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Quantum Mechanical Vistas on the Road to Quantum Gravity

Citation

Singh, Ashmeet (2020) Quantum Mechanical Vistas on the Road to Quantum Gravity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/m1vx-d174. https://resolver.caltech.edu/CaltechTHESIS:05292020-005036817

Abstract

In this thesis, we lay out the goal, and a broad outline, for a program that takes quantum mechanics in its minimal form to be the fundamental ontology of the universe. Everything else, including features like space-time, matter and gravity associated with classical reality, are emergent from these minimal quantum elements. We argue that the Hilbert space of quantum gravity is locally finite-dimensional, in sharp contrast to that of conventional field theory, which could have observable consequences for gravity. We also treat time and space on an equal footing in Hilbert space in a reparametrization invariant setting and show how symmetry transformations, both global and local, can be treated as unitary basis changes.

Motivated by the finite-dimensional context, we use Generalized Pauli Operators as finite-dimensional conjugate variables and define a purely Hilbert space notion of locality based on the spread induced by conjugate operators which we call "Operator Collimation." We study deviations in the spectrum of physical theories, particularly the quantum harmonic oscillator, induced by finite-dimensional effects, and show that by including a black hole-based bound in a lattice field theory, the quantum contribution to the vacuum energy can be suppressed by multiple orders of magnitude.

We then show how one can recover subsystem structure in Hilbert space which exhibits emergent quasi-classical dynamics. We explicitly connect classical features (such as pointer states of the system being relatively robust to entanglement production under environmental monitoring and the existence of approximately classical trajectories) with features of the Hamiltonian. We develop an in-principle algorithm based on extremization of an entropic quantity that can sift through different factorizations of Hilbert space to pick out the one with manifest classical dynamics. This discussion is then extended to include direct sum decompositions and their compatibility with Hamiltonian evolution.

Following this, we study quantum coarse-graining and state-reduction maps in a broad context. In addition to developing a first-principle quantum coarse-graining algorithm based on principle component analysis, we construct more general state-reduction maps specified by a restricted set of observables which do not span the full algebra (as could be the case of limited access in a laboratory or in various situations in quantum gravity). We also present a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras.

Throughout the thesis, we discuss implications of our work in the broader goal of understanding quantum gravity from minimal elements in quantum mechanics.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Quantum Mechanics; Quantum gravity; Emergent spacetime; Quantum Information
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Awards:R. Bruce Stewart Prize for Excellence in Teaching, 2018.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Carroll, Sean M.
Group:Walter Burke Institute for Theoretical Physics
Thesis Committee:
  • Preskill, John P. (chair)
  • Hsieh, David
  • Brandao, Fernando
  • Carroll, Sean M.
Defense Date:11 May 2020
Non-Caltech Author Email:ashmeet.quark (AT) gmail.com
Funders:
Funding AgencyGrant Number
US Department of Energy (DOE)DE-SC0011632
Foundational Questions InstituteUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechTHESIS:05292020-005036817
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05292020-005036817
DOI:10.7907/m1vx-d174
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-3-030-11301-8_10DOIArticle adapted for Ch. 2
https://doi.org/10.1142/S0218271817430131DOIArticle adapted for Ch. 3
https://arxiv.org/abs/2004.09139arXivArticle adapted for Ch. 4
https://arxiv.org/abs/1806.10134arXivArticle adapted for Ch. 5
https://doi.org/10.1142/S0218271819440061DOIArticle adapted for Ch. 6
https://arxiv.org/abs/2005.12938arXivArticle adapted for Ch. 7
https://doi.org/10.1007/s40509-018-0176-8DOIArticle adapted for Ch. 8
https://doi.org/10.1103/PhysRevA.97.032111DOIArticle adapted for Ch. 9
https://doi.org/10.1103/PhysRevA.101.032303DOIArticle adapted for Ch. 10
ORCID:
AuthorORCID
Singh, Ashmeet0000-0002-4404-1416
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13734
Collection:CaltechTHESIS
Deposited By: Ashmeet Singh
Deposited On:01 Jun 2020 22:29
Last Modified:18 Dec 2020 00:30

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