Special Relativity and How It Works Book

Preface     XIII
Introduction     1
The Meaning of Relativity     1
Weirdness of Light     10
A Steamer in the Stream     12
Problems     15
Light and Relativity     17
The Michelson Experiment     17
The Speed of Light and the Principle of Relativity     22
"Obvious" Does Not Always Mean "True!"     24
Light Determines Simultaneity     25
Light, Times, and Distances     29
The Lorentz Transformations     32
The Relativity of Simultaneity     38
A Proper Length and a Proper Time     41
Problems     43
The Velocities' Play     47
The Addition of Collinear Velocities     47
The Addition of Arbitrarily Directed Velocities     50
The Velocities' Play     53
Observable Manifestations     56
The Fizeau Experiment     56
Aberration of Light     60
Problems     62
Space-Time     65
Minkowski's World     65
Rotations in Space-Time (Representation in Euclidean Plane)     73
Lorentz Transformations as Rotations     81
What isHorizontal and What is Vertical?     87
General Lorentz Transformations     99
The Path Integrals     103
4-Vectors and Tensors     106
Problems     120
Relativity at Work I: Mechanics     125
4-Velocity     125
4-Acceleration     130
4-Momentum     132
Relativistic Angular Momentum     137
Force and Motion     141
Mass and Energy     151
Mechanics From the Least Action     170
Relativistic Motion in Coulomb's Field     176
Problems     185
Relativity at Work II: Electromagnetism and Optics     191
Electric Field and Something Else (The Origin of Magnetic Field)     191
Magnetic Field and Something Else...     205
Is Electric Charge Invariant? (The Subtleties of "Neutrality")     209
Maxwell's Equations     218
Lenz's Law     225
4-Potential, Gauge Transformations, and Gauge Invariance     228
Electrodynamics and The Principle of the Least Action     233
Electrodynamics in Tensor Notations     239
Running Waves     244
The Relativistic Doppler Effect I     247
The Origin of Light      248
Aberration of Light - 2     252
Why Do Droplets Sparkle? Or Can We Trap the Light in a Droplet?     256
Problems     263
Relativistic Paradoxes     267
Seeing and Observing (on the Appearance of Fast-Moving Objects)     267
Can We See the Relativistic Length Contraction?     273
The Lorentz Contraction Paradox     280
Predicaments of Relativistic Train     283
The Dynamics of Relativistic Length Contraction     298
The Conveyor Belt Paradox     317
What is Rigid in Relativity? (What Constitutes Deformation?)     323
The Twin Paradox     334
The Three Friends' Paradox     344
Problems     348
Miracles of a Spinning World     351
The Ehrenfest Paradox     351
Circumnavigations with the Atomic Clocks     365
Surprises of the Rotland     375
Photons' Races in a Centrifuge     376
The Thomas Precession     387
Problems     394
Theory of Relativity is the Theory of Absoluteness     397
What Is Relative and What Is Absolute     397
The Speed of Light and the Invariant Speed     398
Space-Time Intervals      403
Relativistic Doppler Effect II     407
Relative Is Real     413
Problems     422
Relativity at Work III: Quantum Mechanics     425
Basic Ideas of Quantum Mechanics     425
Relativistic QM Indeterminacy     454
Relativistic Wave Equations     461
The Klein-Gordon Equation     461
Dirac's Equation     469
Relativistic Doppler Effect III: A Child of Relativity and Quantum Mechanics     477
Field-Particle Interactions: The Compton Effect     482
Problems     493
Relativity and Causality     497
Space-Time and Causality     497
Tachyons and Tardyons     500
The Tolman Paradox     509
Tachyons and Causality     516
Wave Packet Propagation and Position Measurements     523
Superluminal Quantum Tunneling     527
Wave Front Propagation     537
What Constitutes a Signal?     541
Direct Signaling Into the Past     550
The Mystery of Quantum Telecommunication     558
The "No Cloning" Theorem     564
Problems     569
Applied Relativity     571
Relativistic Jet Propulsion: A "Star Trek" Cruiser     571
Principles of Design and Functioning of Particle Accelerators     580
Problems     593
A Bit of General Relativity     595
Basic Ideas of GR     595
Kinematics of GR     603
State Function and the Continuity Equation     615
Representation of Observables by Operators     617
The Pauli Matrices     619
Dimensionality of Dirac's Matrices     621
Optical Barriers for a Photon     623
Cause and Effect     627
Permittivity and Refractive Index     637
References     643
Index     647