Is quantum space-time infinite dimensional

The stringy uncertainty relations, and corrections thereof, were explicitly derived recently from the new relativity principle that treats all dimensi ons and signatures on the same footing and which is based on the postulate that the Planck scale is the minimal length in nature in the same Vein that the speed of light was taken as the maximum velocity in Einstein's theory of Special Relativity. A simple numerical argument is presented which sugge sts that quantum space-time may very well be infinite dimensional. A discus sion of the repercussions of this new paradigm in Physics is given. A truly remarkably simple and plausible solution of the cosmological constant prob lem results from the new relativity principle: The cosmological constant is not a constant, in the same vein that energy in Einstein's Special Relativ ity is observer dependent. Finally, following Fl Naschie, we argue why the observed D = 4 world might just be an average dimension over the infinite p ossible values of the quantum space-time and why the compactification mecha nisms from higher to four dimensions in string theory may not be actually t he right way to look at the world at Planck scales. (C) 2000 Elsevier Scien ce Ltd. All rights reserved.