Quantum gravity and hydrodynamics: a surprising partnership

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This proposal is a composition of two seemingly unrelated themes. The first is the study of quantum gravity, where the quantum mechanical nature of spacetime plays a fundamental role. The second is novel arenas for hydrodynamics, the long-wavelength description of many quantum systems at finite temperature. These lines of thought in fact harmonize. The long-wavelength description of many black holes is precisely that of hydrodynamics, and in a sense, Einstein gravity is the low-energy "hydrodynamic" description of the fundamental degrees of freedom that build up spacetime. Indeed, my own research has helped weave these strands together, with developments in one arena informing new ideas for the other. There are several fundamental questions I propose to address in the realm of quantum gravity. One concerns the role of quantum mechanical fluctuations of the gravitational field that lead to wormhole geometries. These contributions appear in ordinary Einstein gravity and seem to encode information about the possible microstates of black holes. Yet there is good reason to believe that, in complete models of quantum gravity like string theory, these configurations are unstable. A major goal of my research program is to unravel the precise connection between these wormholes and black holes, and the sense in which they might contribute to observable physics. Another major objective is to formulate a consistent model of cosmology in which quantum mechanics is fully accounted for. Such a framework is certainly important to properly treat inflationary physics, during which the energy density of the universe was close to the Planck scale, but it is also important now when understanding the relation between the quantum state of the universe and observable fluctuations in the cosmic microwave background. When it comes to hydrodynamics, my main goal is to find a fluid description for so-called "fracton" phases of quantum matter, which have been postulated but yet to be discovered in the lab. Using the somewhat exotic spacetime symmetries of these theoretical materials, I will be able to find the analogue of the Navier-Stokes equations describing flows of conserved quantities at long distance. There is good reason to think that these equations will imply rather unique predictions for transport, which will assist in the discovery of fracton phases in Nature. The confirmation that such phases exist, and successful predictions of their basic properties, will be yet another triumph in the history of quantum mechanics and the role of symmetries in physical laws. My work broadly falls under the byline of advancing our fundamental knowledge of physics, of the sort that inspires scientists and laypeople alike to marvel at the universe we share.