2 a “ Running ” Gravitational Constant ?

If the gravitational interaction is unified with the electro-weak and strong interactions at a mass M = 10 15 GeV, the evolution of Newton's constant must differ from its classical (general relativistic) form. We can model such behavior by introducing an ad hoc dependence on ℓn(s/4m 2), where s is the usual cm energy between two protons. We can then predict the observable effects for relativistic collisions (√ s ∼ 1.4 × 10 4 GeV) as well as for the case of low velocity motion (β 2 ∼ 10 −5). It is well known that the dimensionless coupling constants of the three gauge groups of the standard model SU(3) × U(2) × U(1) vary with the momentum transfer of the interaction [1]. This effect which is due to the polarization of the vacuum was first recognized for the electromagnetic field. It is most prominent in the case of the color field and leads to assymptotic freedom. Extrapolation to higher energies is governed by the equations of the renormaliza-tion group, and it is customary to consider the inverse coupling constants