Special Relativity: A Heuristic Approach

Description

Special Relativity: A Heuristic Approach provides a qualitative exposition of relativity theory on the basis of the constancy of the speed of light. Using Einstein's signal velocity as the defining idea for the notion of simultaneity and the fact that the speed of light is independent of the motion of its source, chapters delve into a qualitative exposition of the relativity of time and length, discuss the time dilation formula using the standard light clock, explore the Minkowski four-dimensional space-time distance based on how the time dilation formula is derived, and define the components of the two-dimensional space-time velocity, amongst other topics. Provides a heuristic derivation of the Minkowski distance formulaUses relativistic photography to see Lorentz transformation and vector algebra manipulation in actionIncludes worked examples to elucidate and complement the topic being discussedWritten in a very accessible style Cover Special Relativity: A Heuristic Approach Copyright Dedication Preface List of Symbols, Phrases, and Acronyms Note to the Reader 1 Qualitative Relativity 1.1 It Began With Maxwell 1.1.1 Einstein and Signal Velocity 1.2 Relativity of Simultaneity 1.2.1 Simultaneity in a Single RF 1.2.2 Simultaneity in Different RFs 1.3 Relativity of Length 1.4 Problems 2 Relativity of Time and Space 2.1 Time Dilation 2.1.1 Proper Time 2.2 Length Contraction 2.3 Relativisticity 2.4 The Twin Paradox 2.5 Problems 3 Lorentz Transformation 3.1 "Derivation" of Euclidean Distance 3.1.1 Coordinate Transformation 3.2 Spacetime Distance 3.3 Lorentz Transformation 3.4 Examples of the Use of LT 3.5 Relativistic Law of Addition of Velocities 3.6 Problems 4 Spacetime Geometry 4.1 Plane Spacetime Geometry 4.1.1 Events and Worldlines 4.1.2 Light Cone 4.2 Rules of Spacetime Geometry 4.2.1 Invariant Distance 4.2.2 The Rules 4.3 Examples of Spacetime Diagrams 4.3.1 Simultaneity Revisited 4.3.2 The Train and the Tunnel 4.3.3 The Doppler Effect 4.3.4 Time Travel? 4.4 Lorentz Transformation Revisited 4.4.1 Lorentz Transformation and Time Travel 4.5 Curved Worldlines 4.5.1 The Spacetime Triangle Inequality 4.5.2 The Twin Paradox Revisited 4.6 Problems 5 Spacetime Momentum 5.1 Spacetime Velocity 5.2 Spacetime Momentum 5.2.1 Relativistic Energy 5.2.2 No Mass at Light Speed 5.2.3 Invariant Length of Spacetime Momentum 5.2.4 No Velocity-Dependent Mass 5.3 Conservation of Momentum 5.3.1 The Classical Case 5.3.2 The Relativistic Case 5.4 Problems 6 Relativity in Four Dimensions 6.1 Four-Vectors 6.2 Lorentz Transformation in 4D 6.3 General Velocity Addition Formula 6.3.1 Aberration Aberration of Starlight 6.4 General Doppler Effect 6.5 Global Positioning System 6.6 Four-Velocity 6.7 Four-Momentum 6.8 Second Law of Motion 6.8.1 Four-Acceleration 6.8.2 Four-Force 6.8.3 Weirdness of Velocity-Dependent Mass 6.9 Problems 7 Relativistic Photography 7.1 History 7.2 Physics of Photography 7.3 Photograph of Two Points 7.4 Photograph of a Rod 7.5 Photograph of a Cube 7.5.1 Capturing Length Contraction With a Camera 7.6 Photograph of a Sphere at the Origin 7.6.1 Cone Construction via Aberration Formula 7.6.2 Cone Construction via Relativistic LAV 7.6.3 Cone Construction via LT of Emission Events 7.7 Photograph of a Sphere off the Origin 7.7.1 Stationary Sphere 7.7.2 Moving Sphere 7.8 Problems 8 Relativistic Interactions 8.1 Center of Mass and Lab Frames 8.1.1 Lorentz Transformation of CM 8.2 Two-Particle Collision 8.2.1 Minimum Two-Particle Production Energy 8.2.2 Minimum Multi-Particle Production Energy 8.3 Decays 8.4 Special Relativity, Spin, and Antimatter 8.4.1 Dirac Equation 8.4.2 Discovery of Antimatter 8.5 Problems 9 Interstellar Travel 9.1 Massive Particle Propulsion 9.2 Photon Propulsion 9.2.1 Uniform Depletion 9.2.2 Laser Propulsion 9.3 Ground-Based Propulsion 9.3.1 The Physics 9.3.2 The Equation of Motion 9.3.3 The Formal Solution 9.3.4 Numerical Examples 9.3.5 Nonrelativistic Limits 9.4 Problems 10 A Painless Introduction to Tensors 10.1 From Boldface to Indices 10.1.1 Dot and Cross Products 10.1.2 Proof of Note 7.6.2 10.2 Index Management in Special Relativity 10.3 Invariance of the Elemental 4-Volume 10.4 Problems 11 Relativistic Electrodynamics 11.1 Transformation of Ē and B̄ 11.1.1 Transformation of Ē 11.1.2 Transformation of B̄ 11.2 Field of a Uniformly Moving Charge 11.3 Electromagnetic Field Tensor 11.3.1 Lorentz Force Law 11.3.2 The Cyclotron 11.3.3 Maxwell's Equations 11.4 Problems 12 Early Universe 12.1 Photon Gas 12.2 Friedmann Equation 12.3 The Densities 12.4 Evolution of the Universe Matter Dominance Radiation Dominance Dark Energy Dominance 12.5 Cosmic Background Radiation 12.6 Cosmic Genesis The First Epoch 1015 K