  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.
