Metrical Lattice and the Problem of Electricity

A reinterpretation of Einstein's tetrad geometry leads to new results if we abandon the over-simplified picture of the vacuum as an almost empty Minkowskian manifold. The basic tetrad is identified with the four principal axes of the matter tensor which belongs to a strongly curved fourfold periodic Riemannian world. The macroscopic perturbation of the metrical lattice is investigated, corresponding to a mere rotation of the principal axes and assuming the quadratic action principle of general relativity. The perturbation Lagrangian yields the scalar E2 − H2, (and thus the Maxwellian equations), although the basic manifold is strictly Riemannian, with a positive-definite line element.