Navigation of Space-Time Ships in Unified Gravitational and Electromagnetic Waves

摘要

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 PDEs to a particular conformally equivariant system of differential equations, we show the dependency of any kind of function describing "space-time waves, " with respect to 20 parameterizing functions. These latter, appearing in a linear differential Spencer sequence and determining gauge fields of deformations relative to "ship metrics " or to "flat space-time 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 space-time.