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Special Relativity

:	Jürgen Ehlers, Claus Lämmerzahl
:	Special Relativity
:	Springer-Verlag
:	9783540345237
:	1
:	CHF 76.80
:

:	Naturwissenschaft
:	English

:	531
:	DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

Writte for: Researchers, lecturers, graduate students

Keywo ds:
Einstein
L rentz invariance
Minkowski spacetime
special relativity

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

Colby College, Waterville, ME 04901, USA
rtbluhm@colby.edu

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.

	Preface	6
	Contents	8
	List of Contributors	14
	Part I Historical and Philosophical Aspects	18
	Isotropy of Inertia: A Sensitive Early Experimental Test	20
	1 Introduction	20
	2 Early Ideas	21
	3 Possibilities for Experiments	21
	4 Some Factors Expected to A.ect Sensitivity in a Simple NMR Measurement	22
	5 Development of the Experimental Technique	22
	6 Initial Observations	24
	8 Experimental Procedure	26
	9 Discussion of Experimental Results	29
	10 Interpretation	29
	11 Some Personal Remarks	30
	Acknowledgements	30
	References	30
	The Challenge of Practice: Einstein, Technological Development and Conceptual Innovation	32
	1 Knowledge and Power in the Scienti.c Revolution	32
	2 Contrasting Intuitions on the Cascade Model	34
	3 Poincar ´ e, Einstein, Distant Simultaneity,	37
	and the Synchronization of Clocks	37
	4 The Emerging Rule of Global Time	41
	5 Technology-Based Concepts and the Rise of Operationalism	42
	6 Technological Problems, Technological Solutions, and Scientific Progress	45
	References	47
	Part II Foundation and Formalism	50
	Foundations of Special Relativity Theory	52
	1 Introduction	52
	2 Inertial Frames	53
	3 Poincar ´ e Transformations	53
	4 Minkowski Spacetime	56
	5 Axiomatics	57
	6 The Principle of Special Relativity and Its Limits	57
	7 Examples	58
	8 Accelerated Frames of Reference	58
	9 SR Causality	59
	References	60
	Algebraic and Geometric Structures in Special Relativity	62
	1 Introduction	62
	2 Some Remarks on Symmetry and Covariance	63
	3 The Impact of the Relativity Principle on the Automorphism Group of Spacetime	66
	4 Algebraic Structures of Minkowski Space	72
	5 Geometric Structures in Minkowski Space	88
	A Appendices	115
	Acknowledgements	125
	References	125
	Quantum Theory in Accelerated Frames of Reference	129
	1 Introduction	129
	2 Hypothesis of Locality	130
	3 Acceleration Tensor	132
	4 Nonlocality	133
	5 Inertial Properties of a Dirac Particle	136
	6 Rotation	137
	7 Sagnac E.ect	138
	8 Spin-Rotation Coupling	139
	9 Translational Acceleration	142
	10 Discussion	146
	References	146
	Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory	150
	1 Introduction	150
	2 From Quantum Mechanics and Special Relativity to Quantum Field Theory	154
	3 The Reeh–Schlieder–Theorem and Geometric Modular Action	163
	4 Relativistic Quantum Information Theory: Distillability in Quantum Field Theory	171
	References	177
	Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme	180
	1 Introduction	180
	2 Spacetime	181
	3 Matter – Electrically Charged and Neutral	182
	4 Electric Charge Conservation	183
	5 Charge Active: Excitation	183
	6 Charge Passive: Field Strength	184
	7 Magnetic Flux Conservation	185
	8 Premetric Electrodynamics	185
	9 The Excitation is Local and Linear in the Field Strength	187
	10 Propagation of Electromagnetic Rays ( Light )	190
	11 No Birefringence in Vacuum and the Light Cone	192
	12 Dilaton, Metric, Axion	197
	13 Setting the Scale	198
	14 Discussion	199
	15 Summary	201
	Acknowledgments	201
	References	201
	Part III Violations of Lorentz Invariance?	206
	Overview of the Standard Model Extension: Implications and Phenomenology of Lorentz Violation	208
	1 Introduction	208
	2 Motivations	211
	3 Constructing the SME	214
	4 Spontaneous Lorentz Violation	220
	5 Phenomenology	229
	6 Tests in QED	232
	7 Conclusions	238
	References	239
	Anything Beyond Special Relativity?	244
	1 Introduction and Summary	244
	2 Some Key Aspects of Beyond-Special-Relativity Research	249
	3 More on the Quantum-Gravity Intuition	256
	4 More on the Quantum-Gravity-Inspired DSR Scenario	261