This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Includes more than 100 problems and 38 figures. 1986 edition.

This book is about Einstein's Summation Notation (ESN). It explains the rules for correct use of ESN-notation, covering the Kronecker-symbol and the Levi-Civita-symbol. Examples are taken from Linear Algebra (vector - and matrix - calculation) as well as functional analysis (diferential operators gradient, curl, divergence). The book aims at students of physics who want to deal with the Special - and General Theory of Relativity by Albert Einstein, as the correct use of ESN in this area is essential.

Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.

A straightforward, enjoyable guide to the mathematics of Einstein's relativity To really understand Einstein's theory of relativity – one of the cornerstones of modern physics – you have to get to grips with the underlying mathematics. This self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. With a user-friendly style, clear step-by-step mathematical derivations, many fully solved problems and numerous diagrams, this book provides a comprehensive introduction to a fascinating but complex subject. For those with minimal mathematical background, the first chapter gives a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes, relativistic cosmology and gravitational waves. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes. "I must observe that the theory of relativity resembles a building consisting of two separate stories, the special theory and the general theory. The special theory, on which the general theory rests, applies to all physical phenomena with the exception of gravitation; the general theory provides the law of gravitation and its relations tothe other forces of nature." – Albert Einstein, 1919 Understand even the basics of Einstein's amazing theory and the world will never seem the same again. Contents: Preface Introduction 1 Foundation mathematics 2 Newtonian mechanics 3 Special relativity 4 Introducing the manifold 5 Scalars, vectors, one-forms and tensors 6 More on curvature 7 General relativity 8 The Newtonian limit 9 The Schwarzschild metric 10 Schwarzschild black holes 11 Cosmology 12 Gravitational waves Appendix: The Riemann curvature tensor Bibliography Acknowledgements January 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

The purposes of this book are (1) to explore and expound relativity physics and four-dimensional symmetry from the logically simplest viewpoint by making one single postulate instead of two; and (2) to indicate the simplest generalization of the Lorentz transformation in order to cope with frames with constant linear accelerations. The fundamentally new ideas of the first purpose are developed on the basis of the term paper of a Harvard physics undergraduate. They lead to an unexpected affirmative answer to the long-standing question of whether it is possible to construct a relativity theory without postulating the constancy of the speed of light and retaining only the first postulate of special relativity. This question was discussed in the early years following the discovery of special relativity by many physicists, including Ritz, Tolman, Kunz, Comstock and Pauli, all of whom obtained negative answers. Furthermore, the new theory of relativity indicates the truly universal and fundamental constants in physics, and provides a broad view of relativistic physics beyond special relativity. It substantiates the view and sheds light on the understanding that the four-dimensional symmetry framework can accommodate many different concepts of physical time, including common time and Reichenbach's general concept of time. This logically simplest viewpoint of relativity allows a natural extension of the physics of particles and fields from inertial frames to noninertial frames in which the speed of light is not constant. New predictions in physics resulting from this new viewpoint are discussed. The book is based on papers by the author and his collaborators in Physics Letters A, Nuovo Cimento B, and Physical Review A and D.

"I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case, I would rather be a cobbler, or even an employee in a gaming house, than a physicist." -Albert Einstein A scandal hovers over the history of 20th century physics. Albert Einstein-the century's greatest physicist-was never able to come to terms with quantum mechanics, the century's greatest theoretical achievement. For physicists who routinely use both quantum laws and Einstein's ideas, this contradiction can be almost too embarrassing to dwell on. Yet Einstein was one of the founders of quantum physics and he spent many years preaching the quantum's importance and its revolutionary nature. The Danish genius Neils Bohr was another founder of quantum physics. He had managed to solve one of the few physics problems that Einstein ever shied away from, linking quantum mathematics with a new model of the atom. This leap immediately yielded results that explained electron behavior and the periodic table of the elements. Despite their mutual appreciation of the quantum's importance, these two giants of modern physics never agreed on the fundamentals of their work. In fact, they clashed repeatedly throughout the 1920s, arguing first over Einstein's theory of "light quanta"(photons), then over Niels Bohr's short-lived theory that denied the conservation of energy at the quantum level, and climactically over the new quantum mechanics that Bohr enthusiastically embraced and Einstein stubbornly defied. This contest of visions stripped the scientific imagination naked. Einstein was a staunch realist, demanding to know the physical reasons behind physical events. At odds with this approach was Bohr's more pragmatic perspective that favored theories that worked, even if he might not have a corresponding explanation of the underlying reality. Powerful and illuminating, Einstein Defiant is the first book to capture the soul and the science that inspired this dramatic duel, revealing the personalities and the passions-and, in the end, what was at stake for the world.