Causality violations as black holes are one of the most intriguing predictions of classical relativistic formalism. These phenomena have been normally considered as unphysical mainly because, within the classical formalism, causality violations seem to impose more initial data constraints than those normally required in causality respecting spacetimes. These initial constrains, for which we do not have experimental evidence, apparently are revealing the unphysical character of these phenomena.  We  are interested to know whether causality violations should be ignored because in conflict with our physical theories or have to be considered seriously in relation, for instance, with gravitational collapse scenarios

Our work in this area is guided  by the study of  the classical paradoxes linked to time travel, following the approach developed by Deutsch based on computational networks . Within the limits of classical (non-quantum) physics, causality violations indeed impose initial data constraints. Nevertheless, we have shown  that the scenario described by the paradoxes, which depicts an evolution from a causal well behaved region to a local causality violating region and then again to a causal well behaved region, cannot be captured by the classical formalism. We have proven a theorem that shows that the formation of local causality violating regions from causal well behaved regions lead to the formation of singularities or points to infinity. This result is an alternative version of a theorem given by Tipler, the advantage of the approach developed by us  is that it avoids the global hypothesis capturing the intuitive local picture used by Deutsch. It results then that from the perspective of quantum mechanics the necessity of initial constrains close to causality violating regions disappear, as has been shown by Deutsch based on the use of quantum computational networks. In this way it has been proved that the paradoxes normally associated to time travel arise from the false premise that classical physics is true near chronology violating regions, but that once quantum mechanics is considered such paradoxes disappear. 

At this point, the necessity of an interpretation of quantum theory becomes evident, the apparent paradoxes derived from the classical approach seem to be solved by the quantum formalism, but how? Deutsch showed that when versions of quantum theory as the statistical interpretation, dynamical collapse formulations or pilot wave hidden variables are considered, the apparent resolution of the paradoxes given by the formalism does not occur from the perspective of these interpretations. These formulations of quantum theory predict the same classical paradoxes requiring the imposition of initial constraints even if the quantum formalism predicts that such constrains are not necessary. On the other hand, the Everett interpretation gives a natural explanation of the resolution of the paradoxes in total agreement with the predictions of the formalism. The resolution of the paradoxes that follows from the Everett perspective reveals a possible, even if very bizarre, structure of quantum geometry. Considering that the more realistic model of gravitational collapse, i.e. the Kerr solution, predicts the formations of violations of causality inside Kerr black holes summed to the fact that Deutsch’s considerations are all based in the classical quantum formalism without any further hypothesis, the geometric picture obtained from the resolution of the paradoxes is maybe the most solid hint we have of the possible route to follow towards a quantum gravity theory.

Nowadays our work is focused on the study of  the main components of the Deutsch-Everett interpretation of quantum theory, trying to understand what kind of mathematical structure is needed to capture the picture of quantum geometry derived from the resolution of the paradoxes. We have shown why the more common approaches suggested in this direction, which propose to consider branching manifolds or similar structures derived from weakening some classical properties, as the Hausdorff property, are totally inadequate. Our conclusion is that  if such structure exists, it has to arise from the intrinsic structure of the quantum formalism and not as an extension of the Lorentzian relativistic formalism with some quantum properties added as it has been commonly approached.

Documents:

Causality Violations and Quantum Geometry (Work in Progress)