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Abstract

The question of quantum gravity is approached from a new point of view. The phase field concept, which is successfully applied in certain condensed matter problems (Steinbach & Pezzolla, Physica D 1999), will be generalized to a quantum phase field concept. It is applicable to matter in general, formulated in terms of a variational principle. The new concept (I.Steinbach, Z. NaturforschungA, to be published) has energy as the only fundamental substance. Different states of energy are ordered by a discret set of quantum phase fields. The dual elements of matter, mass and space, are described as voulume-and gradient-energy contributions of the set of fields, rspectively. Time and space are formulated as background-independent dynamic variables. The evolution equations of the fields and wave-function of the universe are derived in quasi-static approximation. Gravitational interaction emerges from quantum fluctuations in finite space. Application to a large number of fields predicts scale separation in space and repulsive action of masses distant beyond a marginal distance. The predicted marginal distance is compared to the size of the voids in the observable universe.