Preamble |
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vii | |
Contents |
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xi | |
Guide to contents |
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xvii | |
Many reasons to write this book |
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xix | |
Special relativity matters |
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xxiii | |
Acceleration frontier of physics |
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xxiv | |
Frequently used abbreviations |
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xxv | |
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Part I Space-Time, Light and the Æther |
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3 | (18) |
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1.1 Time, a new 4th coordinate |
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3 | (4) |
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1.2 Measuring space and time |
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7 | (2) |
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1.3 Speed of light and the æther |
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9 | (12) |
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2 The Michelson-Morley Experiment |
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21 | (8) |
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2.1 Earth's motion and the æther |
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21 | (2) |
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2.2 Principle of relativity |
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23 | (4) |
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2.3 Cosmic microwave background frame of reference |
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27 | (2) |
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3 Material Bodies in Special Relativity |
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29 | (18) |
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3.1 Time dilation, body contraction |
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29 | (2) |
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3.2 Reality of the Lorentz-FitzGerald body contraction |
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31 | (8) |
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3.3 Path towards Lorentz coordinate transformations |
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39 | (2) |
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3.4 Highlights: how did relativity `happen'? |
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41 | (6) |
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Part II Time Dilation, and Lorentz-Fitzgerald Body Contraction |
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47 | (14) |
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4.1 Proper time of a traveler |
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47 | (4) |
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4.2 Relativistic light-clock |
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51 | (10) |
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5 The Lorentz-FitzGerald Body Contraction |
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61 | (14) |
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5.1 Universality of time measurement |
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61 | (1) |
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62 | (1) |
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63 | (12) |
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Part III The Lorentz Transformation |
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6 Relativistic Coordinate Transformation |
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75 | (14) |
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6.1 Derivation of the form of the Lorentz coordinate transformation |
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75 | (5) |
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6.2 Explicit form of the Lorentz coordinate transformation |
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80 | (5) |
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6.3 The nonrelativistic Galilean limit |
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85 | (1) |
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6.4 The inverse Lorentz coordinate transformation |
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86 | (3) |
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7 Properties of the Lorentz Coordinate Transformation |
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89 | (28) |
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7.1 Relativistic addition of velocities |
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89 | (9) |
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98 | (6) |
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7.3 Invariance of proper time |
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104 | (2) |
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7.4 Two Lorentz coordinate transformations in sequence |
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106 | (2) |
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108 | (9) |
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8 Body Properties and Lorentz Coordinate Transformations |
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117 | (4) |
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8.1 Graphic representation of LT |
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117 | (2) |
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8.2 Simultaneity and time dilation |
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119 | (2) |
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9 Different Methods of Measuring Spatial Separation |
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121 | (12) |
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9.1 Spatial separation measurement with the signal synchronized in the rest-frame of the observer S |
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122 | (1) |
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9.2 Spatial separation measurement with the signal synchronized in the rest-frame of a body So |
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123 | (2) |
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9.3 Spatial separation measurement due to illumination with light emitted in the rest-frame of the observer |
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125 | (3) |
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9.4 Train in the tunnel: is the tunnel contracted? |
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128 | (5) |
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133 | (10) |
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10.1 Rockets connected by a thread |
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133 | (3) |
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136 | (1) |
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10.3 Lorentz-FitzGerald body contraction measured |
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136 | (7) |
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143 | (6) |
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143 | (3) |
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146 | (3) |
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149 | (22) |
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12.1 Timelike and spacelike event separation |
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149 | (6) |
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12.2 Essay: Quantum entanglement and causality |
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155 | (5) |
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12.3 Time dilation revisited |
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160 | (3) |
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12.4 Spaceship travel in the Milky Way |
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163 | (8) |
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171 | (12) |
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13.1 Introducing SR-Doppler shift |
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171 | (4) |
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13.2 Determination of SR-Doppler shift |
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175 | (8) |
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Part VI Mass, Energy, Momentum |
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183 | (8) |
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183 | (3) |
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14.2 Relativistic energy of a moving body |
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186 | (1) |
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187 | (4) |
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191 | (12) |
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15.1 Relation between energy and momentum |
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191 | (5) |
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196 | (7) |
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16 Generalized Mass-Energy Equivalence |
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203 | (12) |
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16.1 Where is energy coming from? |
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203 | (2) |
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16.2 Mass equivalence for kinetic energy in a gas |
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205 | (1) |
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16.3 Potential energy mass equivalence |
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206 | (2) |
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208 | (1) |
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16.5 Rotational energy mass equivalence |
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208 | (2) |
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16.6 Chemical energy mass defect |
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210 | (1) |
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211 | (2) |
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213 | (2) |
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17 Tests of Special Relativity |
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215 | (14) |
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17.1 Direct tests of special relativity |
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215 | (4) |
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17.2 The Michelson-Morley experiment today |
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219 | (1) |
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17.3 Tests of Lorentz coordinate transformation |
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220 | (3) |
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223 | (6) |
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Part VII Collisions, Decays |
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18 A Preferred Frame of Reference |
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229 | (14) |
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18.1 The center of momentum frame (CM-frame) |
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229 | (2) |
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18.2 The LT to the CM-frame |
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231 | (3) |
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18.3 Decay of a body in the CM-frame |
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234 | (3) |
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18.4 Decay energy balance in CM-frame |
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237 | (1) |
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18.5 Decay of a body in flight |
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237 | (6) |
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243 | (32) |
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19.1 Elastic two-body reactions |
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243 | (2) |
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245 | (4) |
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19.3 Elastic bounce from a moving wall |
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249 | (4) |
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19.4 Inelastic two-body reaction threshold |
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253 | (4) |
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19.5 Energy available in a collision |
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257 | (5) |
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19.6 Inelastic collision and particle production |
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262 | (4) |
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19.7 Relativistic rocket equation |
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266 | (9) |
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Part VIII 4-Vectors and 4-Force |
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20 4-Vectors in Minkowski Space |
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275 | (16) |
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20.1 Lorentz invariants and covariant equations |
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275 | (1) |
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20.2 The `position' 4-vector |
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276 | (1) |
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20.3 Metric in Minkowski space |
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277 | (3) |
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20.4 Lorentz boosts as generalized rotation |
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280 | (4) |
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284 | (2) |
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20.6 Finding new 4-vectors and invariants |
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286 | (5) |
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21 4-Velocity and 4-Momentum |
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291 | (12) |
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291 | (4) |
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21.2 Energy-momentum 4-vector |
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295 | (1) |
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21.3 Properties of Mandelstam variables |
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296 | (7) |
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22 Acceleration and Relativistic Mechanics |
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303 | (14) |
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303 | (2) |
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22.2 Definition of 4-acceleration |
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305 | (3) |
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22.3 Relativistic form of Newton's 2nd Law |
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308 | (3) |
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22.4 The 4-force and work-energy theorem |
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311 | (6) |
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Part IX Motion of Charged Particles |
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317 | (26) |
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23.1 Motion in magnetic and electric fields |
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317 | (8) |
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23.2 EM-potentials and homogeneous Maxwell equations |
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325 | (4) |
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23.3 The Lorentz force: from fields to potentials |
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329 | (1) |
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23.4 Lorentz force from variational principle |
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330 | (13) |
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24 Electrons Riding a Plane Wave |
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343 | (18) |
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24.1 Fields and potentials for a plane wave |
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343 | (4) |
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24.2 Role of conservation laws |
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347 | (5) |
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24.3 Surfing the plane wave |
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352 | (9) |
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Part X Covariant Force and Field |
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25 Covariant Formulation of EM-Force |
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361 | (16) |
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25.1 Lorentz force in terms of 4-potential |
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361 | (5) |
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25.2 Covariant variation-principle |
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366 | (8) |
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25.3 Covariant Hamiltonian for action principle |
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374 | (3) |
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26 Covariant Fields and Invariants |
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377 | (22) |
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26.1 EM-fields: relativistic form |
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377 | (2) |
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26.2 LT of electromagnetic fields and field invariants |
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379 | (5) |
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26.3 Constraints on field invariants |
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384 | (2) |
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26.4 Covariant form of the Lorentz force in terms of fields |
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386 | (4) |
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390 | (9) |
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Part XI Dynamics of Fields and Particles |
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27 Variational Principle for EM-Fields |
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399 | (24) |
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27.1 Maxwell equations with sources |
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399 | (7) |
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27.2 Covariant gauge condition |
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406 | (6) |
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27.3 Homogeneous Maxwell equations |
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412 | (6) |
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27.4 Energy, momentum and mass of the EM-field |
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418 | (5) |
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423 | (14) |
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28.1 Field energy-momentum dynamics |
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423 | (4) |
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28.2 Mass of the electric field |
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427 | (5) |
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28.3 Limiting field/force electromagnetism |
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432 | (5) |
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29 Afterword: Acceleration |
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437 | (24) |
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29.1 Can there be acceleration in SR? |
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437 | (1) |
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29.2 Evidence for acceleration |
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438 | (3) |
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441 | (5) |
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29.4 EM radiation from an accelerated particle |
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446 | (3) |
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29.5 EM radiation reaction force |
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449 | (3) |
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29.6 Landau-Lifshitz radiation force model |
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452 | (4) |
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29.7 Caldirola radiation reaction model |
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456 | (1) |
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29.8 Unsolved radiation reaction |
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457 | (4) |
Index |
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461 | |