EMERGENT GRAVITY BY SCREENING OF GRAVITATIONAL MODES (X v4)

Abstract

This paper explores the hypothesis that gravity is not a fundamental interaction but a macroscopic emergent e ect produced by the local modulation of a stochastic pregeometric background by matter. The guiding physical analogy is the Casimir e ect, where the restriction or screening of vacuum modes generates an e ective pressure imbalance manifesting as an attractive force. We propose a minimal e ective e ld theory based on three e lds: a scalar connectivity e ld d(x t) representing the density of the connective medium, an associated imbalance u x J(x t), and the emergent gravitational acceleration g e (x t). In spherical symmetry, the stationary exterior solution adopts a Yukawa-type form. In the long-range limit, the gradient of this e ld scales as 1 r 2 , recovering the functional form of Newtonian gravity without central singularities. Within the FCD-RB framework, this background ceases to be a heuristic postulate and is physically identi ed with the resonant modes of trans-brane Einstein-Rosen (ER) bridges, which are modeled as systems of inverted and standard harmonic oscillators in di erent regimes. Finally, we discuss how this phenomenological model of mode screening is formalized and hybridized in later parts of the series (Parts XXI and XXII) through Jacobson s spacetime thermodynamics and Verlinde s entropic gravity, where physical mode screening maps directly onto the local alteration of the vacuum s entanglement entropy gradient.