Relativity in curved spacetime : life without special relativity

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

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