Uniformly Accelerating Charged Particles (eBook)

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