The Manga Guide ™ to Comics PRaise for the manga guide series inside! “Highly Recommended.” — Choice Magazine T RReellaattiivviittyy “Stimulus for the next generation of scientists.” — Scientific computing H E “A great fit of FOrm and subject. Recommended.” — Otaku USA Magazine M A N G Hideo Nitta A Masafumi Yamamoto Keita Takatsu G Trend-Pro Co., Ltd. U I D A Charming Cartoon Guide to E ™ The Theory of Relativity T O Everything’s gone screwy at Takai Academy. The Manga Guide to Relativity also R When the crazy headmaster forces Minagi’s teaches you how to: E entire class to study Einstein’s theory Understand and use E = mc², the world’s L of relativity over summer school, Minagi most famous equation A volunteers to go in their place. There’s T just one problem: He’s never even heard Calculate the effects of time dilation I of relativity before! Luckily, Minagi has the using the Pythagorean theorem v plucky Miss Uraga to teach him. I Understand classic thought experiments T follow along with The Manga Guide like the Twin Paradox, and see why Y to Relativity as Minagi learns about the length contracts and mass increases non-intuitive laws that shape our universe. at relativistic speeds Before you know it, you’ll master difficult Grasp the underpinnings of Einstein’s concepts like inertial frames of refer- special and general theories of relativity ence, unified space-time, and the equivalence principle. You’ll even see how relativity If the idea of bending space and time really affects modern astronomy and discover warps your brain, The Manga Guide to y a why GPS systems and other everyday tech- Relativity will straighten things out. M Ta nologies depend on Einstein’s extraordinary RM EoN discovery. NdToItt -P, Ta Ra, ok a T S THE FINEST IN GEEK ENTERTAINMENT™ u www.nostarch.com $19.95 ($22.95 CDN) SHELvE IN: SCIENCE/PhySICS/RElaTIvITy , “I LIE FLAT.” This book uses a lay-flat binding that won't snap shut. Find more Manga Guides at www.edumanga.me 44055 cov1 11-03-23 21:29:52 Cyan, Magenta, Yellow, Black 44055_COV.indd 1 11-03-17 9:41 AM Praise for the Manga Guide series “Highly recommended.” —choice magazine on the manga guide to databases “Stimulus for the next generation of scientists.” —scientific computing on the manga guide to molecular biology “A great fit of form and subject. Recommended.” —otaku usa magazine on the manga guide to physics “The art is charming and the humor engaging. A fun and fairly painless lesson on what many consider to be a less-than-thrilling subject.” —school library journal on the manga guide to statistics “This is really what a good math text should be like. Unlike the majority of books on subjects like statistics, it doesn’t just present the material as a dry series of pointless- seeming formulas. It presents statistics as something fun, and something enlightening.” —good math, bad math on the manga guide to statistics “I found the cartoon approach of this book so compelling and its story so endearing that I recommend that every teacher of introductory physics, in both high school and Wow! college, consider using it.” —american journal of physics on the manga guide to physics “A single tortured cry will escape the lips of every thirty- something biochem major who sees The Manga Guide to Molecular Biology: ‘Why, oh why couldn’t this have been written when I was in college?’” —the san francisco examiner “A lot of fun to read. The interactions between the char- acters are lighthearted, and the whole setting has a sort of quirkiness about it that makes you keep reading just for the joy of it.” —hack a day on the manga guide to electricity “The Manga Guide to Databases was the most enjoyable tech book I’ve ever read.” —rikki kite, linux pro magazine “For parents trying to give their kids an edge or just for kids with a curiosity about their electronics, The Manga Guide to Electricity should definitely be on their bookshelves.” —sacramento book review RELATIVITY_03.indb 1 3/15/2011 3:25:43 PM “This is a solid book and I wish there were more like it in the IT world.” —slashdot on the manga guide to databases “The Manga Guide to Electricity makes accessible a very intimidating subject, letting the reader have fun while still delivering the goods.” —geekdad blog, wired.com “If you want to introduce a subject that kids wouldn’t normally be very interested in, give it an amusing storyline and wrap it in cartoons.” —make on the manga guide to statistics “This book does exactly what it is supposed to: offer a fun, interesting way to learn calculus concepts that would otherwise be extremely bland to memorize.” —daily tech on the manga guide to calculus “The art is fantastic, and the teaching method is both fun and educational.” —active anime on the manga guide to physics “An awfully fun, highly educational read.” —frazzleddad on the manga guide to physics “Makes it possible for a 10-year-old to develop a decent working knowledge of a subject that sends most college students running for the hills.” —skepticblog on the manga guide to molecular biology “This book is by far the best book I have read on the subject. I think this book absolutely rocks and recommend it to anyone working with or just interested in databases.” —geek at large on the manga guide to databases “The book purposefully departs from a traditional physics textbook and it does it very well.” —dr. marina milner-bolotin, ryerson university on the manga guide to physics “Kids would be, I think, much more likely to actually pick this up and find out if they are interested in statistics as opposed to a regular textbook.” —geek book on the manga guide to statistics “The Manga Guide to Statistics offers a visualization of statistics that can’t be found in any mere textbook.” —anime 3000 “A great introduction for readers of any age, and an exemplar of technical communication.” —linux users of victoria on the manga guide to electricity RELATIVITY_03.indb 2 3/15/2011 3:25:43 PM The Manga Guide™ to Relativity RELATIVITY_03.indb 3 3/15/2011 3:25:43 PM RELATIVITY_03.indb 4 3/15/2011 3:25:43 PM The Manga Guide™ to RELATIVITY Hideo Nitta Masafumi Yamamoto Keita Takatsu Trend-pro Co., Ltd. RELATIVITY_03.indb 5 3/15/2011 3:25:43 PM The Manga Guide to Relativity. Copyright © 2011 by Hideo Nitta, Masafumi Yamamoto, and TREND-PRO Co., Ltd. The Manga Guide to Relativity is a translation of the Japanese original, Manga de wakaru soutaiseiriron, published by Ohmsha, Ltd. of Tokyo, Japan, © 2009 by Hideo Nitta, Masafumi Yamamoto, and TREND-PRO Co., Ltd. This English edition is co-published by No Starch Press, Inc. and Ohmsha, Ltd. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without the prior written permission of the copyright owner and the publisher. 15 14 13 12 11 1 2 3 4 5 6 7 8 9 ISBN-10: 1-59327-272-3 ISBN-13: 978-1-59327-272-2 Publisher: William Pollock Supervising Editor: Hideo Nitta Author: Masafumi Yamamoto Illustrator: Keita Takatsu Producer: TREND-PRO Co., Ltd. Production Editor: Serena Yang Developmental Editor: Tyler Ortman Translator: Arnie Rusoff Technical Reviewers: David Issadore and John Roeder Compositor: Riley Hoffman Copyeditor: Paula L. Fleming Proofreader: Serena Yang Indexer: Sarah Schott For information on book distributors or translations, please contact No Starch Press, Inc. directly: No Starch Press, Inc. 38 Ringold Street, San Francisco, CA 94103 phone: 415.863.9900; fax: 415.863.9950; [email protected]; http://www.nostarch.com/ Library of Congress Cataloging-in-Publication Data Nitta, Hideo, 1957- [Manga de wakaru soutaiseiriron. English] The manga guide to relativity / Hideo Nitta, Masafumi Yamamoto, Keita Takatsu ; Trend-pro Co., Ltd. -- English ed. p. cm. Includes index. ISBN-13: 978-1-59327-272-2 ISBN-10: 1-59327-272-3 1. Relativity (Physics)--Comic books, strips, etc. 2. Graphic novels. I. Yamamoto, Masafumi, 1947- II. Takatsu, Keita. III. Trend-pro Co. IV. Title. QC173.57.N5813 2010 530.11--dc22 2010038111 No Starch Press and the No Starch Press logo are registered trademarks of No Starch Press, Inc. Other product and company names mentioned herein may be the trademarks of their respective owners. Rather than use a trademark symbol with every occurrence of a trademarked name, we are using the names only in an editorial fashion and to the benefit of the trademark owner, with no intention of infringement of the trademark. The information in this book is distributed on an “As Is” basis, without warranty. While every precaution has been taken in the preparation of this work, neither the author nor No Starch Press, Inc. shall have any liability to any person or entity with respect to any loss or damage caused or alleged to be caused directly or indirectly by the information contained in it. All characters in this publication are fictitious, and any resemblance to real persons, living or dead, is purely coincidental. RELATIVITY_03.indb 6 3/15/2011 3:25:43 PM Table of Contents Preface................................................................... ix Prologue: Outrageous closing ceremony.......................... 1 1 What Is Relativity?...................................................... 9 1. What Is Relativity ........................................................... 14 2. Galilean Principle of Relativity and Newtonian Mechanics ........................... 17 3. Mystery of the Speed of Light ................................................. 23 4. Einstein Discarded Newtonian Mechanics ........................................ 34 What Is Light? ............................................................... 40 Light Is Constant (and They Prove It Every Day in a Lab Called SPring-8)................. 43 What’s Simultaneous Depends on Whom You Ask! (Simultaneity Mismatch) ............... 44 Case of Newtonian Velocity Addition (Nonrelativistic Addition)....................... 44 Case in Which the Speed of Light Is Constant (Relativistic Addition of Velocity).......... 46 Galilean Principle of Relativity and Galilean Transformation............................. 47 Differences Between the Galilean Principle of Relativity and Einstein’s Special Principle of Relativity.................................................................... 48 Wait a Second—What Happens with the Addition of Velocities?.......................... 48 2 What Do You Mean, Time Slows Down?............................... 51 1. Urashima Effect (Time Dilation)................................................ 54 2. Why Does Time Slow Down? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3. The Slowing of Time Mutually Affects Each Party Equally............................ 64 4. Looking at the Slowing of Time Using an Equation................................. 73 Using the Pythagorean Theorem to Prove Time Dilation............................... 78 How Much Does Time Slow Down? .............................................. 80 3 The Faster an Object moves, the Shorter and Heavier It Becomes?.... 83 1. Does Length Contract When You Go Faster?...................................... 86 2. Do You Get Heavier When You Go Faster?........................................ 92 Using an Equation to Understand Length Contraction (Lorentz Contraction) .............. 106 Muons with Extended Life Spans................................................ 108 Mass When Moving........................................................... 109 Galilean Transformation ................................................... 109 Newton’s Second Law of Motion ............................................ 109 Lorentz Transformation.................................................... 111 Relationship Between Energy and Mass .......................................... 112 Does Light Have Zero Mass? ................................................... 113 RELATIVITY_03.indb 7 3/15/2011 3:25:43 PM 4 What Is General Relativity........................................... 115 1. Equivalence Principle ....................................................... 120 2. Light Is Bent by Gravity ..................................................... 133 3. Time Is Slowed Down by Gravity .............................................. 143 4. Relativity and the Universe................................................... 149 The Slowing of Time in General Relativity ......................................... 158 The True Nature of Gravity in General Relativity .................................... 162 Phenomena Discovered from General Relativity .................................... 162 Bending of Light (Gravitation Lensing) Near a Large Mass (Such as the Sun) ......... 162 Anomalous Perihelion Precession of Mercury .................................. 164 Black Holes............................................................. 164 Global Positioning System and Relativity .......................................... 165 Epilogue ............................................................... 167 Index ................................................................... 175 viii Table of Contents RELATIVITY_03.indb 8 3/15/2011 3:25:43 PM