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Time, The Physical Magnitude

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Table of Contents

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$${textbf {F}} = m{ddot {textbf {r}}} $$.- 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-Poincare-Minkowski transformation.- 2.5.4. On the Galileo-Newton paradigm as a limit of the Poincare-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. Poincare'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 DegreesK 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 Lande 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: Schroedinger formalizes quantum mechanics as a wave mechanics.- 4.3:6. 1926: Mathematical `equivalence' between Heisenberg's and Schroedinger'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 Weiszacker'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 Schroedinger, 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 Pais's theory of the wonderful behavior ofK Degrees mesons.- 4.5.8. 1965: Christenson, Cronin, Fitch and Turlay discover theCP- violating decay ofK Degrees 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: Schroedinger'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.

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