Relational and operational quantum physics in spacetime

Quantum field theory is arguably one of the most successful physical theories of all times. It is the basis of the standard model, which describes all known particles and forces (except for gravity) in excellent, precise agreement with experiment. However, its current formulation is plagued by several problems: most quantum field theories that we care about do not have a fully consistent mathematical description. Moreover, we do not fully understand how, and to what extent, we can actually concretely perform quantum measurements (or other procedures) locally in a laboratory. While these gaps of understanding do not necessarily impact our analysis of scattering experiments, they are relevant for quantum information theoretic approaches, and they may be part of the reason for why it is currently difficult to incorporate gravity into quantum field theory. In this project, we will reconsider and rebuild some of the foundations of quantum field theory, reproducing some of its predictions, in a relational and operational way. Relational means that we take the idea seriously that properties such as position or momentum of quantum systems are not absolute, but only defined relative to some frame of reference. These reference frames are themselves quantum systems an insight that has recently gained a large amount of attention and has already demonstrated the potential to remove some infinities plaguing quantum field theory. Operational means that we aim at describing quantum fields not as an entity that sits in space and time, but by the way that it manifests itself in the statistics of experiments. Concretely, this means that we make heavy use of the tools and terminology of quantum information theory. Much of this research can be understood as analyzing how the structures of space and time (as defined by special relativity) and of probabilities (as given by quantum theory) can interact and constrain each other. While this question is already at the heart of conventional quantum field theory, we will broaden its scope and ask how all probabilistic theories, even those which are more general than quantum, would fit into relativistic spacetime. This will either tell us that quantum theory and relativity are more closely related than previously thought; or it will allow us to describe potential particles and fields which are more general than quantum. If successful, we expect that our operational and relational reformulation, together with the foundational analysis of how space, time and probabilities interplay, will help alleviate some of the foundational problems of quantum field theory, by providing a partial reformulation that is both mathematically more rigorous and more directly suited to quantum information theoretic reasoning.