Relativity in curved spacetime : life without special relativity

394 pages, size: 234×156mm, Includes bibliographic references and index, and >200 figures and illustrations Publisher website: http://www.chocolatetreebooks.com Author's website: http://www.relativitybook.com This is the paperback version of "Relativity in Curved Spacetime", for the hardback version, see: ISBN 0955706823

Overview.. vi
Table of Contents. vii
Welcome. xiii
About the Author. xiv
Notes to the First Edition. xiv
Acknowledgements and Credits. xv
Abbreviations. xvi

PART I: BACKGROUND PHYSICS 1
1: The Speed of Light 3
1.1 : Light is pretty fast. 5
1.2 : Lightspeed varies. 6
1.3 : Lightspeed is not just the speed of light. 7
1.4 : Lightspeed affects inertia. 8
1.5 : Lightspeed controls timeflow.. 8
1.6 : Lightspeed is locally constant. 8
1.7 : Lightspeed is now defined as constant. 9
1.8 : The gravity well. 9
1.9 : Light travels in straight lines. Except when it doesn't. 11
1.10 : Light used to define a straight line. 12
2: Gravity, Energy and Mass 13
2.1 : What is mass?. 15
2.2 : Does light have mass?. 16
2.3 : Genie in a bottle: Thought-experiments with bottled light. 17
2.4 : Difficulty of detecting the effect. 19
2.5 : Mass-to-energy conversion. 20
2.6 : History of E=mc². 21
2.7 : Energy has mass, period. 22
3: Curved Space and Time. 23
3.1 : Gravity is … what, exactly?. 25
3.2 : Gravity bends light. 25
3.3 : Gravity warps geometry. 26
3.4 : Gravity as a variation in inertia. 28
3.5 : Energy-change in light due to gravity. 28
3.6 : Gravitational redshifts and blueshifts. 29
3.7 : Gravitational time dilation. 30
3.8 : Not just curved space, but curved spacetime. 32
4: Relativity. 33
4.1 : Relativity of space. 35
4.2 : Relativity of time. 35
4.3 : Relativity of velocity. 36
4.4 : Isaac Newton's "Principia". 37
4.5 : Mach and relativity. 38
4.6 : Practical advantages of "relativistic" arguments. 39
4.7 : Applying Occam's Razor. 39
4.8 : Different "Principles of Relativity". 40
4.9 : Causes of confusion. 41
4.10 : Relativity of acceleration. 42
4.11 : Relative acceleration vs. absolute acceleration. 43
4.12 : Relativity of rotation. 45
4.13 : "Centrifugal" and "Coriolis" fields. 45
4.14 : Rotational dragging. 47
4.15 : Experimental verification. 49
4.16 : Equivalence principles. 50
5: The Newtonian Catastrophe. 51
5.1 : Newton's unification scheme: 53
5.2 : The lightspeed mistake …... 54
5.3 : The "space-density" mistake. 54
5.4 : The light-energy mistake. 55
5.5 : Loss of wave-particle duality. 55
5.6 : Newton vs. Huyghens. 56
5.7 : The lightspeed trap. 57
5.8 : Consequences for physics. 59

PART II: EFFECTS due to RELATIVE MOTION 61
6: Doppler Shifts 63
6.1 : "Stationary observer" Doppler effect. 65
6.2 : "Stationary source" Doppler effect. 66
6.3 : Comparisons. 66
6.4 : Transverse Doppler effects (audio) 67
6.5 : Optical Doppler effects. 69
6.6 : Longitudinal Doppler effect under Special Relativity. 69
6.7 : Transverse Doppler effect under Special Relativity. 70
7: Apparent Length-Changes in Moving Objects. 71
7.1 : Apparent changes in length. 73
7.2 : Approaching objects appear elongated. 73
7.3 : Receding objects appear contracted. 73
7.4 : Degree of contraction or elongation. 74
7.5 : Special relativity and length-changes. 75
7.6 : Rulers and gravitation. 76
8: Aberration of Angles. 77
8.1 : Aberration of Angles. 79
8.2 : Relativistic aberration at 90 degrees. 80
8.3 : The Relativistic Ellipse. 81
8.4 : Putting it all together. 83
8.5 : Relativistic ellipse: Newtonian theory. 83
8.6 : Relativistic ellipse: Special relativity. 84
9: Moving bodies drag light 85
9.1 : Generality of dragging effects. 87
9.2 : Naming conventions: Gravitomagnetism, frame-dragging. 87
9.3 : Argument #1: Linear GM as a gravitational timelag effect. 87
9.4 : Argument #2: "Effective gravitational potential" depends on relative velocity. 88
9.5 : Argument #3: Gravitational smudging. 89
9.6 : Argument #4: The slingshot effect. 89
9.7 : Argument #5: Rotational GM and gravitational timelag. 90
9.8 : Argument #6: QM and "probabilistic" smudging. 91
9.9 : Argument #7: Experiment: The Fizeau effect. 91
9.10 : Inconsistencies in our approach to velocity. 92
9.11 : Cancellation and unification?. 94
9.12 : Implementation – the tilted gravity-well. 95
9.13 : Zeno revisited: the "impossibility" of motion. 96
9.14 : Worldlines and curvature. 97
9.15 : Uh-oh …... 98
9.16 : The score chart. 99
9.17 : "Relativistic" implementations of lightspeed constancy. 100

PART III: LIMITS TO OBSERVATION 101
10: Quantum Mechanics and Observability. 103
10.1 : The origin of quantum mechanics. 105
10.2 : Is quantum mechanics a theory?. 106
10.3 : The "Copenhagen" and "Hidden Variable" interpretations. 107
10.4 : The two-slit experiment. 108
10.5 : Quantum mechanics and everyday experience. 111
10.6 : Illusion and reality. 112
10.7 : Pair Production. 114
10.8 : Virtual particles. 114
10.9 : Pseudo- pair production. 115
11: Dark Stars and Black Holes 117
11.1 : John Michell's dark stars. 119
11.2 : Properties of a compact gravitational object. 120
11.3 : Escape velocity calculations and the gravitational horizon. 121
11.4 : Tidal forces. 121
11.5 : "Visiting" particles around a dark star. 122
11.6 : Dark stars and "acoustic" metrics. 123
11.7 : Acoustic metrics and nonlinearity. 124
11.8 : Black holes under GR1915. 125
11.9 : The Kerr black hole. 129
11.10 : The expansion problem.. 130
11.11 : The acceleration problem.. 130
11.12 : Black holes according to Quantum Mechanics. 131
11.13 : Hawking radiation. 132
11.14 : Pair-production and pseudo-pair-production. 133
11.15 : Attempts to eliminate the "dark star" explanation. 134
11.16 : Acoustic metrics, once again. 135
11.17 : "Acceleration radiation". 136
11.18 : The Black Hole Information Paradox. 137
11.19 : The BHIP and Microcausality. 138
11.20 : "Observerspace" arguments. 139
11.21 : The Membrane Paradigm.. 140
11.22 : Holographic arguments. 141
11.23 : The Holographic Principle in action. 142
11.24 : The "no-signal" problem.. 143
11.25 : The verdict. 144

PART IV: UPDATING STANDARD THEORY 145
12: What's wrong with General Relativity?. 147
12.1 : "Core" experimental tests of general relativity. 149
12.2 : Experimental significance. 152
12.3 : Incompatibility with quantum mechanics. 153
12.4 : Fudge factor?: The Cosmological Constant. 154
12.5 : Possible breaking of conservation laws. 155
12.6 : Possible incompatibility with Mach's principle. 155
12.7 : Fudge factor?: Galactic curves and Dark Matter. 156
12.8 : Arbitrary suspension of the Equivalence Principle. 157
12.9 : Invoking reduction to flat spacetime. 159
12.10 : Use of tailor-made definitions. 160
12.11 : Do cosmological horizons count as "acoustic"?. 163
12.12 : Doppler effects and the Black Hole Information Paradox. 164
12.13 : Grand unification?. 165
12.14 : Gravitomagnetic incompatibility?. 167
12.15 : Complexity. 168
12.16 : Is GR1915 scientifically falsifiable?. 169
12.17 : Blaming special relativity. 170
13: Horrible Nasty Mathematics. 171
13.1 : A family of relativistic theories. 173
13.2 : Selecting a reference theory. 174
13.3 : Defining the range. 174
13.4 : Ellipses. 175
13.5 : Special relativity as a special solution. 175
13.6 : Positive values of © and positive curvature. 176
13.7 : Rejecting negative solutions for ©.. 176
13.8 : Gravitomagnetism suggests positive ©.. 177
13.9 : Graphed Doppler responses. 177
13.10 : Setting "one" as a higher limit for ©.. 178
13.11 : Using the BHIP to set a minimum of "one" for ©.. 178
13.12 : Oops?. 179
13.13 : Preliminary conclusions. 180

PART V: Flat Spacetime and Special Relativity 181
14: Einstein's "special" theory of relativity. 183
14.1 : The birth of special relativity. 185
14.2 : Failure of earlier theories …... 185
14.3 : … "Draggable" aethers. 185
14.4 : … Absolute aether. 186
14.5 : Aether, either, neither neither. 187
14.6 : Lorentz Ether Theory (LET), ® 1904. 188
14.7 : Special relativity, 1905. 189
14.8 : Additional interpretational overhead. 190
14.9 : Minkowski Spacetime. 192
14.10 : Implications of Minkowski spacetime. 194
15: So, what's wrong with the special theory?. 195
15.1 : SR and Observerspace. 197
15.2 : Is the special theory "robust"?. 198
15.3 : Minkowski spacetime as an argument against SR.. 199
15.4 : The "stratification" problem.. 200
15.5 : Does SR "do" acceleration?. 201
15.6 : Extensibility. 203
15.7 : Cumulative redshift effects …... 203
15.8 : … Thermal redshifts. 205
15.9 : … Cosmological redshifts. 206
15.10 : Round-trip effects in general. 208
16: Experimental Evidence for Special Relativity.... 209
16.1 : Commonly-cited evidence for special relativity. 211
16.2 : … E=mc² 211
16.3 : "Classical Theory" vs. Special Relativity. 212
16.4 : … "Transverse" redshifts. 213
16.5 : … "Longitudinal" Doppler shifts. 214
16.6 : … The lightspeed upper limit in particle accelerators. 215
16.7 : The "searchlight" effect. 216
16.8 : Velocity-addition. 216
16.9 : Particle tracklengths. 216
16.10 : Muon showers. 217
16.11 … Particle storage rings and centrifugal time dilation. 218
16.12 : deSitter / Brecher disproof of simple emission theory. 219
16.13 : "Domain of applicability" issues. 220
16.14 : Conclusions. 222

PART VI: FUTURE PHYSICS 223
17: Cosmologies. 225
17.1 : The expanding universe. 227
17.2 : The "Big Bang". 227
17.3 : Spatial closure. 228
17.4 : Expansion curves. 231
17.5 : Cosmological time coordinates. 232
17.6 : The Hartle-Hawking "bubble universe". 234
17.7 : Entropy, arrows of time, and the Big Crunch. 235
17.8 : Extending the "bubble" model. 236
17.9 : Variable dimensionality?. 237
17.10 : "Mirror" and "kaleidoscope" universes. 237
17.11 : Oranges and raspberries. 239
17.12 : A few Multiverses. 240
17.13 : Fractal universe arguments. 243
17.14 : Why is the universe rational?. 246
17.15 : The Drake Equation. 248
17.16 : Before Event Zero. 249
18: Trouble with Wormholes. 251
18.1 : What is a wormhole?. 253
18.2 : "Spacetime surgery" and simple optics. 253
18.3 : Wormhole instability?. 254
18.4 : The distance problem.. 256
18.5 : The ageing problem.. 256
18.6 : The "antihorizon" problem.. 256
18.7 : "Anti-wormholes" and spatial reversal. 257
18.8 : The Kerr wormhole. 260
18.9 : The fieldline problem.. 261
18.10 : The gravity problem.. 261
18.11 : Wormhole politics. 262
18.12 : The time-connection problem.. 262
18.13 : Wormhole time travel?. 263
18.14 : Mistaken time machine behaviour. 264
18.15 : Quantum foam.. 265
18.16 : Scale-dependent topology. 266
18.17 : Pseudowormholes. 266
18.18 : Does quantum foam contain only pseudowormholes?. 268
18.19 : Do wormholes exist at all?. 268
19: Metric Engineering and Warp Drives 269
19.1 : "Space bungees" and regenerative braking. 271
19.2 : Boomeranging. 272
19.3 : Exotic-matter drives. 273
19.4 : The negative-field problem.. 274
19.5 : Ultrafast travel using simple gravity. 275
19.6 : The "cresting" problem.. 276
19.7 : The Krasnikov tube. 277
19.8 : Warpfield Hawking radiation?. 278
19.9 : The "acoustics" analogue. 279
19.10 : Simple warpfield generators. 281
19.11 : Toroidal configurations. 282
19.12 : Cancellation and non-cancellation. 283
19.13 : The 2-spin torus. 284
19.14 : Self-refraction and cross-refraction. 286
19.15 : General field-refraction issues. 287
19.16 : Momentum conversion. 288
19.17 : "Reactionless" drives and deferred momentum.. 289
19.18 : Can we build a working warp drive?. 289

PART VII: THE HUMAN FACTOR 291
20: Limitations of language and procedure. 293
20.1 : The order in which things are written. 295
20.2 : Lightspeed, velocity, and language traps. 295
20.3 : Fractured logic. 297
20.4 : Logic traps and logical black holes. 298
20.5 : More examples of circular thinking. 300
20.6 : Is consistency all it's cracked up to be?. 302
20.7 : "First answer" syndrome. 303
20.8 : Life, Death, and the Square Root of Two. 304
20.9 : The story of Pi 305
20.10 : Pi and global extinction. 307
20.11 : Naming rituals, binary logic and Giant Pandas. 308
20.12 : Intransitive logics. 309
20.13 : Complex logical spaces. 310
20.14 : Intransitive ordering and gravitation. 312
20.15 : "Certainty" parameters. 314
20.16 : Living with uncertainty. 315
20.17 : Conclusions. 316
21: The Perils of Experimentation 317
21.1 : Evaluating science neutrality. 319
21.2 : Perception filters. 321
21.3 : System bias and "v1.0" syndrome. 323
21.4 : Safety in numbers. 325
21.5 : Accident reporting. 326
21.6 : Quantum sociology?. 327
21.7 : Pattern Recognition and group decisionmaking. 328
21.8 : Market Forces. 331
21.9 : Physics nightmares. 333
22: Conclusions. 335
22.1 : SR-based or NM-based physics?. 337
22.2 : The fork in the road. 339
22.3 : Warning signs. 339
22.4 : Mathematical "truth" vs. relevance 344
22.5 : Alternative alternatives. 346
22.6 : Life after special relativity. 346

PART VIII: Calculations, References and Index 347
Calculations 1 : Doppler shifts. 348
Calculations 2 : E=mc² from Newtonian mechanics. 350
Calculations 3 : Non-SR transverse Doppler effect / "Aberration redshift". 352
Calculations 4 : The "Box of Frogs" depiction of classical Hawking radiation. 354
Calculations 5 : Comparison table. 357
Major Players. 358
Topic References. 359
General References: 365
Index 371