Proposal for a new quantum theory of gravity III: Equations for quantum gravity, and the origin of spontaneous localisation
Abstract
We present a new, falsifiable, quantum theory of gravity, which we name Noncommutative MatterGravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the concept of an atom of spacetimematter [STM], which is described by the spectral action in noncommutative geometry, corresponding to a classical theory of gravity. We used the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derived the spectral equation of motion for the gravity part of the STM atom, which turns out to be the Dirac equation on a noncommutative space. In the present work, we propose how to include the matter (fermionic) part and give a simple action principle for the STM atom. This leads to the equations for a quantum theory of gravity, and also to an explanation for the origin of spontaneous localisation from quantum gravity. We use spontaneous localisation to arrive at the action for classical general relativity [including matter sources] from the action for STM atoms.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.04309
 Bibcode:
 2019arXiv190804309M
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 v1: 25 pages (this paper is a followup of arXiv:1903.05402v2 and arXiv:1906.08248v3). This version v2: minor changes, references updated, to appear in Zeitschrift fur Naturforschung A