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arXiv:1911.03339 · Foundations of Physics

A Quantum Field Theory View of Interaction Free Measurements

Filipe Barroso, Orfeu Bertolami A

Published Jun 30, 2020• 1 citation
arXivHTMLPDF
DOI
10.1007/s10701-020-00350-8

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In Chapter 3, we have discussed the direct measurement scheme in which a measured field is directly absorbed by photodetectors. In the direct detection process, the field is destroyed as the detector absorbs all the field interacting with it. From the point of view of quantum physics, the measurement destroys the state vector of the field such that the state collapses to the appropriate eigenstate of the measured field. For example, if prior to the measurement the state vector of the field is |α〉 + |β〉, at the measurement the state vector collapses to |α〉 if the value α is obtained, or |β〉 if β is obtained.
This paper interprets Haag’s theorem as more than a technical obstruction to the interaction picture in relativistic quantum field theory. It argues that the theorem reveals a deeper structural limitation of global representation-based ontology: an interacting QFT cannot, under the assumptions of the theorem, be understood as a simple unitary deformation of a free theory within one fixed Fock representation. The paper connects this lesson to algebraic quantum field theory, superselection sectors, locally covariant QFT, Wilsonian renormalization, and effective field theory. It proposes that these developments all point toward a common principle: physical objectivity is not grounded in a privileged representation, but in structural content preserved under admissible transformations between perspectives, representations, sectors, scales, or regions. The paper does not claim to solve Haag’s theorem or construct interacting QFTs. Its aim is interpretive: to show how Haag’s theorem is naturally intelligible within the observer-equivariant framework, where objectivity is understood as invariant or equivariant structure rather than as a view from one absolute representation.
In the early 1990's A. Elitzur and L. Vaidman proposed an interaction free measurement (IFM) that allows researchers to find infinitely fragile objects without destroying them. But Elitzur-Vaidman IFM has been used only to determine the position of opaque objects. In this paper, we propose an extension of such a technique that allows measurement of classical electric and magnetic fields. Our main goal is to offer a framework for future investigations about the role of the measurement processes, expanding the physical properties that are measurable by means of IFM.