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Lecture Notes in Physics EditorialBoard R.Beig,Wien,Austria W.Beiglböck,Heidelberg,Germany W.Domcke,Garching,Germany B.-G.Englert,Singapore U.Frisch,Nice,France P.Hänggi,Augsburg,Germany G.Hasinger,Garching,Germany K.Hepp,Zürich,Switzerland W.Hillebrandt,Garching,Germany D.Imboden,Zürich,Switzerland R.L.Jaffe,Cambridge,MA,USA R.Lipowsky,Golm,Germany H.v.Löhneysen,Karlsruhe,Germany I.Ojima,Kyoto,Japan D.Sornette,Nice,France,andZürich,Switzerland S.Theisen,Golm,Germany W.Weise,Garching,Germany J.Wess,München,Germany J.Zittartz,Köln,Germany TheLectureNotesinPhysics TheseriesLectureNotesinPhysics(LNP),foundedin1969,reportsnewdevelopments in physics research and teaching – quickly and informally, but with a high quality and theexplicitaimtosummarizeandcommunicatecurrentknowledgeinanaccessibleway. 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ProposalsshouldbesenttoamemberoftheEditorialBoard,ordirectlytothemanaging editoratSpringer: Dr.ChristianCaron SpringerHeidelberg PhysicsEditorialDepartmentI Tiergartenstrasse17 69121Heidelberg/Germany [email protected] Jürgen Ehlers Claus Lämmerzahl (Eds.) Special Relativity Will it Survive the Next 101 Years? ABC Editors JürgenEhlers ClausLämmerzahl Albert-Einstein-Institut ZARM,UniversitätBremen MPlGravitationsphysik AmFallturm AmMühlenberg1 28359Bremen,Germany 14476Golm,Germany E-mail:laemmerzahl@zarm. E-mail:mpoessel@aei-potsdam. uni-bremen.de mpg.de J.EhlersandC.Lämmerzahl,SpecialRelativity, Lect.NotesPhys.702(Springer,BerlinHeidelberg2006),DOI10.1007/b11758914 LibraryofCongressControlNumber:2006928275 ISSN0075-8450 ISBN-10 3-540-34522-1SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-34522-0SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsare liableforprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springer.com (cid:1)c Springer-VerlagBerlinHeidelberg2006 Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:bytheauthorsandtechbooksusingaSpringerLATEXmacropackage Coverdesign:design&productionGmbH,Heidelberg Printedonacid-freepaper SPIN:11758914 54/techbooks 543210 Preface Einstein’s relativity theories changed radically the physicists’ conception of space and time. The Special Theory, i.e., Minkowski spacetime and Poincaré- invariance, not only removed an inconsistency between the kinematical foundations of mechanics and electrodynamics but provided a framework for all of physics except gravity. Even General Relativity kept the most essential ingredi- entofspecialrelativity–aLorentz-metric–and,therefore,maintainedLorentz- invariance infinitesimally. In the large realm of particle physics where intrin- sic,tidalgravitationalfieldsaretotallynegligible,Poincaré-invariancecombined with gauge invariance led to relativistic quantum field theories and, specifically, to the standard model of particle physics. General Relativity theory and Quantum Field theory generalized classi- cal Poincaré-invariant field theory in different directions. Both generalizations turned out to be successful, but their basic assumptions contradict each other. Attemptstoovercomethis“mostglaringincompatibilityofconcepts”(F.Dyson) sofarhaveledtopartialsuccessesbutnottoaunifiedfoundationofphysicsen- compassinggravityandquantumtheory.Thus,afteraboutacenturyofsuccesses in separate areas, physicists feel the need to probe the limits of validity of the SR-based theories. Canonical approaches to quantum gravity, non-commutative geometry,(super-)stringtheory,andunificationscenariospredicttinyviolations of Lorentz-invariance at high energies. Accordingly, the present seminar tries to coverthebasicsofSpecialRelativity,proposedscenariosthatleadtoviolationsof Lorentz-invariance, and experiments designed to find such effects. Furthermore, some historical and philosophical aspects are treated. The main topis of this seminar are • The foundations and the mathematics of Special Relativity • Conjectured violations of Lorentz-invariance • Confrontation with high-precision experiments • Philosophical and historical aspects The 271st WE–Heraeus Seminar on Special Relativity, where these issues have been discussed, took place in Potsdam from February 13–18, 2005. We VI Preface sincerely thank all speakers for their presentations and especially those who moreoverwerewillingtowritethemupforthepresentvolume.Lastbutnotleast we thank the Wilhelm and Else Heraeus Foundation for its generous support, without which this seminar could not have been realized. Golm and Bremen Ju¨rgen Ehlers January 2006 Claus La¨mmerzahl Experimental set-up of an early high precision search for an anisotropy of inertia. Contents Part I Historical and Philosophical Aspects Isotropy of Inertia: A Sensitive Early Experimental Test R.W.P. Drever .................................................... 3 1 Introduction ................................................... 3 2 Early Ideas .................................................... 4 3 Possibilities for Experiments ..................................... 4 4 Some Factors Expected to Affect Sensitivity in a Simple NMR Measurement .................................. 5 5 Development of the Experimental Technique ....................... 5 6 Initial Observations............................................. 7 7 Experiments and Developments for Higher Sensitivity............... 7 8 Experimental Procedure......................................... 9 9 Discussion of Experimental Results ............................... 12 10 Interpretation.................................................. 12 11 Some Personal Remarks......................................... 13 References ........................................................ 13 The Challenge of Practice: Einstein, Technological Development and Conceptual Innovation M. Carrier........................................................ 15 1 Knowledge and Power in the Scientific Revolution .................. 15 2 Contrasting Intuitions on the Cascade Model ...................... 17 3 Poincaré, Einstein, Distant Simultaneity, and the Synchronization of Clocks ................................ 20 4 The Emerging Rule of Global Time............................... 24 5 Technology-Based Concepts and the Rise of Operationalism................................... 25 6 Technological Problems, Technological Solutions, and Scientific Progress .......................................... 28 References ........................................................ 30 VIII Contents Part II Foundation and Formalism Foundations of Special Relativity Theory J. Ehlers.......................................................... 35 1 Introduction ................................................... 35 2 Inertial Frames................................................. 36 3 Poincaré Transformations ....................................... 36 4 Minkowski Spacetime ........................................... 39 5 Axiomatics .................................................... 40 6 The Principle of Special Relativity and Its Limits .................. 40 7 Examples ..................................................... 41 8 Accelerated Frames of Reference ................................. 41 9 SR Causality .................................................. 42 References ........................................................ 43 Algebraic and Geometric Structures in Special Relativity D. Giulini......................................................... 45 1 Introduction ................................................... 45 2 Some Remarks on “Symmetry” and “Covariance” .................. 46 3 The Impact of the Relativity Principle on the Automorphism Group of Spacetime......................... 49 4 Algebraic Structures of Minkowski Space .......................... 55 5 Geometric Structures in Minkowski Space ......................... 71 A Appendices .................................................... 98 References ........................................................ 108 Quantum Theory in Accelerated Frames of Reference B. Mashhoon ...................................................... 112 1 Introduction ................................................... 112 2 Hypothesis of Locality .......................................... 113 3 Acceleration Tensor............................................. 115 4 Nonlocality .................................................... 116 5 Inertial Properties of a Dirac Particle ............................. 119 6 Rotation ...................................................... 120 7 Sagnac Effect .................................................. 121 8 Spin-Rotation Coupling ......................................... 122 9 Translational Acceleration ....................................... 125 10 Discussion..................................................... 129 References ........................................................ 129 Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory R. Verch.......................................................... 133 1 Introduction ................................................... 133 2 From Quantum Mechanics and Special Relativity to Quantum Field Theory ....................................... 137 Contents IX 3 The Reeh–Schlieder–Theorem and Geometric Modular Action .................................. 146 4 Relativistic Quantum Information Theory: Distillability in Quantum Field Theory............................ 154 References ........................................................ 160 Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme F.W. Hehl and Y.N. Obukhov ....................................... 163 1 Introduction ................................................... 163 2 Spacetime ..................................................... 164 3 Matter – Electrically Charged and Neutral ........................ 165 4 Electric Charge Conservation .................................... 166 5 Charge Active: Excitation ....................................... 166 6 Charge Passive: Field Strength................................... 167 7 Magnetic Flux Conservation ..................................... 168 8 Premetric Electrodynamics ...................................... 168 9 The Excitation is Local and Linear in the Field Strength ............ 170 10 Propagation of Electromagnetic Rays (“Light”) .................... 173 11 No Birefringence in Vacuum and the Light Cone ................... 175 12 Dilaton, Metric, Axion .......................................... 180 13 Setting the Scale ............................................... 181 14 Discussion..................................................... 182 15 Summary...................................................... 184 References ........................................................ 184 Part III Violations of Lorentz Invariance? Overview of the Standard Model Extension: Implications and Phenomenology of Lorentz Violation R. Bluhm ......................................................... 191 1 Introduction ................................................... 191 2 Motivations.................................................... 194 3 Constructing the SME .......................................... 197 4 Spontaneous Lorentz Violation................................... 203 5 Phenomenology ................................................ 212 6 Tests in QED .................................................. 215 7 Conclusions.................................................... 221 References ........................................................ 222 Anything Beyond Special Relativity? G. Amelino-Camelia ............................................... 227 1 Introduction and Summary ...................................... 227 2 Some Key Aspects of Beyond-Special-Relativity Research............ 232 3 More on the Quantum-Gravity Intuition........................... 239 4 More on the Quantum-Gravity-Inspired DSR Scenario .............. 244 X Contents 5 More on the Similarities with Beyond-Standard-Model Research...... 272 6 Another Century? .............................................. 274 References ........................................................ 275 Doubly Special Relativity as a Limit of Gravity K. Imil(cid:1)kowska and J. Kowalski-Glikman .............................. 279 1 Introduction ................................................... 279 2 Postulates of Doubly Special Relativity ........................... 280 3 Constrained BF Action for Gravity ............................... 284 4 DSR from 2+1 Dimensional Gravity .............................. 290 5 Conclusions.................................................... 295 References ........................................................ 296 Corrections to Flat-Space Particle Dynamics Arising from Space Granularity L.F. Urrutia ...................................................... 299 1 Introduction ................................................... 299 2 Basic Elements from Loop Quantum Gravity (LQG) ............... 304 3 A Kinematical Estimation of the Semiclassical Limit................ 312 4 Phenomenological Aspects....................................... 318 References ........................................................ 340 Part IV Experimental Search Test Theories for Lorentz Invariance C. Lämmerzahl .................................................... 349 1 Introduction ................................................... 349 2 Test Theories .................................................. 351 3 Model-Independent Descriptions of LI Tests ....................... 354 4 The General Frame for Kinematical Test Theories .................. 364 5 The Test Theory of Robertson ................................... 367 6 The General Formalism ......................................... 376 7 The Mansouri-Sexl Test Theory .................................. 379 8 Discussion..................................................... 381 References ........................................................ 383 Test of Lorentz Invariance Using a Continuously Rotating Optical Resonator S. Herrmann, A. Senger, E. Kovalchuk, H. Mu¨ller, A. Peters............ 385 1 Introduction ................................................... 385 2 Setup ......................................................... 387 3 LLI-Violation Signal According to SME ........................... 389 4 LLI-Violation Signal According to RMS ........................... 394 5 Data Analysis.................................................. 396 6 Outlook....................................................... 398 References ........................................................ 400