Symmetry and measurement: a foundation for semi-local quantum physics

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This proposal concerns quantum theory, describing (sub)atomic matter, and Einstein's theories of relativity, describing gravitation and high speed motion. These fundamental building blocks of modern physics do not fit easily together. This project tackles several problems at the boundary between these important subjects. Quantum theory and special relativity are combined in quantum field theory (QFT), a hugely successful model for particle physics tested spectacularly at CERN. However its mathematical foundations are incomplete and the combination of quantum theory with general relativity (quantum gravity) is one of the biggest open problems in science.One tension between quantum theory and relativity concerns measurement. Students learn that quantum measurement causes an instantaneous state collapse, but relativity teaches that different observers disagree on what "instantaneous" means. Consequently, the description of measurement in QFT has been plagued by inconsistencies and paradoxes suggesting, for example, that typical measurements allow impossible faster than light signalling. Significant recent progress by members of the project team has provided a measurement framework that is fully compatible with relativity and free of the problems afflicting earlier work. This proposal will significantly generalise these ideas for measurements in quantum gravity.At this point, symmetry enters. Physicists and mathematicians like symmetry because it can often simplify problems and produces very pleasing mathematical structures. However general relativity has so much symmetry that a serious problem occurs: there are no local physical observable quantities. One solution is to work with the grain of the symmetry, introducing "relational observables", which have been implemented by one of us in effective quantum gravity. We will integrate them into the general framework for measurement mentioned above, bridging between the theoretical idea and its implementation (an observable that cannot be measured in practice is of little use).Another theme in our proposal is the relation between symmetry and boundaries, particularly boundaries in spacetime. For example,the event horizon of a black hole represents an effective boundary: classical information can flow in, but not out. However, Hawking showed that when quantum theory is taken into account, black holes radiate as if they are hot and can even evaporate entirely. Now, the information that comes out is much less ordered than the information that enters. What happens to the `lost information' is a famous unsolved problem and it has been suggested that degrees of freedom related to symmetries may hold the key. These degrees of freedom are not localised within the bulk of spacetime but rather live on the boundaries of spacetime, at the horizon and also a boundary at infinity. Another example is that charged particles, e.g. electrons, are always accompanied by a cloud of `soft photons' that reaches to infinity. Again, this exemplifies the significance of boundary degrees of freedom, and the complicated way in which they may be mixed up with the bulk.The long-term goal of our proposal is to move beyond traditional ideas of localisation in QFT to build a framework for "semi-local quantum physics" that can handle boundary and relational observables just as easily as those with absolute localisation away from boundaries.While this proposal is fundamental discovery science, its long term impact may include technological applications. Quantum information theory is rapidly moving from the laboratory into large scale terrestrial and even space-borne and satellite systems. These developments put quantum information theory into the relativistic realm and so a clear framework incorporating an operational understanding of measurement in QFT could become a standard tool for analysing such technologies.