On the Metric of Space-time

Abstract

Maxwell's equations are obeyed in a one-parameter group of isotropic gravity-free flat space-times whose metric depends upon the value of the group parameter. An experimental determination of this value has been proposed. If it is zero, the metric is Minkowski's. If it is non-zero, the metric is not Poincare invariant and local frequencies of electromagnetic waves change as they propagate. If the group parameter is positive, velocity independent red shifts develop and the group parameter plays a role similar to that of Hubble's constant in determining the relation of these redshifts to propagation distance. In the resulting space-times, the velocity dependence of Doppler shifts is a function of propagation distance. If the group parameter and Hubble's constant have the same order of magnitude, observed frequency shifts in radiation received from stellar sources can imply source velocities quite different from those implied in Minkowski space. In these space-times, electromagnetic waves received from bodies in galactic Kepler orbits undergo frequency shifts which are indistinguishable from shifts currently attributed to dark matter and dark energy in Minkowski space, or to a non-Newtonian physics.