Download and read online A Most Incomprehensible Thing in PDF and EPUB A clear and enjoyable guide to the mathematics of relativity To really understand relativity – one of the cornerstones of modern physics – you have to get to grips with the mathematics. This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides 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 and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. 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. Understand even the basics of Einstein's amazing theory and the world will never seem the same again. March 2017. 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.
Download and read online A Most Incomprehensible Thing in PDF and EPUB This book is aimed at the enthusiastic general reader who wants to move beyond the maths-lite popularisations in order to tackle the essential mathematics of Einstein's fascinating theories of special and general relativity. One of the cornerstones of modern physics, relativity is based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive (in plain English: very weird) consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, a theory of gravity, is at the heart of our understanding of cosmology and black holes. To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics. This introductory, self-study guide is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides 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 Schwarzschild solution; simple black holes (and what different observers would see if someone was unfortunate enough to fall into one). Also covered are the mysteries of dark energy and the cosmological constant; plus relativistic cosmology, including the Friedmann equations and Friedmann-Robertson-Walker cosmological models. Following the historic 2015 LIGO detection, there is now also an additional chapter on gravitational waves. Understand even the basics of Einstein's amazing theory and the world will never seem the same again.
Download and read online A Most Incomprehensible Thing in PDF and EPUB Synopsis Based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence - Einstein's theories of special and general relativity together form a cornerstone of modern physics. Special relativity has some strangely counter-intuitive consequences, including time dilation, length contraction, the relativity of simultaneity and mass-energy equivalence, whilst general relativity is at the heart of our understanding of black holes and the evolution of the universe. Using straightforward, accessible language, with numerous fully solved problems and clear derivations and explanations, this book is aimed at the enthusiastic general reader who wants to move beyond maths-lite popularisations and tackle the essential mathematics of this fascinating theory. (To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics.) For those with minimal mathematical background, the first chapter provides 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; the four classical tests of general relativity; simple black holes; the mysteries of dark energy and the cosmological constant; and the Friedmann equations and Friedmann-Robertson-Walker cosmological models. 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 Bibliography Appendix - Planetary motion data Acknowledgements
Download and read online Mathematics of Relativity in PDF and EPUB Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity. Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor.
Download and read online Differential Forms and the Geometry of General Relativity in PDF and EPUB Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.
Download and read online Quantum Field Theory for the Gifted Amateur in PDF and EPUB Quantum field theory provides the theoretical backbone to most modern physics. It explains the standard model of particle physics and the existence of the Higgs boson, the physics of states of matter such as metals, magnets and superconductors, and allows us to understand the behaviour of polymers and biological molecules. However, quantum field theory has a reputation for difficulty, reinforced by a selection of weighty and inaccessible books on the subject aimedfirmly at those who will make future advances in the subject. The authors of this book believe the subject is too important to be restricted to the professionals and have designed this book to bringquantum field theory to a wider audience of physicists. The book is packed with worked examples, witty diagrams, and applications intended to introduce a new audience to this revolutionary theory.
Download and read online Relativity Gravitation and Cosmology in PDF and EPUB This book provides an introduction to Einstein's general theory of relativity. A "physics-first" approach is adopted so that interesting applications come before the more difficult task of solving the Einstein equation. The book includes extensive coverage of cosmology, and is designed to allow readers to study the subject alone.
Download and read online The Geometry of Spacetime in PDF and EPUB Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.
Download and read online It s about Time in PDF and EPUB This book has three main goals. First, it explores a selection of topics from the early period of the theory of relativity, focusing on particular aspects that are interesting or unusual. These include the twin paradox; relativistic mechanics and its interaction with Maxwell's laws; the earliest triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing near the sun; and the surprising bizarre metric of Kurt Godel, in which time travel is possible. Second, it provides an exposition of the differential geometry needed to understand these topics on a level that is intended to be accessible to those with just two years of university-level mathematics as background. Third, it reflects on the historical development of the subject and its significance for our understanding of what reality is and how we can know about the physical universe. The book also takes note of historical prefigurations of relativity, such as Euler's 1744 result that a particle moving on a surface and subject to no tangential acceleration will move along a geodesic, and the work of Lorentz and Poincare on space-time coordinate transformations between two observers in motion at constant relative velocity. The book is aimed at advanced undergraduate mathematics, science, and engineering majors (and, of course, at any interested person who knows a little university-level mathematics). The reader is assumed to know the rudiments of advanced calculus, a few techniques for solving differential equations, some linear algebra, and basics of set theory and groups.
Download and read online Understanding Relativity in PDF and EPUB Nonspecialists with no prior knowledge of physics and only reasonable proficiency with algebra can now understand Einstein's special theory of relativity. Effectively diagrammed and with an emphasis on logical structure, Leo Sartori's rigorous but simple presentation will guide interested readers through concepts of relative time and relative space. Sartori covers general relativity and cosmology, but focuses on Einstein's theory. He tracks its history and implications. He explores illuminating paradoxes, including the famous twin paradox, the "pole-in-the-barn" paradox, and the Loedel diagram, which is an accessible, graphic approach to relativity. Students of the history and philosophy of science will welcome this concise introduction to the central concept of modern physics.
Download and read online Introduction to Special Relativity in PDF and EPUB Concise, well-written treatment of epochal theory of modern physics covers classical relativity and the relativity postulate, time dilation, the twin paradox, momentum and energy, particles of zero mass, electric and magnetic fields and forces and more. Only high school math needed. Replete with examples, ideal for self-study. Introduction. 70 illustrations.
Download and read online General Relativity in PDF and EPUB This textbook is suitable for a one-semester introduction to General Relativity for advanced undergraduates in physics and engineering. The book is concise so that the entire material can be covered in the one-semester time frame. Besides, the readers are introduced to the subject easily without the need for advanced mathematics. Though concise, the theory development is lucid and the readers are exposed to possible analytic calculations. Full solutions to some important problems are provided, and the experimental evidence is discussed in detail. Contents:Review of Special RelativityVectors and Tensors in SpacetimeCovariant Differentiation, Equations of MotionCurvatureGravity and General RelativitySolar System Tests of General RelativityBlack HolesGravitational WavesCosmolgy Readership: Undergraduate and graduate students in physics courses.
Download and read online Introduction to General Relativity Black Holes and Cosmology in PDF and EPUB General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.
Download and read online Einstein s Theory in PDF and EPUB This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory. Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained aims to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.
Download and read online Relativity Gravitation and Cosmology in PDF and EPUB The textbook introduces students to basic geometric concepts, such as metrics, connections and curvature, before examining general relativity in more detail. It shows the observational evidence supporting the theory, and the description general relativity provides of black holes and cosmological spacetimes. --