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    It's about time : elementary mathematical aspects of relativity / Roger Cooke.

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    • Title:It's about time : elementary mathematical aspects of relativity / Roger Cooke.
    •    
    • Variant Title:Elementary mathematical aspects of relativity
    • Author/Creator:Cooke, Roger, 1942- author.
    • Other Contributors/Collections:American Mathematical Society, issuing body.
    • Published/Created:Providence, Rhode Island : American Mathematical Society, [2017]

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    • Library of Congress Subjects:Relativity (Physics)--Mathematics--Textbooks.
      Mathematical physics--Textbooks.
      Space and time--Mathematics--Textbooks.
    • Genre/Form:Textbooks.
    • Description:xix, 403 pages : illustrations ; 27 cm
    • Summary:This book has three main goals. First, it explores a selection of topics from the early period of the theory of relativity, focusing on particular aspects that are interesting or unusual. These include the twin paradox; relativistic mechanics and its interaction with Maxwell's laws; the earliest triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing near the sun; and the surprising bizarre metric of Kurt Gödel, in which time travel is possible. Second, it provides an exposition of the differential geometry needed to understand these topics on a level that is intended to be accessible to those with just two years of university-level mathematics as background. Third, it reflects on the historical development of the subject and its significance for our understanding of what reality is and how we can know about the physical universe. The book also takes note of historical prefigurations of relativity, such as Euler's 1744 result that a particle moving on a surface and subject to no tangential acceleration will move along a geodesic, and the work of Lorentz and Poincaré on space-time coordinate transformations between two observers in motion at constant relative velocity.The book is aimed at advanced undergraduate mathematics, science, and engineering majors (and, of course, at any interested person who knows a little university-level mathematics). The reader is assumed to know the rudiments of advanced calculus, a few techniques for solving differential equations, some linear algebra, and basics of set theory and groups--Publisher's description.
    • Notes:Includes bibliographical references and index.
    • ISBN:9781470434830 hardcover
      1470434830 hardcover
    • Contents:Machine generated contents note: pt. 1 Special Theory
      ch. 1 Time, Space, and Space-Time
      1. Simultaneity and Sequentiality
      2. Synchronization in Newtonian Mechanics
      3. Asymmetry in Newtonian Mechanics: Electromagnetic Forces
      4. Lorentz Transformation
      5. Contraction of Length and Time
      6. Composition of Parallel Velocities
      7. Twin Paradox
      8. Relativistic Triangles
      9. Composition of Relativistic Velocities as a Binary Operation*
      10. Plane Trigonometry*
      11. Lorentz Group*
      12. Closure of Lorentz Transformations under Composition*
      13. Rotational Motion and a Non-Euclidean Geometry*
      14. Problems
      ch. 2 Relativistic Mechanics
      1. Kinematics of a Particle
      2. From Kinematics to Dynamics: Mass and Momentum
      3. Relativistic Force
      4. Work, Energy, and the Famous E = mc2
      5. Newtonian Potential Energy
      6. Hamilton's Principle
      7. Newtonian Lagrangian
      8. Relativistic Lagrangian
      9. Angular Momentum and Torque
      10. Four-Vectors and Tensors*
      11. Problems
      ch. 3 Electromagnetic Theory*
      1. Charge and Charge Density
      2. Current and Current Density
      3. Transformation of Electric and Magnetic Fields
      4. Derivation of the Curl Equations from the Divergence Equations
      5. Problems
      pt. 2 General Theory
      Introduction to Part 2
      ch. 4 Precession and Deflection
      1. Gravitation as Curvature of Space
      2. First Analysis: Newtonian Orbits
      3. Second Analysis: Newton's Law with Relativistic Force
      4. Third Analysis: Newtonian Orbits as Geodesies
      5. Fourth Analysis: General Relativity
      6. Einstein's Law of Gravity
      7. Computation of the Relativistic Orbit
      8. Speed of Light
      9. Deflection of Light Near the Sun
      10. Problems
      ch. 5 Concepts of Curvature, 1700
      1850
      1. Differential Geometry
      2. Curvature, Phase 1: Euler
      3. Curvature, Phase 2: Gauss
      4. Problems
      ch. 6 Concepts of Curvature, 1850
      1950
      1. Second-Order Derivations
      2. Curvature, Phase 3: Riemann
      3. Parallel Transport
      4. Exponential Mapping and Normal Coordinates
      5. Sectional Curvature
      6. Laplace-Beltrami Operator
      7. Curvature, Phase 4: Ricci
      8. Problems
      ch. 7 Geometrization of Gravity
      1. Einstein Field Equations
      2. Further Developments
      3. "Temporonautics" and the Godel Rotating Universe
      4. Black Holes
      5. Problems
      pt. 3 Historical and Philosophical Context
      ch. 8 Experiments, Chronology, Metaphysics
      1. Experimental Tests of General Relativity
      2. Chronology
      3. Space and Time
      4. Reality of Physical Concepts
      5. Harmony Between Mathematics and the Physical World
      6. Knowledge of Hypothetical Objects: An Example
      7. Knowledge of the Physical World
      8. Few Words from the Discoverers
      9. Epilogue: The Reception of Relativity.
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