  We introduce the gauge-invariant vector dynamics of continuous inertial
densities through the metric formalism for extended mechanical charges. Ricci
scalar density is related to invariant sum of inertial and gravitational mass
densities of nonlocal matter-extension. Such a Cartesian continuum of
gravitating inertial densities is self-governed by internal tensor tensions
toward a static equilibrium state with a Euclidean material 3-space under the
equivalence of inertial and gravitational densities of extended masses.
External forces and local frictions transform the self-dynamics of an
elementary closed continuum into a forced motion of still adaptive energy
flows, where high-order space-time derivatives can provide non-Newtonian
self-accelerations. If such tensor inertial feedback with the inverse constant
of Cavendish 1/G is justified by measurements for the modified Navier-Stokes
equation, the Newton empty space model should be replaced by the Cartesian
matter-extension for the non-local macroscopic world.
