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.
Author(s): Thomas Strohm
Publisher: Springer
Year: 2023
Language: English
Pages: 346
City: Cham
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
