Introduction to Spacetime: A First Course on Relativity
| Date: 06 May 2011, 19:55
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Review
By Hanno Essen (Stockholm Sweden)
This material of this book was successfully used in a course of special relativity for advanced undergraduates at the University of Stockholm by the late professor Bertel Laurent, one of Oskar Klein's best students. When he sadly passed away shortly before retirement the manuscript was transformed into a book by his enthusiastic friend Stig Flodmark.
The book is unusual in that it does not discuss the historical, philosophical, and experimental background that most book dwell on a lot. Instead special relativity is clearly and simply presented with modern coordinate free (index free) notation as a correct and accepted theory of physics. I recommend it strongly as a concise, pedagogical, and compact course book with a modern point of view.
Contents
I PRINCIPLES. BASIC APPLICATIONS
1 Clocks and Acceleration
1.1 Measuring Time
1.2 Measuring Acceleration
1.3 The Principle of the Maximal Proper Time
1.4 Events. Space-Time
1.5 Parallel World Lines
2 Vector Algebra
2.1 Basic Properties
2.2 Scalar Product
3 Vector Characteristics
3.1 Timelike. Spacelike. Null-like
3.2 Comparison with Euclidean Space
4 Simultaneity and Space Distance
4.1 Simultaneity
4.2 Space Distance
4.3 The Orthogonal Space
5 Linear Independence
6 Relative Velocity and Four-Velocity
6.1 The Standard Velocity Split
6.2 Light Signals
6.3 Split of Null-Like Vectors
6.4 The Future and the Past
7 Two-Dimensional Spacetime
7.1 Lorenta Transformation
7.2 Addition of Velocities
7.3 Lorentz Contraction
8 Plane Waves
8.1 The Wave Four-Vector
8.2 Modulations
8.3 Doppler Shift and Aberration
9.1 Four-Momentum
9.2 Particle Kinematics
9 Particle Reactions
10 Curved World Lines a1
10.1 Four-Acceleration
10.2 Examples
10.2.1 Constant Acceleration
10.2.2 Fitting a Car into a Garage
10.2.3 Rotating Wheel
II TENSORS
11 Definition and Examples
11.1 Definition
11.2 Examples
12 Algebraic Properties
12.1 First Rank Tensors
12.2 Generalized Tensors
12.2.1 Symmetries
12.2.2 Abstract Indices
12.3 Tensor Algebra
12.4 Expansion
12.5 Contraction
12.6 Tensors and the Scalar Product
12.6.1 Relation between Vectors and Dual Vectors
12.6.2 The Metric Tensor
13 Tensor Fields
13.1 Scalar Fields. Gradients
13.2 Tensor Fields
14 Spacetime Volumes
14.1 Volume Without Metric
14.1.1 Basic Concepts. Parallelepipeds
14.1.2 Calculation of Volumes
14.1.3 Sums of Volumes
14.1.4 Volumes and Coordinates
14.2 Volume and Metric. Orientation
14.3 Hypersurface Volumes
15 Currents
15.1 Particle Flow. Four-Current Density
15.2 Gauss's Theorem
15.3 Different Kinds of Currents
III ELECTRODYNAMICS
16 Sourcefree Electromagnetism
16.1 The Wave Equation
16.2 The Field Tensor
16.3 The Field Equations
16.3.1 General Considerations
16.3.2 The Four-Potential Equations
16.3.3 The Field Tensor Equations
16.3.4 Gauge
16.4 Maxwell's Equations
16.4.1 The Electric and Magnetic Fields
16.4.2 The Field Equations
17 Electro-Magnetism with Sources
17.1 The Field Equations
17.1.1 Sources
17.1.2 Maxwell's Equations
17.1.3 The Potential Equations
17.2 Energy-Momentum
17.2.1 Dust
17.2.2 Electromagnetism
18.1 The Green's Function
18.2 The Lienard-Wiechert Potential
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