Mem-force Theory: Density-Dependent Restoring Force, QCD Vacuum Origin, and a Unified Picture of the Four Fundamental Interactions

This paper proposes the Mem-force Theory, in which gravity is not an independent fundamental interaction but a density-dependent restoring force arising from the response of the QCD vacuum scalar condensate to energy density perturbations. The core axiom of the theory is that the restoring stiffness satisfies a power law μ² (ρ) ∝ ρ^α, where the exponent α = sin (π/8) ≈ 0. 3827 is given by a geometric axiom and is consistent with galaxy rotation curve observations. We rigorously derive the field equations and the force law of Mem-force gravity, demonstrating that in high-density regions the force automatically approaches Newtonian gravity (chameleon screening), while in low-density regions it acquires long-range modifications that can explain galaxy rotation curves without introducing dark matter. We further propose a QCD vacuum origin hypothesis: the scalar memory field φ of gravity corresponds to the relative fluctuation of the QCD chiral condensate, and the transition from nuclear scales (fm) to galactic scales (kpc) is achieved through low-density infrared softening dynamics. Finally, we present a unified interpretive framework for the four fundamental interactions: all four interactions are memory responses of the same QCD vacuum to different types of perturbations. Electromagnetism, the strong force, and the weak force correspond to the standard model gauge dynamics, while gravity corresponds to the density-dependent restoring force unique to Mem-force Theory. The theory does not modify the standard model, does not claim to derive gravity from first principles in QCD, but provides a self-consistent, falsifiable, and testable unified physical picture. Its validity is to be judged by observational tests of the gravitational sector. ```