Time, the Physical Magnitude

ISBN-13: 9789027724441 / Angielski / Twarda / 1987 / 340 str.

O. Costa De Beauregard

Opis

In an age characterized by impersonality and a fear of individuality this book is indeed unusual. It is personal, individualistic and idiosyncratic - a record of the scientific adventure of a single mind. Most scientific writing today is so depersonalized that it is impossible to recognize the man behind the work, even when one knows him. Costa de Beauregard's scientific career has focused on three domains - special relativity, statistics and irreversibility, and quantum mechanics. In Time, the Physical Magnitude he has provided a personal vade mecum to those problems, concepts, and ideas with which he has been so long preoccupied. Some years ago we were struck by a simple and profound observa- tion of Mendel Sachs, the gist of which follows. Relativity is based on very simple ideas but, because it requires highly complicated mathe- matics, people find it difficult. Quantum mechanics, on the other hand, derives from very complicated principles but, since its mathematics is straightforward, people feel they understand it. In some ways they are like the bourgeois gentilhomme of Moliere in that they speak quantum mechanics without knowing what it is. Costa de Beauregard recognizes the complexity of quantum mechanics. A great virtue of the book is that he does not hide or shy away from the complexity. He exposes it fully while presenting his ideas in a non-dogmatic way.

Spis treści

1 Generalities.- 1.1. Introductory Remarks.- 1.1.1. Modelism or formalism?.- 1.1.2. Paradox and paradigm.- 1.1.3. Utility of dimensional analysis. Universal constants.- 1.1.4. ‘Very large’ and ‘very small’ universal constants.- 1.1.5. Today’s scientific humanism.- 1.1.6. Epistemology as understood in this book.- 2 Lawlike Equivalence Between Time and Space.- 2.1. More Than Two Millennia of Euclidean Geometry.- 2.1.1. ‘Euclidean theory of space’.- 2.1.2. ‘Is it false that overnight everything has doubled in size?’.- 2.1.3. Absolute time and classical kinematics.- 2.1.4. The classical ‘principle of relative motion’.- 2.2. The Three Centuries of Newtonian Mechanics: Universal Time and Absolute Space.- 2.2.1. Remarkable aphorisms by Aristotle.- 2.2.2. Kepler (1571-1630) and Galileo (1564-1642): celestial and terrestrial mechanics.- 2.2.3. The universal Galileo—Newtonian law$${\textbf } = m{\ddot {\textbf }} $$.- 2.2.4. ‘Greatness and servitude’ of classical mechanics.- 2.2.5. Gravitation.- 2.2.6. Symplectic manifolds and analytical mechanics.- 2.3. Three Centuries of Kinematical Optics.- 2.3.1. Fermat (1601-1665) and Huygens (1629-1695).- 2.3.2. Roemer (1976) and Bradley (1728): the two first measurements of the velocity of light.- 2.3.3. Could Bradley’s discovery allow a formulation of the relativity theory?.- 2.3.4. A corollary to Bradley’s aberration: photography of a fastly moving object.- 2.3.5. Arago’s 1818 experiment and Fresnel’s very far reaching ‘ether drag’ formula.- 2.3.6. ‘Normal science’ in optics throughout the 19th Century.- 2.3.7. In electromagnetism also there was a dormant relativity problem.- 2.3.8. Unexpected end of the hunting of the snark.- 2.4. Today’s Nec Plus Ultra of Metrology and Chronometry: ‘Equivalence’ of Space and Time.- 2.4.1. Fundamental significance of the Michelson—Morley type of experiment.- 2.4.2. Optical metrology.- 2.4.3. Microwave chronometry.- 2.4.4. Measurements of the velocity of light.- 2.4.5. Imminent fulfilment of the old Aristotelian dream.- 2.4.6. Wonders of laser physics: the 1978 Brillet and Hall ‘repetition’ of the Michelson experiment.- 2.4.7. Wonders of laser physics: metrology via Doppler free spectroscopy.- 2.4.8. October 1983: The speed of light as supreme ‘motion referee’, and the new immaterial length standard.- 2.4.9. Wonders of laser spectroscopy: chronometry via optical heterodyning.- 2.4.10. Mossbauer effect (Heidelberg, 1957).- 2.4.11. Applied metrology, tachymetry and chronometry.- 2.5. Entering the Four-Dimensional Spacetime Paradigm.- 2.5.1. Walking through the entrance gate.- 2.5.2. Playing with hyperbolic trigonometry.- 2.5.3. On the general Lorentz—Poincaré—Minkowski transformation.- 2.5.4. On the Galileo—Newton paradigm as a limit of the Poincaré—Minkowski one.- 2.5.5. Fresnel’s ether drag law as a velocity composition formula.- 2.5.6. Terrell’s relativistic photography revisited.- 2.5.7. Time dilatation and the ‘twins paradox’.- 2.5.8. The Harress (1912) and Sagnac (1913) effects.- 2.5.9. The problem of accelerating a solid body.- 2.5.10. Kinematics identified with vacuum optics. The restricted relativity principle as a kinematical principle.- 2.6. The Magic of Spacetime Geometry.- 2.6.1. Introduction.- 2.6.2. Invariant phase and 4–frequency vector.- 2.6.3. The 4–velocity concept.- 2.6.4. Integration and differentiation in spacetime.- 2.6.5. Invariant or scalar volume element carried by a fluid.- 2.6.6. The Green– and Stokes–like integration transformation formulas.- 2.6.7. Relativistic electromagnetism and electrodynamics.- 2.6.8. Entering relativistic dynamics.- 2.6.9. Fluid moved by a scalar pressure: a quick look at relativistic thermodynamics.- 2.6.10. Dynamics of a point particle.- 2.6.11. Isomorphism between the classical statics of filaments and the relativistic dynamics of spinning-point particles.- 2.6.12. Barycenter and 6–component angular momentum around the barycenter. The relativistic ‘general theorems’.- 2.6.13. Analytical dynamics of an electrically charged point particle.- 2.6.14. Wheeler—Feynman electrodynamics.- 2.6.15. De Broglie’s wave mechanics.- 2.6.16. What was so special with light, after all?.- 2.6.17 Concluding this chapter, and the Second part of the book.- 3 Lawlike Time Symmetry and Factlike Irreversibility.- 3.1. Overview.- 3.1.1. Old wisdom and deeper insights.- 3.1.2. Mathematization of gambling.- 3.1.3. Probability as data dependent.- 3.14. The Shannon—Jaynes principle of entropy maximization, or ‘maxent’.- 3.1.5. ‘How subjective is entropy?’.- 3.1.6. Loschmidt–like and Zermelo–like behavior in card shuffling.- 3.1.7. Laplace, the first, and profound theorist of lawlike reversibility and factlike irreversibility.- 3.1.8. Timeless causality and timeless probability.- 3.1.9. Factlike irreversibility according to Laplace, Boltzmann and Gibbs.- 3.1.10. Lawlike reversibility.- 3.1.11. Matrix conceptualization of conditional or transition probabilities.- 3.1.12. Laplacean reversal and time reversal.- 3.1.13. Markov chains in general.- 3.1.14. Factlike irreversibility as blind statistical retrodiction forbidden.- 3.1.15. Causality identified with conditional or transition probability.- 3.1.16. Concluding the chapter: a spacetime covariant, arrowless calculus of probability.- 3.1.17. Appendix: Comparison between my thesis and those of other authors having discussed the fundamentals of irreversibility.- 3.2. Phenomenological Irreversibility.- 3.2.1. Classical thermodynamics.- 3.2.2. Factlike thermodynamical irreversibility and its relevance to causality and information.- 3.2.3. Entropy increase and wave retardation.- 3.2.4. Light waves.- 3.2.5. Waves and information theory.- 3.2.6. Lawlike time symmetry and factlike time asymmetry in the Wheeler—Feynman electrodynamics.- 3.2.7. Thermal equilibrium radiation.- 3.2.8. Irreversibility and the cosmological cool oven.- 3.3. Retarded Causality as a Statistical Concept. Arrowless Microcausality.- 3.3.1. Poincaré’s discussion of the little planets’ ring.- 3.3.2. Boltzmann, Gibbs and thermodynamical entropies.- 3.3.3. Loschmidt’s objection and Boltzmann’s first inappropriate answer. Recurrence of this sort of paralogism.- 3.3.4. Retarded causality as identical to probability increase. Causality as arrowless at the microlevel.- 3.3.5. Retarded causality and registration.- 3.3.6. Zermelo’s recurrence objection, and the phenomenon of spin echoes.- 3.3.7. Other instances of lawlike symmetry and factlike asymmetry between blind statistical prediction and retrodiction.- 3.3.8. Statistical mechanics: from Maxwell’s three–dimensional billiard–balls game to Shannon’s information concept.- 3.3.9. Boltzmann’s second thoughts concerning the Loschmidt objection.- 3.4. Irreversibility as a Cosmic Phenomenon.- 3.4.1. Liminal advice.- 3.4.2. Branch systems. The ‘statistical Big Bang’.- 3.4.3 Unusual statistics of self-gravitating systems.- 3.4.4. Loschmidt–like behavior of the Universe: Big Bang and time reversal.- 3.4.5. The Olbers paradox.- 3.4.6. The 2.7 °K cosmological radiation.- 3.4.7. Building order by feeding on the universal negentropy cascade.- 3.4.8. Concluding the chapter.- 3.5. Lawlike Reversibility and Factlike Irreversibility in the Negentropy-Information Transition.- 3.5.1. Preliminary considerations.- 3.5.2. Is the subconscious mind time-extended, as matter is?.- 3.5.3. Lawlike reversibility between negentropy and information.- 3.5.4. ‘Seeing in the future and acting in the past’.- 3.5.5. A proposed experiment in psychokinesis.- 3.5.6. Concluding the chapter, and Part 3 of the book.- 4 Relativistic Quantum Mechanics and the Problem of Becoming.- 4.1. Overview.- 4.1.1. Quantum theory as the child of wave physics and of a probability calculus.- 4.1.2. Macrorelativity and microrelativity, Lorentz–and–CPT invariance.- 4.1.3. ‘Correspondence’ between the classical and the quantal, wavelike, probability calculus.- 4.1.4. Topological invariance of Landé chains and of Feynman graphs; Wheeler’s smoky dragon; EPR correlations.- 4.1.5. Covariant Fourier analysis and the second-order Klein?”Gordon equation.- 4.1.6. Covariant Fourier analysis and the first-order spinning-wave equations.- 4.1.7. Particle in an external field.- 4.1.8. Concluding the chapter: quantum and relativity theories as daughters of wave physics.- 4.2. 1900-1925: The Quantum Springs Out, and Spreads.- 4.2.1. 1900: Max Planck discovers the quantum of action.- 4.2.2. Einstein’s numerous contributions to the quantum theory: statistics, and the photon.- 4.2.3. The hydrogen atom of Bohr (1913) and Sommerfeld (1916).- 4.2.4. The ‘Old Testament’ of the quantum theory and Sommerfeld’s bible. Correspondence Principle. Two new ideas in 1925.- 4.2.5. Bose—Einstein and Fermi—Dirac statistics.- 4.2.6. De Broglie’s matter waves.- 4.2.7. Retrospective outlook.- 4.3. 1925—1927: The Dawn of Quantum Mechanics with a Shadow: Relativistic Covariance Lost.- 4.3.1. Liminal advice.- 4.3.2. 1925: Heisenberg starts the game of quantum mechanics.- 4.3.3. 1926—1927: Born and Jordan formalize quantum mechanics as a matrix mechanics.- 4.3.4. 1925: Dirac and the Poisson brackets.- 4.3.5. 1926: Schrödinger formalizes quantum mechanics as a wave mechanics.- 4.3:6. 1926: Mathematical ‘equivalence’ between Heisenberg’s and Schrödinger’s theories.- 4.3.7. 1926: Born introduces, and Jordan formalizes, a radically new ‘wavelike probability calculus’.- 4.3.8. Non-commuting position and momentum operators, and Heisenberg’s uncertainty relations.- 4.3.9. Non-commuting angular momentum operators.- 4.3.10. 1929: Robertson’s formalization of the uncertainty relations.- 4.3.11. 1929: Heisenberg’s microscope thought experiment and statistical retrodiction. 1931: Von Weiszäcker’s modified use of it and retroaction.- 4.3.12. On the time—energy uncertainty relation in nonrelativistic quantum mechanics.- 4.3.13. The Hilgevoord—Uffink conception of the position—momentum and time—energy uncertainties.- 4.3.14. Nonrelativistic quantum mechanics of many particles.- 4.3.15. Ennuple quantal correlations: general formalism.- 4.3.16. The Schrödinger, Heisenberg and interaction representations.- 4.3.17. Nonrelativistic perturbation theory.- 4.3.18. ‘Transformation theory’: Dirac, 1926; Jordan, 1927.- 4.3.19. ‘Grandeur and Servitude’ of the Hamiltonian formalism.- 4.4. 1927–1949: From Quantum Mechanics to Quantum Field Theory: Relativistic Covariance Slowly Recovered.- 4.4.1. Second– and first–order covariant wave equations.- 4.4.2. 1927: Dirac’s first–order equation describing jointly an electron and a positron.- 4.4.3. 1934–1939: De Broglie, Proca, Petiau, Duffin, Kemmer: the covariant spin-1 wave equation.- 4.4.4. Higher order spin equations. Fermions and bosons.- 4.4.5. 1927–1928: The Jordan—Klein and Jordan—Wigner ‘second quantized’ formalisms.- 4.4.6. 1928—1948: The groping years of the quantized fields theory.- 4.4.7. 1948: Schwinger’s ‘Quantum electrodynamics. I: A covariant formulation’.- 4.4.8. 1949: Feynman’s version of quantum electrodynamics.- 4.4.9. 1949–1950: Dyson’s articles.- 4.4.10. Provisional epilogue.- 4.5. Parity Violations andCPT Invariance.- 4.5.1. Liminal advice.- 4.5.2. Classical connection between charge conjugation and spacetime reversal.- 4.5.3. The ‘?—?’ puzzle resolved: Lee’s and Yang’s K meson.- 4.5.4. ForgettingK mesons:‘V —A’ formalization of the weak interaction.- 4.5.5. On the possibility of time–reversal violations.- 4.5.6.CPT invariance and the spin–statistics connection.- 4.5.7. Back toK mesons. 1955: Gell–Mann’s and Païs’s theory of the wonderful behavior ofK ° mesons.- 4.5.8. 1965: Christenson, Cronin, Fitch and Turlay discover theCP- violating decay ofK ° mesons.- 4.5.9.T violations.- 4.5.10. By way of conclusion, a little fable.- 4.6. Paradox and Paradigm: The Einstein— Podolsky—Rosen Correlations.- 4.6.1. 1927: Einstein at the Fifth Solvay Conference.- 4.6.2. 1927–1935: The Bohr—Einstein controversy.- 4.6.3. 1935: The Einstein—Podolsky—Rosen article ‘Can quantum mechanical description … be considered complete?’.- 4.6.4. 1935: On Bohr’s reply to EPR.- 4.6.5. 1935–1936: Schrödinger’s and Furry’s discussions of the EPR argument.- 4.6.6. More thoughts on the EPR thought experiment.- 4.6.7. 1947: A personal recollection.- 4.6.8. 1949: Wu’s and Shaknov’s experiment on correlated linear polarizations of photon pairs issuing from positronium annihilation.- 4.6.9. 1951 and 1957: Bohm’s and Bohm—Aharonov’s correlated spins versions of the EPR.- 4.6.10. 1964: Bell’s theorem.- 4.6.11. 1967–1982: Experimenting and thinking with correlated linear polarizations of photons.- 4.6.12. Deduction and discussion of the correlation formula for linear polarizations of spin-zero photon pairs.- 4.6.13. Directionless causality.- 4.7.S-Matrix, Lorentz-and-CPT Invariance, And the Einstein—Podolsky—Rosen Correlations.- 4.7.1. Liminal advice.- 4.7.2. Derivation of Feynman’sS-matrix algorithm following Dyson.- 4.7.3. Consistency between Feynman’s negative energy and the commonsense positive energy interpretations of antiparticles.- 4.7.4. EssentialCPT invariance of Feynman’s algorithm.- 4.7.5. A concise derivation of the EPR correlation formula for spin-zero photon pairs.- 4.7.6. Irrelevance of the evolving state vector; relevance of the transition amplitude.- 4.7.7. Covariant expression of the EPR correlation for spinzero fermion pairs.- 4.7.8. The paradox of relativistic quantum mechanics.- 4.7.9 A digression on propagators. Causality and the Feynman propagator.- 4.7.10. Concluding the chapter, and Part 4 of this book.- 5 An Outsider’s View of General Relativity.- 5.1. On General Relativity.- 5.1.1. Liminal advice.- 5.1.2. What is so special with universal gravitation?.- 5.1.3. Einstein’s 1916 formalization of the ‘equivalence principle’. General relativity theory.- 5.1.4. Time in general relativity.- 5.1.5. Bending of light waves. Advance of periastrons.- 5.1.6. Quantum mechanics in the Riemannian spacetime.- 5.1.7. Quantization of the gravity field.- 5.1.8. Gravity waves.- 5.2. An Outsider’S Look at Cosmology, and Overall Conclusions.- 5.2.1. God said: Let there be self-gravitating light! Cosmogenesis.- 5.2.2. Black holes.- 5.2.3. Souriau’s and Fliche’s ‘layered universe’.- 5.2.4. Brief overall conclusions.- Notes.- Added in Proof.- Index of Names.- Index of Subjects.