Mathematics – Logic
Scientific paper
Oct 1973
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973natur.245..313c&link_type=abstract
Nature, Volume 245, Issue 5424, pp. 313-314 (1973).
Mathematics
Logic
3
Scientific paper
SINCE the original relationship pointed out by Dirac1,2, several dependent and independent numerological relations have been proposed. Dirac noticed that the ratio between the age of the Universe and the natural unit of time (which he took to be the time the light takes to cross an electron radius) is approximately equal to the ratio between the electrostatic and the gravitational force acting between two electrons. Here I propose a semi-empirical relationship which could throw some light on the Dirac expression : mec3/(He2)~=e2/(Gm2e) (1) where me and e are the electron mass and charge respectively, H is the Hubble constant, G is the gravitational constant and c is the speed of light. Whether me or mp, the proton mass, should appear on the right hand side of equation (1) has long been regarded as irrelevant, since a few orders of magnitude would matter little in expressions of the order of 1040. But here I shall need to be more accurate, and I write instead mec3/(He2)=qe2/(Ggme2), where q is an appropriate constant, and g comes from setting R =gc/H, with g <= 1. Equivalently : H=(g/q) (Gm3ec3/e4) (2)
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