Papageorgiou Maria, Fraser Doreen
Department of Applied Mathematics and Institute for Quantum Computing, University of Waterloo, Waterloo, Canada.
Division of Theoretical and Mathematical Physics, University of Patras, Patras, Greece.
Found Phys. 2024;54(3):26. doi: 10.1007/s10701-024-00756-8. Epub 2024 May 8.
Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293-305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. 10.1103/PhysRevD.104.025012) 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 [1] 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 Lüders' 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-Gómez et al. (Phys Rev D, 2022. 10.1103/physrevd.105.065003) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851-889, 2020). 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 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.
索尔金（《量子场的不可能测量。见：广义相对论的方向：1993年国际研讨会论文集，马里兰州，第2卷，第293 - 305页，1993年》）以及博尔斯坦等人（《物理评论D》104(2)，2021。doi:10.1103/PhysRevD.104.025012）的论证表明，将量子测量理论从非相对论量子力学自然扩展到相对论量子理论会导致一个不可接受的结果，即一个区域内的期望值取决于在类空分离区域执行的酉操作。索尔金[1]将这种情况标记为“不可能测量”。我们将这些论证明确呈现为一个具有归谬论证逻辑形式的不可行结果，并研究其对量子场论（QFT）中测量的影响。索尔金型不可能测量情况清楚地表明，微观因果性本身不足以排除在使用吕德斯规则的相对论量子理论中的超光速信号传递。我们回顾了为QFT制定测量描述的三种不同方法，并分析它们对“不可能测量”问题的回应。其中两种方法是：基于波罗 - 戈麦斯等人（《物理评论D》，2022。doi:10.1103/physrevd.105.065003）提出的探测器模型的测量理论，以及菲斯特和韦尔奇（《数学物理通讯》378(2):851 - 889，2020）提出的代数QFT的测量框架。对QFT基础特别有意义的是，它们具有共同特征，这些特征可能蕴含关于如何在QFT中表示测量的一般道理。这些道理涉及动力学在消除“不可能测量”中所起的作用、放弃将局部代数的操作解释为表示在区域中可能执行的操作，以及对状态更新规则的解释。最后，我们研究“不可能测量”问题在基于历史的方法中所呈现的形式，并讨论剩余的挑战。
