CHANGES OF TOPOLOGY AND CHANGES OF SIGNATURE

Some recent ideas about topology and signature changing spacetimes are described. If spacetime is everywhere Lorentzian but non-orientable, one can sometimes avoid closed timelike curves, but one must must cons ider pinors rather than spinors. One finds that there is now an import ant distinction between signature (+ + +-) and (- - -+). In some cases one signature may be excluded and the other allowed. Topology changin g spacetimes with domains of non-Lorentzian signature are considered. These domains may be Riemannian or Kleinian (+ + --). It is argued tha t our present signature, together with the idea of time must have aris en as the consequence of physical processes. This emergence of the ide a of time is also connected with the origin of the complex numbers in Quantum Mechanics which should also be regarded as the consequence of the evolution of the universe.