Electromagnetism in terms of quantum measurements

Abstract

We consider the question whether electromagnetism can be derived from the theory of quantum measurements. It turns out that this is possible, both for quantum and classical electromagnetism, if we use more recent innovations such as smearing of observables and simultaneous measurability. In this way, we justify the use of von Neumann-type measurement models for physical processes. We apply the operational quantum measurement theory to gain insight into fundamental aspects of quantum physics. Interactions of von Neumann type make the Heisenberg evolution of observables describable using explicit operator deformations. In this way, one can obtain quantized electromagnetism as a measurement of a system by another. The relevant deformations (Rieffel deformations) have a mathematically well-defined “classical” limit which is indeed classical electromagnetism for our choice of interaction.