Cantorian spacetime and Hilbert space: part II - Relevant Consequences

In this paper, we will show the consequences of the link between epsilon((infinity))and H-(infinity). Starting from El Naschie's epsilon((infinity)) nature shows itself as an arena where the laws of physics appear at each scale in a self-similar way, linked to the resolution of the observations; while Hilbert's space H-(infinity) is the mathematical support to describe the interaction between the observer and dynamical systems. The present formulation of space-time, based on the non-classical, Cantorian geometry and topology of the space-time, automatically solves the paradoxical outcome of the two-slit experiment and duality. The experimental fact that a wave-particle duality exists is an indirect confirmation of the existence of epsilon((infinity)). Another direct consequence of the fact that real space-time is the infinite dimensional hierarchical epsilon((infinity)) is the existence of the scaling law R(N). The present author proposed it as a generalization of the Compton wavelength. This rule gives an answer to segregation of matter at different scales; it shows the role of fundamental constants like the speed of light and Plank's constant h in the fundamental lengths scale without invoking the methodology of quantum mechanics. In addition, we consider the genesis of E-Infinity. A Cantorian potential theory can be formulated to take into account the geometry and topology of epsilon((infinity)) in the context of gravitational theories. Consequently, we arrive at the result of the existence of gravitational channels.