On the unification of the fundamental forces and complex time in the ε(∞) space

Motivated by some recent contributions by various authors in the use of the so-called complex time (0 +/- ii) and Cantorian space (g((infinity))) in particle physics and cosmology, the present paper gives a preliminary analysis and some possible applications of these relatively new concepts in the quest for a general theory which may unify all the four fundamental forces known at present. In the course of the analysis presented here, we will give a derivation of a fundamental length in conceptually two different but complementary ways. The so-obtained fundamental length turned our to be of the order of magnitude of the Planck length (10(-33) Cm) and we discuss the possible existence of a transcritical fundamental particle with a mass related to the Planck mass (10(-5) g) and to a mini black hole with a Schwarzschild radius which is of the order of the Planck length. (C) 2000 Elsevier Science Ltd. All rights reserved.