Keywords:
Special relativity (Physics)-Problems, exercises, etc.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (456 pages)
Edition:
2nd ed.
ISBN:
9780128137215
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5216161
DDC:
530.11
Language:
English
Note:
Front Cover -- SPECIAL RELATIVITY, ELECTRODYNAMICS, AND GENERAL RELATIVITY -- SPECIAL RELATIVITY, ELECTRODYNAMICS, AND GENERAL RELATIVITY: From Newton to Einstein -- Copyright -- CONTENTS -- ABOUT THE BOOK COVER -- PREFACE -- 1. SPECIAL RELATIVITY WITH A MISSION -- 2. GENERAL RELATIVITY -- 3. BACKGROUND READING AND RECOMMENDATIONS FOR FUTURE READING -- REFERENCES -- 1 - Physics According to Newton-A World With No Speed Limit -- 1.1 NEWTON'S WORLD: LAWS AND MEASUREMENTS -- 1.2 NEWTON'S WORLD: NO PLACE FOR MAGNETISM -- 2 - Space-Time Measurements According to Einstein -- 2.1 A WORLD WITH A SPEED LIMIT -- 2.2 MAKING A CLOCK WITH MIRRORS AND LIGHT -- 2.3 LORENTZ CONTRACTION -- 2.4 THE RELATIVITY OF SIMULTANEITY -- 2.5 TIME DILATION REVISITED -- 2.6 LORENTZ CONTRACTION REVISITED -- PROBLEMS -- REFERENCE -- 3 - Visualizing Relativity-Minkowski Diagrams and the Twins -- 3.1 SPACE AND TIME AXES FOR INERTIAL FRAMES AND THE CONSTANCY OF THE SPEED OF LIGHT -- 3.2 VISUALIZING THE RELATIVITY OF SIMULTANEITY, TIME DILATION, AND LORENTZ CONTRACTION -- 3.3 THE DOPPLER EFFECT -- 3.4 THE TWIN PARADOX -- 3.5 EINSTEIN MEETS SHAKESPEARE-RELATIVISTIC HISTORY -- 3.6 REALITY, HORSE RACING, AND THE SPEED LIMIT -- PROBLEMS -- REFERENCES -- 4 - Lorentz Transformations (Boosts), Addition of Velocities, and Invariant Intervals -- 4.1 LORENTZ TRANSFORMATION (BOOSTS) -- 4.1.1 Time Dilation -- 4.1.2 Lorentz Contraction -- 4.1.3 Relativity of Simultaneity -- 4.2 RELATIVISTIC VELOCITY ADDITION -- 4.3 CAUSALITY, LIGHT CONES, AND PROPER TIME -- PROBLEMS -- REFERENCES -- 5 - Illustrations and Problems in Space-Time Measurements -- 5.1 A SPACESHIP RENDEZVOUS -- 5.2 A HOLE IN THE ICE -- 5.3 A VELOCITY GREATER THAN THE SPEED LIMIT? -- PROBLEMS -- REFERENCES -- 6 - Relativistic Dynamics: First Steps -- 6.1 ENERGY, LIGHT, AND E = MC2.
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6.2 PATCHING UP NEWTONIAN DYNAMICS-RELATIVISTIC MOMENTUM AND ENERGY -- 6.3 RELATIVISTIC FORCE AND ENERGY CONSERVATION -- 6.4 ENERGY AND MOMENTUM CONSERVATION, AND FOUR-VECTORS -- 6.5 FOCUSING ON FOUR-VECTORS, TENSORS, AND NOTATION -- 6.6 COLLISIONS AND CONSERVATION LAWS-CONVERTING MASS TO ENERGY AND ENERGY TO MASS, PRODUCING AND DESTROYING PARTICLES -- PROBLEMS -- REFERENCES -- 7 - Acceleration and Forces in Relativity: The Birth of Dynamical Fields -- 7.1 ACCELERATION IN RELATIVITY -- 7.2 TRANSFORMATION PROPERTIES OF FORCES -- 7.3 THE DEATH OF NEWTON'S THIRD LAW, AND STATIC FORCES: THE BIRTH OF FIELDS -- PROBLEMS -- 8 - Boosting the Electrostatic Force, Electromagnetic Fields and More on Four-Vectors -- 8.1 THE ELECTRIC FIELD AROUND A MOVING POINT CHARGE -- 8.2 THE FORCE BETWEEN TWO MOVING CHARGES -- 8.3 TRANSFORMING E AND B BETWEEN FRAMES -- 8.4 MORE ON INVARIANTS AND FOUR-VECTORS -- PROBLEMS -- REFERENCES -- 9 - Maxwell's Equations of Electrodynamics and the Wave Equation -- 9.1 BOOSTING GAUSS' LAW AND DISCOVERING MAXWELL'S EQUATIONS -- 9.2 THE WAVE EQUATION FOR LIGHT AND THE DERIVATION THAT LIGHT TRAVELS AT THE SPEED LIMIT -- PROBLEMS -- 10 - Magnetism in the Lab, the Discovery of Relativity, and the Way Forward -- 10.1 HOW CAN MAGNETIC FORCES BE LARGE IF THEY ARE RELATIVISTIC EFFECTS? -- 10.2 ELECTRODYNAMICS FORMULATED IN COVARIANT NOTATION -- 10.3 NEXT STEPS -- PROBLEMS -- REFERENCE -- 11 - Introduction to General Relativity -- 11.1 THE EQUIVALENCE PRINCIPLE, GRAVITY, AND APPARENT FORCES -- 11.2 MOTION IN A ROTATING, RELATIVISTIC REFERENCE FRAME: SPATIAL CURVATURE AND THOMAS PRECESSION -- 11.3 TIDAL FORCES, NON-EUCLIDEAN GEOMETRY, AND THE MEANING OF ``LOCAL INERTIAL REFERENCE FRAME'' -- 11.4 GRAVITATIONAL REDSHIFT -- 11.4.1 A Freely Falling Inertial Frame -- 11.4.2 An Accelerating Spaceship.
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11.4.3 Gravitational Redshift and the Relativity of Simultaneity -- 11.4.4 A Rotating Reference Frame -- 11.4.5 A Famous Experimental Test of Gravitational Redshift -- 11.4.6 Gravitational Redshift and Energy Conservation -- 11.5 THE TWINS AGAIN -- 11.6 AN AGING ASTRONAUT -- 11.7 BENDING OF LIGHT IN A GRAVITATIONAL FIELD -- 11.8 SIMILARITIES AND DIFFERENCES OF ELECTROMAGNETISM AND GRAVITY -- 11.9 MAKING THE MOST OUT OF TIME -- PROBLEMS -- REFERENCES -- 12 - Curvature, Strong Gravity, and Gravitational Waves -- 12.1 A LOOK AT CURVED SURFACES: A FIRST STEP TO THE MATHEMATICS OF GENERAL RELATIVITY -- 12.2 THE EQUATION OF MOTION OF PARTICLES IN CURVED SPACE-TIME -- 12.3 COVARIANT DERIVATIVES AND COVARIANT VECTOR FIELDS -- 12.4 THE EQUIVALENCE PRINCIPLE, METRIC COMPATIBILITY, AND CHRISTOFFEL SYMBOLS -- 12.5 THE CURVATURE OF SPACE-TIME -- 12.6 FROM NEWTON'S GRAVITY TO RELATIVISTIC WEAK GRAVITY TO STRONG GRAVITY -- 12.7 THE SCHWARZSCHILD METRIC AND BLACK HOLE -- 12.8 THE SCHWARZSCHILD BLACK HOLE -- 12.9 CIRCULAR ORBITAL MOTION IN THE SCHWARZSCHILD METRIC -- 12.10 THE SPEED OF LIGHT IN A GRAVITATIONAL FIELD -- 12.11 RELATIVISTIC TIDAL FORCES -- 12.12 THE DISCOVERY OF GRAVITATIONAL WAVES -- 12.13 GRAVITATIONAL RADIATION -- 12.14 CONTRASTING SPECIAL AND GENERAL RELATIVITY: THE COSMOLOGICAL CONSTANT AND DARK ENERGY -- PROBLEMS -- REFERENCES -- A - Physical Constants, Data, and Conversion Factors -- B - Solutions to Selected Problems -- B.1 CHAPTER 2 PROBLEMS -- Problem 2-1 -- Problem 2-2 -- Problem 2-3 -- Problem 2-5 -- B.2 CHAPTER 3 PROBLEMS -- Problem 3-1 -- Problem 3-7 -- B.3 CHAPTER 4 PROBLEMS -- Problem 4-1 -- Problem 4-2 -- Problem 4-3 -- Problem 4-4 -- Problem 4-5 -- Problem 4-7 -- Problem 4-9 -- Problem 4-11 -- Problem 4-14 -- Problem 4-17 -- B.4 CHAPTER 5 PROBLEMS -- Problem 5-2 -- B.5 CHAPTER 6 PROBLEMS -- Problem 6-1 -- Problem 6-2 -- Problem 6-4.
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Problem 6-5 -- Problem 6-10 -- Problem 6-11 -- Problem 6-12 -- Problem 6-13 -- Problem 6-15 -- Problem 6-17 -- Problem 6.18 -- Problem 6.19 -- Problem 6-21 -- Problem 6-22 -- Problem 6-23 -- Problem 6-25 -- Problem 6-26 -- Problem 6-28 -- Problem 6-29 -- Problem 6-31 -- Problem 6-33 -- Problem 6-34 -- Problem 6-35 -- Problem 6-36 -- Problem 6-38 -- Problem 6.39 -- B.6 CHAPTER 8 PROBLEMS -- Problem 8.1 -- Problem 8.4 -- B.7 CHAPTER 9 PROBLEMS -- Problem 9.3 -- Problem 9.5 -- B.8 CHAPTER 12 PROBLEMS -- Problem 12.8 -- Problem 12.9 -- Problem 12.11 -- Problem 12.14 -- Problem 12.15 -- Problem 12.16 -- Problem 12.17 -- Problem 12.19 -- Problem 12.20 -- Problem 12.24 -- C - Mathematics Background -- C.1 HANDY APPROXIMATIONS AND EXPANSIONS -- C.2 CHAIN RULE OF DIFFERENTIATION AND COORDINATE TRANSFORMATIONS: APPLICATIONS TO COVARIANT AND CONTRAVARIANT VECTORS -- C.3 MATRICES -- C.4 COVARIANT AND CONTRAVARIANT FOUR-VECTORS AND DUALITY -- D - Theorems and Concepts of Vector Calculus -- D.1 CARTESIAN AND SPHERICAL COORDINATES -- D.2 CROSS PRODUCT OF TWO VECTORS -- D.3 GRADIENTS, CURLS, DIVERGENCES, AND LAPLACIANS -- D.4 HELMHOLTZ THEOREMS FOR VECTOR FIELDS -- D.5 INTEGRAL THEOREMS FOR VECTOR FIELDS -- D.6 LOCALITY AND THE DIRAC DELTA FUNCTION -- E - Summary of Formulas -- E.1 SPECIAL RELATIVITY -- E.1.1 Lorentz Transformations (``Boosts'') -- E.1.2 Addition of Velocities -- E.1.3 Four-Vectors -- E.1.4 Energy-Momentum -- E.1.5 Force -- E.1.6 Electric and Magnetic Fields -- E.1.7 Electric Current and Current Conservation -- E.1.8 Maxwell's Equations -- E.1.9 Wave Equations Without Sources -- E.1.10 Wave Equations With Sources -- E.1.11 The Electromagnetic Field Strength Tensor and the Lorentz Force Law -- E.1.12 The Electromagnetic Stress Tensor Tμν -- E.2 GENERAL RELATIVITY -- E.2.1 Gravitational Redshift.
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E.2.2 Coordinate Transformations: Covariant Vectors and Tensors -- E.2.3 Coordinate Transformations: Contravariant Vectors and Tensors -- E.2.4 Metric Tensor -- E.2.5 Christoffel Symbol -- E.2.6 Covariant Derivatives -- E.2.7 Geodesic Curves -- E.2.8 Curvature and the Riemann Tensor -- E.2.9 Curvature, Tidal Forces, and the Geodesic Deviation -- E.2.10 Symmetries of the Riemann Tensor -- E.2.11 The Einstein and Ricci Tensors -- E.2.12 Linearized Gravity -- E.2.13 Schwarzschild Metric -- E.2.14 Slightly Curved Space-Time, Isotropic Coordinates, the Newtonian Limit -- F - The Wave Equation With Sources: The Four-Vector Potential and the Lorenz Gauge -- F.1 THE WAVE EQUATION AND RADIATION -- F.2 THE FOUR-VECTOR POTENTIAL AND MAXWELL'S EQUATIONS -- REFERENCE -- G - Equation of Motion in Curved Space and Christoffel Symbols, Two-Dimensional Surfaces, and the Geodesic Deviati ... -- G.1 FREE FALL AND CHRISTOFFEL SYMBOLS -- G.2 RIEMANN TENSOR AND TWO-DIMENSIONAL SURFACES -- G.3 TIDAL FORCES AND GRAVITY WAVES -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- P -- Q -- R -- S -- T -- U -- V -- W -- Back Cover.
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