## Special Theory of Relativity – Ugarov

After the two books on General Relativity (GR) viz. STG and RTG, we come to a great textbook on Special Theory of Relativity (STR). This one is by V. A. Ugarov titled Special Theory of Relativity. This book is a very comprehensive treatment of the Special Theory of Relativity with all advanced topics treated well. Also interesting is the article by V. L. Ginzburg (whose book Key Problems of Physics and Astrophysics we saw recently) which is  Who Developed Special theory of relativity and how? This may be of special importance to those who wish to know historical roots of development of relativity.

It is in this book that I first read about the superluminal speeds which are possible and are indeed result of STR. Section 8.1 deals with these phenomena and there are 5 of them discussed here. These are for real and are indeed observed in nature. For example the hot-spot in case of radio jets appeared to move at faster-than-speed-of-light. The easiest one which you can indeed do is to take a torch and make a spot on the wall, there is no limit on how fast the spot can travel. Let us see what Ugarov has to say on this topic:

Let us place a searchlight at the origin of coordinates and start rotating it at the angular velocity $\Omega$. Let us circumscribe a stationary sphere of radius $c$ around the origin. Then the light spot will run along the surface of this sphere at the linear velocity $v = \Omega c$. This velocity can exceed the velocity of light. The example of such a beam is provided by a rotating pulsar. The light spot of the Crab Nebula pulsar runs along the Earth surface at the velocity equal approximately to $10^{22} m/s$. But as in the previous cases no signal is transmitted at such a velocity. As a matter of fact, every point of a screen (the Earth) receives a new portion of light energy from a searchlight (pulsar), but not from a neighbouring point of the screen. Therefore, it is impossible to transmit information from one point of the screen to another.

The 4-forms, electrodynamics, transformations are discussed with substantial emphasis on the physical meaning. These kind of discussions make this book a wonderful resource to learn.

The book was translated from the Russian by Yuri Atanov and was first published by Mir in 1979.

All credits to the original uploader, thanks to atisundar for providing this link.

You can get the book here.

Contents

CONTENTS
Preface 5
Chapter 1. CLASSICAL MECHANICS AND THE PRINCIPLE OF RELATIVITY  11

1.1. Α coordinate system and a reference frame in classical mechanics 11
1.2. Τhe choice of a reference frame 14
1.3. The Galilean Transformation 15
1.4. Τhe Galilean principle of relativity. Newton’s second Law. 19
1.5 Newton’s laws and inertial frames or reference 24
1.6. Absolute time and absolute space 29
1.7. How physics was approaching the theory or relativity 30
1.8. The generalization of the Galilean principle or relativity 33
1.9 The velocity or light in vacuo 36

Chapter 2 THE EINSTEIN POSTULATES THE INTERVAL BETWEEN EVENTS. THE LORENTZ TRANSFORMATION 38

2.1. Einstein’s postulates 38
2.2 The relativistic frame or reference. 41
2.3. The direct consequences of Einstein’s postulates (a few imaginary experiments) 45
2.4 The relativity of synchronization of clocks belonging to two inertial frames or reference. The direct derivation or the Lorentz transformation 52
2.5 The Lorentz transformation as a consequence of Einstein’s postulates 56
2.6. The propagation of the light wave profile. An interval between events 60
2.7. The Lorentz transformation as a consequence of the invariance or the interval between events 63
2.8. Complex values in the STR. Symmetric designations 65
2.9. A geometric illustration of the Lorentz transformation 69

Chapter 3. CONSEQUENCES OF THE LORENTZ TRANSFORMATION.THE CLASSIFICATION OF INTERVALS AND THE PRINCIPLE OF CAUSALITY. ΤΗΕ Κ CALCULUS 71

3.1. Οn the measurement of lengths and time intervals. Τhe relativity of simultaneity 71
3.2 Relativity of length of moving rulers (scales). Α visible shape of objects moving at relativistic velocities 7
3.3. Relativity of time intervals between events 83
3.4. Τhe classification of intervals and the principle of causality 90
3.5 Τhe transformation of velocity components of a particle on transition from one inertial frame of reference to another 94
3.6 Τhe transformation of an absolute value and the direction of the velocity of a particle 101
3.7 Τhe Κ calculus (the radar method) 105

Chapter 4. ΤΗΕ FOUR-DIMENSΙONAL SPACE-TIME 117

4.1 Τhree-dimensional and Four-dimensional Euclidean spaces 117
4.2 Τhe 4-spacetime, of the Four-dimensional pseudo-Euclidean space 118
4.3 4-vectors and 4-tensors 120
4.4 Α pseudo-Euclidean plane 123

Chapter 5. RELATIVISTIC MECHANICS OF Α PARTlCLE 133

5.1 Α 4-velocity and 4-acceleration 134
5.2 Α 4-force and a Four-dimensional equation of motion 140
5.3 Α three-dimensional relativistic equation of motion of a particle (the second law of Newton in a relativistic form) 143
5.4 Τhe relativistic expression for a particle’s energy 149
5.5 Α 4vector of energy-momentum 153
5.6 Τhe rest mass of a system. Τhe binding energy 157
5.7. Some problems of relativistic Mechanics of a particle 161
5.8. Τhe conservation laws of relativistic mechanics 175

Chapter 6. THE MAXWELL THEORY IN Α RELATIVISTIC FORM. 180

6.1. Τhe three-dimensional system of Maxwell’s equations. Α 4-potential and 4-current 181
6.2 Τhe transformation of a 4-potential and 4-current 184
6.3 Αn electromagnetic field tensor 188
6.4 Τhe transformation of electric and magnetic field components. 192
6.5 Τhe electromagnetic field invariants 198
6.6 Τhe Lorentz Force 199
6.7 Covariance of the system of the Maxwell equations 205
6.8 Τhe Minkowski equations for moving media (the transformation of material equations) 208
6.9 Τhe transformation of electric and magnetic moments 214
6.10 Some problems involving the transformation of an electromagnetic field 216
6.11 Αn energy-momentum-tension tensor of an electromagnetic field in vacuo 222
6.12 Αn energy-momentum-tension tensor of an electromagnetic field in a medium. Τhe Minkowski tensor and Abraham tensor 233
6.13 Αn energy-momentum-tension tensor of a spherically symmetric charge 238
6.14 Τhe field Ρotentials in a moving non-conducting medium 210
6.15 Τhe field Ρotentials in a moving conducting medium 246

Chapter 7. OPTICAL PHENOMENA AND THE SPECIAL THEORY OF RELATIVITY 258

7.1 Properties of plane light waves 258
7.2 Α 4-wave vector. Τhe Doppler effect. Aberration of Light 261
7.3 Α plane wave limited in space. Τhe transformation of the plane wave energy and amplitude 265
7.4 Τhe pressure exert by an electromagnetic wave (light) on a surface 270
7.5 Τhe light frequency variation on reflection from a moving surface (mirror) 272
7.6 Light quanta (Ρhotons) as relativistic particles 276
7.7. Light quanta in a medium. Τhe Vavilov-Cherenkov effect. Τhe anomalous Doppler effect 280

Chapter 8. ON CERTAIN PARADOXES OF THE SPECIAL THEORY OF RELATIVITY 286

8.1 Faster-than-light velocities 287
8.3 Τhe tachyons 297
8.5 Τhe “equivalence” of mass and energy. Τhe zero rest mass. 310

SUPPLEMENΤ 317

Ι. Who developed the special theory of relativity, and how? (V. L. Ginzburg) 317
II. Τhe unsuccessful search for a medium for the propagation of light 328
III. Was Michelson’s experiment “decisive” for the creation of The special theory of relativity? 345
IV. Why shouldn’t the mass-velocity dependence, of the relativistic mass, be introduced? 350
V. Non-inertial frames of reference. Τhe special Theory of relativity and the advance to gravitational theory (The general theory of relativity) 354

ΜΑΙΝ EVENΤS RELAΤED ΤΟ ΤΗΕ HISΤORY OF ΤΗΕ SΤR 361

Appendix Ι 362
1. Τhe symmetric notation. Τhe summation rules 362
2. Τhe translormation of coordinates in the case of a rotation of the Cartesian system of coordinates 364
3, Τhe tensors 365
4. Τhe invariance of a 4-divergence and d’Alembert’s operator 373
s. Τhc convolution (“rejuvenation”) of tensor indices 375
6. Some data οπ determinants. Τhe dual tensors 377
7. Τhe stress tensor 383
8, Τhe rectilinear oblique-angled systems of coordinates. 386
9. Τhe definition of the hyperbolic functions and some relationships between them 392
Bibliography to Appendix Ι 393

Appendix II.

Τhe basic formulae of electrodynamics in the Gaussian system 394
Bibliography 399
Index 403

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