I Space Time Motion
1 Measuring-Rods and Clocks
2 Inertial Systems
3 Coordinates and Velocities
3.1 One Inertial System
3.1.1 Space Coordinates
3.1.2 The Problem of Time Measurement
3.1.3 The Relative Velocity
3.2 Two Inertial Systems
3.2.1 Coordinate Transformations
3.2.2 Composition of Velocities
4 Special Coordinate Transformations
4.1 Definition of Simultaneity
4.2 The Linear Transformation Formulae
4.3 Composition of Velocities
5 Moving Measuring-Rods and Clocks
5.1 Moving and Stationary Measuring-Rods
5.2 Moving and Stationary Clocks
II The Principle of Relativity
6 Einstein's Principle of Relativity
Portrait Albert Einstein
7 Elementary Relativity
8 A Metrical Principle of Relativity
III Elementary Structure of Classical Spacetime
9 The Physical Postulates of Classical Spacetime
10 Elementary Relativity - The Galilean Transformation
IV Elementary Structure of Relativistic Spacetime
11 The Moving Rod is Shortened - The Michelson Experiment
Portrait Albert Abraham Michelson
Portrait Hendrik Antoon Lorentz
12 The Moving Clock Goes Behind -
Einstein's Experimentum Crucis of Special Relativity
12.1 The Light Cock
Portrait Emmy Noether
12.2 The General Law of Time Dilatation
13 The Physical Postulates of Relativistic Spacetime
14 Elementary Relativity - The Lorentz Transformation
15 Einstein's Composition Law for Arbitrary Directed Velocities
16 Test Experiments of Special Relativity
17 The Linear Approximation of Special Relativity
18 Overview of the Axiomatic Structure of Special Relativity
V Entire Theory on One Page
VI Newtonian Mechanics
19 The Newtonian Axioms Portrait Isaac Newton
20 Classical Mechanics
21 The Tolman Thought Experiment - The Relativistic Mechanics
21.1 The Relativistic Mass Formula
21.2 The Basic Relativistic Equations of Mechanics
VII Einstein's Idea of Energy-Mass Equivalence
22 The Inertia of Energy
23 Einstein's Idea of Energy-Mass Equivalence
VIII Relativistic Phenomena and Paradoxes
24 Fresnel's Drag Coefficient
25 A Paradox to the Drag Coefficient
26 Thomas Precession
27 The Measuring-Rod Paradox
28 Doppler Effect
28.1 Classical Theory of Doppler Effect
28.1.1 Longitudinal Observation
28.1.2 Transversal Observation
28.2 Exact Theory of Doppler Effect
28.2.1 Longitudinal Observation
28.2.2 Transversal Observation
29 Aberration
29.1 Aberration in the Particle Picture
29.2 Aberration in the Wave Picture
30 A Paradox for the Aberration of Waves
31 The Twin Paradox
32 The Measuring-Rod Paradox and the Twin Paradox using Non-Conventional Simultaneity
32.1 The Measuring-Rod Paradox
32.2 The Twin Paradox
IX Mathematical Formalism of Special Relativity
33 The Lorentz Group
33.1 The Special Lorentz- Transformation
33.2 The General Lorentz- Transformation
33.3 The General Proper Lorentz- Transformation
33.4 General Theory of Thomas- Precession
33.5 Geometry in Minkowski- Space
33.6 Einstein's Principle of Relativity in Minkowski-Space
34 The Covariant Formulation of Relativistic Mechanics
34.1 The Motion of a Particle in Minkowski-Space
34.1.1 Proper-Time of Particle Motion
34.1 The Motion of a Particle in Minkowski-Space
34.2 Dynamics of Particles in Minkowski-Space
35 Electrodynamics - Covariant Formulation
35.1 Maxwell-Theory
35.1.1 Charges and Currents - Continuity Equation
35.1.2 Lorentz-Force
35.1.3 Magnetic Flux and Law of Induction
35.1.4 Electrical Displacement and Magnetic Excitation
35.1.5 Maxwell's Equations - Electromagnetic Waves
Portrait James Clerk Maxwell
35.2 The Covariant Formulation of Electrodynamics
35.2.1 The Four-dimensional Variables of Electrodynamics
35.2.2 Four-dimensional Electrodynamics in Vacuum.
35.2.3 Four-dimensional Electrodynamics of Moving Media
Portrait Hermann Minkowski
35.3 Electrodynamics in Absolut Units
35.3.1 Electrodynamics in a medium
35.3.2 Electrodynamics in a - Four-dimensional Formulation
35.3.3 The Energy-Momentum- Tensor of the Maxwell-Field
X The Representations of the Lorentz-Group
Weyl-Equation and Dirac-Equation
36 Remembering to Group-Theory
37 The Tensorial Representations of Lorentz-Group
Relativistic Mechanics and Electrodynamics
38 The Spinorial Representations of Lorentz-Group
Weyl-Equation and Dirac-Equation
38.1 The group C2
38.2 The relation between C2 to Lorentz-Group A2
38.3 Spinor Calculus
39 The Covariant Formulation of the Principle of Relativity
Weyl-Equation and Dirac-Equation
39.1 Weyl-Equation
39.2 Dirac-Equation
40 The Physical Background of Dirac-Equation
40.1 Remembering Quantum Mechanics
Portrait David Hilbert
Portrait Werner Karl Heisenberg
40.1.1 Angular Momentum.
Portrait Erwin Schroedinger
40.2 Transition to Dirac-Equation
41 Other Representations of Dirac-Equation
42 Dirac-Equation, Schroedinger-Equation and Pauli-Equation
XI Electrodynamics in Exterior Calculus
43 The Wedge Product
44 Di_erential Forms
45 Maxwell-Equations
XIIA Lattice Modell of Relativistic Space -Time
46 The Lattice Model
47 A Clock Paradox
XIII Einstein's General Theory of Relativity
48 Gravitation according to Newton and Einstein
Portrait Georg Friedrich Bernhard Riemann
XIV Appendix
49 Problems and Solutions
50 Mathematical Tools
50.1 Remembering to Tensor Calculus
50.2 Integral Theorems
Portrait Carl Friedrich Gauss
50.3 The _-Function
References
Index