The geometry of special relativity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
CRC Press
2012
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVII, 131 S. |
| ISBN: | 9781466510470 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | THE GEOMETRY
OF
SPECIAL RELATIVITY
TEVIAN DRAY
This book is very clearly and simply written. The treatment is mathematically
and physically sound. The diagrams are especially good. Though there are many
introductory books on special relativity, this book is unique in its emphasis on
hyperbolic functions and geometry. The book can stand alone as an elementary
introduction to relativity. Or it can serve well as a supplement to other books, on
relativity or electrodynamics. I strongly endorse it.
—David Hestenes, Professor Emeritus, Department of Physics,
Arizona State University
Clear, beautiful, crystalline. Relativity is about hyperbolas in spacetime! The
mathematically inclined will savor Tevian Dray s friendly primer.
—
Rudy Rucker, author of
Gei
Relativity, and the
Foui
This book is essentially a grown-up version of the masterful Spacetime Physics
by Taylor and Wheeler. Anyone who teaches or intends to teach special relativity
needs to own a copy.
;li O Murchadha. Department of Physics. National University of Ireland
The Geometry of Special Relativity provides an introduction to special
relativity that encourages readers to see beyond the formulas to the deeper
geometric structure. The text treats the geometry of hyperbolas as the key to
understanding special relativity. This approach replaces the ubiquitous
7
symbol
of most standard treatments with the appropriate hyperbolic trigonometric
functions. In most cases, this not only simplifies the appearance of the formulas,
but also emphasizes their geometric content in such a way as to make them
almost obvious. Furthermore, many important relations, including the famous
relativistic addition formula for velocities, follow directly from the appropriate
trigonometric addition formulas.
CRC Press
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Mathematics/Physics
K14782
ISBN
978-1-4665-1047-0
9 781466 510470
www. crcpress.com
Contents
List of Figures and Tables Xl
Preface xv
Acknowledgments xv
1
Introduction
1.1
Newton s Relativity
.....................
1.2
Einstein s Relativity
.....................
2
2
The Physics of Special Relativity 3
2.1
Observers and Measurement
.................
3
2.2
The Postulates of Special Relativity
............ 3
2.3
Time Dilation and Length Contraction
........... 7
2.4
Lorentz
Transformations
...................
10
2.5
Addition of Velocities
....................
U
2.6
The Interval
..........................
12
3
Circle Geometry
3.1
The Geometry of Trigonometry
...............
13
3.2
Distance
............................
13
3.3
Circle Trigonometry
.....................
1
3.4
Triangle Trigonometry
....................
„ „ _ ..... 16
3.0
Rotations
....................
3.6
Projections
..........................
3.7
Addition Formulas
......................
VII
viii CONTENTS
4
Hyperbola Geometry
19
4.1
Hyperbolic Trigonometry
.................. 19
4.2
Distance
............................ 20
4.3
Hyperbola Trigonometry
................... 20
4.4
Triangle Trigonometry
.................... 22
4.5
Rotations
........................... 23
4.6
Projections
.......................... 24
4.7
Addition Formulas
...................... 24
5
The Geometry of Special Relativity
25
5.1
The Surveyors
......................... 25
5.2
Spacetime Diagrams
..................... 26
5.3
Lorentz
Transformations
................... 27
5.4
Space and Time
........................ 29
5.5
Dot Product
.......................... 30
6
Applications
37
6.1
Drawing Spacetime Diagrams
................ 37
6.2
Addition of Velocities
.................... 38
6.3
Length Contraction
...................... 39
6.4
Time Dilation
......................... 41
6.5
Doppler
Shift
......................... 44
7
Problems I
47
7.1
Practice
............................ 47
7.2
The Getaway
......................... 51
7.3
Angles Are Not Invariant
.................. 52
7.4
Interstellar Travel
....................... 55
7.5
Cosmic Rays
......................... 57
7.6
Doppler
Effect
........................ 59
8
Paradoxes
61
8.1
Special Relativity Paradoxes
................. 61
8.2
The Pole and Barn Paradox
................. 61
8.3
The Twin Paradox
...................... 63
8.4
Manhole Covers
........................ 65
9
Relativistic Mechanics
67
9.1
Proper Time
......................... 67
9.2
Velocity
............................ 68
9.3
Conservation Laws
...................... 69
CONTENTS iX
9.4 Energy............................. 71
9.5
Useful Formulas
........................ 73
10 Problems
II
75
10.1
Mass Isn t Conserved
..................... 75
10.2
Identical Particles
...................... 76
10.3
Pion
Decay I
......................... 77
10.4
Mass and Energy
....................... 80
10.5
Pion
Decay II
......................... 81
11
Relativistic Electromagnetism
83
11.1
Magnetism from Electricity
................. 83
11.2
Lorentz
Transformations
................... 86
11.3
Vectors
............................ 89
11.4
Tensors
............................ 91
11.5
The Electromagnetic Field
.................. 92
11.6
Maxwell s Equations
..................... 93
11.7
The Unification of Special Relativity
............ 96
12
Problems III
97
12.1
Vanishing Fields
....................... 97
12.2
Parallel and Perpendicular Fields
.............. 98
13
Beyond Special Relativity
99
13.1
Problems with Special Relativity
.............. 99
13.2
Tidal Effects
......................... 100
13.3
Differential Geometry
.................... 102
13.4
General Relativity
...................... 103
13.5
Uniform Acceleration and Black Holes
........... 105
14
Hyperbolic Geometry
107
14.1
Non-Euclidean Geometry
.................. 107
14.2
The
Hyperboloid....................... 108
14.3
The
Poincaré Disk
...................... 110
14.4
The Klein Disk
........................ 113
14.5
The Pseudosphere
...................... 114
15
Calculus 119
15.1
Circle Trigonometry
..................... 119
15.2
Hyperbolic Trigonometry
.................. 120
15.3
Exponentials (and Logarithms)
............... 121
* CONTENTS
Bibliography
127
Index
129
|
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| language | English |
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| physical | XVII, 131 S. |
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| spelling | Dray, Tevian Verfasser (DE-588)102623753X aut The geometry of special relativity Tevian Dray Boca Raton CRC Press 2012 XVII, 131 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematisches Modell Special relativity (Physics) Space and time / Mathematical models Spezielle Relativitätstheorie (DE-588)4182215-8 gnd rswk-swf Spezielle Relativitätstheorie (DE-588)4182215-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025874386&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025874386&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Dray, Tevian The geometry of special relativity Mathematisches Modell Special relativity (Physics) Space and time / Mathematical models Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| subject_GND | (DE-588)4182215-8 |
| title | The geometry of special relativity |
| title_auth | The geometry of special relativity |
| title_exact_search | The geometry of special relativity |
| title_full | The geometry of special relativity Tevian Dray |
| title_fullStr | The geometry of special relativity Tevian Dray |
| title_full_unstemmed | The geometry of special relativity Tevian Dray |
| title_short | The geometry of special relativity |
| title_sort | the geometry of special relativity |
| topic | Mathematisches Modell Special relativity (Physics) Space and time / Mathematical models Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| topic_facet | Mathematisches Modell Special relativity (Physics) Space and time / Mathematical models Spezielle Relativitätstheorie |
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