Lyle Uniformly Accelerating Charged Particles

A Threat to the Equivalence Principle
1. Auflage 2008
ISBN: 978-3-540-68477-0
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 158, 361 Seiten

Reihe: Fundamental Theories of Physics

This book examines the problems with the LD equation in flat spacetime and details its extension to curved spacetime. It compares different equivalence principles as well as vindicates some.

www.stephenlyle.org

Autoren/Hrsg.

Lyle, Stephen

Inhaltsverzeichnis

1;Preface;7
2;Contents;11
3;Acronyms;14
4;A Doubt about the Equivalence Principle;15
5;From Minkowski Spacetime to General Relativity;19
5.1;2.1 Semi-Euclidean Coordinate Systems;19
5.2;2.2 The SE Metric for Uniform Acceleration Is the Only Static SE Metric;24
5.3;2.3 The Step to General Relativity;29
5.4;2.4 Weak Field Approximation;38
5.5;2.5 Geodesic Principle;50
6;Gravity as a Force in Special Relativity;61
7;Applying the Strong Equivalence Principle;64
8;The Debate Continues;71
9;A More Detailed Radiation Calculation;78
10;Defining the Radiation from a Uniformly Accelerating Charge;82
11;Energy Conservation for a Uniformly Accelerated Charge;87
12;The Threat to the Equivalence Principle According to Fulton and Rohrlich;93
13;Different Predictions of Special Relativity and General Relativity;98
13.1;10.1 Four Cases for Special Relativity;98
13.2;10.2 Four Cases for General Relativity;99
13.3;10.3 Conclusion;100
14;Derivation of the Lorentz–Dirac Equation;102
14.1;11.1 Parrott’s Derivation;102
14.2;11.2 Dirac’s Derivation;110
14.3;11.3 Conclusion;113
14.4;11.4 Self-Force Calculation;114
15;Extending the Lorentz–Dirac Equation to Curved Spacetime;116
15.1;12.1 Equation of Motion of a Charged Particle;116
15.2;12.2 The Equivalence Principle in All This;121
15.3;12.3 Conclusions;134
16;Static Charge in a Static Spacetime;136
17;A Radiation Detector;146
17.1;14.1 Equivalence Principle According to Mould;146
17.2;14.2 Construction of the Detector and Calculations in General Coordinates;153
17.3;14.3 Detecting Radiation Where There Is None;162
17.4;14.4 Conclusion;164
18;The Definitive Mathematical Analysis;166
18.1;15.1 Static Gravitational Field;169
18.2;15.2 Relation with Minkowski Spacetime;172
18.3;15.3 What the Uniformly Accelerated Observer Sees;176
18.4;15.4 Coordinate Singularity in the SE Metric;181
18.5;15.5 Some Semi-Euclidean Geometry;183
18.6;15.6 Redshift in a Uniformly Accelerating SE Frame;188
18.7;15.7 Interpreting Semi-Euclidean Coordinates;195
18.8;15.8 Accelerations;197
18.9;15.9 Fields of a Uniformly Accelerated Charge;205
18.9.1;15.9.1 Obtaining the Vector Potential;205
18.9.2;15.9.2 Obtaining the Electromagnetic Fields;213
18.9.3;15.9.3 Electromagnetic Fields on the Null Surface z + t = 0;215
18.9.4;15.9.4 Fixing up the Fields on the Null Surface;221
18.10;15.10 Origin of the Delta Function in the Field;226
18.11;15.11 Conclusions Regarding the Fields;238
18.11.1;15.11.1 Fields in Region I;238
18.11.2;15.11.2 Fields Along Forward Light Cone of Point on Worldline;241
18.11.3;15.11.3 Equivalence of Advanced and Retarded Fields;243
18.11.4;15.11.4 Comparing Radiated and Coulomb Fields in Region I;245
18.11.5;15.11.5 Situation in Region II;250
18.12;15.12 Stress–Energy Tensor;254
18.12.1;15.12.1 Stress–Energy Tensor in Accelerating Frame;255
18.12.2;15.12.2 Energy Flux;256
18.12.3;15.12.3 Boulware’s Conclusion about Energy Flow;261
18.13;15.13 General Conclusions;261
19;Interpretation of Physical Quantities in General Relativity;264
19.1;16.1 Definition of Energy;266
19.2;16.2 Lorentz Boost Killing Vector Field in Minkowski Spacetime;267
19.3;16.3 Killing Vector Field for Static Spacetime;270
19.4;16.4 Killing Vector Fields for Schwarzschild Spacetime;271
19.5;16.5 Another Metric;276
19.6;16.6 And Another Metric;278
19.7;16.7 Rindler or Elevator Coordinates;279
19.8;16.8 The Problem with the Poynting Vector;283
19.9;16.9 Schwarzschild Spacetime Revisited;291
19.10;16.10 Antithesis of the Present View;293
20;Charged Rocket;298
20.1;17.1 Preamble;298
20.2;17.2 Calculation;307
20.3;17.3 Conclusion;314
21;Summary;316
22;Conclusion;351
23;References;356
24;Index;358