  However, we still have no guarantee that if CTCs do bloom to the  future of \(\Sigma_0\), then the state on \(\Sigma_0\)  is responsible for the blooming. Of course, we have already learned  that we cannot have the iron clad guarantee of causal determinism  that the state on \(\Sigma_0\) is responsible for the actual  blooming in all of its particularity. But we might hope for a  guarantee that the state on \(\Sigma_0\) is responsible for  the blooming of some CTCs—the actual ones or others.  The difference takes a bit of explaining. The failure of causal  determinism is aptly pictured by the image of a future  “branching” of world histories, with the different  branches representing different alternative possible futures of (the  domain of dependence of) \(\Sigma_0\) that are compatible with the actual past and the laws of physics. And so it is in the present  setting: if \(H^+ (\Sigma_0) \ne \varnothing\), then there will  generally be different ways to extend  \(D^+ (\Sigma_0)\), all compatible with the  laws of general relativistic physics. But if CTCs are present in all  of these extensions, even through the details of the CTCs may vary  from one extension to another, then the state on \(\Sigma_0\)  can rightly be deemed to be responsible for the fact that  subsequently CTCs did develop.