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On Analogue-Gravity Models As Seen by In-Universe Observers a Thesis

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On Analogue-Gravity Models As Seen by In-Universe Observers a Thesis On analogue-gravity models as seen by in-universe observers A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy Scott Lockerbie Todd BAppSc(Nano)/BAppSc(Phys)(Hons) RMIT School of Science College of Science, Engineering and Health RMIT University October 2020 Declaration I certify that except where due acknowledgement has been made, the work is that of the author alone; the work has not been submitted previously, in whole or in part, to qualify for any other academic award; the content of the thesis is the result of work which has been carried out since the official commencement date of the approved research program; any editorial work, paid or unpaid, carried out by a third party is acknowledged; and, ethics procedures and guidelines have been followed. I acknowledge the support I have received for my research through the provision of an Australian Government Research Training Program Scholarship. Scott L. Todd October 16, 2020 i Acknowledgements Attempting to acknowledge every specific person who was of importance in my journey as a PhD candidate—important in the production of this thesis—seems to be at best a daunting task, and at worst a near-impossible task. If you, the reader, are somebody in particular to whom I owe a debt of gratitude, and if your name does not appear in the acknowledgements to come, then I sincerely apologize for the oversight; the omission is, I promise, unintentional. So where to begin? I guess I’ll try to do this somewhat chronologically. While it should go without saying, first and foremost: thank you, Mum and Dad. It’s difficult for me to properly articulate the multitude of ways in which I am thankful to you, but at the very least—and of direct relevance to this thesis—I think I can safely say that I likely would not be the inquisitive person that I am today (and I likely would not be writing an acknowledgement section for a doctoral thesis) had you not put so much effort into attempting to sate my curiosity at a young age. Much love and thanks to the both of you. I think it only fair to thank all of the education staff—from those earliest of teachers who taught me in primary school to those academics still teaching me in the present—whose collective hard work played no small role in my path through life leading to this point. Despite not knowing any of them personally, and despite basically all of my interactions with them having been remote, I feel like it would be unfair to not thank the staff at the RMIT library: so to the RMIT library staff, thank you! I definitely appreciate all of the effort that must have gone into acquiring all of the documents that I requested over the course of my PhD once my own attempts had failed to bear fruit. I am deeply thankful to the RMIT physics department collectively. Thank you to the academic staff and my fellow students for all of the guidance—both academic and personal—that has individually and collectively been imparted to me in my time as a student at RMIT. In particular of the RMIT physics department academics, thank you to Professor Andrew Greentree, Professor Jared Cole, and Professor Salvy Russo: the three of you have certainly put up with more unpleasantness from me than most of the academic staff at RMIT, in spite of which you have all remained absolutely phenomenal pillars of support both academically and personally. For that, I thank the three of you deeply. To Daniel Stavrevski and Giannis Thalassinos: you are two of the best friends that I have ever had the pleasure of making. The pair of you have ensured that my time at RMIT has been enjoyable since day one of our undergraduate (actually, day zero in Daniel’s case), and in complete honesty, I genuinely do not think that I could have gotten this far without the two of you. Your friendship and comradery means more to me than I’ll probably ever be able to express. I thank you both deeply for the everything. Furthermore on the student-front, I would like to specifically acknowledge Akib Karim, David Ing, Josef Worboys, Sam Wilkinson, and Tommy Bartolo. I could write paragraphs of thanks to each of you... but I won’t. Suffice it to say, your collective support, guidance, and friendship has been of immense importance to me through my time as a PhD student, and I am thankful towards the lot of you! Along with Daniel and Giannis, you guys have provided much entertainment, many fun times, and a whole lot of food for thought. Sam, you get bonus props for being an awesome DM during our D&D sessions (and I use the word “awesome” both in the original sense of the word and its more modern-day usage here)! Thank you to Dr Jamie Booth for all of the interesting discussions, guidance, and endless supply of entertaining anecdotes and stories! It should go without saying (though I shall of course say it anyhow) that I owe an immense debt of gratitude to the supervisory team that has seen me through my PhD candidature. Of my supervisors, I owe a special debt of gratitude to my primary supervisor Professor Nicolas C. Menicucci who has been a phenomenal mentor in more ways than I can adequately articulate: thank you very much for your endless patience, your guidance, and your feedback; I am—without doubt—a much better physicist for it. Thank you also to Doctor Valentina Baccetti, who joined as a secondary supervisor relatively late on during the course of my PhD candidature, but whose input as both a supervisor and a co-author has been invaluable. Salvy, you already got a thanks earlier on, so don’t get greedy! Penultimately, thank you to Past Scott, who in a cruel twist of fate can never read this acknowledgement. Past Scott was far from perfect—Present Scott isn’t either, and I very much doubt Future Scott will be for that matter—however he did put in a good amount of leg work at the start of the PhD that made putting this thesis together much easier than it otherwise might have been (and even then, it was a struggle at times). In spite of his desire to procrastinate, Past Scott made a decent effort to write explicit derivations down for Future (now Present) Scott’s reference/use, and I thank him for that. Finally, though definitely not least, thank you to my wonderful partner Thamale! Your endless love, support, and fantastic sense of humour has kept me sane and has made this whole thing possible. My love for you is nothing short of Jupiter-sized! rrr iv Summary The contents of this thesis include several investigations into analogue-gravity models from an internal or in-universe perspective. The philosophy driving these studies is that operational notions of observation and measurement have been of crucial importance in the construction of our theories of physics to date, and this was especially true in the construction of Einstein’s theories of special and general relativity: despite this, so far very little work appears to have been done on investigating analogue-gravity models from the perspective of such observers. Specifically, within this thesis it is demonstrated that it is possible to construct devices whose measurements behave in an equivalent manner to the reference frames within Einstein’s theory of special relativity. In particular, the collective measurements of these devices would lead observers who use them (in-universe observers) to view their analogue-gravity universe as containing a sonic analogue to special relativity (where the speed of sound 2s plays the role of the speed of light 2 from special relativity). Of course, the sonic analogue to special relativity (sonic relativity) is not fundamental: to this end, this thesis also provides a demonstration of how certain experiments can be performed by in-universe observers to reveal the fact that their universe has a preferred frame of reference (the frame defined by their analogue-gravity medium). The existence of a preferred frame of reference reveals to in-universe observers that there exists a bigger universe (the actual universe) outside of their analogue-gravity universe, and that sonic relativity is not a fundamental description of reality in this bigger universe. Towards the end of this thesis, it is speculated that it may be possible to map a certain type of experiment that violates sonic relativity to a type of experiment that does not violate sonic relativity. Should this be true, studying analogue-gravity models that are not fully sonically relativistic may still provide us with insights into real relativistic systems. CONTENTS List of Figures xi I Background 1 Introduction1 1.1 Structure of this thesis ......................... 2 1.2 The grand scheme of things...................... 3 1.2.1 Gravity: fundamental or emergent? ............. 4 1.2.2 A small detour: Semiclassical gravity ............ 7 1.2.3 The case for quantizing gravity................ 8 1.2.3.1 A glance at the field of quantum gravity . 10 1.2.3.2 One final and curious quantum gravity result . 13 1.2.4 The case for not quantizing gravity.............. 14 1.2.5 Other possibilities: questioning our postulates? . 16 1.3 Analogue gravity............................ 17 1.3.1 Origins.............................. 17 1.3.1.1 Gordon’s optical-metric model........... 17 1.3.1.2 Unruh’s acoustic black-hole model . 18 1.3.2 Developments.......................... 20 1.4 Making sense of it all: the role of analogue-gravity models in the hunt for a microscopic theory of gravity and the aim of this thesis 22 2 Theory 25 2.1 Relativity................................
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