Ehlers / Lämmerzahl Special Relativity

Will it Survive the Next 101 Years?
1. Auflage 2006
ISBN: 978-3-540-34523-7
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 702, 531 Seiten

Reihe: Lecture Notes in Physics

After a century of successes, physicists still feel the need to probe the limits of the validity of theories based on special relativity. Canonical approaches to quantum gravity, non-commutative geometry, string theory and unification scenarios predict tiny violations of Lorentz invariance at high energies.

The present book, based on a recent seminar devoted to such frontier problems, contains reviews of the foundations of special relativity and the implications of Poincaré invariance as well as comprehensive accounts of experimental results and proposed tests.

The book addresses, besides researchers in the field, everyone interested in the conceptual and empirical foundations of our knowledge about space, time and matter.

Written for: Researchers, lecturers, graduate students

Keywords:
Einstein
Lorentz invariance
Minkowski spacetime
special relativity

Autoren/Hrsg.

Ehlers, Jürgen

Lämmerzahl, Claus

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;List of Contributors;14
4;Part I Historical and Philosophical Aspects;18
4.1;Isotropy of Inertia: A Sensitive Early Experimental Test;20
4.1.1;1 Introduction;20
4.1.2;2 Early Ideas;21
4.1.3;3 Possibilities for Experiments;21
4.1.4;4 Some Factors Expected to A.ect Sensitivity in a Simple NMR Measurement;22
4.1.5;5 Development of the Experimental Technique;22
4.1.6;6 Initial Observations;24
4.1.7;8 Experimental Procedure;26
4.1.8;9 Discussion of Experimental Results;29
4.1.9;10 Interpretation;29
4.1.10;11 Some Personal Remarks;30
4.1.11;Acknowledgements;30
4.1.12;References;30
4.2;The Challenge of Practice: Einstein, Technological Development and Conceptual Innovation;32
4.2.1;1 Knowledge and Power in the Scienti.c Revolution;32
4.2.2;2 Contrasting Intuitions on the Cascade Model;34
4.2.3;3 Poincar ´ e, Einstein, Distant Simultaneity,;37
4.2.4;and the Synchronization of Clocks;37
4.2.5;4 The Emerging Rule of Global Time;41
4.2.6;5 Technology-Based Concepts and the Rise of Operationalism;42
4.2.7;6 Technological Problems, Technological Solutions, and Scientific Progress;45
4.2.8;References;47
5;Part II Foundation and Formalism;50
5.1;Foundations of Special Relativity Theory;52
5.1.1;1 Introduction;52
5.1.2;2 Inertial Frames;53
5.1.3;3 Poincar ´ e Transformations;53
5.1.4;4 Minkowski Spacetime;56
5.1.5;5 Axiomatics;57
5.1.6;6 The Principle of Special Relativity and Its Limits;57
5.1.7;7 Examples;58
5.1.8;8 Accelerated Frames of Reference;58
5.1.9;9 SR Causality;59
5.1.10;References;60
5.2;Algebraic and Geometric Structures in Special Relativity;62
5.2.1;1 Introduction;62
5.2.2;2 Some Remarks on Symmetry and Covariance ;63
5.2.3;3 The Impact of the Relativity Principle on the Automorphism Group of Spacetime;66
5.2.4;4 Algebraic Structures of Minkowski Space;72
5.2.5;5 Geometric Structures in Minkowski Space;88
5.2.6;A Appendices;115
5.2.7;Acknowledgements;125
5.2.8;References;125
5.3;Quantum Theory in Accelerated Frames of Reference;129
5.3.1;1 Introduction;129
5.3.2;2 Hypothesis of Locality;130
5.3.3;3 Acceleration Tensor;132
5.3.4;4 Nonlocality;133
5.3.5;5 Inertial Properties of a Dirac Particle;136
5.3.6;6 Rotation;137
5.3.7;7 Sagnac E.ect;138
5.3.8;8 Spin-Rotation Coupling;139
5.3.9;9 Translational Acceleration;142
5.3.10;10 Discussion;146
5.3.11;References;146
5.4;Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory;150
5.4.1;1 Introduction;150
5.4.2;2 From Quantum Mechanics and Special Relativity to Quantum Field Theory;154
5.4.3;3 The Reeh–Schlieder–Theorem and Geometric Modular Action;163
5.4.4;4 Relativistic Quantum Information Theory: Distillability in Quantum Field Theory;171
5.4.5;References;177
5.5;Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme;180
5.5.1;1 Introduction;180
5.5.2;2 Spacetime;181
5.5.3;3 Matter – Electrically Charged and Neutral;182
5.5.4;4 Electric Charge Conservation;183
5.5.5;5 Charge Active: Excitation;183
5.5.6;6 Charge Passive: Field Strength;184
5.5.7;7 Magnetic Flux Conservation;185
5.5.8;8 Premetric Electrodynamics;185
5.5.9;9 The Excitation is Local and Linear in the Field Strength;187
5.5.10;10 Propagation of Electromagnetic Rays ( Light );190
5.5.11;11 No Birefringence in Vacuum and the Light Cone;192
5.5.12;12 Dilaton, Metric, Axion;197
5.5.13;13 Setting the Scale;198
5.5.14;14 Discussion;199
5.5.15;15 Summary;201
5.5.16;Acknowledgments;201
5.5.17;References;201
6;Part III Violations of Lorentz Invariance?;206
6.1;Overview of the Standard Model Extension: Implications and Phenomenology of Lorentz Violation;208
6.1.1;1 Introduction;208
6.1.2;2 Motivations;211
6.1.3;3 Constructing the SME;214
6.1.4;4 Spontaneous Lorentz Violation;220
6.1.5;5 Phenomenology;229
6.1.6;6 Tests in QED;232
6.1.7;7 Conclusions;238
6.1.8;References;239
6.2;Anything Beyond Special Relativity?;244
6.2.1;1 Introduction and Summary;244
6.2.2;2 Some Key Aspects of Beyond-Special-Relativity Research;249
6.2.3;3 More on the Quantum-Gravity Intuition;256
6.2.4;4 More on the Quantum-Gravity-Inspired DSR Scenario;261
6.2.5;5 More on the Similarities with Beyond-Standard-Model Research;289
6.2.6;6 Another Century?;291
6.2.7;References;292
6.3;Doubly Special Relativity as a Limit of Gravity;296
6.3.1;1 Introduction;296
6.3.2;2 Postulates of Doubly Special Relativity;297
6.3.3;3 Constrained BF Action for Gravity;301
6.3.4;4 DSR from 2+1 Dimensional Gravity;307
6.3.5;5 Conclusions;312
6.3.6;Acknowledgements;313
6.3.7;References;313
6.4;Corrections to Flat-Space Particle Dynamics Arising from Space Granularity;316
6.4.1;1 Introduction;316
6.4.2;2 Basic Elements from Loop Quantum Gravity (LQG);321
6.4.3;3 A Kinematical Estimation of the Semiclassical Limit;329
6.4.4;4 Phenomenological Aspects;335
6.4.5;Acknowledgements;357
6.4.6;References;357
7;Part IV Experimental Search;364
7.1;Test Theories for Lorentz Invariance;366
7.1.1;1 Introduction;366
7.1.2;2 Test Theories;368
7.1.3;3 Model-Independent Descriptions of LI Tests;371
7.1.4;4 The General Frame for Kinematical Test Theories;381
7.1.5;5 The Test Theory of Robertson;384
7.1.6;6 The General Formalism;393
7.1.7;7 The Mansouri-Sexl Test Theory;396
7.1.8;8 Discussion;398
7.1.9;Acknowledgements;400
7.1.10;References;400
7.2;Test of Lorentz Invariance Using a Continuously Rotating Optical Resonator;402
7.2.1;1 Introduction;402
7.2.2;2 Setup;404
7.2.3;3 LLI-Violation Signal According to SME;406
7.2.4;4 LLI-Violation Signal According to RMS;411
7.2.5;5 Data Analysis;413
7.2.6;6 Outlook;415
7.2.7;References;417
7.3;A Precision Test of the Isotropy of the Speed of Light Using Rotating Cryogenic Optical Cavities;418
7.3.1;1 Introduction;418
7.3.2;2 Experimental Setup;419
7.3.3;3 Characterization of the Setup;424
7.3.4;4 Data Collection and Analysis;427
7.3.5;5 Conclusions;430
7.3.6;Acknowledgments;431
7.3.7;References;431
7.4;Rotating Resonator-Oscillator Experiments to Test Lorentz Invariance in Electrodynamics;433
7.4.1;1 Introduction;433
7.4.2;2 Common Test Theories to Characterize Lorentz Invariance;434
7.4.3;3 Applying the SME to Resonator Experiments;441
7.4.4;4 Comparison of Sensitivity of Various Resonator Experiments in the SME;450
7.4.5;5 Applying the RMS to Whispering Gallery Mode Resonator Experiments;454
7.4.6;6 The University of Western Australia Rotating Experiment;456
7.4.7;7 Data Analysis and Interpretation of Results;462
7.4.8;8 Summary;465
7.4.9;Acknowledgments;467
7.4.10;References;467
7.5;Recent Experimental Tests of Special Relativity;468
7.5.1;1 Introduction;468
7.5.2;2 Theoretical Frameworks;469
7.5.3;3 Michelson-Morley and Kennedy-Thorndike Tests;476
7.5.4;4 Atomic Clock Test of Lorentz Invariance;485
7.5.5;in the SME Matter Sector;485
7.5.6;5 Conclusion;492
7.5.7;References;494
7.6;Experimental Test of Time Dilation by Laser Spectroscopy on Fast Ion Beams;496
7.6.1;1 Introduction;496
7.6.2;2 Principle of the Ives Stilwell Experiment;497
7.6.3;3 Ives-Stilwell Experiment at Storage Rings;498
7.6.4;4 Outlook;507
7.6.5;Acknowledgments;509
7.6.6;References;509
7.7;Tests of Lorentz Symmetry in the Spin-Coupling Sector;510
7.7.1;1 Introduction;510
7.7.2;2 129Xe/3He maser (Harvard-Smithsonian Center for Astrophysics);511
7.7.3;3 Hydrogen Maser;514
7.7.4;4 Spin-Torsion Pendula (University of Washington and Tsing-Hua University);516
7.7.5;References;521
7.8;Do Evanescent Modes Violate Relativistic Causality?;523
7.8.1;1 Introduction;523
7.8.2;2 Wave Propagation;525
7.8.3;3 Photonic Barriers, Examples of Evanescent Modes;527
7.8.4;4 Evanescent Modes Are not Observable;532
7.8.5;5 Velocities, Delay Times, and Signals;533
7.8.6;6 Partial Re.ection: An Experimental Method to Demonstrate Superluminal Signal Velocity of Evanescent Modes;539
7.8.7;7 Evanescent Modes a Near Field Phenomenon;541
7.8.8;8 Superluminal Signals Do not Violate Primitive Causality;544
7.8.9;9 Summary;546
7.8.10;Acknowledgement;547
7.8.11;References;547
8;Lecture Notes in Physics;549

Leseproben

Overview of the Standard Model Extension: Implications and Phenomenology of Lorentz Violation (p. 191-192)
R. Bluhm

Colby College, Waterville, ME 04901, USA
[e-mail]

Abstract. The Standard Model Extension (SME) provides the most general observerindependent field theoretical framework for investigations of Lorentz violation. The SME lagrangian by definition contains all Lorentz-violating interaction terms that can be written as observer scalars and that involve particle fields in the Standard Model and gravitational fields in a generalized theory of gravity. This includes all possible terms that could arise from a process of spontaneous Lorentz violation in the context of a more fundamental theory, as well as terms that explicitly break Lorentz symmetry. An overview of the SME is presented, including its motivations and construction. Some of the theoretical issues arising in the case of spontaneous Lorentz violation are discussed, including the question of what happens to the Nambu-Goldstone modes when Lorentz symmetry is spontaneously violated and whether a Higgs mechanism can occur. A minimal version of the SME in flat Minkowski spacetime that maintains gauge invariance and power-counting renormalizability is used to search for leading-order signals of Lorentz violation. Recent Lorentz tests in QED systems are examined, including experiments with photons, particle and atomic experiments, proposed experiments in space, and experiments with a spin-polarized torsion pendulum.

1 Introduction

It has been 100 years since Einstein published his first papers on special relativity [1]. This theory is based on the principle of Lorentz invariance, that the laws of physics and the speed of light are the same in all inertial frames. A few years after Einstein’s initial work, Minkowski showed that a new spacetime geometry emerges from special relativity. In this context, Lorentz symmetry is an exact spacetime symmetry that maintains the form of the Minkowski metric in different Cartesian-coordinate frames. In the years 1907–1915, Einstein developed the general theory of relativity as a new theory of gravity. In general relativity, spacetime is described in terms of a metric that is a solution of Einstein’s equations.

The geometry is Riemannian, and the physics is invariant under general coordinate transformations. Lorentz symmetry, on the other hand, becomes a local symmetry. At each point on the spacetime manifold, local coordinate frames can be found in which the metric becomes the Minkowski metric. However, the choice of the local frame is not unique, and local Lorentz transformations provide the link between physically equivalent local frames.

The Standard Model (SM) of particle physics is a fully relativistic theory. The SM in Minkowski spacetime is invariant under global Lorentz transformations, whereas in a Riemannian spacetime the particle interactions must remain invariant under both general coordinate transformations and local Lorentz transformations. Particle fields are also invariant under gauge transformations. Exact symmetry under local gauge transformations leads to the existence of massless gauge fields, such as the photon. However, spontaneous breaking of local gauge symmetry in the electroweak theory involves the Higgs mechanism, in which the gauge fields can acquire a mass.

Classical gravitational interactions can be described in a form analogous to gauge theory by using a vierbein formalism [2]. This also permits a straightforward treatment of fermions in curved spacetimes. Covariant derivatives of tensors in the local Lorentz frame involve introducing the spin connection.