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The Scharnhorst Effect: Superluminality and Causality in Effective Field Theories Item Type text; Electronic Dissertation Authors de Clark, Sybil Gertrude Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 07/10/2021 00:45:17 Link to Item http://hdl.handle.net/10150/622964 THE SCHARNHORST EFFECT: SUPERLUMINALITY AND CAUSALITY IN EFFECTIVE FIELD THEORIES by Sybil Gertrude de Clark Copyright c Sybil Gertrude de Clark 2016 A Dissertation Submitted to the Faculty of the DEPARTMENT OF PHYSICS In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2016 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dis- sertation prepared by Sybil Gertrude de Clark, titled The Scharnhorst Effect: Su- perluminality and Causality in Effective Field Theories, and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. Date: 8 November 2016 Sean Fleming Date: 8 November 2016 Christian W¨uthrich Date: 8 November 2016 Bruce Barrett Date: 8 November 2016 Dimitrios Psaltis Date: 8 November 2016 William Toussaint Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: 8 November 2016 Dissertation Director: Sean Fleming Date: 8 November 2016 Dissertation Director: Christian W¨uthrich 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Sybil Gertrude de Clark 4 ACKNOWLEDGEMENTS Firstly, I want to express my sincere gratitude to my advisors. I want to thank my physics advisor, Sean Fleming, for his patient support through all stages of my research. It should go without saying (but I shall say it anyway) that without his readiness to accommodate my passion for foundations of physics, his guidance in delineating research projects of relevance to the latter, and then his continuous assistance over the years to bring my research to fruition, this work would not exist. I am also immensely grateful to my philosophy advisor, Christian W¨uthrich, for supervising my work and providing numerous detailed and thoughtful comments. His input and advice have been invaluable to me. I could not have wished for better mentors. In addition to my advisors, I also want to thank the other members of my doctoral committee: Bruce Barrett, Dimitrios Psaltis and Doug Toussaint. I am of course, yet truly, grateful for their willingness to serve on my committee in the first place. Furthermore, their keen and insightful feedback during the meetings that took place in the course of my research has been extremely helpful, even crucial. I am also very grateful for the opportunities I have been given to present my work at seminars while it was still in progress. In this respect I wish to thank James Weatherall as the organizer of the ”Southern California Philosophy of Physics Reading Group” at UC Irvine, as well as Chris W¨uthrich for introducing me to this wonderful group. I also want to thank Hasok Chang for the opportunity to present my work to the inter-disciplinary seminar ”Coffee with Scientists” which he organizes in the Department of History and Philosophy of Science at the University of Cambridge, as well as Daniel Jon Mitchell without who I would never have had the opportunity to go. The questions and observations I received during these talks really helped me to broaden my ideas, and I am very grateful to those who provided me with feedback in this way. Furthermore, these talks have had an unanticipated and wonderful outcome: they motivated me to contact several of the physicists whose fascinating work it had been my pleasure to study. In this respect, it is with the greatest pleasure that I thank those who I have had the privilege to correspond with, and often even to meet. Being also an historian of science (notably on Ptolemy’s work and 19th c physics), my previous research could hardly afford me the joy of discussing the science I was studying with the verypeople who had discovered it. Being able to do so now has been a truly special experience, and one of the most rewarding aspects of my work. I am especially grateful to Peter Milonni, Robert Geroch, John Cramer, Shahar Ben-Menahem, Sebastiano Sonego, as well as the two pioneers who unveiled and publicized the effect that is the topic of the present dissertation: Klaus Scharnhorst and Gabriel Barton. I have been 5 overwhelmed by how incredibly generous they have been with their time and help, and the discussions that I have had with them over the course of this work have been incredibly gratifying. 6 DEDICATION For Michael Kruse, without whom I would never have had the opportunity to accomplish this work, and for Roger Haar, who I wish could have seen it. 7 Table of Contents List of Figures . 12 ABSTRACT . 14 Chapter 1 INTRODUCTION . 16 1.1 Introduction . 16 1.1.1 Description of the Scharnhorst effect . 16 1.1.2 Derivations of the Scharnhorst effect: a brief history . 17 1.2 The issue of signal velocity . 19 1.3 Conceptual interpretation of the Scharnhorst effect . 22 1.3.1 The Casimir vacuum as a dielectric medium . 22 1.3.2 The Casimir effect . 23 1.3.3 Analogous conceptual model for the Scharnhorst effect . 25 1.3.4 Alternative conceptual models for the Casimir and Scharn- horst effects . 27 1.4 Overview of dissertation . 28 Chapter 2 SURVEY OF SUPERLUMINAL EFFECTS IN FIELD THEO- RIES . 33 2.1 Introduction . 33 2.2 The Drummond-Hathrell effect . 34 2.2.1 Description . 34 2.2.2 Historical background . 37 2.2.3 Interpretation . 40 2.3 Bimetric theories . 41 2.3.1 Modified Newtonian dynamics (MOND) theories . 41 2.3.2 Varying speed of light bimetric theories . 45 2.4 k-essence . 45 2.4.1 Description . 45 2.4.2 k-essence and superluminal propagation . 49 2.5 Does superluminal propagation imply causal paradoxes? . 51 2.5.1 Causal paradox: the bilking argument and its physical imple- mentation . 52 2.5.2 Causal cone . 54 2.5.3 The tachyonic anti-telephone thought experiment modified . 57 2.5.4 Stable causality . 59 8 Table of Contents – Continued 2.5.5 New difficulties: propagation into the coordinate past . 61 2.5.6 Initial data formulation and Cauchy problem . 68 2.5.7 Robert Geroch’s work . 72 2.5.8 Forming CSCs within a causal cone formalism . 79 2.6 Conclusion . 86 Chapter 3 THE SCHARNHORST EFFECT: A HISTORICAL INTRODUC- TION . 89 3.1 Introduction . 89 3.2 The Scharnhorst effect . 90 3.3 Early derivations of the Scharnhorst effect . 90 3.3.1 Scharnhorst’s derivation (1990) . 91 3.3.2 Barton’s derivation (1990) . 94 3.4 Early reactions (1990) . 97 3.4.1 Milonni & Svotzil’s argument . 98 3.4.2 Ben-Menahem’s wavefront argument . 100 3.4.3 Ben-Menahem’s commutator argument . 102 3.5 Scharnhorst and Barton’s response: implications of the Kramers- Kronig relations . 107 3.6 Later work . 113 3.6.1 Relation between the Scharnhorst effect and the energy den- sity of the Casimir vacuum . 113 3.6.2 Effect at oblique incidence and effective metric approaches .117 Chapter 4 DERIVATION OF THE SCHARNHORST EFFECT IN SOFT- COLLINEAR EFFECTIVE THEORY . 122 4.1 Introduction . 122 4.2 Modelling the Scharnhorst effect in the framework of SCET . .122 4.2.1 The standard Euler-Heisenberg Lagrangian . 123 4.2.2 Degrees of freedom in the SCET Euler-Heisenberg Lagrangian 128 4.3 Advantages of SCET vs the standard approach . 132 4.3.1 Light-cone coordinates . 133 4.3.2 SCET: scaling in the expansion parameter λ . 134 4.3.3 SCET perturbative expansion and control of the errors at higher orders . 141 4.3.4 Interaction between Casimir background and probe photon . 146 4.4 Derivation of the SCET Lagrangian . 147 2 loop 4.5 Derivation of the SCET polarization tensor Πμν− . 151 SC 4.5.1 Relevant terms to model the Scharnhorst effect in LEH theory 152 9 Table of Contents – Continued 4.5.2 Expressions for the propagators . 157 4.5.3 Evaluating the contributions to the tadpole diagram and self- energy tensor . 158 4.5.4 Resulting polarization tensor . 170 4.6 Derivation of the velocity from the SCET polarization tensor using the light cone condition . 176 4.7 Derivation of the velocity from the SCET polarization tensor using the index of refraction .

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