We develop an effective continuum framework in which the physical vacuum is characterized by a bounded scalar capacity field Φ(x,t), with normalized remaining-capacity fraction f=Phi /c^{2}. Matter is represented by localized depletion of this capacity, while gravitation arises from the associated redistribution of the remaining vacuum response. In the weak-field limit, the governing equation reduces to the Poisson equation and reproduces Newtonian gravity. A nonlinear capacity-dependent response yields the exterior solution Phi (r)=c^{2}sqrt{1-2Gm/(rc^{2})}, or equivalently f(r)=sqrt{1-2Gm/(rc^{2})}. Relating the local capacity fraction to temporal and reciprocal radial scaling reconstructs the Schwarzschild exterior line element ds^{2}=-f^{2}c^{2}dt^{2}+f^{-2}dr^{2}+r^{2}d{Omega }^{2}, together with its standard weak-field gravitational optical response. The same continuum dynamics admit localized intrinsic oscillations which, under the quantum normalization mathrm{hbar }{omega }_{0}=mc^{2}, yield the Planck—Einstein and de Broglie relations through Lorentz transformation of the intrinsic phase. The resulting dispersion relation takes the Klein—Gordon form and reduces to the Schrödinger equation in the nonrelativistic limit. Massive excitations propagate subluminally, whereas massless disturbances remain nondispersive with limiting propagation speed c. The framework thus provides a common continuum description of vacuum depletion, emergent gravitation and spacetime scaling, and relativistic matter-wave dynamics, while identifying strong-field dynamical phenomena as a potential regime for distinguishing predictions.