Navigation of Spacetime Ships in Unified Gravitational and Electromagnetic Waves

Abstract

On the basis of a "local" principle of equivalence of general relativity, we consider a navigation in a kind of "4D-ocean" involving measurements of conformally invariant physical properties only. Then, applying the Pfaff theory for PDE to a particular conformally equivariant system of differential equations, we show the dependency of any kind of function describing "spacetime waves", with respect to 20 parametrizing functions. These latter, appearing in a linear differential Spencer sequence and determining gauge fields of deformations relatively to "ship-metrics" or to "flat spacetime ocean metrics", may be ascribed to unified electromagnetic and gravitational waves. The present model is based neither on a classical gauge theory of gravitation or a gravitation theory with torsion, nor on any Kaluza-Klein or Weyl type unifications, but rather on a post-Newtonian approach of gravitation in a four dimensional conformal Cosserat spacetime.Comment: 28 pages. Relative to the second version some changes in the mathematical results have been corrected without consequences in the physical model. The conformally flatness of the substratum spacetime which is an assumption used throughout in the mathematical developements from chapter 2, has been well precised in the first chapter. Clearer explanations at the very end of chapter 3 about accelerating frames are given. New references are indicated and some of them correcte