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Quantum Decoherence and Interlevel Relations A QUANTUM DECOHERENCE AND INTERLEVEL RELATIONS A Dissertation Submitted to the Graduate School of the University of Notre Dame in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Elise M. Crull Don Howard, Director Graduate Program in History and Philosophy of Science Notre Dame, Indiana April 2011 c Copyright by Elise Marie Crull 2011 All Rights Reserved QUANTUM DECOHERENCE AND INTERLEVEL RELATIONS Abstract by Elise M. Crull Quantum decoherence is a dynamical process whereby a system's phase rela- tions become delocalized due to interaction and subsequent entanglement with its environment. This delocalization, or decoherence, forces the quantum system into a state that is apparently classical (or apparently an eigenstate) by prodigiously suppressing features that typically give rise to so-called quantum behavior. Thus it has been frequently proposed by physicists and philosophers alike that deco- herence explains the dynamical transition from quantum behavior to classical behavior. Statements like this assume the existence of distinct realms, however, and the present thesis is an exploration of the metaphysical consequences of quan- tum decoherence motivated by the question of the quantum-to-classical transition and interlevel relations: if there are in-principle \classical" and \quantum" levels, what are the relations between them? And if there are no such levels, what fol- lows? Importantly, the following philosophical investigations are carried out by intentionally leaving aside the measurement problem and concerns about particu- lar interpretations of quantum mechanics. Good philosophical work, it is argued, Elise M. Crull can be done without adopting a specific interpretational framework and without recourse to the measurement problem. After introducing the physics of decoherence and exploring the four canon- ical models applied to system-environment interactions, it is argued that, on- tologically speaking, there exist no levels. This claim|called the \nontological thesis"|exposes as ill-posed questions regarding the transition from the quan- tum regime to the classical regime and reveals the inappropriateness of interlevel relations (like reduction, supervenience and emergence) operating within meta- physical frameworks. The nontological thesis has further important consequences regarding intralevel relations: not only are there no meaningful ways to carve the world into levels, but there are no meaningful ways to carve the world into parts and wholes either. These conclusions, supported by quantum decoherence and the empirical suc- cess of its models, drastically alter the philosophical terrain|not just in physics or in the philosophy of physics, but in traditional metaphysics as well. To Mom and Dad ad astra per aspera ii CONTENTS TABLES . vi ACKNOWLEDGMENTS . vii CHAPTER 1: INTRODUCTION . .1 1.1 Background . .1 1.2 What this dissertation is about, and why . .9 1.3 What this dissertation is not about, and why . 15 1.3.1 The measurement problem problem . 15 1.3.2 The interpretation problem . 30 1.4 Chapter synopsis . 33 1.5 Conclusion . 39 CHAPTER 2: DECOHERENCE FOR NONSPECIALISTS . 41 2.1 Introduction . 41 2.2 Preliminaries: Understanding quantum coherence . 42 2.3 The ubiquity of decoherence . 51 2.3.1 Assumptions . 52 2.3.2 Robustness, interaction Hamiltonians and the pointer basis 57 2.3.3 Minimal environments: Scattering-induced decoherence . 64 2.3.3.1 Takes little prodding . 65 2.3.3.2 Takes little time . 67 2.3.3.3 Wavelength limits of decoherence . 69 2.4 The density matrix formalism . 73 2.4.1 Density matrices . 76 2.4.2 Reduced density matrices . 83 2.4.3 Master equations . 87 iii 2.4.3.1 Born-Markov master equation . 91 2.4.3.2 Non-Markovian dynamics . 95 2.5 An alternate perspective: The Wigner representation . 96 CHAPTER 3: MODELING DECOHERENCE . 99 3.1 The general practice of modeling . 99 3.1.1 Cartwright on models . 101 3.1.2 Responding to Cartwright . 103 3.2 An overview of the four canonical models of decoherence . 106 3.3 Master equations: From general to specific . 113 3.4 Oscillator environments . 120 3.4.1 Osc-osc models: Quantum Brownian motion . 123 3.4.2 The Wigner approach to osc-osc models . 132 3.4.3 Assumptions in the osc-osc model . 135 3.4.4 Spin-osc models . 139 3.5 Spin-1/2 environments . 144 3.5.1 Spin-spin models . 148 3.5.2 Osc-spin models . 150 3.6 Decoherence models in biological & chemical systems . 152 3.7 Conclusion . 154 CHAPTER 4: WHENCE \CLASSICALITY"? . 157 4.1 Introduction to Part II of this thesis . 157 4.2 Defining classicality . 160 4.3 Denials of quantum fundamentalism . 164 4.3.1 Cartwright once again . 164 4.4 Attempts at a middle ground . 168 4.4.1 Wiebe, Ballentine and Emerson . 170 4.4.1.1 The Hyperion dispute . 171 4.4.1.2 Emerson's thesis . 178 4.4.2 Other attempts at a middle ground that won't do . 183 4.4.3 Caveat: Classical spacetime . 193 4.5 Batterman, Bokulich & the obstinance of classical structures . 196 4.6 Closing the (non-vicious) epistemic circle . 201 4.7 Conclusion . 205 iv CHAPTER 5: NONREDUCTIVE QUANTUM MONISM . 208 5.1 Introduction . 208 5.2 Reduction . 214 5.2.1 Kim's functional reduction . 219 5.3 Supervenience . 224 5.4 Emergence . 226 5.5 Conclusion . 230 CHAPTER 6: WHY WE CAN'T HAVE NICE THINGS . 232 6.1 Introduction . 232 6.1.1 A note about terminology . 235 6.1.2 A note about method . 237 6.2 Why we can't have nice things . 239 6.2.1 A thought experiment to illustrate this point . 243 6.2.2 A real experiment to illustrate this point . 245 6.3 Consequences for quantitative mereology . 250 6.3.1 Compositional mereology . 253 6.3.2 Traditional bundle theory . 257 6.3.3 Mereological nihilism . 258 6.4 Consequences for qualitative mereology? . 260 6.4.1 One more thought experiment . 260 6.5 Conclusion . 264 CHAPTER 7: CONCLUDING REMARKS . 266 BIBLIOGRAPHY . 271 v TABLES 2.1 Λ (in cm−2s−1)............................ 66 vi ACKNOWLEDGMENTS I must begin by acknowledging my great debt to Don Howard. An advisor who believes in you, tirelessly advocates on your behalf and whose sole fault in musical taste is Patsy Cline (though perhaps the fault lies with me) is a gift of immeasurable worth. The enthusiasm with which he shepherded me through difficult stages in my graduate career|the present work not withstanding|was such that I can only hope to impart some portion of the same to my own students some day. Abundant thanks of a similar nature are owed to Katherine Brading and Guido Bacciagaluppi, for seeing a colleague in me long before I did. In a way, I suspect their confidence propelled me to that very status. I am also thankful to Michael Rea for inviting a philosopher of physics into a metaphysician's world, and for the ways he has encouraged me (not least by example) to engage in metaphysics with clarity, confidence and a good measure of charity. In addition to those already mentioned, I have benefited frequently from count- less discussions (along with the occasional impassioned debate), helpful sugges- tions and insightful commentary provided by John LoSecco, David Wallace, Jos Uffink, Amit Hagar, Michel Janssen, and my good friend and peer, Tom Pashby. I also wish to thank the committee and participants of Seven Pines XIV: I learned a great deal from a great many people that week, evidence of which is surely to vii be found in these pages. Thanks also to the organizers and participants of the 2009 Geneva Summer School in the Philosophy of Physics, for exploring with me certain issues pertinent to my thesis as well as certain regions of the Pennine Alps. Special thanks are long overdue to Max Schlosshauer and Kristian Camilleri, both of whom showed deep interest and unbridled support regarding this project from its very inception. Since those first conversations in Australia, I have con- tinued to profit from their council and friendship. I hope the future brings us to the same part of the world as one another as often as possible. Andrew White deserves abundant thanks for his Herculean editing skills on earlier drafts. Thanks also to Chicory Caf´eand Martha Precup for many Saturday mornings spent together. Lauren Whitnah, I am blessed through your friendship and will think of you often from across the Pond. Also, thanks for letting me ride your horse. I would be remiss not to mention the understanding and accountability (except, perhaps, with respect to the daily crossword) provided by my law school study companions, Laura Porter and Kate Kennedy. My love always to Brooke Peterson, who brought me yellow tulips during a particularly dark winter, and to Greta & Will-bo, who might never understand just how therapeutic their dance parties, train sets and giggle-fits were for \Eeese." To my academic big brothers, Greg Macklem and Erik Peterson: we laughed, we cried, we became legend. I will keep near to my heart always the folks of SBCRC and the home group: but for the plenteous love you've shown me, graduate school would have been impossible indeed. To Giovanni, Pierre Louis, Seamus, Dean and Little Burl I offer hearty thanks for sorely needed extra-curricular amusement. Karen Vegter (\Mom Too"), viii you are a font of wisdom and good humor, and your friendship in these years has meant a great deal to your \Daughter Also." Gram and Gramps, you've been a continual source of support and advice all through my long career as a student. I cannot tell you how much it has meant to have grandparents who understand life in academia.
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