Date of Award

Winter 2023

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

David M Mattingly

Second Advisor

Per Berglund

Third Advisor

Chanda Prescod-Weinstein


Quantum Field Theory (QFT) is often formulated using local operators, i.e., operators defined at points on a fixed background spacetime. However, General Relativity (GR) requires that observables be fully diffeomorphism invariant. This includes invariance not only under passive diffeomorphisms, which change the coordinate system but also active diffeomorphisms, which imply background independence and a dynamical metric. Localizing such systems and observables in quantum gravity has been a long-standing problem. This dissertation makes progress on two facets of this problem. Part I shows that a typical quantum information paradox using local operators cannot be embedded in a self-consistent, low-energy prescription which makes it diffeomorphism invariant. Part II explores the energy cost of localizing quantum information using the relational frameworks of the $G$-twirl and the $Z$-model. Moreover, it is shown that these two frameworks are related since both can be obtained via limits of positive-operator valued measurements. Part I is based on work currently under review at the International Journal of Modern Physics D and Part II is based on work published in Physical Review D.