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E-raamat: Special Relativity: An Introduction with 200 Problems and Solutions

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  • Ilmumisaeg: 17-May-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642038372
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 17-May-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642038372

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Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using heavier mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a ´ la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones! As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity.
1 Mathematical Part
1(54)
1.1 Introduction
1(1)
1.2 Elements From the Theory of Linear Spaces
2(4)
1.2.1 Coordinate Transformations
2(4)
1.3 Inner Product - Metric
6(4)
1.4 Tensors
10(4)
1.4.1 Operations of Tensors
13(1)
1.5 The Case of Euclidean Geometry
14(3)
1.6 The Lorentz Geometry
17(9)
1.6.1 Lorentz Transformations
18(8)
1.7 Algebraic Determination of the General Vector Lorentz Transformation
26(14)
1.8 The Kinematic Interpretation of the General Lorentz Transformation
40(3)
1.8.1 Relativistic Parallelism of Space Axes
40(2)
1.8.2 The Kinematic Interpretation of Lorentz Transformation
42(1)
1.9 The Geometry of the Boost
43(5)
1.10 Characteristic Frames of Four-Vectors
48(2)
1.10.1 Proper Frame of a Time like Four-Vector
48(1)
1.10.2 Characteristic Frame of a Space like Four-Vector
49(1)
1.11 Particle Four-Vectors
50(2)
1.12 The Center System (CS) of a System of Particle Four-Vectors
52(3)
2 The Structure of the Theories of Physics
55(12)
2.1 Introduction
55(1)
2.2 The Role of Physics
56(3)
2.3 The Structure of a Theory of Physics
59(1)
2.4 Physical Quantities and Reality of a Theory of Physics
60(2)
2.5 Inertial Observers
62(1)
2.6 Geometrization of the Principle of Relativity
63(3)
2.6.1 Principle of Inertia
63(1)
2.6.2 The Covariance Principle
64(2)
2.7 Relativity and the Predictions of a Theory
66(1)
3 Newtonian Physics
67(20)
3.1 Introduction
67(1)
3.2 Newtonian Kinematics
68(6)
3.2.1 Mass Point
68(1)
3.2.2 Space
69(2)
3.2.3 Time
71(3)
3.3 Newtonian Inertial Observers
74(4)
3.3.1 Determination of Newtonian Inertial Observers
75(2)
3.3.2 Measurement of the Position Vector
77(1)
3.4 Galileo Principle of Relativity
78(1)
3.5 Galileo Transformations for Space and Time - Newtonian Physical Quantities
79(2)
3.5.1 Galileo Covariant Principle: Part I
79(1)
3.5.2 Galileo Principle of Communication
80(1)
3.6 Newtonian Physical Quantities. The Covariance Principle
81(1)
3.6.1 Galileo Covariance Principle: Part II
81(1)
3.7 Newtonian Composition Law of Vectors
82(1)
3.8 Newtonian Dynamics
83(4)
3.8.1 Law of Conservation of Linear Momentum
84(3)
4 The Foundation of Special Relativity
87(30)
4.1 Introduction
87(1)
4.2 Light and the Galileo Principle of Relativity
88(4)
4.2.1 The Existence of Non-Newtonian Physical Quantities
88(1)
4.2.2 The Limit of Special Relativity to Newtonian Physics
89(3)
4.3 The Physical Role of the Speed of Light
92(1)
4.4 The Physical Definition of Spacetime
93(3)
4.4.1 The Events
94(1)
4.4.2 The Geometry of Spacetime
94(2)
4.5 Structures in Minkowski Space
96(6)
4.5.1 The Light Cone
96(1)
4.5.2 World' Lines
97(1)
4.5.3 Curves in Minkowski Space
98(1)
4.5.4 Geometric Definition of Relativistic Inertial Observers (RIO)
99(1)
4.5.5 Proper Time
99(1)
4.5.6 The Proper Frame of a RIO
100(1)
4.5.7 Proper or Rest Space
101(1)
4.6 Spacetime Description of Motion
102(3)
4.6.1 The Physical Definition of a RIO
103(1)
4.6.2 Relativistic Measurement of the Position Vector
104(1)
4.6.3 The Physical Definition of an LRIO
105(1)
4.7 The Einstein Principle of Relativity
105(3)
4.7.1 The Equation of Lorentz Isometry
106(2)
4.8 The Lorentz Covariance Principle
108(2)
4.8.1 Rules for Constructing Lorentz Tensors
109(1)
4.8.2 Potential Relativistic Physical Quantities
110(1)
4.9 Universal Speeds and the Lorentz Transformation
110(7)
5 The Physics of the Position Four-Vector
117(38)
5.1 Introduction
117(1)
5.2 The Concepts of Space and Time in Special Relativity
117(1)
5.3 Measurement of Spatial and Temporal Distance in Special Relativity
118(2)
5.4 Relativistic Definition of Spatial and Temporal Distances
120(1)
5.5 Timelike Position Four-Vector - Measurement of Temporal Distance
121(5)
5.6 Spacelike Position Four-Vector - Measurement of Spatial Distance
126(3)
5.7 The General Case
129(1)
5.8 The Reality of Length Contraction and Time Dilation
130(2)
5.9 The Rigid Rod
132(2)
5.10 Optical Images in Special Relativity
134(7)
5.11 How to Solve Problems Involving Spatial and Temporal Distance
141(14)
5.11.1 A Brief Summary of the Lorentz Transformation
141(1)
5.11.2 Parallel and Normal Decomposition of Lorentz Transformation
142(1)
5.11.3 Methodologies of Solving Problems Involving Boosts
143(3)
5.11.4 The Algebraic Method
146(4)
5.11.5 The Geometric Method
150(5)
6 Relativistic Kinematics
155(30)
6.1 Introduction
155(1)
6.2 Relativistic Mass Point
155(4)
6.3 Relativistic Composition of Three-Vectors
159(7)
6.4 Relative Four-Vectors
166(8)
6.5 The three-Velocity Space
174(3)
6.6 Thomas Precession
177(8)
7 Four-Acceleration
185(68)
7.1 Introduction
185(1)
7.2 The Four-Acceleration
186(7)
7.3 Calculating Accelerated Motions
193(4)
7.4 Hyperbolic Motion of a Relativistic Mass Particle
197(7)
7.4.1 Geometric Representation of Hyperbolic Motion
200(4)
7.5 Synchronization
204(1)
7.5.1 Einstein Synchronization
204(1)
7.6 Rigid Motion of Many Relativistic Mass Points
205(1)
7.7 Rigid Motion and Hyperbolic Motion
206(10)
7.7.1 The Synchronization of LRIO
208(1)
7.7.2 Synchronization of Chronometry
209(2)
7.7.3 The Kinematics in the LCF Σ
211(3)
7.7.4 The Case of the Gravitational Field
214(2)
7.8 General One-Dimensional Rigid Motion
216(3)
7.8.1 The Case of Hyperbolic Motion
217(2)
7.9 Rotational Rigid Motion
219(5)
7.9.1 The Transitive Property of the Rigid Rotational Motion
222(2)
7.10 The Rotating Disk
224(15)
7.10.1 The Kinematics of Relativistic Observers
224(1)
7.10.2 Chronometry and the Spatial Line Element
225(3)
7.10.3 The Rotating Disk
228(1)
7.10.4 Definition of the Rotating Disk for a RIO
229(1)
7.10.5 The Locally Relativistic Inertial Observer (LRIO)
230(5)
7.10.6 The Accelerated Observer
235(4)
7.11 The Generalization of Lorentz Transformation and the Accelerated Observers
239(9)
7.11.1 The Generalized Lorentz Transformation
240(2)
7.11.2 The Special Case u0(l1, x1) = u1(l1, x1) = u(x1)
242(5)
7.11.3 Equation of Motion in a Gravitational Field
247(1)
7.12 The Limits of Special Relativity
248(5)
7.12.1 Experiment 1: The Gravitational Redshift
249(2)
7.12.2 Experiment 2: The Gravitational Time Dilation
251(1)
7.12.3 Experiment 3: The Curvature of Spacetime
252(1)
8 Paradoxes
253(12)
8.1 Introduction
253(1)
8.2 Various Paradoxes
254(11)
9 Mass - Four-Momentum
265(18)
9.1 Introduction
265(1)
9.2 The (Relativistic) Mass
266(1)
9.3 The Four-Momentum of a ReMaP
267(8)
9.4 The Four-Momentum of Photons (Luxons)
275(3)
9.5 The Four-Momentum of Particles
278(1)
9.6 The System of Natural Units
278(5)
10 Relativistic Reactions
283(42)
10.1 Introduction
283(1)
10.2 Representation of Particle Reactions
284(1)
10.3 Relativistic Reactions
285(4)
10.3.1 The Sum of Particle Four-Vectors
286(2)
10.3.2 The Relativistic Triangle Inequality
288(1)
10.4 Working with Four-Momenta
289(2)
10.5 Special Coordinate Frames in the Study of Relativistic Collisions
291(1)
10.6 The Generic Reaction A + B → C
292(12)
10.6.1 The Physics of the Generic Reaction
293(4)
10.6.2 Threshold of a Reaction
297(7)
10.7 Transformation of Angles
304(21)
10.7.1 Radiative Transitions
308(4)
10.7.2 Reactions With Two-Photon Final State
312(5)
10.7.3 Elastic Collisions - Scattering
317(8)
11 Four-Force
325(52)
11.1 Introduction
325(1)
11.2 The Four-Force
325(15)
11.3 Inertial Four-Force and Four-Potential
340(3)
11.3.1 The Vector Four-Potential
342(1)
11.4 The Lagrangian Formalism for Inertial Four-Forces
343(7)
11.5 Motion in a Central Potential
350(5)
11.6 Motion of a Rocket
355(8)
11.7 The Frenet-Serret Frame in Minkowski Space
363(14)
11.7.1 The Physical Basis
368(4)
11.7.2 The Generic Inertial Four-Force
372(5)
12 Irreducible Decompositions
377(18)
12.1 Decompositions
377(2)
12.1.1 Writing a Tensor of Valence (0, 2) as a Matrix
378(1)
12.2 The Irreducible Decomposition wrt a Non-null Vector
379(10)
12.2.1 Decomposition in a Euclidean Space En
379(4)
12.2.2 1 + 3 Decomposition in Minkowski Space
383(6)
12.3 1 + 1 + 2 Decomposition wrt a Pair of Timelike Vectors
389(6)
13 The Electromagnetic Field
395(100)
13.1 Introduction
395(1)
13.2 Maxwell Equations in Newtonian Physics
396(3)
13.3 The Electromagnetic Potential
399(6)
13.4 The Equation of Continuity
405(7)
13.5 The Electromagnetic Four-Potential
412(3)
13.6 The Electromagnetic Field Tensor Fij
415(6)
13.6.1 The Transformation of the Fields
415(2)
13.6.2 Maxwell Equations in Terms of Fij
417(1)
13.6.3 The Invariants of the Electromagnetic Field
418(3)
13.7 The Physical Significance of the Electromagnetic Invariants
421(5)
13.7.1 The Case Y = 0
422(1)
13.7.2 The Case Y ≠ 0
423(3)
13.8 Motion of a Charge in an Electromagnetic Field - The Lorentz Force
426(3)
13.9 Motion of a Charge in a Homogeneous Electromagnetic Field
429(11)
13.9.1 The Case of a Homogeneous Electric Field
430(4)
13.9.2 The Case of a Homogeneous Magnetic Field
434(2)
13.9.3 The Case of Two Homogeneous Fields of Equal Strength and Perpendicular Directions
436(2)
13.9.4 The Case of Homogeneous and Parallel Fields E || B
438(2)
13.10 The Relativistic Electric and Magnetic Fields
440(14)
13.10.1 The Levi-Civita Tensor Density
440(2)
13.10.2 The Case of Vacuum
442(3)
13.10.3 The Electromagnetic Theory for a General Medium
445(3)
13.10.4 The Electric and Magnetic Moments
448(1)
13.10.5 Maxwell Equations for a General Medium
448(1)
13.10.6 The 1 + 3 Decomposition of Maxwell Equations
449(5)
13.11 The Four-Current of Conductivity and Ohm's Law
454(5)
13.11.1 The Continuity Equation Jaa = 0 for an Isotropic Material
458(1)
13.12 The Electromagnetic Field in a Homogeneous and Isotropic Medium
459(4)
13.13 Electric Conductivity and the Propagation Equation for Ea
463(2)
13.14 The Generalized Ohm's Law
465(2)
13.15 The Energy Momentum Tensor of the Electromagnetic Field
467(8)
13.16 The Electromagnetic Field of a Moving Charge
475(14)
13.16.1 The Invariants
477(1)
13.16.2 The Fields E1, B1
478(1)
13.16.3 The Lienard-Wiechert Potentials and the Fields E, B
478(11)
13.17 Special Relativity and Practical Applications
489(3)
13.18 The Systems of Units SI and Gauss in Electromagnetism
492(3)
14 Relativistic Angular Momentum
495(26)
14.1 Introduction
495(1)
14.2 Mathematical Preliminaries
495(3)
14.2.1 1 + 3 Decomposition of a Bivector Xab
495(3)
14.3 The Derivative of Xab Along the Vector pa
498(2)
14.4 The Angular Momentum in Special Relativity
500(6)
14.4.1 The Angular Momentum in Newtonian Theory
500(2)
14.4.2 The Angular Momentum of a Particle in Special Relativity
502(4)
14.5 The Intrinsic Angular Momentum - The Spin Vector
506(15)
14.5.1 The Magnetic Dipole
506(4)
14.5.2 The Relativistic Spin
510(5)
14.5.3 Motion of a Particle with Spin in a Homogeneous Electromagnetic Field
515(2)
14.5.4 Transformation of Motion in σ
517(4)
15 The Covariant Lorentz Transformation
521(34)
15.1 Introduction
521(2)
15.2 The Covariant Lorentz Transformation
523(11)
15.2.1 Definition of the Lorentz Transformation
523(1)
15.2.2 Computation of the Covariant Lorentz Transformation
524(5)
15.2.3 The Action of the Covariant Lorentz Transformation on the Coordinates
529(5)
15.2.4 The Invariant Length of a Four-Vector
534(1)
15.3 The Four Types of the Lorentz Transformation Viewed as Spacetime Reflections
534(3)
15.4 Relativistic Composition Rule of Four-Vectors
537(13)
15.4.1 Computation of the Composite Four-Vector
540(2)
15.4.2 The Relativistic Composition Rule for Three-Velocities
542(2)
15.4.3 Riemannian Geometry and Special Relativity
544(4)
15.4.4 The Relativistic Rule for the Composition of Three-Accelerations
548(2)
15.5 The Composition of Lorentz Transformations
550(5)
16 Geometric Description of Relativistic Interactions
555(34)
16.1 Collisions and Geometry
555(1)
16.2 Geometric Description of Collisions in Newtonian Physics
556(2)
16.3 Geometric Description of Relativistic Reactions
558(1)
16.4 The General Geometric Results
559(4)
16.4.1 The 1 + 3 Decomposition of a Particle Four-Vector wrt a Timelike Four-Vector
561(2)
16.5 The System of Two to One Particle Four-Vectors
563(11)
16.5.1 The Triangle Function of a System of Two Particle Four-Vectors
565(2)
16.5.2 Extreme Values of the Four-Vectors (A ± B) 2
567(1)
16.5.3 The System Aa, Ba, (A + Ba) of Particle Four-Vectors in CS
568(2)
16.5.4 The System Aa, Ba, (A + Ba) in the Lab
570(4)
16.6 The Relativistic System Aa + Ba → Ca + Da
574(15)
16.6.1 The Reaction B → C + D
587(2)
Bibliography 589(2)
Index 591