Gravity Informed Thesis by Aidan Chatwin-Davies In Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2018 (Defended May 17, 2018) ii c 2018 Aidan Chatwin-Davies ORCID: 0000-0003-1406-9271 All rights reserved except where otherwise noted iii ACKNOWLEDGEMENTS In the five years that I have spent as a graduate student at the California Institute of Technology, I have had the privilege to be supported academically, professionally, socially, and emotionally by the finest network of peers, mentors, friends, and family that one could ask for. I would like to recognize the following individuals and groups of people for their help and support: Co-authors – Ning Bao, Adam Bouland, Charles Cao, Sean Carroll, Nick Hunter- Jones, Adam Jermyn, Achim Kempf, Robert Martin, Jason Pollack, Grant Remmen, and Henry Yuen. We are joined by a bond of punctuation and grammar. Quantum Spacetime Group Members – Originally known as the Cosmological Quan- tum Mechanics Group, or just “Cosmo QM” for short, many of the ideas presented in this dissertation had their origins in this group. Here I would like to thank some of the student members of the group: • Charles Cao – From struggling through homework to braving the frontiers of research together, we have come a long way since we started our first year of studies. Your extraordinary insight into physics never ceases to amaze me, and I am humbled to call you a friend and collaborator. I think you are also the only person with whom I have been to four different continents. • Tony Bartolotta, Nick Hunter-Jones, Jason Pollack, and Grant Remmen – As part of the old guard, you have been stalwart companions in both research and other matters (particularly concerning Shiganshina, the YITP, Eorzea, and aboard the Artemis, respectively). • Junyu Liu and Ashmeet Singh – As part of the new guard, I am relying on your youthful brilliance to keep me going now that I am newly old; it has certainly worked to inspire me so far. iv Fellow Graduate Students – If graduate students make up the fabric of an institute, then Caltech’s fabric is as fine (and durable) as silk. In addition to those students already named, I would like to thank Dávid Guszejnov, Jake Kim, Anna Kómár, Greg MacCabe, Christopher White, and Minyoung You for their friendship and support. The “Mates” – I would like to thank Alex Turzillo (officemate), with whom it was an absolute pleasure to share an office for both working hours and after-hours shenani- gans; Tomas Jochym-O’Connor (housemate), with whom I enjoyed bonding over physics, French, and of course our favourite mustache-sporting Italian plumber; and Aleksander Kubica (housemate), with whom I shared all aspects of graduate student life during my first four years at Caltech. Dear Friends – Rayner Andersen, Wilson Brenna, John Churchill, Stephen Favron James Hawyard, and Scott Jakes. Having known them for over a decade, I can always turn to these friends for candid counsel, relentless camaraderie, and unshakable support. In particular, I would like to recognize Stephen for continuing to host me for extended periods of time when I visit Waterloo, and John for being an enduring companion on adventures in both real and virtual worlds. Family – I would like to thank my mother, Ann Chatwin; my father, Ian Davies; my grandmother, Loie Chatwin; and my sister, Robyn Chatwin-Davies, for always giving me a place that I can call home. Mentors – The following individuals have helped define me as a physicist: • Gil Refael – Assisting with Physics 50 under your guidance has been the best teaching assistant job that I could have hoped for. Participating in this class has helped me learn how to think like a physicist just as much as any other form of academic training. • Achim Kempf – Having transitioned from master’s advisor to collaborator, I continue to value your sage advice on all matters relating to life as a physicist. I am particularly grateful for the generous support that you provide to host me for visits at the University of Waterloo. v • Ning Bao – You arrived at Caltech at a critical point of my graduate career; your ability to support, advise, and empathize with me went above and beyond any expectation of a postdoctoral scholar. I look forward to continuing to work together as both close collaborators and close friends. Dissertation and Candidacy Committee Members – Sean Carroll, Cliff Cheung, John Preskill, and Alan Weinstein. Their thoughtful guidance led to significant improve- ments in the direction and content of this dissertation. Advisor – Sean Carroll. The quality of graduate student advising can vary wildly, even at an institution as reputable as Caltech. Fortunately for me, the experience I had with you as an advisor sits at the highest of echelons in terms of graduate advising. You were always available to talk about research, academic duties, and life in general—and you were surprisingly tolerant of my tendency to barge into your office unannounced for short physics discussions! Working with you and witnessing your unwavering commitment to integrity and excellence first-hand has inspired me to contribute to the physics community to the best of my abilities and to engage with the full cross-section of its members, from experts, to students, to members of the public. Thank you. vi ABSTRACT Formulating a universally satisfactory theory of quantum gravity is a long-standing open problem in theoretical physics. Relatively recently, the use of techniques from quantum information has emerged as a powerful tool for analyzing phenomena that lie at the intersection of quantum theory and gravitation. This thesis describes several advances and novel proposals that were made regarding information theoretic aspects of quantum gravity in three broad areas: holography, cosmology, and the black hole information problem. Regarding holography, we first assess the differences between typical holographic states and fully random states. Next, we show that determining Ryu-Takayanagi surfaces in AdS3/CFT2 is computationally easy from a complexity-theoretic stand- point. Finally, we identify precise consistency conditions that constrain the validity of an early tensor network model for the AdS/CFT correspondence that uses the Multiscale Entanglement Renormalization Ansatz (MERA). Regarding cosmology, we propose an alternative interpretation of the MERA as a discretization of de Sitter spacetime. Next, we return to holographic ideas and show that an appropriately-defined Generalized Second Law implies a cosmic no- hair theorem for certain classes of cosmological spacetimes. Finally, we advance an information-theoretic proposal for calculating the signature of a quantum gravity- motivated, fully covariant, natural ultraviolet cutoff in the spectrum of inflationary perturbations. Regarding the black hole information problem, we begin by exhibiting a simple protocol which, under highly specific circumstances, allows one to retrieve a single qubit from a black hole. Next, we propose an operational resolution of the black hole information problem in which observers who enter the black hole could never detect an inconsistency between their experiences and quantum mechanics due to the finite amount of time available before reaching the central singularity. Finally, we discuss a proposal to understand the emergence of an ensemble of definite geometries vii during the process of black hole evaporation as a decoherence process, as well as its implications for the black hole information problem. viii PUBLISHED CONTENT AND CONTRIBUTIONS The following articles constitute Chs. 2-7 and 9-11 of this dissertation. I was a major contributing author for all of these articles and participated in all parts of the writing process. [1] N. Bao and A. Chatwin-Davies, “Puzzles and pitfalls involving Haar- typicality in holography,” arXiv:1708.08561. [2] N. Bao and A. Chatwin-Davies, “The complexity of identifying Ryu-Takayanagi surfaces in AdS3/CFT2,” JHEP 11 (2016) 034, arXiv:1609.01727. [3] N. Bao, C. Cao, S. M. Carroll, A. Chatwin-Davies, N. Hunter-Jones, J. Pollack, and G. N. Remmen, “Consistency conditions for an AdS mul- tiscale entanglement renormalization ansatz correspondence,” Phys. Rev. D 91 (2015) 125036, arXiv:1504.06632. [4] N. Bao, C. Cao, S. M. Carroll, and A. Chatwin-Davies, “De Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity,” Phys. Rev. D 96 (2017) 123536, arXiv:1709.03513. [5] S. M. Carroll and A. Chatwin-Davies, “Cosmic equilibration: A holo- graphic no-hair theorem from the generalized second law,” Phys. Rev. D 97 (2018) 046012, arXiv:1703.09241. [6] A. Chatwin-Davies, A. Kempf, and R. T. W. Martin, “Natural covariant Planck scale cutoffs and the cosmic microwave background spectrum,” Phys. Rev. Lett. 119 (2017) 031301, arXiv:1612.06445. [7] A. Chatwin-Davies, A. S. Jermyn, and S. M. Carroll, “How to recover a qubit that has fallen into a black hole,” Phys. Rev. Lett. 115 (2015) 261302, arXiv:1507.03592. [8] N. Bao, A. Bouland, A. Chatwin-Davies, J. Pollack, and H. Yuen, “Rescuing complementarity with little drama,” JHEP 12 (2016) 026, arXiv:1607.05141. [9] N. Bao, S. M. Carroll, A. Chatwin-Davies, J. Pollack, and G. N. Remmen, “Branches of the black hole wave function need not contain firewalls,” arXiv:1712.04955. ix TABLE OF CONTENTS Acknowledgements................................. iii Abstract....................................... vi Published Content and Contributions . viii Table of Contents.................................. ix List of Illustrations................................. xii Preliminaries 2 Chapter 1: Introduction.............................. 2 1.1 How it all fits together .......................... 6 Part I: Holography 10 Chapter 2: Puzzles and Pitfalls Involving Haar-Typicality in Holography . 11 2.1 Introduction................................ 11 2.2 Properties of random states ....................... 14 2.3 Puzzles resolved and pitfalls espied ................... 16 2.3.1 Measures of holographic states ................. 16 2.3.2 Error correction ......................... 18 2.3.3 Butterfly effects and shockwaves ................ 19 2.3.4 Random tensor networks....................