Existence of a Consistent Quantum Gravity Model from Minimum Microscopic Information

Abstract

It is shown that a quantum gravity formulation exists on the basis of quantum number conservation, the laws of thermodynamics, unspecific interactions, and locally maximizing the ratio of resulting degrees of freedom per imposed degree of freedom of the theory. The First Law of thermodynamics is evaluated by imposing boundary conditions to the theory. These boundary conditions determine the details of the complex world structure. No explicite microscopic quantum structure is required, and thus no ambiguity arises on how to construct the model. Although no dynamical computations of quantum systems are possible on this basis, all well established physics may be recovered, and all measurable quantities may be computed. The recovery of physical laws is shown by extremizing the entropy, which means varying the action on the bulk and boundary of small volumes of curved space-time. It is sketched how Quantum Field Theory (QFT) and General Relativity (GR) are recovered with no further assumptions except for imposing the dimension of a second derivative of the metric on the gravitational field equations. The new concepts are 1. the abstract organization of statistical quantum states, allowing for the possibility of absent quantum microstructure, 2. the optimization of the locally resulting degrees of freedom per imposed degree of freedom of the theory, allowing for the reconstruction of the spacetime dimensions, 3. the reconstruction of physical and geometric quantities by means of stringent mathematical or physical justifications, 4. the fully general recovery of GR by quasi-local variation methods applied on small portions of spacetime.