Unified Field Theory of the Primordial Tendency-Difference Force

This paper takes the global unidirectional tendency-difference force (potential difference seeking equilibrium) as the sole cosmic origin, driving all differences spontaneously toward dynamic equilibrium. A continuous Lorentz-covariant real scalar field is introduced as the mathematical expression of this force (the field itself is not an independent entity, merely a computational tool). Based on this, a unified field theory framework is established relying solely on three axioms, without extra dimensions, gauge presuppositions, or phenomenological parameters. From the variation of the Lorentz-covariant action, the dynamical equation of the scalar field is derived. Under weak-field and strong-field approximations, the Newtonian gravitational Poisson equation and the Schwarzschild metric are obtained. The electromagnetic field tensor is endogenously constructed from the antisymmetric combination of field gradients, yielding the source-free and sourced Maxwell equations. Linearizing field fluctuations leads to a wave equation, which in the non-relativistic limit reduces to the Schrödinger equation, and the hydrogen atom energy levels are solved analytically. The rest mass of elementary particles is defined via the energy integral of topological solitons, naturally satisfying the equivalence principle of gravitational and inertial mass. The statistical distribution of field gradients gives an entropy expression, from which the second law of thermodynamics is rigorously derived. Three effective parameters of the cosmic medium are introduced to achieve a first-principles closed-form calculation of the speed of light, the gravitational constant, and the electromagnetic combination constant. This theory provides a unified axiomatic foundation for understanding fundamental phenomena in the universe. The axioms are self-consistent, the mathematical derivation is complete without gaps, and the physical picture is unified. It offers a new paradigmatic theory for the grand unification of fundamental physics.