Advanced Mechanics And General Relativity

"Aimed at advanced undergraduates with background knowledge of classical mechanics and electricity and magnetism, this textbook presents both the particle dynamics relevant to general relativity, and the field dynamics necessary to understand the theory. Focusing on action extremization, the book develops the structure and predictions of general relativity by analogy with familiar physical systems. Topics ranging from classical field theory to minimal surfaces and relativistic strings are covered in a homogenous manner. Nearly 150 exercises and numerous examples throughout the textbook enable students to test their understanding of the material covered. A tensor manipulation package to help students overcome the computational challenge associated with general relativity is available on a site hosted by the author"--

Aimed at advanced undergraduates with background knowledge of classical mechanics and electricity and magnetism, this textbook presents both the particle dynamics relevant to general relativity, and the field dynamics necessary to understand the theory. Focusing on action extremization, the book develops the structure and predictions of general relativity by analogy with familiar physical systems. Topics ranging from classical field theory to minimal surfaces and relativistic strings are covered in a homogeneous manner. Nearly 150 exercises and numerous examples throughout the textbook enable students to test their understanding of the material covered. A tensor manipulation package to help students overcome the computational challenge associated with general relativity is available on a site hosted by the author. A link to this and to a solutions manual can be found at www.cambridge.org/9780521762458.

This book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics. Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing. Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.

Covariant Physics: From Classical Mechanics to General Relativity and Beyond endeavours to provide undergraduate students as well as self-learners with training in the fundamentals of the modern theories of spacetime, most notably the general theory of relativity as well as physics in curved spacetime backgrounds in general. This text does so with the barest of mathematical preparation. In fact, very little beyond multivariable calculus and a bit of linear algebra is assumed. Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance. The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers.

Here it is, in a nutshell: the history of one genius’s most crucial work – discoveries that were to change the face of modern physics. In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. Respected American academic Professor Tai Chow tells us the story of these discoveries. He details the basic ideas of Einstein, including his law of gravitation. Deftly employing his inimitable writing style, he goes on to explain the physics behind black holes, weaving into his account an explanation of the structure of the universe and the science of cosmology.

Einstein's theory of gravity can be difficult to introduce at the undergraduate level, or for self-study. One way to ease its introduction is to construct intermediate theories between the previous successful theory of gravity, Newton's, and our modern theory, Einstein's general relativity. This textbook bridges the gap by merging Newtonian gravity and special relativity (by analogy with electricity and magnetism), a process that both builds intuition about general relativity, and indicates why it has the form that it does. This approach is used to motivate the structure of the full theory, as a nonlinear field equation governing a second rank tensor with geometric interpretation, and to understand its predictions by comparing it with the, often qualitatively correct, predictions of intermediate theories between Newton's and Einstein's. Suitable for a one-semester course at junior or senior level, this student-friendly approach builds on familiar undergraduate physics to illuminate the structure of general relativity.

This book provides a concise introduction to both the special theory of relativity and the general theory of relativity. The format is chosen to provide the basis for a single semester course which can take the students all the way from the foundations of special relativity to the core results of general relativity: the Einstein equation and the equations of motion for particles and light in curved spacetime. To facilitate access to the topics of special and general relativity for science and engineering students without prior training in relativity or geometry, the relevant geometric notions are also introduced and developed from the ground up. Students in physics, mathematics or engineering with an interest to learn Einstein's theories of relativity should be able to use this book already in the second semester of their third year. The book could also be used as the basis of a graduate level introduction to relativity for students who did not learn relativity as part of their undergraduate training.

The text covers the entire domain of basic classical mechanics and relativity theory (special and general) and has been revised mainly for the purpose of adding exercises without worked solutions that were missing in the first edition. To retain the format of a readable, yet advanced introductory text that can serve as the companion text for a course in mechanics, the more than 100 new exercises on diverse topics are of moderate range; answers are given and occasionally hints are provided. As before, the text aims to cover the entire spectrum of theoretical mechanics from Newton to Einstein. The reader can observe how in the course of time, deeper and deeper insights were achieved with the development of the basic equations of Newton to those of Euler and Lagrange, and to the geodesic equations of space-time and Einstein's relativity. To include diverse problems, a small section on this topic has been added.