A NEW PERSPECTIVE ON RELATIVITY : AN ODYSSEY IN NON-EUCLIDEAN GEOMETRIES
Bernard H. Lavenda
Bok Engelsk 2011 · Electronic books.
| Annen tittel | |
|---|---|
| Utgitt | Singapore : : World Scientific Publishing Company, , 2011.
|
| Omfang | 1 online resource (695 p.)
|
| Opplysninger | Description based upon print version of record.. - Preface; Contents; List of Figures; 1. Introduction; 1.1 Einstein's Impact on Twentieth Century Physics; 1.1.1 The author(s) of relativity; 1.1.1.1 Einstein's retraction of these two postulates and the existence of the aether; 1.1.1.2 Which mass?; 1.1.1.3 Conspiracy theories; 1.1.1.4 Space-time in Einstein's world; 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 Poincaré's missed opportunities; 1.2.2.1 From Fuchsian groups to Lorentz transforms. - 1.2.2.2 An author of E = mc21.3 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 Möbius transform; 2.2.5.1 Invariance of the cross-ratio; 2.2.5.2 Fixed points; 2.2.5.3 Associativity; 2.2.5.4 Transformations for which the unit circle is invariant; 2.3 Geodesics. - 2.4 Models of the Hyperbolic Plane and Their Properties2.5 A Brief History of Hyperbolic Geometry; References; 3. A Brief History of Light, Electromagnetism and Gravity; 3.1 The Drag Coef.cient: 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 drag3.6 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; 3.7.3.1 Quaternionic mass; 3.7.3.2 Vectorial mass; 3.7.4 e/m measurements of the transverse mass; 3.7.4.1 Thomson's method; 3.7.4.2 Kaufmann's method; 3.7.4.3 Microscopic interpretation of the de.ection methods; 3.8 Modeling Gravitation. - 3.8.1 Maxwellian gravitation3.8.2 Ritzian gravitation; 3.8.2.1 Mass from the gravitational field; 3.8.2.2 Advance of the perihelion; 3.8.2.3 Deflection of light; References; 4. Electromagnetic Radiation; 4.1 Spooky Actions-at-a-Distance versus Wiggly Continuous Fields; 4.1.1 Irreversibility from a reversible theory; 4.1.2 From fields to particles; 4.1.3 Absolute versus relative motion; 4.1.4 Faster than the speed of light; 4.2 Relativistic Mass; 4.2.1 Gedanken experiments; 4.2.2 From Weber to Einstein; 4.2.3 Maxwell on Gauss and Weber; 4.2.4 Ritz's electrodynamic theory of emission. - 4.2.4.1 Absolute versus relative velocities. - Starting off from noneuclidean geometries, apart from the method of Einstein's equations, this book derives and describes the phenomena of gravitation and diffraction. A historical account is presented, exposing the missing link in Einstein's construction of the theory of general relativity: the uniformly rotating disc, together with his failure to realize, that the Beltrami metric of hyperbolic geometry with constant curvature describes exactly the uniform acceleration observed. This book also explores these questions: How does time bend? Why should gravity propagate at the speed of light? Ho
|
| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9789814340489. - 9814340480
|
