Relativity: The Theory and Its Philosophy (eBook)
270 Seiten
Elsevier Science (Verlag)
978-1-4831-5003-1 (ISBN)
Relativity: The Theory and its Philosophy provides a completely self-contained treatment of the philosophical foundations of the theory of relativity. It also surveys the most essential mathematical techniques and concepts that are indispensable to an understanding of the foundations of both the special and general theories of relativity. In short, the book includes a crash course in applied mathematics, ranging from elementary trigonometry to the classical tensor calculus. Comprised of 11 chapters, this book begins with an introduction to fundamental mathematical concepts such as sets, relations, and functions; N-tuples, vectors, and matrices; and vector algebra and calculus. The discussion then turns to the concept of relativity and elementary foundations of Newtonian mechanics, as well as the principle of special relativity and its interpretation by means of empiricism and rationalism. Subsequent chapters focus on the status of the doctrine of conventionalism in the theory of special relativity; the commensurability of classical and relativistic mechanics; mathematical foundations of special relativistic physics; and the classical or Newtonian theory of gravitation. The principle of general covariance and its relation to the principle of general relativity are also examined. The final chapter addresses the fundamental question as to the actual information concerning the structure of spacetime that is conveyed to us through the theory of general relativity. This monograph will be of interest to students, teachers, practitioners, and researchers in physics, mathematics, and philosophy.
Front Cover 1
Relativity: The Theory and its Philosophy 4
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 10
List of Logical Symbols 12
Chapter 1. Mathematical Preliminaries 14
Sets, Relations, Functions 14
N-tuples, Vectors, Matrices, and other Items 20
A Trigonometric Digression 28
Vector Algebra 29
The Calculus 41
Bibliography for Chapter 1 53
Chapter 2. Relativity and Newtonian Mechanics 54
The Concept of Relativity 54
Elementary Foundations of Newtonian Mechanics 57
The Principle of Classical Relativity 62
Bibiliography for Chapter 2 72
Chapter 3. The Principle of Special Relativity 74
The Breakdown of Classical Relativity 74
Relativistic Kinematics 76
Four-Vector Formalism and Space-Time Geometry 94
Relativistic Mechanics 104
The Principle of Special Relativity 109
Bibliography for Chapter 3 114
Chapter 4. Empiricism, Rationalism and Special Relativity 116
Relativity and the A Priori in the Philosophy of Eddington 117
The Transcendentalism of J. R. Lucas 123
The Radical Empiricism of Percy Bridgman 128
The Liberalized Empiricism of the Logical Positivists 132
Bibliography for Chapter 4 135
Chapter 5. Special Relativity and Conventionalism 136
The Conventionality of Simultaneity 138
Bibliography for Chapter 5 151
Chapter 6. The Commensurability of Classical and Relativistic Mechanics 153
Bibliography for Chapter 6 161
Chapter 7. More Mathematics 162
Motivation 162
Curvilinear Coordinates 164
Tensors and their Algebra 168
Tensor Calculus 173
The Riemann-Christoffel Tensor 182
Bibliography for Chapter 7 184
Chapter 8. The Path to General Relativity 186
The Classical Theory of Gravitation 186
The Field-Theoretic Standpoint 190
Mach's Principle 193
The Principle of Equivalence 195
The Principle of General Covariance 199
Bibliography for Chapter 8 203
Chapter 9. An Outline of General Relativity 204
Bibliography for Chapter 9 220
Chapter 10. Relativity and Covariance 221
Bibliography for Chapter 10 238
Chapter 11. Spacetime and Geometry 239
The Distinction Between Pure and Applied Mathematics 239
The Geometric Conventionalism of Henri Poincaré 242
The Geometric Empiricism of Hans Reichenbach 245
Geochronometric Conventionalism 249
A Critique of Geochronometric Conventionalism 253
General Relativity and Space-time Structure 257
The Ontology of Spacetime 262
Bibliography for Chapter 11 265
Index 268
| Erscheint lt. Verlag | 20.5.2014 |
|---|---|
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Relativitätstheorie |
| Sozialwissenschaften ► Ethnologie | |
| Sozialwissenschaften ► Politik / Verwaltung | |
| Sozialwissenschaften ► Soziologie | |
| ISBN-10 | 1-4831-5003-8 / 1483150038 |
| ISBN-13 | 978-1-4831-5003-1 / 9781483150031 |
| Haben Sie eine Frage zum Produkt? |
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