Special Relativity

ISBN-13: 9781852334260 / Angielski / Miękka / 2002 / 196 str.

N. M. J. Woodhouse; Nicholas M. J. Woodhouse

Opis

Special relativity is one of the high points of the undergraduate mathematical physics syllabus. Nick Woodhouse writes for those approaching the subject with a background in mathematics: he aims to build on their familiarity with the foundational material and the way of thinking taught in first-year mathematics courses, but not to assume an unreasonable degree of prior knowledge of traditional areas of physical applied mathematics, particularly electromagnetic theory. His book provides mathematics students with the tools they need to understand the physical basis of special relativity and leaves them with a confident mathematical understanding of Minkowski's picture of space-time. Special Relativity is loosely based on the tried and tested course at Oxford, where extensive tutorials and problem classes support the lecture course. This is reflected in the book in the large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. The author has included material on acceleration and tensors, and has written the book with an emphasis on space-time diagrams. Written with the second year undergraduate in mind, the book will appeal to those studying the 'Special Relativity' option in their Mathematics or Mathematics and Physics course. However, a graduate or lecturer wanting a rapid introduction to special relativity would benefit from the concise and precise nature of the book.

Recenzje

From the reviews:

N.M.J. Woodhouse's comparatively short Special Relativity is a pleasure to read and therefore qualifies right off as a good source to use for learning about special relativity on your own. A lot of very nice material is touched on in its pages, presented in natural sequence consonant with history, and is not improperly belabored. It's also rather informal in style. One gets the sense of breezing along pretty fast while, in actuality, a lot of material is being dealt with... the selection of topics in the book is very nice indeed , and is historically sound and will therefore reward the reader with an element of culture to boot: he'll learn some history of modern physics... I wish this book had been around when I was a student.

MAA Online

...an exciting and challenging book with which to introduce a modern mathematics student in a single course to the great ideas of Maxwell's theory and special relativity.

The Australian Mathematical Society Gazette

"There are many books on special relativity for undergraduates, and this one is notable in that it is specifically addressed to mathematicians. ... this book will be found illuminating by students of mathematics ... ." (Dr. P. E. Hodgson, Contemporary Physics, Vol. 45 (5), 2004)

"This book is ... aimed squarely at the undergraduate mathematician ... . The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. ... There are lots of examples and nicely graded exercises throughout the text, and each chapter ends with a usefully annotated bibliography. The author's friendly style, and the fact the material has been developed from taught courses make the book ideal for self-study ... ." (Peter Macgregor, The Mathematical Gazette, Vol. 88 (512), 2004)

"Meant as a resource for advanced undergraduate students, this book approaches special relativity theory from a mathematical perspective ... . It is best used for mathematics majors ... . the text is clear, well written, and has an adequate bibliography. Summing Up: Recommended. Upper-division undergraduates." (A. Spero, CHOICE, December, 2003)

"This presentation is very elegant ... . The book contains a large number of examples. Each chapter is followed by exercises, ranging from the rather simple to the more involved. This book is certainly a good introduction to special relativity, understandable for second-year students. But it is also interesting for readers searching for a concise and precise presentation of special relativity within the tensor formalism." (Claude Semay, Physcalia, Vol. 25 (4), 2003)

Spis treści

1. Relativity in Classical Mechanics.- 1.1 Frames of Reference.- 1.2 Relativity.- 1.3 Frames of Reference.- 1.4 Newton’s Laws.- 1.5 Galilean Transformations.- 1.6 Mass, Energy, and Momentum.- 1.7 Space-time.- 1.8 *Galilean Symmetries.- 1.9 Historical Note.- 2. Maxwell’s Theory.- 2.1 Introduction.- 2.2 The Unification of Electricity and Magnetism.- 2.3 Charges, Fields, and the Lorentz Force Law.- 2.4 Stationary Distributions of Charge.- 2.5 The Divergence of the Magnetic Field.- 2.6 Inconsistency with Galilean Relativity.- 2.7 The Limits of Galilean Invariance.- 2.8 Faraday’s Law of Induction.- 2.9 The Field of Charges in Uniform Motion.- 2.10 Maxwell’s Equations.- 2.11 The Continuity Equation.- 2.12 Conservation of Charge.- 2.13 Historical Note.- 3. The Propagation of Light.- 3.1 The Displacement Current.- 3.2 The Source-free Equations.- 3.3 The Wave Equation.- 3.4 Monochromatic Plane Waves.- 3.5 Polarization.- 3.6 Potentials.- 3.7 Gauge Transformations.- 3.8 Photons.- 3.9 Relativity and the Propagation of Light.- 3.10 The Michelson-Morley Experiment.- 4. Einstein’s Special Theory of Relativity.- 4.1 Lorentz’s Contraction.- 4.2 Operational Definitions of Distance and Time.- 4.3 The Relativity of Simultaneity.- 4.4 Bondi’s fc-Factor.- 4.5 Time Dilation.- 4.6 The Two-dimensional Lorentz Transformation.- 4.7 Transformation of Velocity.- 4.8 The Lorentz Contraction.- 4.9 Composition of Lorentz Transformations.- 4.10 Rapidity.- 4.11 *The Lorentz and Poincaré Groups.- 5. Lorentz Transformations in Four Dimensions.- 5.1 Coordinates in Four Dimensions.- 5.2 Four-dimensional Coordinate Transformations.- 5.3 The Lorentz Transformation in Four Dimensions.- 5.4 The Standard Lorentz Transformation.- 5.5 The General Lorentz Transformation.- 5.6 Euclidean Space and Minkowski Space.- 5.7 Four-vectors.- 5.8 Temporal and Spatial Parts.- 5.9 The Inner Product.- 5.10 Classification of Four-vectors.- 5.11 Causal Structure of Minkowski Space.- 5.12 Invariant Operators.- 5.13 The Frequency Four-vector.- 5.14 * Affine Spaces and Covectors.- 6. Relative Motion.- 6.1 Transformations Between Frames.- 6.2 Proper Time.- 6.3 Four-velocity.- 6.4 Four-acceleration.- 6.5 Constant Acceleration.- 6.6 Continuous Distributions.- 6.7 *Rigid Body Motion.- 6.8 Visual Observation.- 7. Relativistic Collisions.- 7.1 The Operational Definition of Mass.- 7.2 Conservation of Four-momentum.- 7.3 Equivalence of Mass and Energy.- 8. Relativistic Electrodynamics.- 8.1 Lorentz Transformations of E and B.- 8.2 The Four-Current and the Four-potential.- 8.3 Transformations of E and B.- 8.4 Linearly Polarized Plane Waves.- 8.5 Electromagnetic Energy.- 8.6 The Four-momentum of a Photon.- 8.7 *Advanced and Retarded Solutions.- 9. *Tensors and Isomet ries.- 9.1 Affine Space.- 9.2 The Lorentz Group.- 9.3 Tensors.- 9.4 The Tensor Product.- 9.5 Tensors in Minkowski Space.- 9.6 Tensor Components.- 9.7 Examples of Tensors.- 9.8 One-parameter Subgroups.- 9.9 Isometries.- 9.10 The Riemann Sphere and Spinors.- Notes on Exercises.- Vector Calculus.