A Student's Guide to Einstein's Major Papers

Cover......Page 1
Contents......Page 8
Acknowledgments......Page 14
Introduction......Page 16
1.1 Overview......Page 24
1.2.1 600 BC to AD 200: The Contribution of the Early Greeks......Page 25
1.2.2 The 1600s: The Contribution of Galileo and Newton......Page 29
1.2.3 The 1800s: The Contribution of Maxwell and Lorentz......Page 36
1.3.1 The Pre-College Years......Page 38
1.3.2 The College Years......Page 40
1.3.3 From College to 1905......Page 42
1.4 Discussion and Comments......Page 43
1.5.1 Science Today......Page 44
1.5.2 Newton’s Law of Gravitation from Kepler’s Laws......Page 48
1.6 Notes......Page 50
1.7 Bibliography......Page 54
2.1.1 Thermodynamics and Entropy......Page 56
2.1.2 Blackbody Radiation......Page 57
2.1.3 Max Planck’s Derivation of the Radiation Density......Page 61
2.2 Albert Einstein’s Paper, “On a Heuristic Point of View Concerning the Production and Transformation of Light”......Page 62
2.2.1 On a Difficulty Encountered in the Theory of “Blackbody Radiation”......Page 63
2.2.2 On Planck’s Determination of the Elementary Quanta......Page 64
2.2.3 On the Entropy of Radiation......Page 65
2.2.5 Molecular-Theoretical Investigation of the Dependence of the Entropy of Gases and Dilute Solutions on the Volume......Page 66
2.2.6 Interpretation of the Expression for the Dependence of the Entropy of Monochromatic Radiation on Volume According to Boltzmann’s Principle......Page 67
2.2.7 On Stokes’ Rule......Page 68
2.2.8 On the Generation of Cathode Rays by Illumination of Solid Bodies......Page 69
2.3 Discussion and Comments......Page 70
2.4.1 Entropy and Irreversibility......Page 72
2.4.2 Planck’s derivation of ρ (ν, T)......Page 73
2.4.3 Wien’s Expression for Entropy......Page 74
2.5 Notes......Page 75
2.6 Bibliography......Page 78
3.1 Historical Background......Page 79
3.1.1 The Atom......Page 80
3.1.3 The Worldview in 1900......Page 83
3.2 Albert Einstein’s Paper, “A New Determination of Molecular Dimensions”......Page 85
3.2.1 On the Influence on the Motion of a Liquid Exercised by a Very Small Sphere Suspended in It......Page 86
3.2.2 Calculation of the Coeficient of Viscosity of a Liquid in Which Very Many Irregularly Distributed Small Spheres are Suspended......Page 89
3.2.3 On the Volume of a Dissolved Substance Whose Molecular Volume is Large Compared to that of the Solvent......Page 90
3.2.4 On the Diffiusion of an Undissociated Substance in a Liquid Solution......Page 91
3.2.5 Determination of the Molecular Dimensions with the Help of the Relations Obtained......Page 92
3.3 Albert Einstein’s Paper, “On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat”......Page 93
3.3.1 On the Osmotic Pressure Attributable to Suspended Particles......Page 94
3.3.2 Osmotic Pressure from the Standpoint of the Molecular-Kinetic Theory of Heat......Page 95
3.3.3 Theory of Diffiusion of Small Suspended Spheres......Page 96
3.3.4 On the Random Motion of Particles Suspended in a Liquid and Their Relation to Diffiusion......Page 98
3.4 Discussion and Comments......Page 99
3.5.1 Derivation of the Expressions for u, v, and w......Page 101
3.5.2 Derivation of the Expression for W = Energy per Unit Time Converted into Heat......Page 108
3.5.3 Derivation of the Coefficient of Viscosity of a Liquid in Which Very Many Irregularly Distributed Spheres are Suspended......Page 113
3.5.5 Derivation of the Expression for Entropy......Page 116
3.5.6 Derivation of B = JV*(sup[n])......Page 118
3.5.7 Derivation of ν = f (x, t)......Page 119
3.6 Notes......Page 121
3.7 Bibliography......Page 126
4.1.1 The Relativity of Galileo Galilei and of Isaac Newton......Page 128
4.1.2 The Lorentz Transformations (from Lorentz)......Page 131
4.2 Albert Einstein’s Paper, “On the Electrodynamics of Moving Bodies”......Page 136
4.2.1 Definition of Simultaneity......Page 138
4.2.2 On the Relativity of Lengths and Times......Page 139
4.2.3 Theory of Transformation of Coordinates and Time from a System at Rest to a System in Uniform Translational Motion Relative to It......Page 141
4.2.4 The Physical Meaning of the Equations Obtained Concerning Moving Rigid Bodies and Moving Clocks......Page 143
4.2.5 The Addition Theorem of Velocities......Page 144
4.2.6 Transformation of the Maxwell–Hertz Equations for Empty Space. On the Nature of the Electromotive Forces that Arise upon Motion in a Magnetic Field......Page 145
4.2.7 Theory of Doppler’s Principle and of Aberration......Page 147
4.2.8 Transformation of the Energy of Light Rays. Theory of the Radiation Pressure Exerted on Perfect Mirrors......Page 149
4.2.10 Dynamics of the (Slowly Accelerated) Electron......Page 151
4.3 Albert Einstein’s Paper, “Does the Inertia of a Body Depend Upon Its Energy Content?”......Page 152
4.4 Discussion and Comments......Page 154
4.5.1 Lorentz and the Transformed Maxwell Equations......Page 156
4.5.2 Derivation of the Lorentz Transformation Equations......Page 163
4.5.3 The Electromagnetic Field Transformations......Page 169
4.5.4 The Doppler Principle......Page 173
4.5.5 The Electrodynamic Lorentz Force......Page 176
4.6 Notes......Page 178
4.7 Bibliography......Page 182
5.1.1 Lingering Questions......Page 184
5.1.2 Generalizing the Special Theory of Relativity......Page 186
5.1.3 The Equivalence of a Gravitational Field and an Accelerated Reference Frame......Page 187
5.1.4 The Timeline from 1905 to 1916......Page 190
5.2.1 Observations on the Special Theory of Relativity......Page 194
5.2.2 The Need for an Extension of the Postulate of Relativity......Page 195
5.2.3 The Space-Time Continuum. Requirement of General Covariance for the Equations Expressing General Laws of Nature......Page 197
5.2.4 The Relation of the Four Coordinates to Measurement in Space and Time......Page 198
Part B: “Mathematical Aids to the Formulation of Generally Covariant Equations”......Page 201
5.2.5 Contravariant and Covariant Four-Vectors......Page 202
5.2.6 Tensors of the Second and Higher Ranks......Page 204
5.2.7 Multiplication of Tensors......Page 205
5.2.8 Some Aspects of the Fundamental Tensor gμν......Page 206
5.2.9 The Equation of the Geodetic Line. The Motion of a Particle......Page 209
5.2.10 The Formation of Tensors by Differentiation......Page 210
5.2.11 Some Cases of Special Importance......Page 211
5.2.12 The Riemann–Christoffel Tensor......Page 214
5.2.13 Equations of Motion of a Material Point in the Gravitational Field. Expression for the Field-Components of Gravitation......Page 215
5.2.14 The Field Equations of Gravitation in the Absence of Matter......Page 216
5.2.15 The Hamiltonian Function for the Gravitational Field. Laws of Momentum and Energy......Page 217
5.2.16 The General Form of the Field Equations of Gravitation......Page 219
5.2.18 The Laws of Momentum and Energy for Matter, as a Consequence of the Field Equations......Page 221
5.2.19 Euler’s Equations for a Frictionless Adiabatic Fluid......Page 222
5.2.20 Maxwell’s Electromagnetic Field Equations for Free Space......Page 223
5.2.21 Newton’s Theory as a First Approximation......Page 228
5.2.22 The Behaviour of Rods and Clocks in the Static Gravitational Field. Bending of Light Rays. Motion of the Perihelion of a Planetary Orbit......Page 231
5.3.1 Verification of the General Theory of Relativity......Page 236
5.3.2 Beyond the General Theory of Relativity: Cosmology and the Unified Field Theory......Page 239
5.4.1 Multiplication of Tensors......Page 246
5.4.2 Some Aspects of the Fundamental Tensor gμν......Page 247
5.4.3 The Equation of the Geodetic Line......Page 248
5.4.4 The Formation of Tensors by Differentiation......Page 252
5.4.5 Some Cases of Special Importance......Page 255
5.4.6 The Riemann–Christoffel Tensor......Page 262
5.4.7 The Hamiltonian Function for the Gravitational Field......Page 264
5.4.9 Calculation of the Precession of the Perihelion of Mercury......Page 272
5.4.10 The Bending of Starlight Experiment......Page 276
5.4.11 Newton’s Bucket......Page 277
5.5 Notes......Page 278
5.6 Bibliography......Page 285
6.1 Historical Background......Page 288
6.2.1 The Theory of Specific Heat (1906)......Page 290
6.2.2 The Dual Nature of Radiation (1909)......Page 291
6.2.3 The Bohr Atom (1913)......Page 292
6.2.5 The Compton Scattering Experiment (1923)......Page 294
6.2.6 Bose–Einstein Statistics (1924)......Page 295
6.2.7 Einstein, de Broglie (1924), and Schrödinger (1926)......Page 298
6.2.8 Einstein and Bohr (1927, 1930)......Page 300
6.3 Discussion and Comments......Page 304
6.4.2 The Commutator of P and Q......Page 305
6.5 Notes......Page 306
6.6 Bibliography......Page 310
7.1 The Inflexible Boundary Condition......Page 313
7.2 Notes......Page 316
7.3 Bibliography......Page 318
C......Page 320
E......Page 321
I......Page 322
M......Page 323
R......Page 324
U......Page 325
Z......Page 326