An Illustrated Guide to Relativity

by Tatsu Takeuchi

• ISBN13: 9780521763943
• ISBN10: 0521763940
• Format: Hardcover
• Copyright: 2010-10-18
• Publisher: Cambridge University Press

Summary

Aimed at both physics students and non-science majors, this unique book explains Einstein's special theory of relativity pictorially, using diagrams rather than equations. The diagrams guide the reader, step-by-step, from the basics of relativity to advanced topics including the addition of velocities, Lorentz contraction, time dilation, the twin paradox, Doppler shift, and Einstein's famous equation E=mc². The distinctive figures throughout the book enable the reader to visualize the theory in a way that cannot be fully conveyed through equations alone. The illustrative explanations in this book maintain the logic and rigour necessary for physics students, yet are simple enough to be understood by non-scientists. The book also contains entertaining problems which challenge the reader's understanding of the materials covered.

Author Biography

Tatsu Takeuchi is an Associate Professor in the Department of Physics at Virginia Tech. This book grew from the "Highlights of Contemporary Physics" course he taught for many years. Primarily aimed at non-physics majors, it has been highly popular among physics students as well.

Table of Contents

Preface to English edition	p. viii
Preface to Japanese edition	p. ix
Kinematics: Relativity without any equations	p. 1
Welcome to the world of relativity	p. 2
Basics	p. 4
Questions about motion	p. 4
Frames of reference	p. 5
Relativity of motion	p. 12
The Law of Inertia	p. 14
Inertial and non-inertial frames	p. 18
What's so "special" about Special Relativity?	p. 26
Galilean relativity	p. 30
Basic questions	p. 30
Spacetime diagrams	p. 34
The Galilei transformation	p. 40
Addition of velocities	p. 54
Acceleration and Newton's Second Law	p. 56
Einsteinian relativity	p. 59
The mystery of the speed of light	p. 59
Modification to the spacetime diagram	p. 64
The problem	p. 66
The solution	p. 72
Einstein's argument	p. 80
The solution, continued	p. 85
Conservation of spacetime volume	p. 88
The Lorentz transformation	p. 94
The low velocity limit of the Lorentz transformation	p. 108
Addition of velocities	p. 110
Dependence of inertia on speed	p. 116
Causality	p. 120
Before and after	p. 120
Paradox?	p. 122
Instantaneous communication?	p. 124
Impossibility of faster than light travel	p. 126
The light-cone	p. 128
Consequences	p. 130
Synchronization of clocks	p. 130
Time dilation	p. 132
What time dilation DOES NOT mean	p. 138
Lorentz contraction	p. 140
What Lorentz contraction DOES NOT mean	p. 146
Twin paradox	p. 148
Doppler effect	p. 154
Red shift	p. 156
Blue shift	p. 158
Red shift and the expansion of the universe	p. 160
Summary of Part I	p. 162
Problems	p. 165
Qualitative problems	p. 166
Reading the spacetime diagram	p. 166
Street lamps	p. 166
Supernovae	p. 168
Questions on before and after	p. 170
The hare and the tortoise 1	p. 170
The hare and the tortoise 2	p. 172
The hare and the tortoise 3	p. 174
The starship and the supernova	p. 176
Relativistic sports	p. 178
Tagging up in baseball 1	p. 178
Tagging up in baseball 2	p. 180
The offside rule in soccer	p. 182
Lorentz contraction	p. 184
Train and tunnel	p. 184
The starship and the enemy space cruiser 1	p. 186
The starship and the enemy space cruiser 2	p. 188
The duel of the space cruisers	p. 190
Trains in a tunnel	p. 192
Solutions to Chapter 8 problems	p. 194
Quantitative problems	p. 200
Addition of velocities	p. 200
Dynamics: Relativity with a few equations	p. 207
The world's most famous equation	p. 209
The problem	p. 210
Newtonian dynamics	p. 212
The mass-momentum vector	p. 212
The impulse vector	p. 218
Inertial mass	p. 220
Newton's Second Law	p. 222
Newton's Third Law and the conservation of mass-momentum	p. 224
Relativistic dynamics	p. 230
The energy-momentum vector	p. 230
The energy-momentum vector of a photon	p. 236
The work-impulse vector	p. 240
Conservation of energy-momentum	p. 244
E = mc2	p. 246
Common misconception about E = mc2	p. 248
Summary of Part III	p. 251
Afterword	p. 252
References	p. 254
Index	p. 255
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