Maxwell equation derived from (Coulomb’ Law + velocity), Maxwell-type Gravity derived from (Newton’s Law + velocity), Spin-Electromagnetism derived from (Coulomb’ Law + spin): By Universal Mathematical Field Theory (UMFT)

Abstract

A Universal Mathematical Field Theory (UMFT) is established, which states that the combination of inverse-square laws and vector field or an axial vector field create the curl of an axial vector field. Utilizing UMFT, we mathematically: (1) derive the Extended-Maxwell equations and the Lorentz force from Coulomb’s law and the velocity of the source; (2) establish Maxwell-type gravity equations (Gravito-EM) and Lorentz-type gravitational force from Newton’s law and velocity of gravitational source; (3) establish Spin-Electromagnetics (Spin-EM) from the Coulomb’s law and the spin angular velocity; (4) predicate the spin related force. For a source moving with spatially uniform velocity, the Extended-Maxwell equations reduce to Maxwell equations (EM), which 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 EM, Gravito-EM and Spin-EM. Therefore, the concepts, effects and phenomena of EM may be directly converted to that of gravity and Spin. The Gravito-EM are employed to study the accelerating universe, rotation curve and gravitation waves. The Gravito-EM can be quantized, along the line of quantizing EM, and unified with EM force. Spin-EM: (1) correlates phenomena of family of Hall effects, zero longitudinal Hall coefficient/resistivity, Extended Rashbe SOC, and GMR/TMR. (2) predicts that Spin-potential coupling directly induces force; (3) provides classical counterparts of Larmor-precession, Stark Effect, Landau–Lifshitzequation, Zeeman effect, and Aharonov–Casher effect. We derive the Spin-Lorentz-type force and Lagrangian-Lorentz-type force. If experimentally proved, the Spin-related force may be the 5th force.