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1 A Doubt about the Equivalence Principle |
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1 | |
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2 From Minkowski Spacetime to General Relativity |
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5 | |
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2.1 Semi-Euclidean Coordinate Systems |
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5 | |
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2.2 The SE Metric for Uniform Acceleration Is the Only Static SE Metric |
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10 | |
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2.3 The Step to General Relativity |
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15 | |
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2.4 Weak Field Approximation |
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24 | |
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36 | |
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3 Gravity as a Force in Special Relativity |
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47 | |
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4 Applying the Strong Equivalence Principle |
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51 | |
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59 | |
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6 A More Detailed Radiation Calculation |
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67 | |
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7 Defining the Radiation from a Uniformly Accelerating Charge |
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71 | |
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8 Energy Conservation for a Uniformly Accelerated Charge |
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77 | |
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9 The Threat to the Equivalence Principle According to Fulton and Rohrlich |
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83 | |
10 Different Predictions of Special Relativity and General Relativity |
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89 | |
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10.1 Four Cases for Special Relativity |
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89 | |
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10.2 Four Cases for General Relativity |
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90 | |
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91 | |
11 Derivation of the Lorentz–Dirac Equation |
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93 | |
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11.1 Parrott's Derivation |
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93 | |
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101 | |
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104 | |
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11.4 Self-Force Calculation |
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105 | |
12 Extending the Lorentz–Dirac Equation to Curved Spacetime |
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107 | |
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12.1 Equation of Motion of a Charged Particle |
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107 | |
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12.2 The Equivalence Principle in All This |
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112 | |
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125 | |
13 Static Charge in a Static Spacetime |
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127 | |
14 A Radiation Detector |
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137 | |
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14.1 Equivalence Principle According to Mould |
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137 | |
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14.2 Construction of the Detector and Calculations in General Coordinates |
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144 | |
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14.3 Detecting Radiation Where There Is None |
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153 | |
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155 | |
15 The Definitive Mathematical Analysis |
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157 | |
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15.1 Static Gravitational Field |
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160 | |
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15.2 Relation with Minkowski Spacetime |
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163 | |
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15.3 What the Uniformly Accelerated Observer Sees |
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167 | |
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15.4 Coordinate Singularity in the SE Metric |
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172 | |
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15.5 Some Semi-Euclidean Geometry |
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174 | |
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15.6 Redshift in a Uniformly Accelerating SE Frame |
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179 | |
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15.7 Interpreting Semi-Euclidean Coordinates |
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186 | |
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188 | |
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15.9 Fields of a Uniformly Accelerated Charge |
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196 | |
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15.9.1 Obtaining the Vector Potential |
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196 | |
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15.9.2 Obtaining the Electromagnetic Fields |
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204 | |
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15.9.3 Electromagnetic Fields on the Null Surface z+ t = 0 |
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206 | |
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15.9.4 Fixing up the Fields on the Null Surface |
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212 | |
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15.10 Origin of the Delta Function in the Field |
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217 | |
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15.11 Conclusions Regarding the Fields |
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229 | |
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15.11.1 Fields in Region I |
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229 | |
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15.11.2 Fields Along Forward Light Cone of Point on Worldline |
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232 | |
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15.11.3 Equivalence of Advanced and Retarded Fields |
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234 | |
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15.11.4 Comparing Radiated and Coulomb Fields in Region I |
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236 | |
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15.11.5 Situation in Region II |
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241 | |
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15.12 Stress–Energy Tensor |
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245 | |
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15.12.1 Stress–Energy Tensor in Accelerating Frame |
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246 | |
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247 | |
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15.12.3 Boulware's Conclusion about Energy Flow |
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252 | |
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15.13 General Conclusions |
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252 | |
16 Interpretation of Physical Quantities in General Relativity |
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255 | |
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16.1 Definition of Energy |
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257 | |
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16.2 Lorentz Boost Killing Vector Field in Minkowski Spacetime |
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258 | |
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16.3 Killing Vector Field for Static Spacetime |
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261 | |
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16.4 Killing Vector Fields for Schwarzschild Spacetime |
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262 | |
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267 | |
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269 | |
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16.7 Rindler or Elevator Coordinates |
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270 | |
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16.8 The Problem with the Poynting Vector |
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274 | |
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16.9 Schwarzschild Spacetime Revisited |
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282 | |
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16.10 Antithesis of the Present View |
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284 | |
17 Charged Rocket |
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289 | |
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289 | |
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298 | |
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305 | |
18 Summary |
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307 | |
19 Conclusion |
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343 | |
References |
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349 | |
Index |
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351 | |