Self-Consistent Quantum-Gravitational Quadrupole Fluctuations

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 mG = Nμ. In the field of mG any small test mass orbits at unit distance ru 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 ∝ (c/u) 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 μ2πG = 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.