Emergence of Gravitational Coupling from Quantum Action and Vacuum Geometry

Abstract

We propose a quantum-geometric framework in which gravitational coupling emerges from the requirement that spacetime maintains a quantum-scale action of order ℏ. Starting from the zero-point energy of quantum oscillations and a minimal spacetime volume element, we construct an action-based balance between vacuum energy and geometric curvature. This leads to a natural derivation of a coupling relation of the form . Unlike conventional approaches, the derivation avoids direct use of the gravitational constant G, thereby addressing circularity issues in Planck-scale arguments. We interpret gravity as an emergent geometric response required to preserve quantum coherence of action in spacetime.