Relativistic Dynamics Of A Charged Sphere: Updating The Lorentz-abraham Model (lecture Notes In Physics New Series M)

This book takes a fresh and novel approach to century-old problems and their solution. The primary purpose is to determine an equation of motion for the classical Lorentz model of the electron that is consistent with causal solutions to the Maxwell - Lorentz equations. The author observes among other things that one does not need quantum mechanics to exclude the unphysical solution (to the equation of motion of a charge). In fact he shows for the first time that the classical theory is consistent in itself. The book will be highly welcome to physicists, and historians and philosophers of science, both students and researchers. This Is A Remarkable Book. [...] A Fresh And Novel Approach To Old Problems And To Their Solution. –fritz Rohrlich, Emeritus Professor Of Physics, Syracuse University This Book Takes A Fresh, Systematic Approach To Determining The Equation Of Motion For The Classical Model Of The Electron Introduced By Lorentz More Than 100 Years Ago. The Original Derivations Of Lorentz, Abraham, Poincaré And Schott Are Modified And Generalized For The Charged Insulator Model Of The Electron To Obtain An Equation Of Motion Consistent With Causal Solutions To The Maxwell-lorentz Equations And The Equations Of Special Relativity. The Solutions To The Resulting Equation Of Motion Are Free Of Pre-acceleration And Runaway Behavior. Binding Forces And A Total Stress–momentum–energy Tensor Are Derived For The Charged Insulator Model. General Expressions For Synchrotron Radiation Emerge In A Form Convenient For Determining The Motion Of The Electron. Appendices Provide Simplified Derivations Of The Self-force And Power At Arbitrary Velocity. In This Second Edition, The Method Used For Eliminating The Noncausal Pre-acceleration From The Equation Of Motion Has Been Generalized To Eliminate Pre-deceleration As Well. The Generalized Method Is Applied To Obtain The Causal Solution To The Equation Of Motion Of A Charge Accelerating In A Uniform Electric Field For A Finite Time Interval. Alternative Derivations Of The Landau-lifshitz Approximation To The Lorentz-abraham-dirac Equation Of Motion Are Also Given, Along With Spohn’s Elegant Solution Of This Approximate Equation For A Charge Moving In A Uniform Magnetic Field. The Book Is A Valuable Resource For Students And Researchers In Physics, Engineering And The History Of Science. 1. Introduction And Summary Of Results -- 2. Lorentz-abraham Force And Power Equations -- 3. Derivation Of Force And Power Equations -- 4. Internal Binding Forces -- 5. Electromagnetic, Electrostatic, Bare, Measured, And Insulator Masses -- 6. Transformation And Redefinition Of Force-power And Momentum-energy -- 7. Momentum And Energy Relations -- 8. Solutions To The Equations Of Motion -- App. A. Derivation And Transformation Of Small-velocity Force And Power -- App. B. Derivation Of Force And Power At Arbitrary Velocity -- App. C. Electric And Magnetic Fields In A Spherical Shell Of Charge -- App. D. Derivation Of The Linear Terms For The Self Electromagnetic Force. Arthur D. Yaghjian. Includes Bibliographical References. This is a remarkable book. Arthur Yaghjian is by training and profession an electrical engineer; but he has a deep interest in fundamental questions usually reserved for physicists. Working largely in isolation he has studied the relevant papers of an enormous literature accumulated over a century. The result is a fresh and novel approach to old problems and to their solution. Physicists since Lorentz have looked at the problem of the equations of motion of a charged object primarily as a problem for the description of a fundamental particle, typically an electron. Yaghjian considers a mac- scopic object, a spherical insulator with a surface charge. was therefore not tempted to take the point limit, and he thus avoided the pitfalls that have misguided research in this field since Dirac's famous paper of 1938. Perhaps the author's greatest achievement was the discovery that one does not need to invoke quantum mechanics and the correspondence pr- ciple in order to exclude the unphysical solutions (runaway and pre-acc- eration solutions). Rather, as he discovered, the derivation of the classical equations of motion from the Maxwell-Lorentz equations is invalid when the time rate of change of the dynamical variables too large (even in the relativistic case). Therefore, solutions that show such behavior are inc- sistent consequences. The classical theory thus shown to be physically consistent by itself. It embarrassing--to say the least--that this obs- vation had not been made before. The primary purpose of this text is to determine an equation of motion for the classical Lorentz model of the electron that is consistent with causal solutions to the Maxwell-Lorentz equations.