Geometrization of Radial Particles in Non-Empty Space Complies with Tests of General Relativity

Abstract

Curved space-time 4-interval of any probe particle does not contradict to flat non-empty 3-space which, in turn, assumes the global material overlap of elementary continuous particles or the nonlocal Universe with universal Euclidean geometry. Relativistic particle's time is the chain function of particles speed and this time differs from the proper time of a motionless local observer. Equal passive and active relativistic energy-charges are employed to match the universal free fall and the Principle of Equivalence in non-empty (material) space, where continuous radial densities of elementary energy-charges obey local superpositions and mutual penetrations. The known planetary perihelion precession, the radar echo delay, and the gravitational light bending can be explained quantitatively by the singularity-free metric without departure from Euclidean spatial geometry. The flatspace precession of non-point orbiting gyroscopes is non-Newtonian one due to the Einstein dilation of local time within the Earth's radial energy-charge rather than due to unphysical warping of Euclidean space.

Cartesian nature of equal active and passive energies

“…But Einstein himself began to share the Cartesian matter-extension for the pure field physics at least since 1938. And nonempty space metric constructions for Einstein's General Relativity lead again to the same post-Newton findings for the main gravitational tests [15] as the empty-space metric of Schwarzschild can propose. What is the use of reinforcing the Aristotle-Descartes material space if it might not be ever justified in practice?…”

“…Now we associate electricity with imaginary numbers by using ρ(x, t)dv ≡ q ≡ ie ⇒ −ie o for the 'negative' elementary charge of the electron. Its selfpotential ϕ o ≡ E q /q = q/r q = c 2 / √ G is to be defined via the light speed limit c and the Cavendish constant G. The similar charge to spatial scale ratio, √ Gm/r m = c 2 / √ G, arises in gravitation of continuous radial masses [14,15], where mc 2 ≡ √ Gmϕ o is the body internal (kinetic or active) energy. In other words, we use the fundamental potential ϕ o ≡ c 2 / √ G = 1.04×10 27 V for self-energies of both mechanical (real) and electric (imaginary) charges,…”

Einstein Equation for Nondual Field Matter Modifies Naiver-Stokes Dynamics

“…The elementary mass density is to be a continuous spatial function in the Cartesian world and in the Einstein-Infeld pure field approach to matter. 4 passive mass-energy densities in non-empty pseudo-Riemannian world is the Ricci scalar, 8,9…”

4D Sommerfeld quantization of the complex extended charge

“…Pseudo-Riemannian 4-geometry with 6 inherent metric symmetries γ i j (x) = δ i j has the universal, Euclidean 3D space sub-interval in nonlocal GR equations and provides new physical interpretation of the known gravitational tests [3]. Strict spatial flatness of the warped space-time manifold reinforces the surface independent magnetic flux (3) over a closed line, the gauss electric flux over a closed surface, and gravity/inertia independent quantization of elementary matter in covariant relativistic relations.…”