Quantum Diffeomorphisms and Experiment for Quantum Spacetime

The implementation of diffeomorphisms invariance and background independence at the quantum level, and the search for observational evidence, are the main challenges across all different approaches to quantum gravity. I will merge the new perspectives, insights, and tools from the quantum foundations and quantum information communities, with the recent developments in gravity and high energy community, to shed new light on these longstanding challenges. My project has three objectives: 1) to investigate the conceptual and mathematical structure of quantum diffeomorphisms for quantum spacetime, and to explore the corresponding generalization of the covariant quantities and invariant observables, as well as the physical implications; 2) to formulate the quantum relative perspectives for subregions in a quantum spacetime by establishing a precise connection between quantum edge modes and quantum reference frames; and 3) to propose new table-top experimental ideas and precise predictions for testing the quantum features of gravity that might be technically feasible in the near future. The methodology will combine my research experience in quantum gravity, the host groups expertise the relational and operational approaches in quantum physics, as well as the stateof-the- art experimental techniques on the quantum test of gravity in IQOQI-Vienna. The central methods and formulations are the recent development of quantum reference frames, Schrödinger representation of linearized gravitational fields in the field basis, edge modes and boundary symmetries for gravity, insights from nonperturbative quantum gravity, and the experimental test for nonclassicality and contextuality. My project is a synergy of the experiences and ideas coming from my own academic trajectory across different research communities. I aim at providing new perspectives, opening new grounds to the interplay between gravity and quantum physics, developing a robust conceptual core for our understanding of gauge symmetry in quantum gravity, as well as bringing new ideas for testing the low-energy quantum gravity phenomenology