  Now suppose that the state on a partial Cauchy surface  \(\Sigma_0\) with no CTCs to its past is to be thought of as  giving a snapshot of the universe at a moment before the machine is  turned on. The subsequent realization of a Thornian time machine  scenario requires that the chronology violating region  \(V \subseteq \mathcal{M}\), the region of spacetime traced out by   CTCs,[11]  is non-null and lies to the future of \(\Sigma_0\). The fact  that \(V \ne \varnothing\) does not lead to any consistency  constraints on initial data on \(\Sigma_0\) since, by  hypothesis, \(\Sigma_0\) is not intersected more than once by  any timelike curve, and thus, insofar as the so-called paradoxes of  time travel are concerned with such constraints, the paradoxes do not arise with respect to \(\Sigma_0\). But by the same token, the option of traveling back into the past of \(\Sigma_0\) is  ruled out by the set up as it has been sketched so far, since  otherwise \(\Sigma_0\) would not be a partial Cauchy surface.  This just goes to underscore the point made above that the fans of  science fiction stories of time machines will not find the present  context of discussion broad enough to encompass their vision of how  time machines should operate; they may now stop reading this article  and return to their novels.