each other, they have same symmetry, such as U(1) symmetry of Maxwell-EM, and they can be unified in the frame of UMFT.