SPACETIME CURVATURE FROM RESIDUAL MICROSCOPIC INTERACTIONS: AN EMERGENT-GRAVITY APPROACH BASED ON SPIN AND BINDING FORCES

Abstract

Emergent gravity proposes that gravitation is not a fundamental interaction but rather a macroscopic manifestation of underlying microscopic degrees of freedom. Existing approaches, including thermodynamic gravity, entropic gravity, and holographic gravity, provide important insights into the relationship between information, statistical mechanics, and space-time geometry. However, a direct mathematical framework connecting microscopic particle interactions, spin effects, binding forces, and space-time curvature remains incomplete.
This paper presents a theoretical framework in which residual microscopic interactions generate an effective scalar field whose stress-energy contributes to space-time curvature. A residual interaction density is constructed from electromagnetic, strong, weak, spin, and vacuum contributions. Using variational methods based on the Einstein–Hilbert action, modified Einstein field equations are derived and proof is provided that non-vanishing residual interactions necessarily induce curvature. The framework establishes a mathematical bridge between microscopic interaction physics and macroscopic gravitational geometry, providing a potential foundation for emergent gravity rooted in particle-level dynamics.