Einstein Equations and Electromagnetism

Einstein's equations for infinitesimal gravitational fields are investigated from the standpoint of replacing Einstein's flat Minkowskian background space by a strongly agitated Riemannian lattice space, with the added demand that the perturbation field be of very low frequency compared with the lattice frequency. It is found that the strongly nonlinear lattice transmits low-frequency perturbations only if the perturbation field satisfies a set of field equations which become practically identical with Maxwell's equations. While this result demonstrates the close relation between Einstein equations and electromagnetism, it also opens a new door toward the deeper understanding of the quantum phenomena.