Navigation of Spacetime Ships in Unified Gravitational and Electromagnetic Waves

TL;DR

This paper develops a novel model for navigating spacetime ships using conformally invariant measurements and differential equations, linking electromagnetic and gravitational waves without relying on traditional unification theories.

Contribution

It introduces a new conformal Cosserat spacetime framework and applies Pfaff theory to describe spacetime waves through gauge fields and differential sequences.

Findings

Dependency of spacetime wave functions on 20 parameters

Unified electromagnetic and gravitational wave description

Model avoids classical gauge and Kaluza-Klein theories

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.