THE EMERGENCE OF A KALUZA-KLEIN MICROGEOMETRY FROM THE INVARIANTS OF OPTIMALLY EUCLIDEAN LORENTZIAN SPACES

It is shown that relativistic spacetimes can be viewed as Finslerian s paces endowed with a positive definite distance (omega(0), mod omega(i )) rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of ''Euclidicity in the small'' advocates ab solute parallelism, teleparallel nonlinear Euclidean (i.e., Finslerian ) connections are scrutinized. The fact that (omega(mu), omega(0)(1)) is the set of horizontal fundamental 1-forms in the Finslerian fibrati on implies that it can be used in principle for obtaining compatible n ew structures. If the connection in teleparallel, a Kaluza-Klein space (KKS) indeed emerges from (omega(mu) omega(0)(i)), endowed ab initio with intertwined tangent and cotangent Clifford algebras. A deeper lev el of Kahler calculus, i.e., the language of Dirac equations, thus eme rges. This makes the existence of an intimate relationship between cla ssical differential geometry and quantum theory become ever more plaus ible. The issue of a geometric canonical Dirac equation is also raised .