Citation: Beckman, David, et al. "Measurability of Wilson loop operators." Physical Review D 65.6 (2002): 065022.
Web: https://arxiv.org/abs/hep-th/0110205
Tags: Physical, Philosophical
In this lovely little paper, the authors think about measurements in quantum field theory (gauge theory). They argue that instantaneous non-destructive measurements of Wilson loops is in conflict with causality. By non-destructive, the authors mean that the measurement would not damage a state with is an eigenstate of the Wilson loop. The idea is simple. If Alice and Bob are very far away, and both Alice and Bob have flux loops available to them, then the result of the measurement of a large Wilson loop depending on whether or not the Wilson loop is linked around both Alice and Bob's loops or not. So, depending on the result of the measurement, Alice can infer some information about the location of Bob's loop.
Of course, with these sorts of quantum-information things there's all sorts of subtleties and exceptions and philosophical points. An early discussion is due to Sorkin:
> Sorkin, Rafael D. "Impossible measurements on quantum fields." arXiv preprint gr-qc/9302018 (1993).
There are many more modern papers on this topic, as well:
> Fewster, Christopher J., and Rainer Verch. "Measurement in quantum field theory." arXiv preprint arXiv:2304.13356 (2023).