  The first degree of quantum involvement, if not opening the door to  Thornian time machines, at least seemed to remove some obstacles  since quantum fields are known to lead to violations of the energy  conditions used in the setting of classical general relativity theory to prove chronology protection theorems and no-go results for time  machines. However, the second degree of quantum involvement seemed,  at least initially, to slam the door shut. The intuitive idea was  this. Start with a general relativistic spacetime where CTCs develop  to the future of \(H^+ (\Sigma)\) (often referred to  as the “chronology horizon”) for some suitable partial  Cauchy surface \(\Sigma\). Find that the propagation of a quantum field  on this spacetime background is such that  \(\langle \Psi \mid T_{ab} \mid\Psi \rangle\) “blows up” as \(H^+ (\Sigma)\) is approached from the past. Conclude that the backreaction on the spacetime metric creates unbounded  curvature, which effectively cuts off the future development that  would otherwise eventuate in CTCs. These intuitions were partly  vindicated by detailed calculations in several models. But eventually a number of exceptions were found in which the backreaction remains  arbitrarily small near   \(H^+ (\Sigma)\).[29]  This seemed to leave the door ajar for Thornian time machines.