Dover Books on Physics Ser.: Relativity and Geometry by Roberto Torretti (1996, Trade Paperback, Reprint,New Edition)

Dover Publications, Incorporated

0486690466

9780486690469

731244

416 Pages

English

Relativity and Geometry

1996

Geometry / Differential, Geometry / General, Physics / Relativity, Physics / General

Textbook

Science, Mathematics

Roberto Torretti

Dover Books on Physics Ser.

Trade Paperback

0.8 in

18.8 Oz

9.3 in

6.2 in

95-049003

20

College Audience

Yes

530.11

Reprint,New Edition

Qc173.55.T

Introduction1. Newtonian Principles 1.1 The Task of Natural Philosophy 1.2 Absolute Space 1.3 Absolute Time 1.4 Rigid Frames and Coordinates 1.5 Inertial Frames and Newtonian Relativity 1.6 Newtonian Spacetime 1.7 Gravitation2. Electrodynamics and the Aether 2.1 Nineteenth-Century Views on Electromagnetic Action 2.2 The Relative Motion of the Earth and the Aether3. Einstein's 'Electrodynamics of Moving Bodies' 3.1 Motivation 3.2 The Definition of Time in an Inertial Frame 3.3 The Principles of Special Relativity 3.4 The Lorentz Transformation. Einstein's Derivation of 1905 3.5 The Lorentz Transformation. Some Corollaries and Applications 3.6 The Lorentz Transformation. Linearity 3.7 The Lorentz Transformation. Ignatowsky's Approach 3.8 "The "Relativity Theory of Poincaré and Lorentz"4. Minkowski Spacetime 4.1 The Geometry of the Lorentz Group 4.2 Minkowski Spacetime as an Affine Metric Space and as a Riemannian Manifold 4.3 Geometrical Objects 4.4 Concept Mutation at the Birth of Relativistic Dynamics 4.5 A Glance at Spacetime Physics 4.6 The Causal Structure of Minkowski Spacetime5. Einstein's Quest for a Theory of Gravity 5.1 Gravitation and Relativity 5.2 The Principle of Equivalence 5.3 Gravitation and Geometry circa 1912 5.4 Departure from Flatness 5.5 General Covariance and the Einstein-Grossmann Theory 5.6 Einstein's Arguments against Genral Covariance: 1913-14 5.7 Einstein's Papers of November 1915 5.8 Einstein's Field Equations and the Geodesic Law of Motion6. Gravitational Geometry 6.1 Structures of Spacetime 6.2 Mach's Principle and the Advent of Relativistic Cosmology 6.3 The Friedmann Worlds 6.4 Sigularities.7 Disputed Questions 7.1 The Concept of Simultaneity 7.2 Geometric Conventionalism 7.3 Remarks on Time and CausalityAppendixA. Differentiable Manifolds.B. Fibre BundlesC. Linear Connections 1. Vector-valued Differential Forms. 2. The Lie Algebra of a Lie Group. 3. Connections in a Principal Fibre Bundle. 4. Linear Connections. 5. Covariant Differentiation 6. The Torsion and Curvature of a Linear Connection. 7. Geodesics. 8. Metric Connections in Riemannian Manifolds.D. Useful Formulae.NotesReferencesIndex

1996