Non-locality of Quantum geometry

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Our understanding of modern physics and the physical universe rests on two cornerstones: quantum mechanics and general relativity. Unifying these two theories is a theoretical necessity in the sense that when combined, they predict their own demise. The search for a unified theory has been an extremely challenging and fruitful pursuit, and tremendous progress has been made in the past 20 years; however it still remains the outstanding fundamental question for theoretical physicists in the twenty-first century. The challenge is twofold: on the experimental side, there is a total absence of clear data, while on the theory side the opposite is true: We seem to have a plethora of possible candidates or approaches, such as string theory or AdS/CFT holography, which change the nature of the spacetime probes; or loop gravity, spin foam models causal sets or dynamical triangulations, which have a built-in discretisation of space; or non-commutative field theory, asymptotic safety or emergent gravity developed in the more conventional context of field theory. There is, however, a thread common in this diversity: these approaches all include at their foundation a form of non-locality; moreover recent results show that major progress is possible via a frontal attack on the question of non-locality itself. The goal of my research program is to focus on this common thread and propose a program to study the non-locality of quantum geometry from first principles. My past work work in quantum gravity has given me great expertise into the structure of quantum geometry. My recent work has proposed an underlying principle: relative locality, which sharpens the question of non-locality and gives us a framework to address it. I also have uncovered a realization of string theory called metastring, that incorporates relative locality in its foundation. Armed with these, my plan is to develop the study of quantum geometry, relative locality and the metastring into a framework that allows us to address directly the question of non-locality in quantum gravity. The goal is twofold: I intend to make specific progress on each subject, in particular by studying the consistency of the dynamics of quantum geometry, developing a better and deeper formulation of the principle of relative locality, and progressing towards a proof of the full consistency of the metastring. I also intend to provide a theoretical framework that will allow to study the question of non-Locality in its own right and give us with a common umbrella to understand all the different approaches. Another part of my research program is to advance the exciting idea that the dynamics of gravity could be formulated in terms of non equilibrium thermodynamics. I plan to develop this correspondence in the non-equilibrium context. Such a correspondence would open the way toward a constituent picture of gravity at the quantum level and give us clues on the quantum nature of geometry.