From Locked Energy to Newtonian Gravity: A Minimal Story of Conceptual Necessity

Abstract

Why must gravity, in its macroscopic manifestation, take the precise form of Newton’s universal law? We answer this long-standing descriptive—not dynamical—question by constructing a minimal chain of operational reasoning. Starting from the relativistic definition of mass as timelike locked energy, we demonstrate that statistical coarse-graining erases all directional details, leaving only a scalar density. In empty, flat space, linearity and symmetry then enforce the Poisson equation as the unique consistent long-range closure. This structure is shown to be identical to the Newtonian-limit constraint of General Relativity. The contribution is interpretive: it reduces the apparent arbitrariness of Newtonian gravity by revealing it as the inevitable macroscopic imprint of three simple and well-established principles. This work exemplifies how theoretical physics advances not only by discovering new laws, but also by deepening our understanding of why established laws cannot be otherwise.

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