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Phenomena at the Border Between Quantum Physics and General Relativity

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Phenomena at the Border Between Quantum Physics and General Relativity Phenomena at the border between quantum physics and general relativity by Valentina Baccetti A thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in the School of Mathematics, Statistics and Operations Research. Victoria University of Wellington 2014 Abstract In this thesis we shall present a collection of research results about phenomena that lie at the interface between quantum physics and general relativity. The motivation behind our research work is to find alternative ways to tackle the problem of a quantum theory of/for gravitation. In the general introduction, we shall briefly recall some of the characteristics of the well-established approaches to this problem that have been developed since the beginning of the middle of the last century. Afterward we shall illustrate why one would like to engage in alternative paths to better understand the problem of a quantum theory of/for gravitation, and the extent to which they will be able to shed some light into this problem. In the first part of the thesis, we shall focus on formulating physics without Lorentz invariance. In the introduction to this part we shall describe the motiva- tions that are behind such a possible choice, such as the possibility that the physics at energies near Planck regime may violate Lorentz symmetry. In the following part we shall first consider a minimalist way of breaking Lorentz invariance by renouncing the relativity principle, that corresponds to the introduction of a preferred frame, the aether frame. In this case we shall look at the transformations between a generic inertial frame and the aether frame still requiring the transformations to be linear. The second step is to establish the transformations for the energy and momentum in order to define some dynamics and design possible experiments to test such as- sumptions. As an application we shall present two compelling models that minimally break Lorentz invariance, the first one only in the energy-momentum sector, the sec- ond one in the transformation between inertial frames. Following along the line of physics without Lorentz invariance, we shall next explore some threshold theorems in both scattering and decay processes by considering only the existence of some energy momentum relation E(p), without making any further assumption. We shall see that quite a lot can be said and that 3-momenta can behave in a complicated and counter-intuitive manner. In the second part of the thesis we shall address the thermodynamics of space- time and the important role played by entropy. In the introduction we shall outline the idea of induced gravity, which is the motivation behind this possible interpre- tation of general relativity as a mean field theory of some underlying microscopic degrees of freedom. In the next chapter we shall partially review Jacobson's thermo- dynamic derivation of the Einstein equations and generalise it to a generic birfucate null surface. The interesting result we shall see is that, given the construction of the thermodynamic system via some virtual constantly accelerating observers, we can assign a \virtual" definition of Clausius entropy to essentially arbitrary causal hori- zons. To conclude this part we shall present some of the mathematical properties of entropy. In particular we shall focus on the simpler case of single-channel Shannon entropy and study under which conditions it is infinite, even though the probability distribution is normalisable. In the last part, we shall describe a proposal for a space-base experiment to test the effects of acceleration and gravity of quantum physics. In principle, the results of such an experiment could shed some light on fundamental questions about the overlap of quantum theory and general relativity; at the same time, they may enable experimentalists interested to implement quantum communication into space based technology, to correct adverse gravitational effects. We conclude with a brief discussion of lessons learned from these different ap- proaches. c 2014, Valentina Baccetti iii iv The journey is long and the path is pathless and one has to be alone. There is no map and no one to guide. But there is no alternative One cannot escape it, one cannot evade it. One has to go on the journey. The goal seems impossible but the urge to go on it is intrinsic. The need is deep in the soul. Really, you are the urge, you are the need and consciousness cannot be otherwise because of this challenge and because of this adventure. So do not waste time { begin. Do not calculate { begin. Do not hesitate { begin. Do not look back { begin And always remember old Lao Tzu's words: A tree that takes both arms to encircle grows from a tiny rootlet. A many-storied pagoda is built by placing one brick upon another brick. A journey of three thousand miles is begun by a single step. OSHO - A Cup of Tea v vi Acknowledgments And here it comes, the moment to thank all the people who helped me to achieve this great goal that a PhD is. First things first, I would like to thank Matt, my supervisor, for all the support and guidance you have given me in the last three years. I have truly appreciated all the scientific discussions we have had and all the work we have done together. I hope I have been able to grab even the tiniest amount of your passion for science and for research, and your huge knowledge. I am profoundly grateful to my officemates, Prado and Kyle. We have shared part of this journey together, with its ups and downs. I wish you good luck for your future careers, but knowing you guys, I am sure your future will be bright. Another key ingredient in the completion of this thesis is the RQI group in Nottingham. Ivette, Carlos, Nico, Ant, Gerardo, Mehdi, David, Jason, Giannis, Angela, thank you guys for having welcomed me in your group of \metrology boys and space girls" so quickly. I have learned so much about physics, team work and friendship in the six months I have spent with you. I hope I can visit you soon again. I also want to thank Nicolas Menicucci for all the scientific discussions we have had, for all the physics you have taught me, and for the support you gave me when I needed it more. I want to thank all the staff members at the School of Mathematics, Statistics and Operations Research at Vic, in particular my secondary supervisor Mark McGuinness; Prema, Kelsey, Ginny and Tania, and all the members of the school office, your help was always more than appreciated and your smily faces made several of my mornings at Uni. I also want to thank Steven Archer for the nice support you have given me for the tutoring and marking, and Radek for being such a nice guy. I also want to thank Vladimir, Xenia and Sviatoslav Pestov, for the Irene Pestov's Memorial Scholarship, set up in memory of their late wife and mother Irene Pestov, of which I am a humble recipient. And now let us go to all the friends who have supported me with their company and laughs during these three long years. The biggest thank you goes to Filippo and Giulia S., for basically being my family here in Wellington. All the movie nights we vii have had together, the holiday in Coromandel under the tropical typhoon with your amazing families, the Weta party, the Sundays at the farmers market, all the simple moments we have shared, have been incredible for me. I am more than glad to see you both succeeding in your dreams. Also I need to thank Patato and Kali; without you little silly creatures, life would not be as entertaining at Rodrigo Rd. A big hug and thank you go to Elisa and Raphael, with whom I have had delicious dinners and interesting conversations based on physics and rum (at some stage more rum than physics). Thank you Elisa for making me laugh with your blog every time I needed. Also a big thank you to Cristina, Lorena, Marcello, Sonja, Giulia M. and Rachele, for all the time we have spent together, and for reminding me that there is a world outside; Marcello for the beautiful experience on the Milford track and the motto \stai sereno". Roberto for the amazing fresh pasta and pizza you make at Merkato Fresh and for the spirit of Rome you brought to Wellington, every time I visit you I feel at home. Marco Z., I am very glad to see you pursuing your dreams, and I am more than thrilled for you, I hope I can help you find some interesting science that you can show in one of your documentaries. Daniel and Juan, my friends of many chats and coffees, your latin warmth made me feel like at home, your friendship is very dear to me. Lia, for being my family in Nottingham, I really appreciated all the times we went to Tesco around midnight, just because we wanted. The time we spent together was some of the best in my life. I hope you have enjoyed it too. Manuel, Kai, Wilhelm, Giannis, Benito, Anna, Rowan, Gael, Richard, Nico, Hugo, Giulia G., Silvio, Simona, Michalis, Sid, Sara, Ant, Luis, Cristiano, Daniele and Federica for all the parties, improvised dinners and picnics in Wollaton park. You made me spend a phenomenal summer in the UK, I really want to meet you all at some stage and I deeply miss you. Do not worry Giannis, I will start Salsa classes as soon as I finish this thesis.
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