Maxwell Electromagnetism Derived From (Coulomb’ Law + Velocity), Spin-Electromagnetism Derived From (Coulomb Law + Spin), Gravito-Electromagnetism Derived From (Newton’s Law + Velocity), Spin-Gravito-Electromagnetism Derived From (Newton’s Law + Spin) --- Duality, Symmetry, Spin-Force, and Unification of Above Four Forces

Abstract

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 the vector/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 or Spintronics) 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 well-known 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, including the Spin-Lorentz-type force and Lagrangian-Lorentz-type force. If experimentally confirmed, the Spin-related force may be the NEW FORCEs. Spin-EM can be utilized to describe the interaction between protons, while Spin-gravity can be utilized to describe the interaction between neutrons. The Maxwell-EM, Gravito-EM, Spin-EM, and Spin-gravity are all derived from UMFT and thus: (1) they all have the same symmetry, such as the U(1) symmetry of Maxwell-EM; (2) they all can be quantized in the same way as QED; and (3) can be unified in the frame of UMFT.