Wolfram Physics Q&A

The existence of closed timelike curves is forbidden by the requirement of causal invariance in our models (in much the same way as their existence is forbidden by the requirement of strong hyperbolicity in more conventional formulations of Hamiltonian general relativity). More specifically, a closed timelike curve manifests as a cycle in the multiway evolution graph, and since the condition of causal invariance corresponds to the requirement that all paths in the multiway evolution graph yield causal graphs that are ultimately isomorphic, the existence of such a cycle clearly violates this property (since one could always make a causal graph that is “arbitrarily different” from all of the others, by simply traversing that cycle an arbitrary number of times). However, since we are open to the possibility that causal invariance may be violated over sufficiently short timescales (indeed, this appears to be critical to our derivation of quantum mechanics), the existence of short-lived (and presumably microscopic) CTCs is not ruled out by our formalism.