Towards a Theory of Quantum Gravity Through Geometrization of Quantum Mechanics

Citation

Cao, ChunJun (2018) Towards a Theory of Quantum Gravity Through Geometrization of Quantum Mechanics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SCD0-VB49. https://resolver.caltech.edu/CaltechTHESIS:05082018-133854488

Abstract

In this thesis, we adapt an approach by assuming quantum mechanics as a fundamental theory of nature and attempt to recover familiar concepts such as space-time geometry and gravity from quantum wavefunctions and their unitary evolutions. More specifically, we explore a number of approaches in "geometrizing" quantum systems using techniques such as tensor networks and manifold learning. We find that consistency conditions in quantum gravity can be used to put constraints on tensor network models that approximate the anti-de Sitter/Conformal Field Theory correspondence. Furthermore, quantum circuits and tensor networks can also be used to describe cosmological models and reproduce important features of space-time configurations such as de Sitter space. We find that a generic framework using quantum circuit to describe cosmology puts an upper bound on the number of e-folds during the inflationary phase of the Universe's expansion. In addition to tensor network models, we also propose a Bulk Entanglement Gravity framework that analyzes the entanglement data of a quantum state in a Hilbert space without any a priori assumptions on geometry, such as the likes of a boundary conformal field theory. We find that from an amorphous configuration, one can directly recover geometry of bulk space-time from a generic class of wavefunctions that is fully characterized in this thesis via quantum entropy cone techniques. We find that under a number of assumptions, it is possible to derive linearized Einstein's equation from a version of Jacobson's entanglement equilibrium conditions for an emergent spacetime geometry in the weak field limit near Minkowski space. We show that non-local entanglement perturbations display features of wormhole-like configurations. We also clarify connections between Bulk Entanglement Gravity and highly generic features in quantum error correction codes that can be used to derive gravity.

Thesis Files