Abstract

Weyl’s Gauge Principle of 1929 has been used to show that a five‐dimensional gauge field wherein the fifth dimension is conserved in the same mathematical sense as the conservation of mass embeds a four‐dimensional hyper surface into the five dimensional manifold. The equations specifying the geometry of the embedded hyper surface are similar in form to Einstein’s field equations of his General Theory of Relativity. These field equations become Einstein’s field equations when one takes the fifth dimension to be mass density. This means the predictions of Einstein’s General Theory may be achieved in two different ways. One by using Einstein’s method and the other by using a five dimensional manifold of space, time and mass density while restricting mass to be conserved. The five dimensional gauge fields associated with these phenomena are converted into a four dimensional curved hyper surface by the conservation of mass. The mathematical equivalence of the two methods provides the justification to seek what predictions might be made considering the five dimensional gauge field wherein the electromagnetic fields are inductively coupled to the gauge gravitational field. This presentation will present the logic showing how Einstein’s General Theory of Relativity may be derived from the five dimensional manifold using the conservation of mass. Comparison of predictions of perihelion advance by using the view from the embedded four‐dimensional hyper surface and from the five dimensional manifold shows the equivalence of the two methods of viewing physical phenomena. The inductive coupling between the electromagnetic and gravitational fields may be given experimental support by showing that predictions of the Earth’s magnetic moment due to its spinning gravitational mass is within 7% of the experimentally measured value. Such an inductively coupling between the gravitational gauge field and the electromagnetic gauge field provides an opportunity to seek predictions of the resulting five dimensional wave equations. Whereas in Maxwellian electromagnetism there are two, coupled, vector wave equations in the five dimensional gauge field there are three, coupled, vector wave equations that are also coupled to a scalar wave equation. The presentation will discuss the resulting transverse and longitudinal solutions to this system of wave equations. It will show that the inductive coupling with the gravitational field provides a very weak gravitational component to the transverse waves. It will also show that the longitudinal wave solutions may be independent of the transverse solutions and that the longitudinal solutions consist of only electric and gravitational vector components with an accompanying scalar wave. Longitudinal electrogravitic waves do not interact with the propagation medium as do transverse waves and make good candidates for space communication. Not only will longitudinal waves pass through intervening material, but they may be made very directive and, thereby, avoid a 1/r2 loss. The presentation will also present an antenna design for converting transverse electromagnetic waves into longitudinal electrogravitic waves for using current transmitting laser communication equipment and the reciprocal antenna design for converting longitudinal waves back into transverse waves to use current receivers.

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