A new perspective on relativity: An odyssey in non-Euclidean geometries

Description

Content: Machine generated contents note: 1.Introduction -- 1.1.Einstein's Impact on Twentieth Century Physics -- 1.1.1.The author(s) of relativity -- 1.1.2.Models of the electron -- 1.1.3.Appropriation of Lorentz's theory of the electron by relativity -- 1.2.Physicists versus Mathematicians -- 1.2.1.Gauss's lost discoveries -- 1.2.2.Poincare's missed opportunities -- 1.3.Exclusion of Non-Euclidean Geometries from Relativity -- References -- 2.Which Geometry? -- 2.1.Physics or Geometry -- 2.1.1.The heated plane -- 2.2.Geometry of Complex Numbers -- 2.2.1.Properties of complex numbers -- 2.2.2.Inversion -- 2.2.3.Maxwell's 'fish-eye': An example of inversion from elliptic geometry -- 2.2.4.The cross-ratio -- 2.2.5.The Mobius transform -- 2.3.Geodesics -- 2.4.Models of the Hyperbolic Plane and Their Properties -- 2.5.A Brief History of Hyperbolic Geometry -- References -- 3.A Brief History of Light, Electromagnetism and Gravity -- 3.1.The Drag Coefficient: A Clash Between Absolute and Relative Velocities -- 3.2.Michelson-Morley Null Result: Is Contraction Real? -- 3.3.Radar Signaling versus Continuous Frequencies -- 3.4.Ives-Stilwell Non-Null Result: Variation of Clock Rate with Motion -- 3.5.The Legacy of Nineteenth Century English Physics -- 3.5.1.Pressure of radiation -- 3.5.2.Poynting's derivation of E = mc2 -- 3.5.3.Larmor's attempt at the velocity composition law via Fresnel's drag -- 3.6.Gone with the Aether -- 3.6.1.Elastic solid versus Maxwell's equations -- 3.6.2.The index of refraction -- 3.7.Motion Causes Bodily Distortion -- 3.7.1.Optical effect: Double diffraction experiments -- 3.7.2.Trouton-Noble null mechanical effect -- 3.7.3.Anisotropy of mass -- 3.7.4.E/M Measurements Of The Transverse Mass -- 3.8.Modeling Gravitation -- 3.8.1.Maxwellian gravitation -- 3.8.2.Ritzian gravitation -- References -- 4.Electromagnetic Radiation -- 4.1.Spooky Actions-at-a-Distance versus Wiggly Continuous Fields -- 4.1.1.Irreversibility from a reversible theory -- 4.1.