Special Relativity for the Enthusiast

Description

This textbook introduces special relativity with a focus on a profound understanding of the physics behind the theory. The main part of the book is targeted to undergraduates, for physics education, for undergraduate students in natural sciences in general, and even to interested laypersons. To serve these target groups, the book uses only basic mathematics and, in contrast to many other introductions to special relativity, the book is based on a pedagogical approach that relies on geometry and space-time diagrams to make the surprising predictions of the theory particularly clear. Special relativity is a geometric theory, and space-time diagrams are an efficient and easily understandable way to comprehend its implications. The textbook, however, is also suitable for advanced students and enthusiasts that already learned the basics of the special theory of relativity and want to know more. Special digression sections provide plenty of interesting material. Carefully selected problems with solutions and in-depth explanations for all key experiments help deepen the knowledge. Preface Contents 1 Introduction 2 The Limits of Classical Mechanics 2.1 The Bertozzi Experiment 2.1.1 Introduction 2.1.2 Principle 2.1.3 More Details 2.1.4 Result 2.1.5 Discussion 3 The Relativity Principle of Classical Mechanics 3.1 Reference Frames 3.2 Newton's Laws 3.3 Inertial Frames 3.3.1 Fictitious Forces 3.3.2 Inertial Frames 3.4 The Galilean Principle of Relativity 3.4.1 Introduction 3.4.2 Quantitative Description and Galilei Transformation 3.4.3 Summary 3.5 Addition of Velocities 3.6 Summary 4 Waves and Light 4.1 Introduction 4.2 Waves in Media 4.2.1 What Are Waves in Media? 4.2.2 Waves in Moving Media: Qualitative Discussion I 4.2.3 Waves in Moving Media: Qualitative Discussion II 4.2.4 Doppler Effect 4.2.5 Aberration 4.2.6 Waves in Media and the Relativity Principle 4.3 Light as a Wave and the Supposed Luminiferous Aether 4.3.1 Light is a Wave 4.3.2 The Medium of the Light Wave? 4.4 Stellar Aberration 4.4.1 Bradley's Discovery 4.4.2 Bradley's Explanation 4.4.3 Justification of the Explanation 4.5 Digression: The Transformation of Waves 4.5.1 Transformation of Frequency and Wavevector 4.5.2 The Dispersion Relation 4.5.3 The Velocity of a Wave 5 The Unsuccessful Hunt for the Special Inertial Frame 5.1 First Reflections 5.2 The Experiment by Michelson and Morley and Its Consequences 5.2.1 How It Works 5.2.2 Result 5.2.3 Digression: Arbitrary Orientation of the Interferometer 5.3 Explanation Possibilities 5.3.1 Possibility 1: We Are in the Special Inertial Frame 5.3.2 Possibility 2: A Non-homogeneous Luminiferous Aether 5.3.3 Possibility 3: The Speed of Light is Relative to the Emitter 5.3.4 Possibility 4: Lorentz-FitzGerald Contraction and Lorentz's Ether Theory 5.3.5 Possibility 5: There Is No Special Inertial Frame 5.4 Summary 6 Einstein's Solution: The Special Theory of Relativity (SR) 6.1 Einstein's Two Principles and Their Consequences 6.2 The Relevance of the Principle of Relativity 6.3 Digression: Measuring the Speed of Light 6.3.1 Determining Distances and Sizes in the Solar System 6.3.2 Rømer's Method 6.3.3 Bradley and Stellar Aberration 6.3.4 The Method of the Rotating Mirror 6.3.5 Modern Measurement and Definition of the Value 7 Relativity of Simultaneity 7.1 Introduction 7.2 The Spacetime Diagram I 7.3 Simultaneity and Synchronous Clocks 7.4 Alice and Bob in Space 7.5 Simultaneity Is Relative! 7.5.1 Gedanken Experiment 7.5.2 The Difference from Classical Physics 7.5.3 Spacetime Diagram 7.6 The Spacetime Diagram II: Simultaneity 7.7 Digression: Further Thoughts on Simultaneity 7.7.1 Introduction 7.7.2 Generalized Lorentz Transformation 7.7.3 Lorentz's Ether Theory Versus Einstein's Special Relativity 7.8 Causality and Faster-than-Light Velocity 7.8.1 The Casino Fraud 7.8.2 Past, Present and Future 7.9 Digression: Rotating Reference Frames 7.9.1 Again: Synchronization of Clocks 7.9.2 The Sagnac Interferometer 8 Length Contraction 8.1 Introduction 8.2 Derivation 8.2.1 Length Measurement 8.2.2 Length Contraction in the Direction of Motion 8.2.3 Digression: Length Change Transversal to the Direction of Motion? 8.3 Examples 8.3.1 Muons 8.3.2 Ladder Paradox 8.4 Digression: Hyperbolic Motion 8.4.1 Motion with Constant Acceleration 8.4.2 The Accelerated Rod 8.5 Visibility of Length Contraction 9 Time Dilation 9.1 Introduction 9.2 Derivation 9.3 Digression: Time Measurement 9.4 Digression: Atomic Clocks 9.4.1 Overview 9.4.2 The Caesium Atom and Spin 9.4.3 Measuring the Spin 9.4.4 The Compound Particle 9.4.5 Acting on the Compound Spin 9.4.6 The Caesium Beam Atomic Clock 9.5 The Spacetime Diagram III: Scales 9.6 The Relativistic Doppler Effect 9.6.1 Longitudinal Doppler Effect 9.6.2 Transversal Doppler Effect and the General Formula 9.7 The Experiment by Ives and Stilwell 9.8 The Experiment by Kennedy and Thorndike 9.9 Twin Paradox 9.10 Digression: Proper Time 9.11 Examples 9.11.1 Again: Muons 9.11.2 The Experiment by Hafele and Keating 9.11.3 Satellite Navigation 10 Lorentzian Addition of Velocities 10.1 Introduction 10.2 Addition of Velocities 10.3 Digression: The Fizeau Experiment 11 The Lorentz Transformation: Derivation 11.1 Graphical Derivation of the Lorentz Transformation 11.2 Digression: The Lorentz Transformation in Matrix Form 11.3 Digression: Analytic Derivation of the Lorentz Transformation 11.4 Digression: The Lorentz Transformation from Empirics 12 The Lorentz Transformation: Applications 12.1 Again: The Effects of Special Relativity 12.2 Digression: The Velocity Four-Vector 12.3 Digression: Addition of Non-parallel Velocities 12.4 Relativistic Stellar Aberration 12.4.1 Including Relativistic Effects 12.4.2 Digression: Clarifications Regarding Stellar Aberration 12.5 Lorentz Transformation of Waves 12.5.1 Invariance of the Phase and Transformation of a Wave 12.5.2 The Doppler Effect and Aberration for Light Waves 12.5.3 The Transformation of the Wavevector in Classical and Relativistic Physics 12.5.4 Again: The Velocity of a Wave 12.6 The Michelson-Morley Experiment Revisited 13 Energy and Momentum 13.1 The Relativistic Energy 13.1.1 Gedanken Experiment 13.1.2 The Relativistic Energy 13.1.3 Again: Speed of Light as Maximum Velocity 13.1.4 The Discussion About the ``Relativistic Mass'' 13.2 ``Conversion'' of Mass into Energy: Mass Defect 13.3 The Relativistic Momentum 13.4 Interplay of Energy and Momentum 13.5 Energy and Momentum Conservation Laws 13.5.1 Conservation Laws 13.5.2 Principle of Relativity 13.5.3 Classical Mechanics 13.5.4 Theory of Relativity with Classical Momentum 13.5.5 Theory of Relativity 13.6 The Compton Effect 14 Electrodynamics 14.1 Transformation of Charges and Fields 14.2 Electrodynamics and Spacetime Effects 14.2.1 The Charged Capacitor 14.2.2 The Current-Carrying Wire 14.2.3 The Four-Vector of the Current Density 14.3 Electromagnetic Field of a Moving Point Charge 15 Towards General Relativity 15.1 The Need for a More General Theory 15.2 Recap of Newton's Theory of Gravitation 15.3 The Equivalence Principle 15.3.1 The Equivalence Principle 15.3.2 Consequences from the Equivalence Principle 15.4 Curved Surfaces 15.4.1 The Geometry of Curved Surfaces 15.4.2 Quantitative Description of Curved Surfaces 15.5 Curved Spacetime and General Relativity 15.5.1 Curved Surfaces Versus Curved Spacetime 15.5.2 The Principle of Stationary Action and Geodesics 15.5.3 The Complete Picture 15.6 Example: Curved Spacetime Caused by a Large Spherically Symmetric Source 15.6.1 Schwarzschild Metrics 15.6.2 The Embedding Diagram 16 Summary Appendix Useful Formulas A.1 Frequently Used Approximations A.2 From Special Relativity A.2.1 The Doppler Effect A.2.2 Aberration A.2.3 Lorentzian Addition of Velocities A.2.4 Others Appendix References Index