Measurement in Quantum Field Theory

Abstract

The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the wavefunction'' with relativity of simultaneity, and the difficulty of maintaining causality in the rules for measurement highlighted by ``impossible measurement'' scenarios. Thereafter, the issue is considered from the perspective of mathematical physics. To this end, quantum field theory is described in a model-independent, operator algebraic setting, on generic Lorentzian spacetime manifolds. The process of measurement is modelled by a localized dynamical coupling between a quantum field called the ``system'', and another quantum field, called the ``probe''. The result of the dynamical coupling is a scattering map, whereby measurements carried out on the probe can be interpreted as measurements of induced observables on the system. The localization of the dynamical coupling allows it to derive causal relations for the induced observables. It will be discussed how this approach leads to the concept of selective or non-selective system state updates conditioned on the result of probe measurements, which in turn allows it to obtain conditional probabilities for consecutive probe measurements consistent with relativistic causality and general covariance, without the need for a physical collapse of the wavefunction. In particular, the problem of impossible measurements is resolved. Finally, there is a brief discussion of accelerated detectors and other related work.