Gravity from Displacement of Vacuum Entropy

This paper develops an entropic formulation of gravity in which the geometry of space and the flow of time arise from the density of vacuum entropy. In this framework—the Entropic Cosmological Model (ECM)—the vacuum possesses an intrinsic entropy per unit volume, and physical measures of length, volume, mass, and proper time are determined by the local value of this entropy field. Ordinary matter does not contribute to vacuum entropy; instead, it displaces a small portion of the surrounding vacuum entropy, creating a spatially varying entropy density σ(r). The vacuum responds to this displacement through a Poisson-type field equation whose solution generates both stretching of radial distances and slowing of proper time near mass concentrations. The combined rescaling preserves the locally measured speed of light, ensuring consistency with local Lorentz invariance. Using only this entropic geometry—not the machinery of 4D spacetime curvature—the model reproduces the weak-field gravitational behavior normally attributed to Newtonian gravity and the Schwarzschild metric. The resulting geometry exhibits no singularities, and the gravitational field arises entirely from the redistribution of vacuum entropy rather than from curvature of spacetime or energy flux across holographic screens. These results demonstrate that gravity can be understood as a local, entropic displacement phenomenon within a purely 2D/3D framework, in which an expanding, negatively-curved 2D temporal boundary surrounds a flat 3D spatial interior—an expanding pseudosphere—with a 1:1 correspondence between energy and entropy on the boundary and energy and entropy in the interior. The derivations presented here serve as a proof-of-concept that an entropy-based foundation for gravitational phenomena is viable. By showing that the essential features of gravitational attraction and time dilation emerge directly from entropy displacement, the ECM framework suggests a pathway toward extending these results into a full 4D entropic spacetime theory. Appendices provide detailed mathematical derivations and a numerical example calibrated to Earth’s surface gravity.