The Geometry of Special Relativity, 2nd Edition
- Length: 196 pages
- Edition: 2
- Language: English
- Publisher: Chapman and Hall/CRC
- Publication Date: 2021-06-10
- ISBN-10: 1032008202
- ISBN-13: 9781032008202
- Sales Rank: #1779777 (See Top 100 Books)
This unique book presents a particularly beautiful way of looking at special relativity. The author encourages students to see beyond the formulas to the deeper structure.
The unification of space and time introduced by Einstein’s special theory of relativity is one of the cornerstones of the modern scientific description of the universe. Yet the unification is counterintuitive because we perceive time very differently from space. Even in relativity, time is not just another dimension, it is one with different properties
The book treats the geometry of hyperbolas as the key to understanding special relativity. The author simplifies the formulas and emphasizes their geometric content. Many important relations, including the famous relativistic addition formula for velocities, then follow directly from the appropriate (hyperbolic) trigonometric addition formulas.
Prior mastery of (ordinary) trigonometry is sufficient for most of the material presented, although occasional use is made of elementary differential calculus, and the chapter on electromagnetism assumes some more advanced knowledge.
Changes to the Second Edition
- The treatment of Minkowski space and spacetime diagrams has been expanded.
- Several new topics have been added, including a geometric derivation of Lorentz transformations, a discussion of three-dimensional spacetime diagrams, and a brief geometric description of “area” and how it can be used to measure time and distance.
- Minor notational changes were made to avoid conflict with existing usage in the literature.
Author Biography
Tevian Dray is a Professor of Mathematics at Oregon State University. His research lies at the interface between mathematics and physics, involving differential geometry and general relativity, as well as nonassociative algebra and particle physics; he also studies student understanding of “middle-division” mathematics and physics content. Educated at MIT and Berkeley, he held postdoctoral positions in both mathematics and physics in several countries prior to coming to OSU in 1988. Professor Dray is a Fellow of the American Physical Society for his work in relativity, and an award-winning teacher.
Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface List of Figures List of Tables 1 Introduction 1.1 Newton's Relativity 1.2 Einstein's Relativity 2 The Physics of Special Relativity 2.1 Observers and Measurement 2.2 The Postulates of Special Relativity 2.3 Time Dilation and Length Contraction 2.4 Lorentz Transformations 2.5 Addition of Velocities 2.6 The Interval 3 Circle Geometry 3.1 The Geometry of Trigonometry 3.2 Distance 3.3 Circle Trigonometry 3.4 Triangle Trigonometry 3.5 Rotations 3.6 Projections 3.7 Addition Formulas 4 Hyperbola Geometry 4.1 Hyperbolic Trigonometry 4.2 Distance 4.3 Hyperbola Trigonometry 4.4 Triangle Trigonometry 4.5 Rotations 4.6 Projections 4.7 Addition Formulas 4.8 Combining Circle and Hyperbola Trigonometry 5 The Geometry of Special Relativity 5.1 The Surveyors 5.2 Spacetime Diagrams 5.3 Lorentz Transformations 5.4 Space and Time 5.5 The Geometry of Lorentz Transformations 5.6 Dot Product 6 Applications 6.1 Drawing Spacetime Diagrams 6.2 Addition of Velocities 6.3 Length Contraction 6.4 Time Dilation 6.5 Doppler Shift 7 Problems I 7.1 Warmup 7.2 Practice 7.3 The Getaway 7.4 Angles Are Not Invariant 7.5 Interstellar Travel 7.6 Observation 7.7 Cosmic Rays 7.8 Doppler Effect 8 Paradoxes 8.1 Special Relativity Paradoxes 8.2 The Pole and Barn Paradox 8.3 The Twin Paradox 8.4 Manhole Covers 9 Relativistic Mechanics 9.1 Proper Time 9.2 Velocity 9.3 Conservation Laws 9.4 Energy 9.5 Useful Formulas 9.6 Higher Dimensions 10 Problems II 10.1 Mass Isn't Conserved 10.2 Identical Particles 10.3 Pion Decay I 10.4 Mass and Energy 10.5 Pion Decay II 11 Relativistic Electromagnetism 11.1 Magnetism from Electricity 11.2 Lorentz Transformations 11.3 Vectors 11.4 Tensors 11.5 The Electromagnetic Field 11.6 Maxwell's Equations 11.7 The Unification of Special Relativity 12 Problems III 12.1 Vanishing Fields 12.2 Parallel and Perpendicular Fields 13 Beyond Special Relativity 13.1 Problems with Special Relativity 13.2 Tidal Effects 13.3 Differential Geometry 13.4 General Relativity 13.5 Uniform Acceleration and Black Holes 14 Three-Dimensional Spacetime Diagrams 14.1 Introduction 14.2 The Rising Manhole 14.3 The Moving Spotlight 14.4 The Lorentzian Inner Product 14.5 Transverse Directions 15 Minkowski Area via Light Boxes 15.1 Area in Special Relativity 15.2 Measuring with Light Boxes 16 Hyperbolic Geometry 16.1 Non-Euclidean Geometry 16.2 The Hyperboloid 16.3 The Poincaré Disk 16.4 The Klein Disk 16.5 The Pseudosphere 17 Calculus 17.1 Circle Trigonometry 17.2 Hyperbolic Trigonometry 17.3 Exponentials (and Logarithms) Bibliography Index
Donate to keep this site alive
1. Disable the AdBlock plugin. Otherwise, you may not get any links.
2. Solve the CAPTCHA.
3. Click download link.
4. Lead to download server to download.