Impossible Measurements on Quantum Fields

TL;DR

This paper demonstrates that extending ideal measurement concepts to quantum field theory conflicts with locality, as it implies superluminal information transfer, challenging the Hilbert space approach and favoring the sum-over-histories framework for quantum gravity.

Contribution

It reveals fundamental conflicts between ideal measurements and locality in quantum field theory, questioning the Hilbert space formulation's validity for measurement theory.

Findings

Ideal measurements in quantum fields imply faster-than-light information transfer.

Hilbert space formulation faces fundamental issues with measurement in quantum fields.

Sum-over-histories approach remains consistent with locality and is promising for quantum gravity.

Abstract

It is shown that the attempt to extend the notion of ideal measurement to quantum field theory leads to a conflict with locality, because (for most observables) the state vector reduction associated with an ideal measurement acts to transmit information faster than light. Two examples of such information-transfer are given, first in the quantum mechanics of a pair of coupled subsystems, and then for the free scalar field in flat spacetime. It is argued that this problem leaves the Hilbert space formulation of quantum field theory with no definite measurement theory, removing whatever advantages it may have seemed to possess vis a vis the sum-over-histories approach, and reinforcing the view that a sum-over-histories framework is the most promising one for quantum gravity.