Relativity and Geometry: (Dover Books on Physics)

This high-level study discusses Newtonian principles and 19th-century views on electrodynamics and the aether. Additional topics include Einstein's electrodynamics of moving bodies, Minkowski spacetime, gravitational geometry, time and causality, and other subjects. Highlights include a rich exposition of the elements of the special and general theories of relativity. 1983 edition.

Table of Contents:
Introduction 1. 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 Gravitation 2. Electrodynamics and the Aether 2.1 Nineteenth-Century Views on Electromagnetic Action 2.2 The Relative Motion of the Earth and the Aether 3. 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 Poincare 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 Spacetime 5. 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 Motion 6. 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 Causality Appendix A. Differentiable Manifolds. B. Fibre Bundles C. 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. Notes References Index

About the Author :
Roberto Torretti: In Praise of Dover Robert Torretti was born in Chile in 1930 and received his PhD from the University of Freiberg in 1954. Professor Emeritus of the University of Puerto Rico and the University of Chile, he is now a Fellow of the Institut International de Philosophie. A prominent author on the history and philosophy of science, his books include The Philosophy of Physics (Cambridge, 1999) and Creative Understanding (The University of Chicago Press, 1990). Dover reprinted his Relativity and Geometry in 1996. In the Author's Own Words: "I first ran across Dover books in the 1950s as I browsed the shelves of a small bookshop in Santiago de Chile: clearly printed, firmly bound classics of science at incredibly affordable prices. I immediately realized their significance for a Third World would-be philosopher of science trying to make ends meet with a salary - or was it still my student's allowance? - eroded by chronic two-digit inflation. "Since then, I have remained a devout buyer and reader of Dover books. Early on, I acquired three books which would be decisive for my subsequent research: Felix Klein's Elementary Mathematics from an Advanced Standpoint, Roberto Bonola's Non-Euclidean Geometry, and Hans Reichenbach's The Philosophy of Space and Time. I still keep them, as I do my copies of Campbell's Foundations of Science, and Lindsay and Margenau's Foundations of Physics, which secured me a philosophically solid approach to the field. Though profusely underlined and worn on the outside from too much handling, these books printed over half a century ago do not otherwise show any signs of their age. "Naturally, I almost burst from pride when a book of mine was added to the Dover catalog in 1996." - Roberto Torretti, PhD, Dhc Critical Acclaim for Relativity and Geometry: "It is only rarely that historians and philosophers of science have the opportunity to welcome a work of the outstanding caliber of Torretti's Relativity and Geometry. It is distinguished by the tenacity of its scholarship and the uncompromising rigor of its exposition." - Foundations of Physics