Ehlers / Lämmerzahl Special Relativity

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

E-Book, Englisch, Band 702, 531 Seiten, eBook

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.

Zielgruppe

Research

Autoren/Hrsg.

Ehlers, Jürgen

Lämmerzahl, Claus

Inhaltsverzeichnis

Historical and Philosophical Aspects.- Isotropy of Inertia: A Sensitive Early Experimental Test.- The Challenge of Practice: Einstein, Technological Development and Conceptual Innovation.- Foundation and Formalism.- Foundations of Special Relativity Theory.- Algebraic and Geometric Structures in Special Relativity.- Quantum Theory in Accelerated Frames of Reference.- Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory.- Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme.- Violations of Lorentz Invariance?.- Overview of the Standard Model Extension: Implications and Phenomenology of Lorentz Violation.- Anything Beyond Special Relativity?.- Doubly Special Relativity as a Limit of Gravity.- Corrections to Flat-Space Particle Dynamics Arising from Space Granularity.- Experimental Search.- Test Theories for Lorentz Invariance.- Test of Lorentz Invariance Using a Continuously Rotating Optical Resonator.- A Precision Test of the Isotropy of the Speed of Light Using Rotating Cryogenic Optical Cavities.- Rotating Resonator-Oscillator Experiments to Test Lorentz Invariance in Electrodynamics.- Recent Experimental Tests of Special Relativity.- Experimental Test of Time Dilation by Laser Spectroscopy on Fast Ion Beams.- Tests of Lorentz Symmetry in the Spin-Coupling Sector.- Do Evanescent Modes Violate Relativistic Causality?.

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.