Special Relativity - For Inquiring Minds

Description

This textbook introduces the special theory of relativity at a level which is accessible to undergraduate students and even high school students with a strong foundation in algebra. The presentation emphasizes clean algebraic and geometrical methods, visualized with plenty of illustrations, resulting in a textbook that is modern and serious yet accessible. Replete with many solved exercises and copious spacetime diagrams, this book will help students develop relativistic intuition when encountering the subject for the first time. The emphasis on geometric methods, combined with the pedagogically appealing k-calculus approach, makes this book ideal for a self-contained course on special relativity or as supplementary reading for modern physics courses. It will also appeal to high schoolers with a strong math background who want to get ahead. About the authors Yury Deshko holds a master’s in theoretical physics (with a focus on general relativity) from Belarus State University and a doctorate in physics from the Graduate Center of the City University of New York (CUNY). His research at CUNY focused on experimental spectroscopy and diamond photonics. He served as a research associate at City College of New York until joining the semiconductor industry as a photonics engineer. Yury Deshko’s pedagogical passion led him to teaching, for a number of years, the introduction into the special theory of relativity in summer schools of Johns Hopkins University and Columbia University. Preface Acknowledgment Contents Part I Relativity 1 Introduction 1.1 Brief Historical Context 1.2 Prelude 1.2.1 Static Observers 1.2.2 Relativity Principle 1.3 Quick Tour Through Special Relativity 1.3.1 Travel Time 1.3.2 Relative Velocity 1.3.3 Simultaneous Events 1.3.4 Kinetic Energy 1.3.5 Momentum 1.3.6 Transformation Equations 1.4 Who Needs Relativity? 1.5 Why Is Relativity Hard? References 2 Geometry 2.1 What Is Geometry? 2.2 Coordinates 2.2.1 Cartesian Coordinates 2.2.2 Polar Coordinates 2.2.3 Arctan Coordinates 2.2.4 Cantor Coordinates 2.2.5 Remarks on Coordinates 2.2.6 Transformations of Coordinates 2.3 Spaces and Dimensions 2.3.1 Space 2.3.2 Dimensions References 3 Spacetime 3.1 Events 3.2 Frame of Reference 3.3 Measuring Time 3.3.1 What Is Time? 3.3.2 Mechanical Clock 3.3.3 Electronic Clocks 3.3.4 Atomic Clocks 3.3.5 Random Clocks 3.3.6 Absolute Time and Universal Time 3.3.7 ``Time Itself'' 3.4 Measuring Distance 3.4.1 Interatomic Distance 3.4.2 Triangulated Distances 3.4.3 RADAR Method 3.5 Spacetime Diagrams 3.5.1 2D Spacetime Diagrams 3.5.2 3D Spacetime Diagrams 3.5.3 4D Spacetime Diagrams References 4 Galilean Relativity 4.1 Relative and Absolute in Mechanics 4.1.1 Relativity of Motion 4.1.2 Invariance of Durations and Lengths 4.1.3 Galilean Transformation 4.1.4 Galilean Transformation in 2D and 3D 4.1.5 Relativity of Velocity 4.1.6 Invariance of Acceleration 4.1.7 Length of a Moving Object 4.1.8 Invariance of Laws 4.2 Absolute Space and Time 4.3 Application of Galilean Relativity 4.4 Practice 4.4.1 Additional Remarks References 5 Special Relativity A 5.1 Light Postulate 5.2 Units 5.3 Observers 5.4 Minkowski Diagrams 5.4.1 Minkowski Terminology 5.4.2 Drawing Tips 5.5 Relativity of Simultaneity 5.6 Doppler k-factor 5.7 Relativistic Doppler Effect 5.7.1 Doppler Shift and Astrophysics 5.8 Muon Experiment 5.8.1 Frisch and Smith Experiment 5.8.2 Analysis of the Experiment 5.9 Composition of Velocities 5.10 Blue Shift and Reciprocity 5.11 Path Dependence of Time 5.11.1 Path Dependent Quantities 5.12 Looking at Moving Clock 5.13 Lorentz Transformation References 6 Special Relativity B 6.1 Simultaneity 6.2 Order of Events 6.3 Velocity Composition 6.3.1 Fizeau Experiment 6.4 Length Measurement 6.4.1 FitzGerald and Lorentz Hypotheses 6.5 Fundamental Invariant 6.5.1 Three Kinds of Interval 6.5.2 Distance in Spacetime 6.6 Past, Future, and Present 6.7 Proper Quantities 6.8 Lorentz Transformation as Rotation 6.9 ``Barn and Ladder'' Problem 6.9.1 Analysis in Barn's Reference Frame References 7 Special Relativity C 7.1 Lorentz Transformation in 4D 7.2 Velocity Composition Revisited 7.3 Relativistic Aberration 7.3.1 Relativistic Beaming 7.4 ``Momentum'' Not Conserved 7.5 Spacetime Vectors 7.5.1 Spacetime Displacement 7.5.2 Spacetime Velocity 7.5.3 Lorentz Transformation of Velocity 7.5.4 Spacetime Momentum 7.5.5 Spacetime Acceleration 7.6 Energy-Mass Equivalence 7.7 Practice in Energy-Momentum 7.7.1 Compton Scattering 7.8 Accelerated Motion References Closing Remarks What We Left Out? Suggested Reading A Mathematical A.1 Geometric Series A.2 -δ-notation A.3 Factor γ B Physical B.1 Symmetric Elastic Collision B.2 Relativistic Momentum B.3 Penrose Diagrams B.4 Generalized Lorentz Transformation B.5 Lengths of Objects B.5.1 Objects B.5.2 Lengths B.6 Additional Problems B.6.1 Geometry B.6.2 Galilean Relativity B.6.3 Special Relativity B.6.4 Energy-Momentum Answers B.7 Geometry B.8 Galilean Relativity B.9 Spacetime B.10 Special Relativity Extended Problem: Relativity of Simultaneity B.11 Additional Problems Hints B.12 Geometry B.13 Galilean Relativity B.14 Spacetime B.15 Special Relativity B.16 Additional Problems Solutions B.17 Geometry B.18 Galilean Relativity B.19 Spacetime B.20 Special Relativity B.21 Additional Problems Index