Special Relativity for the Enthusiast

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