Time, the physical magnitude

목차 (Table of Contents)

• CONTENTS
• EDITORIAL PREFACE = xvii
• PREFACE = xix
• ACKNOWLEDGEMENTS = xxiii
• PART 1 GENERALITIES
• 1.1. INTRODUCTORY REMARKS = 3
• 1.1.1. Modelism or formalism? = 3
• 1.1.2. Paradox and paradigm = 4
• 1.1.3. Utility of dimensional analysis. Universal constants = 5
• 1.1.4. 'Very large' and 'very small' universal constants = 7
• 1.1.5. Today's scientific humanism = 8
• 1.1.6. Epistemology as understood in this book = 9
• PART 2 LAWLIKE EQUIVALENCE BETWEEN TIME AND SPACE
• 2.1. MORE THAN TWO MILLENNIA OF EUCLIDEAN GEOMETRY = 13
• 2.1.1. 'Euclidean theory of space' = 13
• 2.1.2. 'Is it false that overnight everything has doubled in size?' = 14
• 2.1.3. Absolute time and classical kinematics = 15
• 2.1.4. The classical 'principle of relative motion' = 15
• 2.2. THE THREE CENTURIES OF NEWTONIAN MECHANICS : UNIVERSAL TIME AND ABSOLUTE SPACE = 17
• 2.2.1. Remarkable aphorisms by Aristotle = 17
• 2.2.2. Kepler （1571―1630） and Galileo （1564―1642） ： celestial and terrestrial mechanics = 18
• 2.2.3. The universal Galileo ― Newtonian law F ＝ m$$\ddot r$$ = 20
• 2.2.4. 'Greatness and servitude' of classical mechanics = 22
• 2.2.5. Gravitation = 25
• 2.2.6. Symplectic manifolds and analytical mechanics = 26
• 2.3 THREE CENTURIES OF KINEMATICAL OPTICS = 28
• 2.3.1 Fermat （1601―1665） and Huygens （1629―1695） = 28
• 2.3.2 Roemer （1976） and Bradley （1728） ： the two first measurements of the velocity of light = 30
• 2.3.3 Could Bradley's discovery allow a formulation of the relativity theory? = 31
• 2.3.4 A corollary to Bradley's aberration ： photography of a fastly moving object = 32
• 2.3.5 Arago's 1818 experiment and Fresnel's very far reaching 'ether drag' formula = 34
• 2.3.6 'Normal science' in optics throughout the 19th Century = 35
• 2.3.7 In electromagnetism also there was a dormant relativity problem = 40
• 2.3.8 Unexpected end of the hunting of the snark = 41
• 2.4 TODAY'S NEC PLUS ULTRA OF METROLOGY AND CHRONOMETRY ： 'EQUIVALENCE' OF SPACE AND TIME = 42
• 2.4.1 Fundamental significance of the Michelson ― Morley type of experiment = 42
• 2.4.2 Optical metrology = 43
• 2.4.3 Microwave chronometry = 43
• 2.4.4 Measurements of the velocity of light = 44
• 2.4.5 Imminent fulfilment of the old Aristotelian dream = 46
• 2.4.6 Wonders of laser physics ： the 1978 Brillet and Hall 'repetition' of the Michelson experiment = 46
• 2.4.7 Wonders of laser physics ： metrology via Doppler free spectroscopy = 47
• 2.4.8 October 1983 ： The speed of light as supreme 'motion referee', and the new immaterial length standard = 48
• 2.4.9 Wonders of laser spectroscopy ： chronometry via optical heterodyning = 50
• 2.4.10 Mossbauer effect （Heidelberg, 1957） = 51
• 2.4.11 Applied metrology, tachymetry and chronometry = 51
• 2.5 ENTERING THE FOUR―DIMENSIONAL SPACETIME PARADIGM = 53
• 2.5.1 Walking through the entrance gate = 53
• 2.5.2 Playing with hyperbolic trigonometry = 55
• 2.5.3. On the general Lorentz ― Poincar$$\acute e$$ ― Minkowski transformation = 58
• 2.5.4. On the Galileo ― Newton paradigm as a limit of the Poincar$$acute e$$ ― Minkowski one = 59
• 2.5.5. Fresnel's ether drag law as a velocity composition formula = 60
• 2.5.6. Terrell's relativistic photography revisited = 61
• 2.5.7. Time dilatation and the 'twins paradox' = 61
• 2.5.8. The Harress （1912） and Sagnac （1913） effects = 64
• 2.5.9. The problem of accelerating a solid body = 65
• 2.5.10. Kinematics identified with vacuum optics. The restricted relativity principle as a kinematical principle = 65
• 2.6. THE MAGIC OF SPACETIME GEOMETRY = 67
• 2.6.1. Introduction = 67
• 2.6.2. Invariant phase and 4―frequency vector = 69
• 2.6.3. The 4―velocity concept = 70
• 2.6.4. Integration and differentiation in spacetime = 70
• 2.6.5. Invariant or scalar volume element carried by a fluid = 73
• 2.6.6. The Green― and Stokes―like integration transformation formulas = 74
• 2.6.7. Relativistic electromagnetism and electrodynamics = 74
• 2.6.8. Entering relativistic dynamics = 77
• 2.6.9. Fluid moved by a scalar pressure ： a quick look at relativistic thermodynamics = 79
• 2.6.10. Dynamics of a point particle = 81
• 2.6.11. Isomorphism between the classical statics of filaments and the relativistic dynamics of spinning―point particles = 82
• 2.6.12. Barycenter and 6―component angular momentum around the barycenter. The relativistic 'general theorems' = 83
• 2.6.13. Analytical dynamics of an electrically charged point particle = 85
• 2.6.14. Wheeler ― Feynman electrodynamics = 86
• 2.6.15. De Broglie's wave mechanics = 90
• 2.6.16. What was so special with light, after all? = 93
• 2.6.17 Concluding this chapter, and the Second part of the book = 94
• PART 3 LAWLIKE TIME SYMMETRY AND FACTLIKE IRREVERSIBILITY
• 3.1 OVERVIEW = 97
• 3.1.1 Old wisdom and deeper insights = 97
• 3.1.2 Mathematization of gambling = 99
• 3.1.3 Probability as data dependent = 101
• 3.1.3 The Shannon ― Jaynes principle of entropy maximization, or 'maxent' = 102
• 3.1.5 'How subjective is entropy?' = 103
• 3.1.6 Loschmidt―Iike and Zermelo―like behavior in card shuffling = 106
• 3.1.7 Laplace, the first, and profound theorist of lawlike reversibility and factlike irreversibility = 107
• 3.1.8 Timeless causality and timeless probability = 108
• 3.1.9 Factlike irreversibility according to Laplace, Boltzmann and Gibbs = 108
• 3.1.10 Lawlike reversibility = 109
• 3.1.11 Matrix conceptualization of conditional or transition probabilities = 111
• 3.1.12 Laplacean reversal and time reversal = 112
• 3.1.13 Markov chains in general = 112
• 3.1.14 Factlike irreversibility as blind statistical retrodiction forbidden = 113
• 3.1.15 Causality identified with conditional or transition probability = 114
• 3.1.16 Concluding the chapter ： a spacetime covariant, arrowless calculus of probability = 114
• 3.1.17 Appendix ： Comparison between my thesis and those of other authors having discussed the fundamentals of irreversibility = 116
• 3.2 PHENOMENOLOGICAL IRREVERSIBILITY = 119
• 3.2.1 Classical thermodynamics = 119
• 3.2.2 Factlike thermodynamical irreversibility and its relevance to causality and information = 120
• 3.2.3 Entropy increase and wave retardation = 121
• 3.2.4 Light waves = 122
• 3.2.5. Waves and information theory = 124
• 3.2.6. Lawlike time symmetry and factlike time asymmetry in the Wheeler ― Feynman electrodynamics = 124
• 3.2.7. Thermal equilibrium radiation = 126
• 3.2.8. Irreversibility and the cosmological cool oven = 127
• 3.3. RETARDED CAUSALITY AS A STATISTICAL CONCEPT. ARROWLESS MICROCAUSALITY = 129
• 3.3.1. Poincare's discussion of the little planets' ring = 129
• 3.3.2. Boltzmann, Gibbs and thermodynamical entropies = 130
• 3.3.3. Loschmidt's objection and Boltzmann's first inappropriate answer. Recurrence of this sort of paralogism = 132
• 3.3.4. Retarded causality as identical to probability increase. Causality as arrowless at the microlevel = 134
• 3.3.5. Retarded causality and registration = 136
• 3.3.6. Zermelo's recurrence objection, and the phenomenon of spin echoes = 137
• 3.3.7. Other instances of lawlike symmetry and factlike asymmetry between blind statistical prediction and retrodiction = 138
• 3.3.8. Statistical mechanics ： from Maxwell's three―dimensional billiard―balls game to Shannon's information concept = 139
• 3.3.9. Boltzmann's second thoughts concerning the Loschmidt objection = 140
• 3.4. IRREVERSIBILITY AS A COSMIC PHENOMENON = 142
• 3.4.1. Liminal advice = 142
• 3.4.2. Branch systems. The 'statistical Big Bang' = 142
• 3.4.3. Unusual statistics of self―gravitating systems = 144
• 3.4.4. Loschmidt―Iike behavior of the Universe ： Big Bang and time reversal = 145
• 3.4.5. The Olbers paradox = 147
• 3.4.6. The 2.7°K cosmological radiation = 148
• 3.4.7. Building order by feeding on the universal negentropy cascade = 148
• 3.4.8. Concluding the chapter = 149
• 3.5. LAWLIKE REVERSIBILITY AND FACTLIKE IRREVERSIBILITY IN THE NEGENTROPY―INFORMATION TRANSITION = 150
• 3.5.1 Preliminary considerations = 150
• 3.5.2 Is the subconscious mind time―extended, as matter is? = 154
• 3.5.3 Lawlike reversibility between negentropy and information = 155
• 3.5.4 'Seeing in the future and acting in the past' = 158
• 3.5.5. A proposed experiment in psychokinesis = 160
• 3.5.6. Concluding the chapter, and Part 3 of the book = 162
• PART 4 RELATIVISTIC QUANTUM MECHANICS AND THE PROBLEM OF BECOMING
• 4.1. OVERVIEW = 167
• 4.1.1. Quantum theory as the child of wave physics and of a probability calculus = 167
• 4.1.2. Macrorelativity and microrelativity, Lorentz―and―CPT invariance = 169
• 4.1.3. 'Correspondence' between the classical and the quantal, wavelike, probability calculus = 172
• 4.1.4. Topological invariance of Land$$\acute e$$ chains and of Feynman graphs ： Wheeler's smoky dragon ： EPR correlations = 174
• 4.1.5. Covariant Fourier analysis and the second―order Klein ― Gordon equation = 177
• 4.1.6. Covariant Fourier analysis and the first―order spinningwave equations = 180
• 4.1.7. Particle in an external field = 182
• 4.1.8. Concluding the chapter ： quantum and relativity theories as daughters of wave physics = 183
• 4.2. 1900―1925 ： THE QUANTUM SPRINGS OUT, AND SPREADS = 185
• 4.2.1. 1900 ： Max Planck discovers the quantum of action = 185
• 4.2.2. Einstein's numerous contributions to the quantum theory ： statistics, and the photon = 188
• 4.2.3. The hydrogen atom of Bohr （1913） and Sommerfeld （1916） = 190
• 4.2.4. The 'Old Testament' of the quantum theory and Sommerfeld's bible. Correspondence Principle. Two new ideas in 1925 = 192
• 4.2.5. Bose ― Einstein and Fermi ― Dirac statistics = 193
• 4.2.6. De Broglie's matter waves = 194
• 4.2.7. Retrospective outlook = 195
• 4.3. 1925―1927 ： THE DAWN OF QUANTUM MECHANICS WITH A SHADOW ： RELATIVISTIC COVARIANCE LOST = 196
• 4.3.1. Liminal advice = 196
• 4.3.2. 1925 ： Heisenberg starts the game of quantum mechanics = 196
• 4.3.3. 1926―1927 ： Born and Jordan formalize quantum mechanics as a matrix mechanics = 197
• 4.3.4. 1925 ： Dirac and the Poisson brackets = 198
• 4.3.5. 1926 ： Schr$$\ddot o$$dinger formalizes quantum mechanics as a wave mechanics = 198
• 4.3.6. 1926 ： Mathematical 'equivalence' between Heisenberg's and Schr$$\ddot o$$dinger's theories = 200
• 4.3.7. 1926 ： Born introduces, and Jordan formalizes, a radically new 'wavelike probability calculus' = 202
• 4.3.8. Non―commuting position and momentum operators, and Heisenberg's uncertainty relations = 202
• 4.3.9. Non―commuting angular momentum operators = 204
• 4.3.10. 1929 ： Robertson's formalization of the uncertainty relations = 205
• 4.3.11. 1929 ： Heisenberg's microscope thought experiment and statistical retrodiction. 1931 ： Von Weisz$$\ddot a$$cker's modified use of it and retroaction = 206
• 4.3.12. On the time ― energy uncertainty relation in nonrelativistic quantum mechanics = 207
• 4.3.13. The Hilgevoord ― Uffink conception of the position―momentum and time ― energy uncertainties = 209
• 4.3.14. Nonrelativistic quantum mechanics of many particles = 210
• 4.3.15. Ennuple quantal correlations ： general formalism = 212
• 4.3.16. The Schr$$\ddot o$$dinger, Heisenberg and interaction representations = 213
• 4.3.17. Nonrelativistic perturbation theory = 214
• 4.3.18. 'Transformation theory' ； Dirac, 1926 ： Jordan, 1927 = 215
• 4.3.19. 'Grandeur and Servitude' of the Hamiltonian formalism = 218
• 4.4. 1927―1949 ： FROM QUANTUM MECHANICS TO QUANTUM FIELD THEORY ： RELATIVISTIC COVARIANCE SLOWLY RECOVERED = 219
• 4.4.1. Second ― and first―order covariant wave equations = 219
• 4.4.2. 1927 ： Dirac's first―order equation describing jointly an electron and a positron = 219
• 4.4.3. 1934―1939 ： De Broglie, Proca, Petiau, Duffin, Kemmer ： the covariant spin―1 wave equation = 224
• 4.4.4. Higher order spin equations. Fermions and bosons = 225
• 4.4.5. 1927―1928 ： The Jordan ― Klein and Jordan ― Wigner 'second quantized' formalisms = 225
• 4.4.6. 1928―1948 ： The groping years of the quantized fields theory = 226
• 4.4.7. 1948 ： Schwinger's 'Quantum electrodynamics. I ： A covariant formulation' = 227
• 4.4.8. 1949 ： Feynman's version of quantum electrodynamics = 230
• 4.4.9. 1949―1950 ： Dyson's articles = 230
• 4.4.10. Provisional epilogue = 231
• 4.5. PARITY VIOLATIONS AND CPT INVARIANCE = 233
• 4.5.1. Liminal advice = 233
• 4.5.2. Classical connection between charge conjugation and spacetime reversal = 233
• 4.5.3. The 'θ ― τ' puzzle resolved ： Lee's and Yang's K meson = 234
• 4.5.4. Forgetting K mesons ： 'V ― A' formalization of the weak interaction = 235
• 4.5.5. On the possibility of time―reversal violations = 237
• 4.5.6. CPT invariance and the spin―statistics connection = 237
• 4.5.7. Back to $$K^\circ $$ mesons. 1955 ： Gell―Mann's and Pa$$\ddot i$$s's theory of the wonderful behavior of K mesons = 239
• 4.5.8. 1965 ： Christenson, Cronin, Fitch and Turlay discover the CP―violating decay of K mesons = 241
• 4.5.9. T violations = 241
• 4.5.10. By way of conclusion, a little fable = 241
• 4.6. PARADOX AND PARADIGM ： THE EINSTEINPODOLSKY―ROSEN CORRELATIONS = 244
• 4.6.1. 1927 ： Einstein at the Fifth Solvay Conference = 244
• 4.6.2. 1927―1935 ： The Bohr ― Einstein controversy = 247
• 4.6.3. 1935 ： The Einstein ― Podolsky ― Rosen article 'Can quantum mechanical description... be considered complete?' = 248
• 4.6.4. 1935 ： On Bohr's reply to EPR = 250
• 4.6.5. 1935―1936 ： Schr$$\ddot o$$dinger's and Furry's discussions of the EPR argument = 250
• 4.6.6. More thoughts on the EPR thought experiment = 251
• 4.6.7. 1947 ： A personal recollection = 252
• 4.6.8. 1949 ： Wu's and Shaknov's experiment on correlated linear polarizations of photon pairs issuing from positronium annihilation = 253
• 4.6.9. 1951 and 1957 ： Bohm's and Bohm ― Aharonov's correlated spins versions of the EPR = 253
• 4.6.10. 1964 ： Bell's theorem = 253
• 4.6.11. 1967―1982 ： Experimenting and thinking with correlated linear polarizations of photons = 254
• 4.6.12. Deduction and discussion of the correlation formula for linear polarizations of spin―zero photon pairs = 256
• 4.6.13. Directionless causality = 261
• 4.7. S―MATRIX, LORENTZ―AND―CPT INVARIANCE, AND THE EINSTEIN―PODOLSKY―ROSEN CORRELATIONS = 265
• 4.7.1. Liminal advice = 265
• 4.7.2. Derivation of Feynman's S―matrix algorithm following Dyson = 265
• 4.7.3. Consistency between Feynman's negative energy and the commonsense positive energy interpretations of antiparticles = 270
• 4.7.4. Essential CPT invariance of Feynman's algorithm = 270
• 4.7.5. A concise derivation of the EPR correlation formula for spin―zero photon pairs = 271
• 4.7.6. Irrelevance of the evolving state vector ； relevance of the transition amplitude = 272
• 4.7.7. Covariant expression of the EPR correlation for spinzero fermion pairs = 275
• 4.7.8. The paradox of relativistic quantum mechanics = 276
• 4.7.9 A digression on propagators. Causality and the Feynman propagator = 279
• 4.7.10. Concluding the chapter, and Part 4 of this book = 282
• PART 5 AN OUTSIDER'S VIEW OF GENERAL RELATIVITY
• 5.1. ON GENERAL RELATIVITY = 287
• 5.1.1. Liminal advice = 287
• 5.1.2. What is so special with universal gravitation? = 287
• 5.1.3. Einstein's 1916 formalization of the 'equivalence principle'. General relativity theory = 289
• 5.1.4. Time in general relativity = 290
• 5.1.5. Bending of light waves. Advance of periastrons = 292
• 5.1.6. Quantum mechanics in the Riemannian spacetime = 292
• 5.1.7. Quantization of the gravity field = 293
• 5.1.8. Gravity waves = 294
• 5.2. AN OUTSIDER'S LOOK AT COSMOLOGY, AND OVERALL CONCLUSIONS = 295
• 5.2.1. God said ： Let there be self―gravitating light! Cosmogenesis = 295
• 5.2.2. Black holes = 296
• 5.2.3. Souriau's and Fliche's 'layered universe' = 297
• 5.2.4. Brief overall conclusions = 297
• NOTES = 299
• BIBLIOGRAPHY = 304
• ADDED IN PROOF = 319
• INDEX OF NAMES = 324
• INDEX OF SUBJECTS = 331