The basic concepts of relativity theory are conveyed through worked and unworked examples in this text, which requires only elementary algebra and emphasizes physical principles and concepts. 1985 edition.
The Theory of Relativity is one of the most complex in the history of science. Together with Darwin’s theory, it is also one of the most controversial, despite the number of experiments that have supposedly confirmed it. Some aspects are conventionally consistent; for example, as it is currently defined, time is relative. However, it does not make much sense the official definition of the unit of time is sensitive to the gravitational field or speed; since it would have been logical to establish it, including these two specific conditions, as it does with temperature and others. This book analyzes the basic concepts: • Maxwell's equations and the Lorentz transformations –3D Pitagoras theorem, the principles of Poincaré, and interpretations of the Michelson-Morley experiment as immediate antecedents of relativistic physics. • Ad hoc postulates of Einstein's relativity, or better said axioms! • The unusual terminology of the theory: thought experiments, observer as a reference frame, inertial and non-inertial frames, and many more. • The Euclidean space and the types in Einstein’s theory as the geometry of Minkowsky and Riemann. • Concept of inertial, gravitational, and relativistic mass. • The weakness of the twin paradox in Special Relativity. • Principle of equivalence incorporating gravity with General Relativity. Since it only explains 5% of the energy-mass of the observable universe and its peculiar characteristics, it belongs to the books of Global Metaphysics.
Quantum mechanics provides the fundamental theoretical apparatus for describing the structure and properties of atoms and molecules in terms of the behaviour of their fundamental components, electrons and nudeL For heavy atoms and molecules containing them, the electrons can move at speeds which represent a substantial fraction of the speed of light, and thus relativity must be taken into account. Relativistic quantum mechanics therefore provides the basic formalism for calculating the properties of heavy-atom systems. The purpose of this book is to provide a detailed description of the application of relativistic quantum mechanics to the many-body prob lem in the theoretical chemistry and physics of heavy and superheavy elements. Recent years have witnessed a continued and growing interest in relativistic quantum chemical methods and the associated computa tional algorithms which facilitate their application. This interest is fu elled by the need to develop robust, yet efficient theoretical approaches, together with efficient algorithms, which can be applied to atoms in the lower part of the Periodic Table and, more particularly, molecules and molecular entities containing such atoms. Such relativistic theories and computational algorithms are an essential ingredient for the description of heavy element chemistry, becoming even more important in the case of superheavy elements. They are destined to become an indispensable tool in the quantum chemist's armoury. Indeed, since relativity influences the structure of every atom in the Periodic Table, relativistic molecular structure methods may replace in many applications the non-relativistic techniques widely used in contemporary research.
Elements and Formulae of Special Relativity presents elements and formulas of the theory of special relativity and covers topics ranging from kinematics and propagation of light to mechanics of single bodies, hydrodynamics, and thermodynamics. Vector operators, electromagnetic fields, electrodynamics, and statistical mechanics are also explored. This book is comprised of 13 chapters and begins by introducing the reader to the kinematics of special relativity, paying particular attention to formulas required for transformations between two frames of reference. Attention then turns to the propagation of light, the Doppler effect, the mechanics of single bodies, and the more general and more powerful approach to relativistic mechanics due to Lagrange and to Hamilton. The chapters that follow focus on formulas for a fluid maintained at a constant uniform pressure; relativistic formulas for thermodynamics; and representation of M-vectors with real components by cartesian 4-vectors with imaginary components. This book also considers the equations for an electromagnetic field in a vacuum and a gaseous phase composed of one or several perfect monatomic gases. A brief historical synopsis is given in the last chapter. This monograph will be useful to chemical physicists and other not-too-theoretical physicists.
This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -particularly the Lorentz and the SL(2,C) groups — to the theory of general relativity. Each chapter is concluded with a set of problems.The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2,C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.
Parallel computing technologies have brought dramatic changes to mainstream computing; the majority of today's PC's, laptops and even notebooks incorporate multiprocessor chips with up to four processors. Standard components are increasingly combined with GPU's (Graphics Processing Unit), originally designed for high-speed graphics processing, and FPGA's (Free Programmable Gate Array) to build parallel computers with a wide spectrum of high-speed processing functions. The scale of this powerful hardware is limited only by factors such as energy consumption and thermal control However, in addition to hardware factors, the practical use of petascale and exascale machines is often hampered by the difficulty of developing software which will run effectively and efficiently on such architecture This book includes selected and refereed papers, presented at the 2009 international Parallel Computing conference (ParCo2009), which set out to address these problems. It provides a snapshot of the state-of-the-art of parallel computing technologies in hardware, application and software development Areas covered include: numerical algorithms, grid and cloud computing, programming - including GPU and cell programming. The book also includes papers presented at the six mini-symposia held at the conference
Elementary introduction pays special attention to aspects of tensor calculus and relativity that students find most difficult. Contents include tensors in curved spaces and application to general relativity theory; black holes; gravitational waves; application of general relativity principles to cosmology. Numerous exercises. Solution guide available upon request. 1982 edition.