Open Systems for Observers

This award funds the research activities of Professor Sarah Shandera at The Pennsylvania State University. Any observer in the universe can access only a limited piece of the cosmos: a finite region of space, over a finite span of time, and at finite resolution. The laws of physics such an observer can actually access are therefore the laws of an "open" system: a small part of a much larger whole whose remaining pieces cannot be directly seen yet still influence what is observed. Learning how to describe physics rigorously from the vantage point of such a limited observer is central to some of the deepest questions in science, including the origin of structure in the early universe, the nature of dark energy, and the quantum behavior of gravity and of horizons. Under this award, Professor Shandera will use mathematical language from quantum information science to build new tools suited to cosmological observers of quantum systems and connect them to outstanding questions in gravity and cosmology. As such, research in this area advances the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical law. The project will also have significant broader impacts within the community of scientists and beyond. Professor Shandera will train graduate and undergraduate student researchers, providing critical early-career research experience, and will continue developing new graduate coursework on open quantum systems. She will give public lectures and presentations to audiences ranging from high-school students to the general public, and will foster interdisciplinary collaboration among physicists, quantum-information scientists, and mathematicians. More technically, under this award Professor Shandera will develop the connection between the open-quantum-system framework for observers and specific aspects of gravity and cosmology. An observer with only partial access to a large, unitarily evolving quantum system must construct an effective theory from an ensemble of possible local open dynamics, described dynamical maps or propagators that act on observer-defined subsystems, subject to consistency constraints inherited from the global unitarity. Non-Markovian behavior and violations of positivity and complete positivity across the ensemble, rather than being treated as pathologies, can be used as resources that encode the quantum correlations between observed and unobserved degrees of freedom and enable inference about the unseen environment. Building on the PI's prior results, the work has three principal goals. First, Professor Shandera will study how quantum reference frames, the different ways distinct observers partition a system into local subsystems, shape the ensemble of open dynamics, and how robust its features are under changes of internal frame. This is a topic of current intense interest in quantum gravity. Second, she will move beyond a fixed, homogeneous notion of locality to allow local structure that is inhomogeneous and dynamical, determined by the quantum correlations themselves, and will relate the resulting behavior to the theory of quantum phases of mixed states. Finally, she will use these results to formulate a new notion of "open effective theory" for observers, built directly from ensembles of open systems with prescribed distributions of subsystem behavior rather than from an assumed decomposition into system and environment. The program will combine analytically solvable spin-system models, whose subsystem dynamics can be computed exactly, with numerical quantum-circuit models that generate a wide range of non-equilibrium, non-homogenizing dynamics, analyzed using measures of information spreading and quantum complexity. By bringing the tools of quantum information science to bear on the problem of subsystems in gravity, the project aims to clarify whether the open-quantum-systems perspective can yield genuine progress on long-standing puzzles about the quantum nature of spacetime, horizons, and cosmological observation. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.