Linking Inverse Square Law with Quantum Mechanical Probabilities

Mathematics – Logic

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Scientific paper

(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 α = 1/137 with the cosmological constant λ = 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 λ = 1/10^120 (see equation 14 in Einstein's 1917 paper) with α by the relationship 1/α ln(1/ λ). 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. et al, A genomic code for nucleosome positioning. Nature 442, pp. 772-778, 2006.

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