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Explore a theoretical physics lecture from Harvard CMSA's Workshop on Symmetries and Gravity where Rutgers University's Tom Banks delves into the mathematical foundations of quantum gravity. Learn how Einstein's equations emerge as hydrodynamic approximations of quantum gravitational systems, based on work by Jacobson, Carlip, and Solodukhin from the 1990s, and subsequent extensions by Banks and Zurek. Examine how the quantum system can be understood as a Hilbert bundle over timelike geodesics, with isometries mapping between different fiber bundles. Discover the concept of time evolution along geodesics through "one-sided modular flow" analogies, and understand how the Quantum Principle of Relativity connects entanglement spectra across different geodesics. Investigate the implications for asymptotic symmetries in various spacetimes, including asymptotically AdS space using Tensor Network Renormalization Group concepts, challenges in asymptotically flat space, and the unique case of de Sitter space where traditional group actions on asymptotic observables break down.
