Energy and geometry : an introduction to deformed special relativity / Fabio Cardone, Roberto Mignani.

Format:

Book

Author/Creator:

Cardone, Fabio.

Contributor:

Mignani, Roberto.

Series:

World Scientific series in contemporary chemical physics ; v. 22.

World Scientific series in contemporary chemical physics ; v. 22

Language:

English

Subjects (All):

Special relativity (Physics).

Generalized spaces.

Physical Description:

xiv, 146 pages ; 24 cm.

Place of Publication:

[River Edge] New Jersey : World Scientific, [2004]

Summary:

Cardone (National Research Council, CNR, Italy) discusses in detail the mathematical aspects and physical applications of a new geometrical structure of space-time based on a generalization ("deformation") of the usual Minkowski space. He explains the physical and mathematical foundations of deformed special relativity (DSR), presents a metric description of fundamental interactions, and considers the connection of DSR with the problem of the breakdown of local Lorentz invariance. The link between DSR and a generalized five- dimension Kaluza-Klein scheme is also outlined. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Contents:

I Generalizing Special Relativity 1

1 An Axiomatic View to Special Relativity 3

1.1 Foundations of Special Relativity 3

1.2 The Principle of Solidarity 4

1.3 Locality and Interaction 5

1.3.1 Locality and Nonlocality 5

1.3.2 Potential and Nonpotential Interactions 6

2 Deformed Minkowski Space-Time 7

3 Description of Interactions by Energy-Dependent Metrics 11

3.1 Energy and the Finzi Principle 11

3.2 Energy as Dynamical Variable 13

II Relativity in a Deformed Space-Time 19

4 Generalized Principle of Relativity and Lorentz Transformations 21

4.1 Deformed Special Relativity 21

4.2 Deriving the Deformed Lorentz Transformations 21

4.3 Maximal Causal Speed Revisited 24

4.4 Boosts in DSR 27

4.4.1 Boost in a Generic Direction 27

4.4.2 Symmetrization of Deformed Boosts 30

4.4.3 Velocity Composition Law in M and the Invariant Maximal Speed 32

4.4.4 Choosing the Boost Direction in DSR 34

4.4.5 Appendix - Another Derivation of a Generic Boost 35

5 Relativistic Kinematics in a Deformed Minkowski Space 37

6 Wave Propagation in a Deformed Space-Time 41

6.1 Deformed Helmholtz Equation 41

6.2 Propagation in an Undersized Waveguide 42

6.3 Total Internal Reflection 44

6.4 Deformation Tensor 48

III Metric Description of Fundamental Interactions 51

7 Nonlocal Effects in Electromagnetic Interaction 53

7.1 Non-Minkowskian Metric for the E.M. Interaction 53

7.1.1 Photon Tunneling and Superluminal Velocities 53

7.1.2 Deformed E.M. Metric from the Cologne Experiment 55

7.2 An Application: Unified View to Cologne and Florence Experiments 59

7.2.1 Superluminal Propagation and the Friis Law 59

7.2.2 Two-Antenna System as a Barrier 64

8 Energy-Dependent Metric for Gravitation 67

8.1 Analysis of Experimental Data on Clock Rates 67

8.2 Local Metric of Gravitation 70

8.3 How Fast Do Travel Gravitational Effects? 72

8.4 Discussion of the Einstein versus Bohr Gedankenexperiment 73

8.5 Einstein and the Energy-Dependence of the Light Speed 75

9 Weak Interaction 77

10 Strong Interaction 81

10.1 The Bose-Einstein Correlation 81

10.2 DSR Treatment of BE Correlation 82

10.3 Deformed BE Correlation Function and the Strong Metric 85

10.4 Hadronic Time Deformation 89

10.5 A Geometric View to Confinement and Asymptotic Freedom 90

11 Metrics of Interactions 93

11.1 Review of Phenomenological Metrics 93

11.1.1 Energy-Dependent Phenomenological Metrics for the Four Interactions 93

11.1.2 Threshold Energies and Recursive Metrics 96

11.2 Asymptotic Metrics 97

IV Breakdown of Local Lorentz Invariance 101

12 Experimental Tests of Local Lorentz Invariance 103

13 A New Electromagnetic Test of LLI 107

13.1 Theoretical Foundations 107

13.2 Experimental Setup and Measurement Procedure 110

13.3 Experimental Results 112

13.3.1 First Experiment 112

13.3.2 Second Experiment 113

13.3.3 An Interpretation by DSR 116

13.4 LLI Violation Parameter 118

13.5 Appendix - Einstein and the Aether 123

14 The Gravitational Mass of Electron from Geometry 125

14.1 LLI Breaking Factor and Relativistic Energy in DSR 125

14.2 The Electron as a Fundamental Particle and its "Geometrical" Mass 127

15 Toward the Fifth Dimension 131

15.1 From LLI Breakdown to Energy as Fifth Dimension 131

15.2 Embedding of Deformed Minkowski Space in a Five-Dimensional Riemannian Space 132

15.3 Einstein's Equations in Vacuum 134.

Notes:

Includes bibliographical references (pages 137-140) and index.

ISBN:

9812387285

OCLC:

55044753