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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
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Preface
Einstein’s relativity theories changed radically the physicists’ conception of
space and time. The Special Theory, i.e., Minkowski spacetime and Poincar´e-
invariance, not only removed an inconsistency between the kinematical foun-
dations 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,Poincar´e-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 Poincar´e-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 Poincar´e, 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 Poincar´e 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. L¨ammerzahl .................................................... 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
