  Time machines may never see daylight, and perhaps so for principled  reasons that stem from basic physical laws. But even if mathematical  theorems in the various theories concerned succeed in establishing  the impossibility of time machines, understanding why time machines  cannot be constructed will shed light on central problems in the  foundations of physics. As we have argued in Section 4, for instance, the hunt for time machines in general relativity theory should be  interpreted as a core issue in studying the fortunes of Penrose’s  cosmic censorship conjecture. This conjecture arguably constitutes  the most important open problem in general relativity theory.  Similarly, as discussed in Section 5, mathematical theorems related  to various aspects of time machines offer results relevant for the  search of a quantum theory of gravity. In sum, studying the  possibilities for operating a time machine turns out to be not a  scientifically peripheral or frivolous weekend activity but a useful  way of probing the foundations of classical and quantum theories of  gravity.