Physical Justifications and Possible Astrophysical Manifestations of the Projective Theory of Relativity

Abstract

The ‘projective theory of relativity’ is a theory developed historically by Oswald Veblen and Banesh Hoffmann, Jan Arnoldus Schouten and David van Dantzig. This theory differs radically from Kaluza-Klein/conformal type theories of spacetime, although it shares with these theories geometric aspects in five-dimensional spaces. The peculiarity of the projective geometries involved in this theory was that it is based on spaces coordinated by five so-called ‘homogeneous coordinates.’ Since then, no physical observables could be ascribed to these five homogeneous coordinates and, in particular, during the elaboration of this theory which consequently fell completely into oblivion. We will present how this projective theory of relativity can be fully justified physically from the causal structures and localizing protocols involved in so-called ‘relativistic localizing systems’ that extend ‘relativistic positioning systems.’ We explain the correspondence between ‘homogeneous coordinates’ of the projective theory of relativity and the physical observables defined in relativistic localizing systems. Then, possible astrophysical manifestations will be presented based on projective effects, invariance of interactions, or observations with respect to projective transformations.