Illustrated Special Relativity Through Its Paradoxes: Standard Edition: A Fusion of Linear Algebra, Graphics, and Reality PDF
Preview Illustrated Special Relativity Through Its Paradoxes: Standard Edition: A Fusion of Linear Algebra, Graphics, and Reality
Illustrated Special Relativity Through Its Paradoxes A Fusion of Linear Algebra, Graphics, and Reality c 2013 by the Mathematical Association of America, Inc. (cid:13) Library of Congress Catalog Card Number 2013956313 Electronic edition ISBN: 978-1-61444-517-3 Illustrated Special Relativity Through Its Paradoxes A Fusion of Linear Algebra, Graphics, and Reality John de Pillis Professor of Mathematics University of California, Riverside and Jos´e Wudka Professor of Physics University of California, Riverside Illustrations and animations by John dePillis Published and Distributed by The Mathematical Association of America Council on Publications and Communications Frank Farris, Chair Committee on Books Gerald Bryce, Chair Spectrum Editorial Board Gerald L. Alexanderson, Co-Editor James J. Tattersall,Co-Editor Robert E. Bradley Susanna S. Epp Richard K. Guy Keith M. Kendig Shawnee L. McMurran Jeffrey L. Nunemacher Jean J. Pedersen Kenneth A. Ross Marvin Schaefer Franklin F. Sheehan SPECTRUM SERIES TheSpectrumSeriesoftheMathematicalAssociationofAmericawas so named to reflect its purpose: to publish a broad range of books including biographies, accessible expositions of old or new mathe- matical ideas, reprints and revisions of excellent out-of-print books, popular works, and other monographs of high interest that will ap- peal to a broad range of readers, including students and teachers of mathematics, mathematical amateurs, and researchers. 777 MathematicalConversationStarters,by John de Pillis 99 Points of Intersection: Examples—Pictures—Proofs,by Hans Walser. TranslatedfromtheoriginalGermanbyPeterHiltonandJeanPedersen AhaGotchaand AhaInsight,by Martin Gardner All the Math That’sFit to Print,by KeithDevlin BeautifulMathematics,by Martin Erickson CalculusandIts Origins,by David Perkins Calculus Gems: Brief Lives and Memorable Mathematics, by George F. Simmons Carl Friedrich Gauss: Titan of Science, by G. 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A FIRST PASS 1 Preface 2 0.1 Exposition and Paradoxes . . . . . . . . . . . . . . . . 2 0.2 Organization of this Book . . . . . . . . . . . . . . . . 5 1 Introduction to the Paradoxes 11 1.1 Aristotle vs. Galileo . . . . . . . . . . . . . . . . . . . 11 1.2 Frames of Reference . . . . . . . . . . . . . . . . . . . 12 1.3 Straight-Line Trajectories in 3-Space . . . . . . . . . . 13 1.4 GalileanRelativity . . . . . . . . . . . . . . . . . . . . 14 1.5 Special Relativity: A First Pass . . . . . . . . . . . . . 16 1.6 A Symmetry Principle . . . . . . . . . . . . . . . . . . 18 1.7 Lorentzian Relativity . . . . . . . . . . . . . . . . . . . 19 1.8 The Ubiquitous Shrinkage Constant . . . . . . . . . . 19 1.9 Paradox: The Accommodating Universe . . . . . . . . 22 1.10 Paradox: Time and Distance Asymmetry . . . . . . . 26 1.11 Paradox: The Traveling Twin . . . . . . . . . . . . . . 29 1.12 Paradox: The Train in the Tunnel . . . . . . . . . . . 33 1.13 Paradox: The Pea-Shooter . . . . . . . . . . . . . . . . 36 1.14 Paradox: The Bug and Rivet . . . . . . . . . . . . . . 40 1.15 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 42 2 Clocks and Rods in Motion 43 2.1 The Perfect Clock . . . . . . . . . . . . . . . . . . . . 43 2.2 Synchronizing Clocks within a Single Frame . . . . . . 45 2.3 MovingClocks Run Slow,Moving Rods Shrink . . . . 47 2.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 50 3 The Algebra of Frames 54 3.1 Inertial Frames of Reference . . . . . . . . . . . . . . . 54 3.2 Vector Space Structure of Frames . . . . . . . . . . . . 55 3.3 Several Parallel MovingFrames . . . . . . . . . . . . . 56 3.4 Six Rules for Frames . . . . . . . . . . . . . . . . . . . 58 3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 64 4 The Graphing of Frames 66 4.1 The Filmstrip Model of Spacetime . . . . . . . . . . . 66 4.2 Constant Velocities in Spacetime . . . . . . . . . . . . 69 4.3 Worldlinesare Parallelto the Home Frame Time Axis 71 ix
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