Abstract

To establish a self-consistent system of mutually interacting gravitational quadrupoles, a characteristic number N of quantum masses µ are related to a characteristic velocity scaling. For this purpose a critical reference is defined by the flux and flux number of mass quanta constituting a confining unit field generating mass m_{G}=Nµ. In the field of m_{G} any small test mass orbits at unit distance r_{u} with unit velocity u (human artificial units). The velocity limit c with angular momentum quantum h is assigned to the Schwarzschild black hole photon sphere with radius given by the Compton wavelength. For this quantum mass we find the constitutional scaling relation N \approx 3m_{G}/µ \propto (c/u)^5 which indicates a quadrupole exchange. The corresponding coupling strength can be exactly related to previous results confirming the quantum mass µ hidden in the action quantum related at the Planck scale to the gravitational coupling constant G by µ^4 G=1. The coupling deficits can be assigned to a duality of coupling and non-coupling fluxes with 4th power flux scaling. This fits very well to existing models assuming a non-gravitating vacuum energy to give a satisfactory answer to the cosmological constant problem.