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

Arguments by Sorkin and Borsten, Jubb, and Kells 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 non-selective measurement 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{\"u}ders' 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 recent proposals for measurement theories for QFT: a measurement theory based on detector models proposed in Polo-G{\'o}mez, Garay, and Mart{\'i}n-Mart{\'i}nez and a measurement framework for algebraic QFT proposed in Fewster and Verch. 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, in spite of being much different in spirit and in details such as the form taken by the state update rules. Careful attention to the dynamics is an important component of both strategies for responding to the `impossible measurements' problem. Both also abandon the traditional operational interpretation of a local algebra of observables $\mathcal{A}(O)$ as representing possible operations carried out in region $O$. Their respective state update rules cannot be literally interpreted as representing a physical change of state of the system upon measurement that occurs in any region of spacetime. The third response to the `impossible measurements' problem that we examine is the histories-based approach that is preferred by Sorkin. While there are open questions about how to address the `impossible measurements' problem using this approach, it is much different in spirit than the detector models approach and the FV framework yet also shares some common features. We hope that this paper lays the groundwork for productive dialogue among the many communities of physicists and philosophers who are working on theoretical, practical, and interpretative issues surrounding the treatment of local measurements in QFT