Eliminating the "impossible": Recent progress on local measurement theory for quantum field theory

Arguments by Sorkin arXiv:gr-qc/9302018 and Borsten, Jubb, and Kells arXiv:1912.06141 establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin labels such scenarios "impossible measurements". We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use L\"uders' rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the "impossible measurements" problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-G\'omez, Garay, and Mart\'in-Mart\'Inez arXiv:2108.02793 and a measurement framework for algebraic QFT proposed in Fewster and Verch arXiv:1810.06512. Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating "impossible measurements", the abandonment of the operational interpretation of local algebras as representing possible operations carried out in a region, and the interpretation of state update rules. Finally, we examine the form that the "impossible measurements" problem takes in histories-based approaches and we discuss the remaining challenges.