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Arguments by Sorkin arXiv:gr-qc/9302018 and Borsten, Jubb, and KellsarXiv:1912.06141 establish that a natural extension of quantum measurementtheory from non-relativistic quantum mechanics to relativistic quantum theoryleads to the unacceptable consequence that expectation values in one regiondepend on which unitary operation is performed in a spacelike separated region.Sorkin labels such scenarios "impossible measurements". We explicitly presentthese arguments as a no-go result with the logical form of a reductio argumentand investigate the consequences for measurement in quantum field theory (QFT).Sorkin-type impossible measurement scenarios clearly illustrate the moral thatMicrocausality is not by itself sufficient to rule out superluminal signallingin relativistic quantum theories that use L\"uders' rule. We review threedifferent approaches to formulating an account of measurement for QFT andanalyze their responses to the "impossible measurements" problem. Two of theapproaches are: a measurement theory based on detector models proposed inPolo-G\'omez, Garay, and Mart\'in-Mart\'Inez arXiv:2108.02793 and a measurementframework for algebraic QFT proposed in Fewster and Verch arXiv:1810.06512. Ofparticular interest for foundations of QFT is that they share common featuresthat may hold general morals about how to represent measurement in QFT. Thesemorals are about the role that dynamics plays in eliminating "impossiblemeasurements", the abandonment of the operational interpretation of localalgebras as representing possible operations carried out in a region, and theinterpretation of state update rules. Finally, we examine the form that the"impossible measurements" problem takes in histories-based approaches and wediscuss the remaining challenges.

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