Linking Inverse Square Law with Quantum Mechanical Probabilities

({\copyright}2007 by S Goradia) I modify the Newtonian inverse square law with a postulate that the probability of interaction between two elementary particles varies inversely as the statistical number of Planck lengths separating them. For two nucleons a million Planck lengths apart, the probability of an interaction is a trillionth (almost never), seemingly contradicting gravity. Likewise, statistical expression of the size of the universe implicitly addresses the issue of dark energy by linking fine-structure constant \textit{$\alpha $} = 1/137 with the cosmological constant \textit{$\lambda $} = 1/$R^{2}$ (abstract submitted 11/11/07 for APS APR2008 meeting). Since light travels one Planck length per Planck time, the radius $R$ of the spherical shape of the universe is 10$^{60}$ Planck lengths, linking the cosmological constant \textit{$\lambda $ = }1/10$^{120}$ (see equation 14 in Einstein's 1917 paper) with $\alpha $ by the relationship 1/\textit{$\alpha $} $\approx $ \textit{ln}$\surd $(1/ \textit{$\lambda $}). Intuitive answers to the questions raised suggest that the elementary particles interact via Planck scale mouths $^{(1),}$ with higher probabilities at smaller distances. This intuition may be supported by genetics, explaining issues such DNA -- nucleosome interaction $^{(2) (3)}$. [1] http://www.arxiv.org/pdf/physics/0210040 [v. 3] [2] www.gravityresearchinstitute.org [3] Segal E. \textit{et al}$,$ A genomic code for nucleosome positioning.\textit{ Nature} 442, pp. 772-778, 2006.