An Illustrated Guide to Relativity

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. Cover......Page 1 Half-title......Page 3 Title......Page 5 Copyright......Page 6 Contents......Page 7 Preface to English edition......Page 10 Preface to Japanese edition......Page 11 Part I: Kinematics......Page 13 1 Welcome to the world of relativity......Page 14 Notes......Page 15 2.1 Questions about motion......Page 16 2.2 Frames of reference......Page 17 2.3 Relativity of motion......Page 24 2.4 The Law of Inertia......Page 26 2.5 Inertial and non-inertial frames......Page 30 2.6 What's so "special'' about Special Relativity?......Page 38 Notes......Page 40 3.1 Basic questions......Page 42 3.2 Spacetime diagrams......Page 46 3.3 The Galilei transformation......Page 52 3.4 Addition of velocities......Page 66 3.5 Acceleration and Newton's Second Law......Page 68 Notes......Page 70 4.1 The mystery of the speed of light......Page 71 4.2 Modification to the spacetime diagram......Page 76 4.3 The problem......Page 78 4.4 The solution......Page 84 4.5 Einstein's argument......Page 92 4.6 The solution, continued......Page 97 4.7 Conservation of spacetime volume......Page 100 4.8 The Lorentz transformation......Page 106 4.9 The low velocity limit of the Lorentz transformation......Page 120 4.10 Addition of velocities......Page 122 4.11 Dependence of inertia on speed......Page 128 Notes......Page 130 5.1 Before and after......Page 132 5.2 Paradox?......Page 134 5.3 Instantaneous communication?......Page 136 5.4 Impossibility of faster than light travel......Page 138 Notes......Page 140 6.1 Synchronization of clocks......Page 142 6.2 Time dilation......Page 144 6.3 What time dilation DOES NOT mean......Page 150 6.4 Lorentz contraction......Page 152 6.5 What Lorentz contraction DOES NOT mean......Page 158 6.6 Twin paradox......Page 160 6.7 Doppler effect......Page 166 6.7.1 Red shift......Page 168 6.7.2 Blue shift......Page 170 6.7.3 Red shift and the expansion of the universe......Page 172 7 Summary of Part I......Page 174 Part II: Problems......Page 177 8.1.1 Street lamps......Page 178 8.1.2 Supernovae......Page 180 8.2.1 The hare and the tortoise 1......Page 182 8.2.2 The hare and the tortoise 2......Page 184 8.2.3 The hare and the tortoise 3......Page 186 8.2.4 The starship and the supernova......Page 188 8.3.1 Tagging up in baseball 1......Page 190 8.3.2 Tagging up in baseball 2......Page 192 8.3.3 The offside rule in soccer......Page 194 8.4.1 Train and tunnel......Page 196 8.4.2 The starship and the enemy space cruiser 1......Page 198 8.4.3 The starship and the enemy space cruiser 2......Page 200 8.4.4 The duel of the space cruisers......Page 202 8.4.5 Trains in a tunnel......Page 204 8.2.1 The hare and the tortoise 1 – solution......Page 206 8.2.4 The starship and the supernova – solution......Page 207 8.3.3 The o.side rule in soccer – solution......Page 208 8.4.3 The starship and the enemy space cruiser 2 – solution......Page 209 8.4.5 Trains in a tunnel–solution......Page 210 Notes......Page 211 9.1 Addition of velocities......Page 212 Part III: Dynamics: Relativity with a few equations......Page 219 Notes......Page 221 11 The problem......Page 222 12.1 The mass–momentum vector......Page 224 12.2 The impulse vector......Page 230 12.3 Inertial mass......Page 232 12.4 Newton's Second Law......Page 234 12.5 Newton’s Third Law and the conservation of mass–momentum......Page 236 Notes......Page 240 13.1 The energy–momentum vector......Page 242 13.2 The energy–momentum vector of a photon......Page 248 13.3 The work–impulse vector......Page 252 13.4 Conservation of energy--momentum......Page 256 13.5 E=mc2......Page 258 13.6 Common misconception about E=mc2......Page 260 Notes......Page 261 14 Summary of Part III......Page 263 Afterword......Page 264 References......Page 266 Index......Page 267 Presents A Step-by-step Explanation Of Einstein's Special Theory Of Relativity Through A Series Of Diagrams Rather Than Equations. Pt. I. Kinematics: Relativity Without Any Equations -- 1. Welcome To The World Of Relativity -- 2. Basics -- Questions About Motion -- Frames Of Reference -- Relativity Of Motion -- The Law Of Inertia -- Inertial And Non-inertial Frames -- What's So Special About Special Relativity? -- 3. Galilean Relativity -- Basic Questions -- Spacetime Diagrams -- The Galilei Transformation -- Addition Of Velocities -- Acceleration And Newton's Second Law -- 4. Einsteinian Relativity -- The Mystery Of The Speed Of Light -- Modification To The Spacetime Diagram -- The Problem -- The Solution -- Einstein's Argument -- The Solution, Continued -- Conservation Of Spacetime Volume -- The Lorentz Transformation -- The Low Velocity Limit Of The Lorentz Transformation -- Addition Of Velocities -- Dependence Of Inertia On Speed -- 5. Causality -- Before And After -- Paradox? -- Instantaneous Communication? -- Impossibility Of Faster Than Light Travel -- The Light-cone -- 6. Consequences -- Synchronization Of Clocks -- Time Dilation -- What Time Dilation Does Not Mean -- Lorentz Contraction -- What Lorentz Contraction Does Not Mean -- Twin Paradox -- Doppler Effect -- Red Shift -- Blue Shift -- Red Shift And The Expansion Of The Universe. Pt. Ii. Problems -- 8. Qualitative Problems -- Reading The Spacetime Diagram -- Street Lamps -- Supernovae -- Questions On Before And After -- The Hare And The Tortoise 1, 2, 3 -- The Starship And The Supernova -- Relativistic Sports -- Tagging Up In Baseball 1, 2 -- The Offside Rule In Soccer -- Lorentz Contraction -- Train And Tunnel -- The Starship And The Enemy Space Cruiser 1, 2 -- The Duel Of The Space Cruisers -- Trains In A Tunnel -- 9. Quantitative Problems -- Addition Of Velocities. Pt. Iii. Dynamics: Relativity With A Few Equations -- 10. The World's Most Famous Equation -- 11. The Problem -- 12. Newtonian Dynamics -- The Mass-momentum Vector -- The Impulse Vector -- Inertial Mass -- Newton's Second Law -- Newton's Third Law And The Conservation Of Mass-momentum -- 13. Relativistic Dynamics -- The Energy-momentum Vector -- The Energy-momentum Vector Of A Photon -- The Work-impulse Vector -- Conservation Of Energy-momentum -- E=mc2 -- Common Misconception About E=mc2 -- 14. Summary Of Pt. Iii. Tatsu Takeuchi. Includes Bibliographical References (p. [254]) And Index. Unique book explaining Einstein's special theory of relativity through diagrams rather than equations, for physics students and non-science majors