Coupled oscillations and mode locking of quantum gravity fields, scale relativity and space

The present paper provides a fundamental conjecture regarding the unification of gravity with the electroweak and strong forces. Based on the renormalization group approach, SU(3) theory, GUT as well as scale relativity and conformal field theory in a space, it is concluded that the Cantorian value corresponding to the Weinberg mixing parameter at the Planck, string-like unification scale, is equal to the Hausdorff dimension of the zero set of namely It is furthermore conjectured that the corresponding charge–mass dimension dcm is equal to the inverse of the value of the Weinberg parameter at the same energy scale: while the expectation value for two coupled oscillating quantum fields related by the unitarity conformal weight dimension dUCW remains exactly as in the theory. This meansdUCW= dc =4+φ3 4.236.It is generally concluded that all the three theories, Heterotic strings, M theory and theory, are organized at the core via the Golden Mean renormalization group in a way reminiscent of deterministically chaotic maps such as the Feigenbaum period doubling bifurcation. In particular the H strings dimension are given by For n=0–4, one finds . Finally we show that can be derived via theory as This means An even more accurate estimation of based on Heterotic string theory and is found to be