Undulatory Riemannian Spaces

Abstract

A demonstration is given that Riemannian spaces of very high curvature in submicroscopic domains do not contradict the existence of a macroscopic line element which is nearly Minkowskian. The signature of the microscopic line element is positive definite and the wave property of the metric in macroscopic domains comes about by a peculiar ``wave‐guide action'' of a strongly curved, two‐dimensional line element, in harmony with the particlelike behavior of the photon. The four‐dimensional lattice structure of the metrical vacuum field does not establish an absolute frame of reference and can be harmonized with the macroscopic validity of the Lorentz transformations.