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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 Mï¿½bius 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 Fermatï¿½s 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 Mï¿½bius 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 Poincarï¿½ 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 Poincarï¿½ Models | |

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Angular Defect and its Relation to Aberration and Thomas Precession | |

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From the Klein to the Poincarï¿½ 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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ï¿½-decay and parity violation | |

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Stokes Parameters and Their Physical Interpretations | |

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Poincarï¿½'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 | |