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A new perspective on relativityan od...

Lavenda, Bernard H.

A new perspective on relativityan odyssey in non-Euclidean geometries /

Record Type:	Electronic resources : Monograph/item
Title/Author:	A new perspective on relativityBernard H. Lavenda.
Reminder of title:	an odyssey in non-Euclidean geometries /
Author:	Lavenda, Bernard H.
Published:	Singapore ;World Scientific,c2012
Description:	1 online resource (xxvi, 668 p.) :ill.
Subject:	Relativity (Physics)
Online resource:	http://www.worldscientific.com/worldscibooks/10.1142/8083#t=toc
ISBN:	9814340499 (electronic bk.)

A new perspective on relativityan odyssey in non-Euclidean geometries /
Lavenda, Bernard H.

A new perspective on relativityan odyssey in non-Euclidean geometries /[electronic resource] :Bernard H. Lavenda. - Singapore ;World Scientific,c2012 - 1 online resource (xxvi, 668 p.) :ill.

Includes bibliographical references and index.

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.

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? How does the expansion function of the universe relate to the absolute constant of the noneuclidean geometries? Why was the Sagnac effect ignored? Can Maxwell's equations accommodate mass? Is there an inertia due solely to polarization? Can objects expand in elliptic geometry like they contract in hyperbolic geometry?

ISBN: 9814340499 (electronic bk.)Subjects--Topical Terms:

189569
Relativity (Physics)

LC Class. No.: QC173.55 / .L38 2012

Dewey Class. No.: 530.1

A new perspective on relativityan odyssey in non-Euclidean geometries /
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505 0 $a 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.
520 $a 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? How does the expansion function of the universe relate to the absolute constant of the noneuclidean geometries? Why was the Sagnac effect ignored? Can Maxwell's equations accommodate mass? Is there an inertia due solely to polarization? Can objects expand in elliptic geometry like they contract in hyperbolic geometry?
650 0 $a Relativity (Physics) $3 189569
650 0 $a Geometry, Non-Euclidean. $3 648181
650 0 $a Gravitation. $3 275002
856 4 0 $u http://www.worldscientific.com/worldscibooks/10.1142/8083#t=toc