It's About Time : Elementary Mathematical Aspects of Relativity / Roger Cooke

Von:

Cooke, Roger, 1942- [aut]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Verlag: Providence : American Mathematical Society, 2017Beschreibung: 1 Online-Ressource (426 p)ISBN:

1470436698
9781470436698

Schlagwörter:

Andere physische Formen: 1470434830 | 9781470434830 | Erscheint auch als: It's about time. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2017. xix, 403 SeitenMSC: MSC: *83-01 | 01-01 | 83-03 | 01A55 | 01A60 | 53Z05 | 83C10 | 78A25 | 83A05 | 83C05 | 83C57 | 03A05 | 97M50RVK: RVK: SK 950 | UH 8000LOC-Klassifikation:

QC173.55.C66 2017

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Zusammenfassung: 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 leveZusammenfassung: 10. Four-Vectors and Tensors*11. Problems; Chapter 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; Part 2 . The General Theory; Introduction to Part 2; Chapter 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 Geodesics; 5. Fourth Analysis: General RelativityZusammenfassung: 6. Einstein's Law of Gravity7. Computation of the Relativistic Orbit; 8. The Speed of Light; 9. Deflection of Light Near the Sun; 10. Problems; Chapter 5. Concepts of Curvature, 1700-1850; 1. Differential Geometry; 2. Curvature, Phase 1: Euler; 3. Curvature, Phase 2: Gauss; 4. Problems; Chapter 6. Concepts of Curvature, 1850-1950; 1. Second-Order Derivations; 2. Curvature, Phase 3: Riemann; 3. Parallel Transport; 4. The Exponential Mapping and Normal Coordinates; 5. Sectional Curvature; 6. The Laplace-Beltrami Operator; 7. Curvature, Phase 4: Ricci; 8. ProblemsZusammenfassung: Chapter 7. The Geometrization of Gravity1. The Einstein Field Equations; 2. Further Developments; 3. "Temporonautics" and the Gödel Rotating Universe; 4. Black Holes; 5. Problems; Part 3 . Historical and Philosophical Context; Chapter 8. Experiments, Chronology, Metaphysics; 1. Experimental Tests of General Relativity; 2. Chronology; 3. Space and Time; 4. The Reality of Physical Concepts; 5. The Harmony Between Mathematics and the Physical World; 6. Knowledge of Hypothetical Objects: An Example; 7. Knowledge of the Physical World; 8. A Few Words from the DiscoverersZusammenfassung: Chapter 7. The Geometrization of Gravity1. The Einstein Field Equations; 2. Further Developments; 3. "Temporonautics" and the Gödel Rotating Universe; 4. Black Holes; 5. Problems; Part 3 . Historical and Philosophical Context; Chapter 8. Experiments, Chronology, Metaphysics; 1. Experimental Tests of General Relativity; 2. Chronology; 3. Space and Time; 4. The Reality of Physical Concepts; 5. The Harmony Between Mathematics and the Physical World; 6. Knowledge of Hypothetical Objects: An Example; 7. Knowledge of the Physical World; 8. A Few Words from the DiscoverersZusammenfassung: 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 levePPN: PPN: 897974506Package identifier: Produktsigel: ZDB-4-NLEBK

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