A Renormalizable Model of Quantum Gravity

Abstract

Two main problems stand in the way of unifying quantum mechanics and general relativity. First, the treatment of time and space in quantum electrodynamics (QED) is not fully covariant. Second, the ultraviolet divergences in QED are not renormalizable. In previous work, we ad- dressed the rst problem by promoting time from parameter to operator: with this the treatment of time and space in QED became fully covari- ant. The most obvious prediction was additional dispersion in time at the attosecond scale; such eects are falsiable with current technology. As an unexpected but welcome side-eect, this regularized the ultraviolet divergences in QED. We therefore ask \will promoting time to opera- tor regularize the ultraviolet divergences in quantum general relativity (QGR)?" Using the existing literature on QGR as a base, we show we can rewrite QGR with time as an operator. And that the ultraviolet diver- gences are contained in QGR just as they are in QED. We show that there are feasible tests which can distinguish between standard QGR and TGR. We conclude that TGR represents a renormalizable model of quantum gravity which is consistent with existing observational and experimental evidence and which is falsiable in principle.