DYNAMICAL DETERMINATION OF THE METRIC SIGNATURE IN SPACETIME OF NONTRIVIAL TOPOLOGY

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom, induced by quantum fields in spacetimes with non-trivial topology of the kind R(D-1) x T1, is considered, for varying D. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space R4 x T1 with small torus radius (periodic boundary conditions), as well as in four-dimensional space with trivial topology. Hence the possibility exists that the early universe might have been of the Kaluza-Klein type, i.e. multi-dimensional and of Lorentzian signature.