Outline for a quantum theory of gravity

Abstract

By invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four dimensional non-commutative curvature scalar (which is torsion dependent) that is sourced by the Nambu-Goto world-sheet action for a string, plus the Kalb-Ramond string action. This `quantum gravity' is actually a non-commutative {\it classical} matrix dynamics, and the only two fundamental constants in the theory are the square of Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and $\hbar$) and quantum general relativity (and $G$) emerge from the underlying matrix dynamics in the thermodynamic limit. The statistical fluctuations that are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope here to highlight the deep connection between quantum foundations, and the sought for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!