2 1 Ju l 2 00 1 A Note on Transfinite M Theory and the Fine Structure Constant

In this short note , using concepts of p-Adic QFT and p-branes, we derive the transfinite M theory generalization of the inverse fine structure constant given by (αM ) −1 = 100 + 61φ . The orginal El Naschie and Selvam-Fadnavis inverse fine structure constant value (αHS) −1 = 100+60φ was based on a transfinite heterotic string theory and a quasiperiodic Penrose tiling formalism, respectively. Here φ is the Golden Mean 0.6180339.... Our results are consistent with the recent astrophysical observations of the Boomerang and Maxima experiments ,the previous results based on the four dimensional gravitational conformal anomaly calculations, and with an enhanced spacetime hierarchy of a suitable number of lines living on Del Pezzo surfaces. Motivated by the fact that the bosonic membrane is devoid of anomalies in d = 27, and the supermembrane is anomaly free in d = 11 [2] , and that the anomaly free ( super) string actions ( d = 26, 10 ) are directly obtained by a double-dimensional reduction process of both the world-volume of the ( super) membrane and the target spacetime dimension , where the ( super) membrane is embedded, we shall derive the transfinite M theoretical generalization (αM) −1 to El Naschie’s inverse fine structure constant (αHS) −1 which was based on a transfinite Heterotic string theory formalism [1]. Selvam and Fadnavis [15] , independently, obtained this value using a quasiperiodic Penrose tiling model ( a quasicrystal ) associated with the logarithmic spiral, with a golden-mean winding number, which represents a bidirectional ∗Center for Theoretical Studies Clark Atlanta University Atlanta, GA. 30314, USA