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| Preface | |
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| List of Figures | |
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| Introduction | |
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| Einstein's Impact on Twentieth Century Physics | |
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| The author(s) of relativity | |
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| Models of the electron | |
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| Appropriation of Lorentz's theory of the electron by relativity | |
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| Physicists versus Mathematicians | |
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| Gauss's lost discoveries | |
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| Poincare's missed opportunities | |
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| Exclusion of Non-Euclidean Geometries from Relativity | |
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| References | |
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| Which Geometry? | |
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| Physics or Geometry | |
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| The heated plane | |
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| Properties of complex numbers | |
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| Inversion | |
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| Maxwell's 'fish-eye': An example of inversion from elliptic geometry | |
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| The cross-ratio | |
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| The M�bius transform | |
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| Geodesies | |
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| Models of the Hyperbolic Plane and Their Properties | |
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| A Brief History of Hyperbolic Geometry | |
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| References | |
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| A Brief History of Light, Electromagnetism and Gravity | |
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| The Drag Coefficient: A Clash Between Absolute and Relative Velocities | |
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| Michelson-Morley Null Result: Is Contraction Real? | |
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| Radar Signaling versus Continuous Frequencies | |
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| Ives-Stilwell Non-Null Result; Variation of Clock Rate with Motion | |
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| The Legacy of Nineteenth Century English Physics | |
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| Pressure of radiation | |
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| Poynting's derivation of E = mc<sup>2</sup> | |
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| Larmor's attempt at the velocity composition law via Fresnel's drag | |
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| Gone with the Aether | |
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| Elastic solid versus Maxwell's equations | |
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| The index of refraction | |
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| Motion Causes Bodily Distortion | |
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| Optical effect: Double diffraction experiments | |
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| Trouton-Noble null mechanical effect | |
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| Anisotropy of mass | |
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| e/m measurements of the transverse mass | |
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| Modeling Gravitation | |
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| Maxwellian gravitation | |
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| Ritzian gravitation | |
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| References | |
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| Electromagnetic Radiation | |
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| Spooky Actions-at-a-Distance versus Wiggly Continuous Fields | |
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| Irreversibility from a reversible theory | |
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| From fields to particles | |
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| Absolute versus relative motion | |
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| Faster than the speed of light | |
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| Relativistic Mass | |
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| Gedanken experiments | |
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| From Weber to Einstein | |
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| Maxwell on Gauss and Weber | |
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| Ritz's electrodynamic theory of emission | |
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| Radiation by an Accelerating Electron | |
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| What does the radiation reaction force measure? | |
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| Constant rate of energy loss in hyperbolic velocity space | |
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| Radiation at uniform acceleration | |
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| Curvatures: Turning and twisting | |
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| Advanced potentials as perpetual motion machines | |
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| References | |
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| The Origins of Mass | |
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| Introduction | |
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| From Motional to Static Deformation | |
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| Potential theory | |
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| Gravitational Mass | |
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| Attraction of a rod: Increase in mass with broadside motion | |
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| Attraction of a spheroid on a point in its axis of revolution: Forces of attraction as minimal curves of convex bodies | |
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| Electromagnetic Mass | |
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| What does the ratio e/m measure? | |
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| Models of the electron | |
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| Thomson's relation between charges in motion and their mass | |
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| Oblate versus prolate spheroids | |
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| Minimal Curves for Convex Bodies in Elliptic and Hyperbolic Spaces | |
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| The Tractrix | |
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| Rigid Motions: Hyperbolic Lorentz Transforms and Elliptic Rotations | |
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| The Elliptic Geometry of an Oblate Spheroid | |
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| Matter and Energy | |
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| References | |
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| Thermodynamics of Relativity | |
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| Does the Inertia of a Body Depend on its Heat Content? | |
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| Poincare Stress and the Missing Mass | |
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| Lorentz Transforms from the Velocity Composition Law | |
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| Density Transformations and the Field Picture | |
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| Relativistic Virial | |
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| Which Pressure? | |
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| Thermodynamics from Bessel Functions | |
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| Boltzmann's law via modified Bessel functions | |
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| Asymptotic probability densities | |
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| References | |
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| General Relativity in a Non-Euclidean Geometrical Setting | |
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| Centrifugal versus Gravitational Forces | |
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| Gravitational Effects on the Propagation of Light | |
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| From Doppler to gravitational shifts | |
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| Shapiro effect via Fermat�s principle | |
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| Optico-gravitational Phenomena | |
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| The Models | |
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| General Relativity versus Non-Euclidean Metrics | |
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| The Mechanics of Diffraction | |
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| Gravitational shift of spectral lines | |
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| The deflection of light | |
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| Advance of the perihelion | |
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| References | |
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| Relativity of Hyperbolic Space | |
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| Hyperbolic Geometry and the Birth of Relativity | |
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| Doppler Generation of M�bius Transformations | |
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| Geometry of Doppler and Aberration Phenomena | |
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| Kinematics: The Radar Method of Signaling | |
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| Constant relative velocity: Geometric-arithmetic mean inequality | |
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| Constant relative acceleration | |
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| Comparison with General Relativity | |
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| Hyperbolic Geometry of Relativity | |
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| Coordinates in the Hyperbolic Plane | |
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| Limiting Case of a Lambert Quadrilateral: Uniform Acceleration | |
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| Additivity of the Recession and Distance in Hubble's Law | |
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| References | |
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| Nonequivalence of Gravitation and Acceleration | |
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| The Uniformly Rotating Disc in Einstein's Development of General Relativity | |
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| The Sagnac Effect | |
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| Generalizations of the Sagnac Effect | |
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| The Principle of Equivalence | |
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| Fermat's Principle of Least Time and Hyperbolic Geometry | |
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| The Rotating Disc | |
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| The FitzGerald-Lorentz Contraction via the Triangle Defect | |
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| Hyperbolic Nature of the Electromagnetic Field and the Poincar� Stress | |
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| The Terrell-Weinstein Effect and the Angle of Parallelism | |
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| Hyperbolic Geometries with Non-Constant Curvature | |
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| The heated disc revisited | |
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| A matter of curvature | |
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| Schwarzschild's metric: How a nobody became a one-body | |
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| Schwarzschild's metric: The inside story | |
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| Cosmological Models | |
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| The general projective metric in the plane | |
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| The expanding Minkowski universe | |
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| Event horizons | |
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| Newtonian dynamics discovers the 'big bang' | |
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| References | |
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| Aberration and Radiation Pressure in the Klein and Poincar� Models | |
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| Angular Defect and its Relation to Aberration and Thomas Precession | |
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| From the Klein to the Poincar� Model | |
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| Aberration versus Radiation Pressure on a Moving Mirror | |
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| Aberration and the angle of parallelism | |
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| Reflection from a moving mirror | |
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| Electromagnetic Radiation Pressure | |
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| Angle of Parallelism and the Vanishing of the Radiation Pressure | |
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| Transverse Doppler Shifts as Experimental Evidence for the Angle of Parallelism | |
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| References | |
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| The Inertia of Polarization | |
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| Polarization and Relativity | |
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| A history of polarization and some of its physical consequences | |
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| Spin | |
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| Angular momentum | |
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| Elastic strain | |
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| Plane waves | |
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| Spherical waves | |
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| �-decay and parity violation | |
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| Stokes Parameters and Their Physical Interpretations | |
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| Poincar�'s Representation and Spherical Geometry | |
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| Isospin and the electroweak interaction | |
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| Polarization of Mass | |
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| Mass and momentum | |
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| Relativistic space-time paths: An example of mass polarization | |
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| Mass in Maxwell's Theory and Beyond | |
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| A model of radiation | |
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| Enter mass: Proca's equations | |
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| Proca's approach to superconductivity | |
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| Phase and mass | |
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| Compressional electromagnetic waves: Helmholtz's theory | |
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| Directed electromagnetic waves | |
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| Relativistic Stokes Parameters | |
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| Weyl and Dirac versus Stokes | |
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| Origin of the zero helicity state | |
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| Lamb shift and left-hand elliptical polarization | |
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| References | |
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| Index | |