Cargando…
A new perspective on relativity : an odyssey in non-Euclidean geometries /
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 relativit...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2012.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Introduction. 1.1. Einstein's impact on twentieth century physics. 1.2. Physicists versus mathematicians. 1.3. Exclusion of non-Euclidean geometries from relativity
- 2. Which geometry? 2.1. Physics or geometry. 2.2. Geometry of complex numbers. 2.3. Geodesics. 2.4. Models of the hyperbolic plane and their properties. 2.5. A brief history of hyperbolic geometry
- 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. 3.6. Gone with the aether. 3.7. Motion causes bodily distortion. 3.8. Modeling gravitation
- 4. Electromagnetic radiation. 4.1. Spooky actions-at-a-distance versus Wiggly continuous fields. 4.2. Relativistic mass. 4.3. Radiation by an accelerating electron
- 5. The origins of mass. 5.1. Introduction. 5.2. From motional to static deformation. 5.3. Gravitational mass. 5.4. Electromagnetic mass. 5.5. Minimal curves for convex bodies in elliptic and hyperbolic spaces. 5.6. The tractrix. 5.7. Rigid motions: hyperbolic Lorentz transforms and elliptic rotations. 5.8. The elliptic geometry of an oblate spheroid. 5.9. Matter and energy
- 6. Thermodynamics of relativity. 6.1. Does the inertia of a body depend on its heat content? 6.2. Poincare stress and the missing mass. 6.3. Lorentz transforms from the velocity composition law. 6.4. Density transformations and the field picture. 6.5. Relativistic virial. 6.6. Which pressure? 6.7. Thermodynamics from Bessel functions
- 7. General relativity in a non-Euclidean geometrical setting. 7.1. Centrifugal versus gravitational forces. 7.2. Gravitational effects on the propagation of light. 7.3. Optico-gravitational phenomena. 7.4. The models. 7.5. General relativity versus non-Euclidean metrics. 7.6. The mechanics of diffraction
- 8. Relativity of hyperbolic space. 8.1. Hyperbolic geometry and the birth of relativity. 8.2. Doppler generation of Mobius transformations. 8.3. Geometry of Doppler and aberration phenomena. 8.4. Kinematics: the radar method of signaling. 8.5. Comparison with general relativity. 8.6. Hyperbolic geometry of relativity. 8.7. Coordinates in the hyperbolic plane. 8.8. Limiting case of a Lambert quadrilateral: uniform acceleration. 8.9. Additivity of the recession and distance in Hubble's Law.