Matter–Energy Model without the Gravitational Constant: A Unified Approach to Gravitational and Nuclear Interactions

Abstract

Newton's law of universal gravitation and Einstein's General Theory of Relativity (GTR) face limitations in explaining gravitational anomalies and unifying fundamental physical forces. This study proposes that the gravitational constant G is not constant but distance-dependent (G_var), establishing a unified theoretical framework for gravitational and nuclear interactions. We first derive the functional form of G_var calibrated by planetary perihelion shifts, then analyze its impact on the physical unit system, and finally construct a matter--energy model based on the Primordial Energy Matrix (PEM) composed of force points. The results show that G_var effectively explains gravitational anomalies (e.g., Pioneer anomaly, flyby anomalies) and achieves the unification of gravity with strong/weak nuclear and electromagnetic forces without introducing extra dimensions. The matter--energy model reveals that elementary particles (neutrons, protons, electrons) originate from vortices formed by PEM force points, and atomic/molecular structures are derived from the cascading combination of these vortices. This work provides a new perspective for understanding the nature of gravity and the origin of matter.