A model of Sakharov (1967) baryo-genesis where the 5th , compactified, dimension of Kaluza-Klein (1926) theory does ‘double duty’ as the creator of lepton-baryon numbers and creator of separate EM and gravity equations is proposed. The appearance of the compactified dimension breaks the symmetry of the Planckian vacuum, allowing the vacuum quantities hbar, G, and c to generate the particle quantities e, mp and me , which are the charges and masses of the proton and electron respectively. Under this model the lepton-baryon asymmetry is a reflection time-space dimensional asymmetry and the relationship of the hidden dimension size, ( in esu units) ro = e^2/(moc^2) ,where c is the speed of light, where mo=(mpme)^1/2 , to the Planck Length, rp =(Ghbar/c^3)^1/2 : is ln(ro/rp) = (mp/me)^1/2 and mirrors the lepton-baryon separation. Inversion of this formula leads to a highly accurate formula for G, the Newton Gravitaion constant. Improvement of this model to apply corrections near the Planck scale results a formula for G further improvement in accuracy( in esu):
G = alpha (e^2/mo^2 )exp( -2((mp/me)^1/2 -.86/(mp/me) …) = 6.6728 x 10^-8 dyn-cm^2-g^-2, where alpha is the fine structure constant. In the GEM theory of long range field unification ( Brandenburg 1988, ,1995, 2010) gravity fields are equivalent to an array of ExB drift cells or Poynting vectors and EM and gravity fields separate with the appearance of the Kaluza-Kline 5th dimension. The predicted hidden dimension size is 3000.0 MeV and lies right between the eta-c and J/psi particles and almost exactly on the Sigma (3000) baryon. Assuming a model where the proton-electron ( lepton-baryon) field unification occurs in a U(1) symmetry with imaginary rotation angle determined by normalized charge q/e and a multiplier ln(s’) where s’ = (mp/me)^1/2 ( the square root of the mass ratio) we obtain approximately, with qP =chbar ( the Planck charge) , we obtain the approximate relation: MP/mp = exp(ln(s’)qP/e) , where MP is the Planck Mass, when combined with the previous relations, we obtain, to leading order, “The Transcendental Cosmos Equation” relating the value of alpha to s':
s’ = ln(s’) (1/alpha^1/2 +1) –ln(1/alpha)~42.85...This is similar to the "MIT Bag Model" (Chodos et al. ,1974)result s' ~ (4pi/alpha)^1/2 Humorously, this recalls the number "42" which appeared in Hichhikers Guide to the Galaxy as the " answer to life, the universe, and everything" however, this author makes no such claims.
Brandenburg J.E. ( 1988) APS Bull.,33, 1, p.32.Brandenburg, J. E., (1995), Astrophysics and Space Science, 227, pp. 133.Brandenburg J.E. ( 2010) OSAPS Meeting .Chodos, R. L. Jaffe, K. Johnson, and C. B. Thorn,(1974) Phys. Rev. D 10, 2599 Klein, Oskar Zeitschrift fur Physik, 37, 895, (1926).Sakharov A.D. JETP 5,24-27, (1967).