J. Benavides

My research interests are in the areas of the Foundations of Physics (Singularity Theorems and Causality in General Relativity  and the interpretations of Quantum Mechanics (QM)) and The Foundations of Mathematics (Set theoretic forcing and Sheaf Logic). Nowadays, I am working on a possible reformulation of quantum mechanics based on the sheaf logic approach to set theoretic forcing. So far it has been possible to obtain a reformulation of Takeuti’s results on Boolean Valued Analysis on projections algebras that result to be more constructive, showing a close relation with the Gelfand representation theorem and revealing a close connection with the Deutsch-Everett multiversal interpretation of Quantum Theory. My next immediate goal will be to try to explain interference phenomena in QM using the notion of Genericity and the respective generic model theorem over this model. Future goals will include the explanation of entanglement, the emergence of probability and the inclusion of a relativistic conception of time in this context. In General Relativity I am studying how the breakdown of relativistic properties related with classical determinism, as global hyperbolicity and causality, when seeing from a quantum perspective can motivate the necessity of a sheaf based approach to relativistic geometry. It has been studied the stability of the global hyperbolic property, showing that this can be proved in very weak situations with considerable effort; the conclusion of this fact is that in realistic situations this property will breakdown and a new perspective of determinism probably based in a quantum conception will be needed. Nowadays, I am studying how the quantum approach to the paradoxes linked to time travel reveal the necessity of a wider conception of relativistic geometry. The future and ultimate goal will be to construct this geometry and give a new perspective of strong gravity singularities.