The Geometry of Special Relativity

by Dray; Tevian

• ISBN13: 9781466510470
• ISBN10: 1466510471
• Format: Hardcover
• Copyright: 2012-07-02
• Publisher: A. K. Peters

Summary

Well-known for connecting mathematical rigor to physics applications, the author of this book presents special relativity in a geometric framework using basic trigonometry. A distinctive feature of the text is its emphasis on the equivalence between special and hyperbolic trigonometry. Suitable for mathematicians and physicists, the book shows how the fascinating and easily accessible mathematics topic of hyperbolic triangle trigonometry is useful in solving problems in relativity.

Table of Contents

List of Figures and Tables	p. xi
Preface	p. xv
Acknowledgments	p. xvii
Introduction	p. 1
Newton's Relativity	p. 1
Einstein's Relativity	p. 2
The Physics of Special Relativity	p. 3
Observers and Measurement	p. 3
The Postulates of Special Relativity	p. 3
Time Dilation and Length Contraction	p. 7
Lorentz Transformations	p. 10
Addition of Velocities	p. 11
The Interval	p. 12
Circle Geometry	p. 13
The Geometry of Trigonometry	p. 13
Distance	p. 13
Circle Trigonometry	p. 13
Triangle Trigonometry	p. 15
Rotations	p. 16
Projections	p. 17
Addition Formulas	p. 18
Hyperbola Geometry	p. 19
Hyperbolic Trigonometry	p. 19
Distance	p. 20
Hyperbola Trigonometry	p. 20
Triangle Trigonometry	p. 22
Rotations	p. 23
Projections	p. 24
Addition Formulas	p. 24
The Geometry of Special Relativity	p. 25
The Surveyors	p. 25
Spacetime Diagrams	p. 26
Lorentz Transformations	p. 27
Space and Time	p. 29
Dot Product	p. 30
Applications	p. 37
Drawing Spacetime Diagrams	p. 37
Addition of Velocities	p. 38
Length Contraction	p. 39
Time Dilation	p. 41
Doppler Shift	p. 44
Problems I	p. 47
Practice	p. 47
The Getaway	p. 51
Angles are not Invariant	p. 52
Interstellar Travel	p. 55
Cosmic Rays	p. 57
Doppler Effect	p. 59
Paradoxes	p. 61
Special Relativity Paradoxes	p. 61
The Pole and Barn Paradox	p. 61
The Twin Paradox	p. 63
Manhole Covers	p. 65
Relativistic Mechanics	p. 67
Proper Time	p. 67
Velocity	p. 68
Conservation Laws	p. 69
Energy	p. 71
Usefull Formulas	p. 73
Problems II	p. 75
Mass Isn't Conserved	p. 75
Identical Particles	p. 76
Pion Decay I	p. 77
Mass and Energy	p. 80
Pion Decay II	p. 81
Relativistic Electromagnetism	p. 83
Magnetism from Electricity	p. 83
Lorentz Transformations	p. 86
Vectors	p. 89
Tensors	p. 91
The Electromagnetic Field	p. 92
Maxwell's Equations	p. 93
The Unifications of Special Relativity	p. 96
Problems III	p. 97
Vanishing Fields	p. 97
Parallel and Perpendicular Fields	p. 98
Beyond Special Relativity	p. 99
Problems with Special Relativity	p. 99
Tidal Effects	p. 100
Differential Geometry	p. 102
General Relativity	p. 103
Uniform Accleration and Black Holes	p. 105
Hyperbolic Geometry	p. 107
Non-Euclidean Geometry	p. 107
The Hyperboloid	p. 108
The Poincaré Disk	p. 110
The Klein Disk	p. 113
The Pseudosphere	p. 114
Calculus	p. 119
Circle Trigonometry	p. 119
Hyperbolic Trigonometry	p. 120
Exponentials (and Logarithms)	p. 121
Bibliography	p. 127
Index	p. 129
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