Fuksa, Jonáš (2021) Limits on Relativistic Quantum Measurement. [Preprint]

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Abstract

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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Fuksa, Jonáš jonas.fuksa@gmail.com 0000-0003-4606-2584
Additional Information:	This work has been submitted as part of the Part III Mathematics course at the University of Cambridge. It was written under supervision of Dr. Jeremy Butterfield.
Keywords:	Relativistic quantum measurement
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory
Depositing User:	Mr. Jonáš Fuksa
Date Deposited:	11 Sep 2021 15:29
Last Modified:	11 Sep 2021 15:29
Item ID:	19551
Official URL:	https://arxiv.org/abs/2109.03187
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory
Date:	6 May 2021
URI:	https://philsci-archive.pitt.edu/id/eprint/19551

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