Special relativity: a heuristic approach
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| Format: | Book |
| Language: | English |
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Amsterdam, Netherlands
Elsevier
[2017]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xix, 360 Seiten Illustrationen, Diagramme |
| ISBN: | 9780128104118 |
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| adam_text | PREFACE
XIII
LIST OF SYMBOLS, PHRASES, AND ACRONYMS.....................................xvii
NOTE TO THE READER.........................................................xix
CHAPTER 1 Qualitative Relativity........................................1
1.1 It Began With Maxwell...................................1
1.1.1 Einstein and Signal Velocity......................3
1.2 Relativity of Simultaneity..............................5
1.2.1 Simultaneity in a Single RF.......................5
1.2.2 Simultaneity in Different RFs.....................8
1.3 Relativity of Length...................................11
1.4 Problems...............................................13
CHAPTER 2 Relativity of Time and Space.................................17
2.1 Time Dilation..........................................17
2.1.1 Proper Time......................................20
2.2 Length Contraction.....................................26
2.3 Relativisticky.........................................32
2.4 The Twin Paradox.......................................35
2.5 Problems...............................................38
CHAPTER 3 Lorentz Transformation.......................................41
3.1 “Derivation” of Euclidean Distance.....................41
3.1.1 Coordinate Transformation........................43
3.2 Spacetime Distance.....................................46
3.3 Lorentz Transformation.................................47
3.4 Examples of the Use of LT..............................50
3.5 Relativistic Law of Addition of Velocities.............57
3.6 Problems...............................................61
CHAPTER U Spacetime Geometry................................................71
4.1 Plane Spacetime Geometry...............................71
4.1.1 Events and Worldlines............................72
4.1.2 Light Cone.......................................75
4.2 Rules of Spacetime Geometry............................76
4.2.1 Invariant Distance...............................77
4.2.2 The Rules........................................79
4.3 Examples of Spacetime Diagrams.........................82
4.3.1 Simultaneity Revisited...........................83
4.3.2 The Train and the Tunnel.........................84
4.3.3 The Doppler Effect...............................87
4.3.4 Time Travel?.....................................90
4.4 Lorentz Transformation Revisited.......................95
4.4.1 Lorentz Transformation and Time Travel...........95
4.5 Curved Worldlines......................................99
4.5.1 The Spacetime Triangle Inequality...............100
4.5.2 The Twin Paradox Revisited......................104
4.6 Problems..............................................108
CHAPTER 5 Spacetime Momentum................................................117
5.1 Spacetime Velocity....................................117
5.2 Spacetime Momentum....................................122
5.2.1 Relativistic Energy.............................122
5.2.2 No Mass at Light Speed..........................124
5.2.3 Invariant Length of Spacetime Momentum..........126
5.2.4 No Velocity-Dependent Mass......................128
5.3 Conservation of Momentum...............................129
5.3.1 The Classical Case...............................129
5.3.2 The Relativistic Case............................130
5.4 Problems...............................................133
CHAPTER 6 Relativity in Four Dimensions.....................................137
6.1 Four-Vectors...........................................137
6.2 Lorentz Transformation in 4D...........................139
6.3 General Velocity Addition Formula......................142
6.3.1 Aberration.......................................145
6.4 General Doppler Effect.................................148
6.5 Global Positioning System..............................151
6.6 Four-Velocity..........................................154
6.7 Four-Momentum..........................................156
6.8 Second Law of Motion...................................157
6.8.1 Four-Acceleration................................157
6.8.2 Four-Force.......................................160
6.8.3 Weirdness of Velocity-Dependent Mass.............163
6.9 Problems...............................................164
CHAPTER 7 Relativistic Photography..........................................169
7.1 History................................................169
7.2 Physics of Photography.................................170
7.3 Photograph of Two Points...............................173
7.4 Photograph of a Rod....................................176
7.5 Photograph of a Cube...................................179
7.5.1 Capturing Length Contraction With a Camera.......181
7.6 Photograph of a Sphere at the Origin...................183
7.6.1 Cone Construction via Aberration Formula.........185
7.6.2 Cone Construction via Relativistic LAV...........189
7.6.3 Cone Construction via LT of Emission Events......189
7.7 Photograph ofa Sphere off the Origin...................193
7.7.1 Stationary Sphere...............................195
7.7.2 Moving Sphere...................................196
7.8 Problems...............................................200
CHAPTER 8 Relativistic Interactions...................................207
8.1 Center of Mass and Lab Frames..........................207
8.1.1 Lorentz Transformation of CM....................209
8.2 Two-Particle Collision.................................211
8.2.1 Minimum Two-Particle Production Energy..........213
8.2.2 Minimum Multi-Particle Production Energy........215
8.3 Decays.................................................216
8.4 Special Relativity, Spin, and Antimatter...............220
8.4.1 Dirac Equation..................................221
8.4.2 Discovery of Antimatter.........................223
8.5 Problems...............................................224
CHAPTER 9 Interstellar Travel.........................................229
9.1 Massive Particle Propulsion............................229
9.2 Photon Propulsion......................................232
9.2.1 Uniform Depletion...............................234
9.2.2 Laser Propulsion................................237
9.3 Ground-Based Propulsion................................239
9.3.1 The Physics.....................................239
9.3.2 The Equation of Motion..........................241
9.3.3 The Formal Solution.............................244
9.3.4 Numerical Examples..............................246
9.3.5 Nonrelativistic Limits..........................248
9.4 Problems...............................................250
CHAPTER 10 A Painless Introduction to Tensors...............................255
10.1 From Boldface to Indices.............................255
10.1.1 Dot and Cross Products........................256
10.1.2 Proof of Note 7.6.2...........................261
10.2 Index Management in Special Relativity...............262
10.3 Invariance of the Elemental 4-Volume.................268
10.4 Problems.............................................272
CHAPTER 11 Relativistic Electrodynamics...................................273
11.1 Transformation of E and B...........................273
11.1.1 Transformation of £............................274
11.1.2 Transformation of B............................275
11.2 Field of a Uniformly Moving Charge...................277
11.3 Electromagnetic Field Tensor.........................279
11.3.1 Lorentz Force Law..............................280
11.3.2 The Cyclotron..................................281
11.3.3 Maxwell’s Equations............................283
11.4 Problems.............................................286
CHAPTER 12 Early Universe.................................................289
12.1 Photon Gas...........................................289
12.2 Friedmann Equation...................................296
12.3 The Densities........................................299
12.4 Evolution of the Universe............................302
12.5 Cosmic Background Radiation..........................304
12.6 Cosmic Genesis.......................................307
12.7 Problems.............................................317
APPENDIX A Maxwell’s Equations.............................................323
A.1 The Briefest Introduction to Vector Analysis..........323
A.2 Maxwell’s Contribution................................327
A.3 Electromagnetic Waves in Vacuum.......................329
A.4 Electromagnetic Waves in a Cubic Cavity...............330
A.5 Problems..............................................332
APPENDIX B Derivation of 4D Lorentz Transformation.....................335
B.1 General Properties................................335
B.2 Derivation of the Lorentz Boost...................336
B.2.1 Transformation of Position and Time..........338
B.2.2 The 3x3 Submatrix............................339
B.2.3 Inverse of a Boost...........................340
B. 3 Problems..........................................340
APPENDIX C Relativistic Photography Formulas...........................341
C. 1 Mapping From Space to a Plane...................341
C.2 Equation of the Contour...........................346
C.3 Problems..........................................347
BIBLIOGRAPHY...........................................................349
INDEX..................................................................351
Sadri Hassani
Special Relativity
A Heuristic Approach
Special Relativity: A Heuristic Approach is an intermediate textbook on relativity, unique both in its
approach and its content. The book approaches relativity with the Lorentz transformations, which are
the key to understanding the subject. Once they are derived as coordinate transformations that leave
the distance in the two-dimensional spacetime unchanged and later generalized to four dimensions,
the Lorentz transformations are applied to a multitude of examples (many unique to this book) to
illustrate their power and immunity from mistakes that other approaches may entail (as demonstrated
in Problem 7.1).
The content of the book is also unique. Whereas topics such as interstellar travel and relativistic
photography are either completely ignored or only mentioned in passing in one or two paragraphs
in other textbooks, this book devotes two complete chapters to these topics. The interstellar travel is
in particular timely because of the interest in projects such as Breakthrough Starshot, which aims to
send nanocrafts to Alpha Centauri. Other topics unique to the book are an accessible discussion
of the Dirac equation and the discovery of antimatter, as well as an easy-to-understand introduction
to the big bang and early universe.
Key Features
• Provides a heuristic derivation of the Minkowskian distance formula after deriving the Euclidean
distance formula for the flatlanden.
• Emphasizes Lorentz transformations as the key to understanding special relativity and provides
countless examples (some appearing for the first time) of their use.
• Provides a reader-friendly introduction to tensor algebra and how it is used in special relativity.
• Features two complete chapters devoted to interstellar travel and relativistic photography.
• Written in a very accessible style.
• All derivations are worked out and explained in detail.
• A companion website provides a complete Solutions Manual for close to three hundred end-of-
chapter problems.
Dr. Sadri Hassani is an Adjunct Professor of physics at the University of Illinois at Urbana-
Champaign, Urbana, IL, USA, and a Professor Emeritus at Illinois State University, Normal, IL, USA.
With over 30 years experience in teaching various physics courses, he is the author of several
books at the introductory, intermediate, and advanced undergraduate and graduate levels.
elsevier.com/books-and-joumals
Physics and Astronomy
|
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| spelling | Hassani, Sadri Verfasser (DE-588)114976838X aut Special relativity a heuristic approach Sadri Hassani, University of Illinois at Urbana-Champaign, Urbana, IL, USA, Illinois State University, Normal, IL, USA Amsterdam, Netherlands Elsevier [2017] © 2017 xix, 360 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Spezielle Relativitätstheorie (DE-588)4182215-8 gnd rswk-swf General relativity (Physics) Heuristic Spezielle Relativitätstheorie (DE-588)4182215-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029799695&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029799695&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| title | Special relativity a heuristic approach |
| title_auth | Special relativity a heuristic approach |
| title_exact_search | Special relativity a heuristic approach |
| title_full | Special relativity a heuristic approach Sadri Hassani, University of Illinois at Urbana-Champaign, Urbana, IL, USA, Illinois State University, Normal, IL, USA |
| title_fullStr | Special relativity a heuristic approach Sadri Hassani, University of Illinois at Urbana-Champaign, Urbana, IL, USA, Illinois State University, Normal, IL, USA |
| title_full_unstemmed | Special relativity a heuristic approach Sadri Hassani, University of Illinois at Urbana-Champaign, Urbana, IL, USA, Illinois State University, Normal, IL, USA |
| title_short | Special relativity |
| title_sort | special relativity a heuristic approach |
| title_sub | a heuristic approach |
| topic | Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| topic_facet | Spezielle Relativitätstheorie |
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