Volume 17: Pages 269-287, 2004

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

Jacques L. Rubin

Institut du Non‐Linéaire de Nice, UMR 6618 CNRS — Université de Nice — Sophia Antipolis, 1361 route des lucioles, 06560 Valbonne, France

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 conformai Cosserat space‐time.

Keywords: conformal invariance, Cosserat space, differential sequences, electromagnetism, gauge theory, gravitation, model of unification, Pfaff systems, space‐time, Spencer theory of partial differential equations

Received: May 10, 2002; Published online: December 15, 2008