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Quantum Mechanical Vistas on the Road to Quantum Gravity

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Quantum Mechanical Vistas on the Road to Quantum Gravity Thesis by Ashmeet Singh In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2020 Defended May 11, 2020 ii © 2020 Ashmeet Singh ORCID: 0000-0002-4404-1416 All rights reserved iii ACKNOWLEDGEMENTS My journey as a PhD student at Caltech over the last five years has been a rather unique one. It has been formative in ways more than one taking me through highs and lows spanning the spectrum, and I feel I am a more holistic person for it. I owe my gratitude to all those people who have made this journey, and this thesis, possible, and because of whom my experience of working toward a doctoral degree has been one that I will cherish. I am grateful to the Almighty (a concept I have now begun to more closely associate with the creative power in Nature) for the gift of good health and ascending spirits, which made working on this thesis enriching, both academically and otherwise. Let me begin with the academic facet of my PhD life. My most intellectually valu- able take-away from my research life at Caltech is the profound research direction I got to be a part of – an effort to understand quantum gravity from minimal elements in quantum mechanics. I am very thankful to our research group at Caltech for letting me be part of this bold and stimulating endeavor. First and foremost, my strongest gratitude to my advisor, Sean Carroll. Ever since I wandered into his office during my first month at Caltech, wanting to discuss ideas in foundational quantum mechanics, Sean has not just been a mentor to me, but rather an inspiration. I feel the biggest thing I learned from him is the ability to think big, think independent, and not be tamed by conventional boundaries. Sean allowed me the freedom to explore bold and risky ideas on my own, while always having my back when my steps faltered. It never ceases to amaze me how Sean connects big picture ideas spanning across various fields in physics, and has such great intuition for seemingly far-fetched, convoluted concepts. Every discussion with him made me push my boundaries, and appreciate the subtle ideas better. His diverse interests, captivating communication style which makes the densest topics seem lucid, and not to mention being a physicist par excellence are an inspiration – something I hope to emulate in my own journey. I would like to thank my collaborators, Ning Bao, Charles Cao, Aidan Chatwin- Davies, Sean Carroll, Oleg Kabernik and Jason Pollack, with whom I had the privilege of discussing physics and working on exciting problems together. Our Quantum Spacetime Reading Group, lovingly called as the “CosmoQM” group, was instrumental in ushering a lot of interesting interactions, discussions and col- iv laborations during my first few years. Being the youngest in the group, I got to learn a lot from the group’s senior student members: Anthony Bartolotta, Jason Pollack, Grant Remmen, Charles Cao, and Aidan Chatwin-Davies. Another pillar which defined me and my time at Caltech was my engagement with teaching of the undergraduate core physics curriculum. While for most graduate students around me, the academic experience revolved primarily around research, I got a chance to witness the “best of both worlds.” What usually gets labeled as “due to lack of funding in theoretical physics” for most, my reasons to be a teaching assis- tant and instructor found their roots in a deeper connection and passion for teaching. I was very fortunate to have the opportunity to engage in full lecture-style and recitation teaching for over 4 years spanning Classical Mechanics, Electrodynam- ics, Special Relativity, Vibrations and Waves, Quantum Mechanics and Statistical Mechanics and Thermodynamics. Teaching those very courses in the very places Richard Feynman taught back in the day is an experience in itself, and I want to thank all my students who made the experience so memorable and unique, often putting up with my random tangents and silly jokes in class. I want to thank Prof. Steve Frautschi – chatting with him and seeing his dedication to teaching and his students continues to be a source of inspiration for me. A special mention for Prof. Frank Porter with whom I taught two terms of Ph2a: Vibrations and Waves. Frank has been incredibly supportive of all my teaching endeavors, one of which culmi- nated in our course being offered as an online course on YouTube. Witnessing his commitment to teaching up-close is a delight, and it has been an absolute pleasure and privilege teaching with him. I would also like to thank Freddy Mora, Meagan Heirwegh and Sofie Leon for their administrative support during my teaching years. Also, thanks to Cassandra Horii and Jenn Weaver at Caltech’s Center for Teaching, Learning and Outreach (CTLO) for their encouragement and involvement in many of my teaching endeavors. The time I spent in my office, 414 Downs-Lauritsen, would have been somewhat monotonous had it not been for my office mates. Matt Heydeman during my first three years, and Nabha Shah for my final year with whom the endless conversations about physics, politics, academia, and more, were a lot of fun. A warm thank you to Carol Silbertstein, our administrator for the High Energy Physics Theory group. It still amazes me how efficiently and smoothly Carol man- v aged the group, and I have fond memories of long, interesting chats with her in the office. I would also like to thank members of my PhD Thesis Committee, Profs. Fer- nando Brandao, Sean Carroll, David Hsieh, and John Preskill, for their time and input at my PhD Candidacy Meeting and my PhD defense. A PhD in Theoretical Physics is not all academics, by far. On a personal note, I would like to thank my mother, Sdn. Harneet Kaur and father, S. Arvinder Pal Singh, and my grandparents, S. Surjit Singh and Sdn. Surinder Kaur. They have been my constant support, both in exciting times as well as the inevitable dull stretches one faces in research. A special shout out to my mother, who is now well versed in concepts of Hilbert space, Hamiltonians and differomorphisms, despite having no background in physics, as she took keen interest in my progress and weathered with me through my struggles. Their blessings and unceasing support have helped me come far and strong this way. A few friends I would like to take special notice of – friends who were instru- mental in shaping the last five years of my life. Let me first mention Aditya Pandey (aka Pandey) and Sudeepto Gangopadhyay (aka Dada). They have been privy to the closest details of my life, academic and otherwise, and their unwavering presence and the constant conversation they keep alive have been strong pillars in my life – something for which I am very grateful for. From spending late work nights at Au Coquolet cafe during Pandey’s Berkeley days (where I would end up driving almost every other week) to the countless road trips and hikes; the endless brain- storming and our mutual admiration for sleep, Pandey has been with me through it all. I am also proud to call him an academic collaborator – we combined Pandey’s background in statistics and civil engineering with mine in physics (which begs for a “Civil Engineer and a Physicist walk into a bar...” joke) to work on using field theoretic techniques to earthquake engineering and it is been an absolute pleasure. Dada is someone whom I got introduced to in the most unexpected way, and ever since that first evening we met, we have found a shared bond in our penchant for late work nights in cafes (which would almost always culminate in long conversations in the parking lot), racquetball, road trips, late night walks (to Dada’s almost constant chagrin), and the constant ribbing of Pandey. Dada is one of the most fun-loving, caring people I have met, and his largess in life never ceases to fascinate me! vi I would be remiss if I did not mention Garima Singh, in whom I found a friend and sister I could invariably depend on. She has been my partner-in-crime, brought together by our mutual love for road trips, telescopes, and the shimmering night sky. My thanks to Swati Chaudhary who has always been there with her kindness, be it talking about my bizarre physics ideas, having me over for dinner ever so often (a blessing for someone whose towering culinary feat is scrambled eggs), to always being ready for a quick trip to Namaste for some evening pakoras. My group of friends at Caltech – Charles Cao, Aidan Chatwin-Davies, Zander Moss, Alec Ridgway, and James St. Germaine-Fuller – y’all made my time at Caltech better with all the support and fun. Long rants and laughs with Alec, discussions with Charles, the renewed energy Zander brought to the group, and barging into James’ office unannounced, it’s all been a lot of fun! Charles Cao and Aidan Chatwin-Davies were my academic brothers, of whom I was comfortable asking any and every silly physics question I had, be it in the office or on a back-country camping trip to White Sands National Monument. I would also like to thank Rajashik Tarafder and Jagannadh Kumar. Rajashik’s multi-dimensional view of life and Jag’s positive vibe made my last year at Caltech much more exciting (though you both still have a lot to learn from me in the racquetball court!) A special thanks to the Sikh community of Southern California – I found emotional and spiritual stability through the many Gurudwaras (Sikh House of Worship) around Los Angeles.
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