The field equations of the quadratic action principle of relativity are solved, assuming a weak perturbation of the basic structure, which is a highly agitated Riemannian lattice field of a very small lattice constant. A field emerges which can be interpreted as the weak gravitational field of an apparently Minkowskian space. This field does not coincide with Einstein's theory of weak gravitational fields. Whereas the redshift remains unchanged, the light deflection becomes reduced by11.1% of the value predicted by Einstein.

Einstein's linear Lagrangian is replaced by a Lagrangian which is quadratic in the curvature quantities (gauge invariance). The hypothesis is made that the basic metrical field is highly agitated (due to periodic boundary conditions) thus establishing a submicroscopic basic lattice structure of the space-time world which, however, is macroscopically isotropic. All consequences follow from these assumptions. The “free vector” of Einstein's theory (void of physical significance and used for the normalization of the reference system) is no longer free but of (...) physical significance. It becomes subject to the wave equation and the Lorentz condition. It can thus be identified with the electromagnetic vector potential. Although the present investigation does not go beyond the linear approximation, the contours of auniverse of maxium rationality emerge. (shrink)

This paper uncovers the basic reason for the mysterious change of sign from plus to minus in the fourth coordinate of nature's Pythagorean law, usually accepted on empirical grounds, although it destroys the rational basis of a Riemannian geometry. Here we assume a genuine, positive-definite Riemannian space and an action principle which is quadratic in the curvature quantities (and thus scale invariant). The constant σ between the two basic invariants is equated to1/2. Then the matter tensor has the trace zero. (...) In consequence of the constancy of the scalar curvature and the divergence identity of the matter tensor, the perturbation metric has to satisfy a scalar and a vector condition, with a negative sign in the fourth coordinate. These conditions lead to the Lorentz condition and the wave equation for the vector potential. Thus the entire Maxwell-Lorentz type of electrodynamics becomes logically derivable, making no concession to any irrationality. (shrink)