The Problem of Time and its Quantum Resolution

Abstract

In this essay, we argue that the problem of time should not be regarded as an issue to be resolved within the prevailing framework for studying quantum gravity, but rather as an indication that there is an issue within the framework itself. We suggest a possible resolution inspired by the observation that the quantization of gravity on null hypersurfaces leads to an anomaly, in that the constraint algebra is projectively represented in the quantum theory. We describe how accommodating these anomalies forces the theory to replace the standard interpretation of canonical time evolution with a fully quantum, diffeomorphism invariant notion of time. The full theory admits states that can be interpreted as emergent geometric spacetime regions which we refer to as quantum diamonds.