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Uniformly Accelerating Charged Particles: A Threat to the Equivalence Principle 2008 ed. [Kõva köide]

  • Formaat: Hardback, 361 pages, kõrgus x laius: 235x155 mm, kaal: 735 g, XV, 361 p., 1 Hardback
  • Sari: Fundamental Theories of Physics 158
  • Ilmumisaeg: 10-Jul-2008
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540684697
  • ISBN-13: 9783540684695
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  • Formaat: Hardback, 361 pages, kõrgus x laius: 235x155 mm, kaal: 735 g, XV, 361 p., 1 Hardback
  • Sari: Fundamental Theories of Physics 158
  • Ilmumisaeg: 10-Jul-2008
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540684697
  • ISBN-13: 9783540684695
Teised raamatud teemal:
Back in1954,a paper[ 2] by Bondi and Gold was to pick upona much olderqu- tion and raise anew one that would trigger another longdebate. The old question hadbeenaroundsince the beginning of the twentiethcentury, whenBorn rstraised it[ 1] and others followed suit. This was the question of whethera uniformly acc- erated charge (in at spacetime) would radiateelectromagnetic energy. The new question arose from the claim by Bondi and Gold that (inthe contextof general relativity now)a static charge ina static gravitational ?eld cannot radiateenergy. If this were the case,thenaparticular version of the equivalence principle would thereby be contradicted. This book reviews the problem discovered by Bondi and Gold and discusses the ensuingdebate ascarried on by Fulton and Rohrlich [ 3], DeWitt and Brehme [ 4], Mould [ 5], Boulware [ 6], andParrott [ 7].Various solutionshave been proposed by the above (and otherswhoare not discussed here). One of the aims here will be to putforward arather different solution to Bondi and Gold's radiation problem. So eventhough the paperscited are discussed to a large extent in chronological order, the reason for writing this is not justto produce an historical reference. Andeven though the version of general relativity applied hereis entirely consensual, every one of these papersis criticised on at leastoneimportant count, soI suspectthat the resultas a whole should not be described asconsensual.
1 A Doubt about the Equivalence Principle
1
2 From Minkowski Spacetime to General Relativity
5
2.1 Semi-Euclidean Coordinate Systems
5
2.2 The SE Metric for Uniform Acceleration Is the Only Static SE Metric
10
2.3 The Step to General Relativity
15
2.4 Weak Field Approximation
24
2.5 Geodesic Principle
36
3 Gravity as a Force in Special Relativity
47
4 Applying the Strong Equivalence Principle
51
5 The Debate Continues
59
6 A More Detailed Radiation Calculation
67
7 Defining the Radiation from a Uniformly Accelerating Charge
71
8 Energy Conservation for a Uniformly Accelerated Charge
77
9 The Threat to the Equivalence Principle According to Fulton and Rohrlich
83
10 Different Predictions of Special Relativity and General Relativity 89
10.1 Four Cases for Special Relativity
89
10.2 Four Cases for General Relativity
90
10.3 Conclusion
91
11 Derivation of the Lorentz–Dirac Equation 93
11.1 Parrott's Derivation
93
11.2 Dirac's Derivation
101
11.3 Conclusion
104
11.4 Self-Force Calculation
105
12 Extending the Lorentz–Dirac Equation to Curved Spacetime 107
12.1 Equation of Motion of a Charged Particle
107
12.2 The Equivalence Principle in All This
112
12.3 Conclusions
125
13 Static Charge in a Static Spacetime 127
14 A Radiation Detector 137
14.1 Equivalence Principle According to Mould
137
14.2 Construction of the Detector and Calculations in General Coordinates
144
14.3 Detecting Radiation Where There Is None
153
14.4 Conclusion
155
15 The Definitive Mathematical Analysis 157
15.1 Static Gravitational Field
160
15.2 Relation with Minkowski Spacetime
163
15.3 What the Uniformly Accelerated Observer Sees
167
15.4 Coordinate Singularity in the SE Metric
172
15.5 Some Semi-Euclidean Geometry
174
15.6 Redshift in a Uniformly Accelerating SE Frame
179
15.7 Interpreting Semi-Euclidean Coordinates
186
15.8 Accelerations
188
15.9 Fields of a Uniformly Accelerated Charge
196
15.9.1 Obtaining the Vector Potential
196
15.9.2 Obtaining the Electromagnetic Fields
204
15.9.3 Electromagnetic Fields on the Null Surface z+ t = 0
206
15.9.4 Fixing up the Fields on the Null Surface
212
15.10 Origin of the Delta Function in the Field
217
15.11 Conclusions Regarding the Fields
229
15.11.1 Fields in Region I
229
15.11.2 Fields Along Forward Light Cone of Point on Worldline
232
15.11.3 Equivalence of Advanced and Retarded Fields
234
15.11.4 Comparing Radiated and Coulomb Fields in Region I
236
15.11.5 Situation in Region II
241
15.12 Stress–Energy Tensor
245
15.12.1 Stress–Energy Tensor in Accelerating Frame
246
15.12.2 Energy Flux
247
15.12.3 Boulware's Conclusion about Energy Flow
252
15.13 General Conclusions
252
16 Interpretation of Physical Quantities in General Relativity 255
16.1 Definition of Energy
257
16.2 Lorentz Boost Killing Vector Field in Minkowski Spacetime
258
16.3 Killing Vector Field for Static Spacetime
261
16.4 Killing Vector Fields for Schwarzschild Spacetime
262
16.5 Another Metric
267
16.6 And Another Metric
269
16.7 Rindler or Elevator Coordinates
270
16.8 The Problem with the Poynting Vector
274
16.9 Schwarzschild Spacetime Revisited
282
16.10 Antithesis of the Present View
284
17 Charged Rocket 289
17.1 Preamble
289
17.2 Calculation
298
17.3 Conclusion
305
18 Summary 307
19 Conclusion 343
References 349
Index 351
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