Energy-Density Gravity: A Scalar-Potential Toy Model Reproducing Schwarzschild Time Dilation

This technical note is a supplementary document to the foundational paper, "Dynamic Present Theory I: Unifying Quantum Mechanics and General Relativity" (DOI: 10.5281/zenodo.17069890). It addresses a concrete question motivated by that work's concept of Energy-Density Gravity (EDG) by constructing a simplified toy model.We present a scalar-potential model in which gravitational time dilation and weak-field dynamics arise from gradients in local energy density within a flat 3D space. This approach does not invoke the curvature of a four-dimensional spacetime manifold. For a static, spherically-symmetric source, we derive a potential Φ(r)=GM/r that satisfies a Poisson-type equation nabla^2 * Φ = 4*pi*G*rho / c^2. By postulating that the proper time interval scales as dτ = dt * sqrt(1 - 2*Φ / c^2), the model reproduces the Schwarzschild time-dilation factor to first order. We tabulate predicted deviations from General Relativity for key astrophysical tests and outline a clear observational pathway for model falsification.