Universal Mathematical Field Theory (UMFT) Deriving Mathematically Maxwell- Electromagnetics From (Coulomb Law + velocity) and GravitoElectromagnetics From (Newton Law + velocity)
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
GravitoElectromagnetics (Gravito-EM or Maxwell-type gravity) and Lorentz-type gravitational force
from Newton’s law and the velocity of a gravitational source. The so-derived Maxwell-EM justifies
UMFT and shows that the experiments-based Maxwell equations have mathematical origin. Gravito-EM
is one step further than Newton’s theory to understand gravity, although may not be the ultimate theory
of gravity. Indeed, since the Gravito-EM is derived mathematically, thus, any further theory of gravity
should have not only Newton’s law but Gravito-EM as approximations under certain condition. UMFT
shows that mathematical identities lead to physical dualities, such as the duality between Maxwell-
EM and Gravito-EM. Therefore, the concepts, effects and phenomena of Maxwell-EM may be directly
converted to that of gravity. The Gravito-EM can be quantized, along the line of quantizing Maxwell-
EM. The Maxwell-EM and Gravito-EM are derived from UMFT and thus, are dual to each other, have
same symmetry, U(1) symmetry, and can be unified in the frame of UMFT.
