  It thus seems that if some quantum mechanism is to serve as the basis for chronology protection, it must be found in the third degree of  quantum involvement in gravity. Both loop quantum gravity and string  theory have demonstrated the ability to cure some of the curvature  singularities of classical general relativity theory. But as far as  we are aware there are no demonstrations that either of these  approaches to quantum gravity can get rid of the acausal features  exhibited in various solutions to Einstein’s field equations. An  alternative approach to formulate a fully-fledged quantum theory of  gravity attempts to capture the Planck-scale structure of spacetime  by constructing it from causal   sets.[31]  Since these sets must be acyclic, i.e., no element in a causal set  can causally precede itself, CTCs are ruled out a priori. Actually, a theorem due to Malament (1977) suggests that any Planck-scale  approach encoding only the causal structure of a spacetime cannot  permit CTCs either in the smooth classical spacetimes or a  corresponding phenomenon in their quantum   counterparts.[32] 