2021/09/07 by Jonáš Fuksa, Fuksa, Jonáš · 1 citation
Physics and Astronomy · #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2109.03187
openalex publication_date 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Requiring causality on measurements in quantum field theory seems to impose strong conditions on a self-adjoint operator to be really measurable. This may seem limiting and artificial in the operator language of algebraic quantum field theory (AQFT), but is essential for a truly relativistic theory. Recent publications attempt to deal with this issue by including the apparatus into the formalism, connecting AQFT with measurement theory, but other options have been suggested. In this essay, I discuss the causality conditions on self-adjoint operators both in the language of AQFT and in the language of quantum information theory. I then present measurement theory in AQFT, modelling the apparatus as a quantum field with coupling to the measured system restricted to a region of spacetime. I highlight how this approach leads to a causally well behaved theory. Finally, I attempt to formulate the causality conditions on measurements in the Feynman path integral approach, using the concept of decoherent histories. I claim that the path integral approach has problems with causality similar to the operator based approaches and that even here causality is an a posteriori condition.