Singularities, Entropy and the Arrow of Time, {\it or} Is CRT a Gauge Symmetry in Quantum Gravity?

Abstract

We examine the question of whether the discrete transformation CRT is a gauge symmetry of ``Quantum Gravity". Since the phrase in quotes is not yet completely well defined, we first try to define specific frameworks in which one might ask the question. We find that the general answer is NO. In asymptotically flat and AdS spaces, CRT is an asymptotic gauge symmetry in the same sense that the continuous parts of the Poincare/AdS isometry groups and scalar internal symmetries are. In eternal dS space it can be considered a spontaneously broken gauge symmetry if a certain ``Alice String" configuration is allowed in the Thermofield double Hilbert space. This requires an extension of the conventional Chern-Simons rewriting of $2 + 1$ dimensional gravity. This interpretation only makes sense if we consider the underlying quantum mechanics to be time independent. General quantum measurement and semi-classical gravitational restrictions on measuring devices put {\it a priori} limits on the existence of detectors with clocks that can actually measure proper time along a classical dS geodesic.