This self-contained monograph provides a mathematically simple and physically meaningful model which unifies gravity, electromagnetism, optics and even some quantum behavior. The simplicity of the model is achieved by working in the frame of an inertial observer and by using a physically meaningful least action principle.
The authors introduce an extension of the Principle of Inertia. This gives rise to a simple, physically meaningful action function. Visualizations of the geometryare obtained by plotting the action function. These visualizations may be used to compare the geometries of different types of fields. Moreover, a new understanding of the energy-momentum of a field emerges.
The relativistic dynamics derived here properly describes motion of massive and massless objects under the influence of a gravitational and/or an electromagnetic field, and under the influence of isotropic media.
The reader will learn how to compute the precession of Mercury, the deflection of light, and the Shapiro time delay. Also covered is the relativistic motion of binary stars, including the generation of gravitational waves, a derivation of Snell's Law and a relativistic description of spin. We derive a complex-valued prepotential of an electromagnetic field. The prepotential is similar to the wave function in quantum mechanics.
The mathematics is accessible to students after standard courses in multivariable calculus and linear algebra. For those unfamiliar with tensors and the calculus of variations, these topics are developed rigorously in the opening chapters. The unifying model presented here should prove useful to upper undergraduate and graduate students, as well as to seasoned researchers.
1. Introduction.- 2. Classical Dynamics.- 3. The Lorentz Transformations
and Minkowski Space.- 4. The Geometric Model of Relativistic Dynamics.-
5. The Electromagnetic Field in Vacuum.- 6. The Gravitational Field.-
7. Motion of Light and Charges in Isotropic Media .- 8. Spin and Complexified
Minkowski Spacetime.- 9. The Prepotential.
Prof. Yaakov Friedman of the Jerusalem College of Technology Lev Academic Center was born in Munkatch, USSR. He graduated from the Faculty of Mathematics and Mechanics of Moscow University in 1971 and got his Ph.D. in Mathematics from Tel Aviv University in 1979. He worked for eight years at the University of California, Los Angeles and Irvine. Since that time, he has worked at the Jerusalem College of Technology as a lecturer, the rector, the vice-president for research and the head of the research authority. He initiated and was R&D director of several high-tech start-ups and companies. Prof. Friedman's research, published in about 100 papers, is in pure and applied mathematics, theoretical and applied statistics, and mathematical, theoretical and experimental physics. His current research interest is the novel approach to dynamics presented in this book, the theory's predictions, and experimental testing of them. This theory has the potential to give new insights into understanding microscopic behavior.
Dr. TzviScarr received his Masters degree in mathematics from the University of California, Berkeley in 1989 and his Ph.D. in mathematics from Bar Ilan University, Israel, in 2000. He has taught and done research at the Jerusalem College of Technology since 1997. His doctoral research was in equivariant topology and set-theoretic forcing. In 2002, he turned to mathematical physics and began his collaboration with Yaakov Friedman, assisting with the writing of the book Physical Applications of Homogeneous Balls. Over the past twenty years, he has developed mathematical models for special relativity, general relativity, electromagnetism and quantum mechanics. His research has focused on the use of a minimal number of assumptions as well as the unification of disparate areas in physics.
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