Reprint of a classical book first published in 1950. This lucid and profound exposition of Einstein's 1915 theory of gravitation is essential reading.

The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.

This comprehensive student manual has been designed to accompany the leading textbook by Bernard Schutz, A First Course in General Relativity, and uses detailed solutions, cross-referenced to several introductory and more advanced textbooks, to enable self-learners, undergraduates and postgraduates to master general relativity through problem solving. The perfect accompaniment to Schutz's textbook, this manual guides the reader step-by-step through over 200 exercises, with clear easy-to-follow derivations. It provides detailed solutions to almost half of Schutz's exercises, and includes 125 brand new supplementary problems that address the subtle points of each chapter. It includes a comprehensive index and collects useful mathematical results, such as transformation matrices and Christoffel symbols for commonly studied spacetimes, in an appendix. Supported by an online table categorising exercises, a Maple worksheet and an instructors' manual, this text provides an invaluable resource for all students and instructors using Schutz's textbook.

A comprehensive review of gravitational effects in quantum field theory. Treatment is general, but special emphasis is given to the Hawking black hole evaporation effect and to particle creation processes in the early universe.

This book deals with underlying basic concepts in relativity. The fundamental work of Stueckelberg, who formulated a consistent relativistic classical and quantum dynamics, generalized for application to many-body systems by Horwitz and Piron (SHP theory), is explained with emphasis on its conceptual content. The two-body bound state and scattering theory are also discussed. The ideas are involved in the Lindner experiment showing interference in time and the proposed experiment of Palacios et al. searching for the persistence of entanglement at unequal times is discussed. The meaning of the Newton-Wigner position operator and the Landau-Peierls construction in terms of relativistic dynamics is given. Finally, the embedding of the SHP theory into the framework of general relativity, providing a canonical structure with particle coordinates and momenta, is studied, carrying with it new concepts in relativistic dynamics.

Discovering Relativity for yourself explains Einstein's Theory of Relativity to readers who are daunted by the standard mathematical approach to that profound theory. For twenty years Sam Lilley taught this subject to adults with no science background. Now he has written an explanation of the theory that demands no prior knowledge of mathematics or physics beyond an ability to do simple arithmetic. The first quarter of the book uses no more than arithmetic and a little simple geometry to introduce some of the main concepts of the theory, as well as discussing an impressive experimental test, which comes down strongly in its favour. When eventually further progress demands use of algebra and other mathematical techniques, these are carefully explained in a way that makes them accessible to absolute beginners, using many new and unorthodox methods.

In these inspiring lectures David Bohm explores Albert Einstein's celebrated Theory of Relativity that transformed forever the way we think about time and space. Yet for Bohm the implications of the theory were far more revolutionary both in scope and impact even than this. Stepping back from dense theoretical and scientific detail in this eye-opening work, Bohm describes how the notion of relativity strikes at the heart of our very conception of the universe, regardless of whether we are physicists or philosophers.

This book, explores the conceptual foundations of Einstein's theory of relativity: the fascinating, yet tangled, web of philosophical, mathematical, and physical ideas that is the source of the theory's enduring philosophical interest.

Originally published in 1986.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Based on papers presented at the Jerusalem Einstein Centennial Symposium in March 1979, this volume sets forth an articulated sequence of chapters on the impact of Einstein's work, not only in science but in humanistic studies and problems such as international security in the nuclear age.

Originally published in 1984.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

From 1900 to 1924 Spain experienced a stage of vigorous academic freedom and unfettered scientific inquiry that strikingly contrasted with the repressive atmosphere of the periods before and after. Thomas Glick explores this "recovery of science" by focusing on the national discussion provoked by Einstein's trip to Spain in 1923. His visit stimulated a debate on the nature and social value of science that was remarkable in a society so recently awakened to the scientific role in the process of modernization. Einstein's universal appeal created the unlikely occasion for a fascination with science that cut across social classes and previously established domains of discourse.

The political Right, which in other countries opposed relativity in the name of "traditional" Newtonian science, backed the new theories with surprising enthusiasm. Engineers, a politically conservative group, contributed much of the rank-and-file support for Einstein; physicians, who tended to the Left, also eagerly embraced his ideas, as did a host of mutually antagonistic political groups, including anarcho-syndicalists and bourgeois Catalan nationalists. Professor Glick's analysis of this multidimensional scientific forum provides an unusual amount of information on science in Spain and an opportunity to contrast the Spaniards' reception of Einstein's work and that of other nations during this historical period.

Originally published in 1988.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Albert Einstein is often viewed as the icon of genius, and his theories are admired for their beauty and correctness. Yet the final judge of any theory is the rigorous test of experiment, not the fame of its inventor or the allure of its mathematics. For decades, general relativity has passed test after test with flying colors, including some remarkable new tests using the recently detected gravitational waves. Still, there are reasons for doubt. Einstein's theory of gravity, as beautiful as it is, seems to be in direct contradiction with another theory he helped create: quantum mechanics. Until recently, this was considered to be a purely academic affair. But as more and more data pour in from the most distant corners of the universe, hinting at bizarre stuff called "dark energy" and "dark matter," some scientists have begun to explore the possibility that Einstein's theory may not provide a complete picture of the cosmos. This book chronicles the latest adventures of scientists as they put Einstein's theory to the test in ever more precise and astonishing ways, and in ever more extreme situations, when gravity is unfathomably intense and rapidly churning. From the explosions of neutron stars and the collisions of black holes to the modern scientific process as a means to seek truth and understanding in the cosmos, this book takes the reader on a journey of learning and discovery that has been 100 years in the making.

This monograph presents the first detailed exposition of the formal theory of Branching Space-Times. The theory presented here by Nuel Belnap, Thomas Muller, and Tomasz Placek describes how real possibilities can play out in our spatio-temporal world. In our world, some things that are really possible in Cleveland are not really possible in San Francisco; other things were really possible in 1988 but are not really possible in 2021. The authors develop a rigorous, relativity-friendly theory of indeterminism as a local and modal concept, demonstrating that our world contains events with alternative possible outcomes. The book is divided into two parts. The first contains the exposition of the theory, including detailed proofs. The second contains three applications of Branching Space-Times in metaphysics and philosophy of science, focusing on the use of Branching Space-Times to represent pertinent forms of indeterminism in each area. Some specific applications include a formal analysis of modal correlations and of causation and a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. The authors link their theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, particularly in quantum non-locality and spatio-temporal relativity. They also relate the theory to philosophy of time, showing how it may be used to explicate the dynamic concept of the past, present, and future based on local indeterminism. The Branching Space-Times theory has been in development over the past 25 years. This volume provides a much needed first systematic and comprehensive book-length exposition of both the theory and its applications. This is an open access title available under the terms of a CC BY-NC-ND 4.0 International license. It is free to read at Oxford Scholarship Online and offered as a free PDF download from OUP and selected open access locations.

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself.

These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large.

Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.

These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole. In the first case, the singularity in our past. A discussion of the Cauchy problem for General Relativity is also included in the book.

Starting with the description of our home galaxy the Milky Way, this cogently written textbook introduces the reader to the astronomy of galaxies, their structure, active galactic nuclei, evolution and large scale distribution. Then, from the extensive and thorough introduction to modern observational and theoretical cosmology, the text turns to the formation of structures and astronomical objects in the early universe. The basics of classical astronomy and stellar astrophysics needed for extragalactic astronomy are given in the appendix.

In particular, Peter Schneider s Extragalactic Astronomy and Cosmology has the goal of imparting the fundamental knowledge of this fascinating subfield of astronomy, while leading readers to the forefront of astronomical research. But it seeks to accomplish this not only with extensive textual information and insights. In addition, the author s evident admiration for the workings of the universe that shines through the lines and the many supporting color illustrations will deeply inspire the reader.

While this book has grown out of introductory university courses on astronomy and astrophysics, it will not only be appreciated by undergraduate students and lecturers. Through the comprehensive coverage of the field, even graduate students and researchers specializing in related fields will appreciate it as reliable reference."

Einstein's general theory of relativity is widely considered to be one of the most elegant and successful scientific theories ever developed, and it is increasingly being taught in a simplified form at advanced undergraduate level within both physics and mathematics departments. Due to the increasing interest in gravitational physics, in both the academic and the public sphere, driven largely by widely-publicised developments such as the recent observations of gravitational waves, general relativity is also one of the most popular scientific topics pursued through self-study. Modern General Relativity introduces the reader to the general theory of relativity using an example-based approach, before describing some of its most important applications in cosmology and astrophysics, such as gamma-ray bursts, neutron stars, black holes, and gravitational waves. With hundreds of worked examples, explanatory boxes, and end-of-chapter problems, this textbook provides a solid foundation for understanding one of the towering achievements of twentieth-century physics.

Each of this book's 32 essays discusses a chosen topic, at a level that is generally within that of a four-year degree course in Physics. The essays supplement (indeed sometimes correct) treatments usually given, or supplies reasoning that tends to fall through the cracks. The author uses his life long experience of tutorial teaching at Oxford to know what topics often need such discussion, for clarification, or for avoidance of common confusions. The book contains accounts of even-standard topics, accounts that offer an unusual emphasis, or a fresh insight, or more than customary rigour, or a cross-link to apparently unrelated material. The student (and their teachers) who really wants to understand physics will find this book indispensable. Often the outcome of tutorial discussion has been an understanding that lies a little to the side of what is presented in standard texts. Such understanding is presented here in the essays. The topics covered are diverse and have something useful to say across most areas of a physics degree.

It is commonly assumed that if the Sun suddenly turned into a black hole, it would suck Earth and the rest of the planets into oblivion. Yet, as prominent author and astrophysicist Jeffrey Bennett points out, black holes don't suck. With that simple idea in mind, Bennett begins an entertaining introduction to Einstein's theories of relativity, describing the amazing phenomena readers would actually experience if they took a trip to a black hole. The theory of relativity reveals the speed of light as the cosmic speed limit, the mind-bending ideas of time dilation and curvature of spacetime, and what may be the most famous equation in history: E = mc2. Indeed, the theory of relativity shapes much of our modern understanding of the universe. It is not "just a theory"-every major prediction of relativity has been tested to exquisite precision, and its practical applications include the Global Positioning System (GPS). Amply illustrated and written in clear, accessible prose, Bennett's book proves anyone can grasp the basics of Einstein's ideas. His intuitive, nonmathematical approach gives a wide audience its first real taste of how relativity works and why it is so important to science and the way we view ourselves as human beings.

The internationally renowned physicist Harald Fritzsch deftly explains the meaning and far-flung implications of the general theory of relativity and other mysteries of modern physics by presenting an imaginary conversation among Newton, Einstein, and a fictitious contemporary particle physicist named Adrian Haller -- the same device Fritzsch employed to great acclaim in his earlier book An Equation That Changed the World, which focused on the special theory of relativity.

Einstein's theory of gravitation, his general theory of relativity, touches on basic questions of our existence. Matter, according to Einstein, has no existence independent of space and time. It is even capable of bending the structure of space and changing the course of time -- it introduces a "curvature." Gravity emerges not as an actual physical force but as a consequence of space-time geometry. Even the apple that drops from the tree follows the curvature of time and space.

In this entertaining and involving account of relativity, Newton serves as the skeptic and asks the questions a modern reader might ask. Einstein himself does the explaining, while Haller explains the new developments that have occurred since the general theory was proposed. The result is an intellectual roller-coaster ride in which concepts that have entered the vernacular become clear for the first time: the Big Bang, "black holes," elementary particles, and much more.

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.

Applications of quantum field theoretical methods to gravitational physics, both in the semiclassical and the full quantum frameworks, require a careful formulation of the fundamental basis of quantum theory, with special attention to such important issues as renormalization, quantum theory of gauge theories, and especially effective action formalism. The first part of this graduate textbook provides both a conceptual and technical introduction to the theory of quantum fields. The presentation is consistent, starting from elements of group theory, classical fields, and moving on to the effective action formalism in general gauge theories. Compared to other existing books, the general formalism of renormalization in described in more detail, and special attention paid to gauge theories. This part can serve as a textbook for a one-semester introductory course in quantum field theory. In the second part, we discuss basic aspects of quantum field theory in curved space, and perturbative quantum gravity. More than half of Part II is written with a full exposition of details, and includes elaborated examples of simplest calculations. All chapters include exercises ranging from very simple ones to those requiring small original investigations. The selection of material of the second part is done using the "must-know" principle. This means we included detailed expositions of relatively simple techniques and calculations, expecting that the interested reader will be able to learn more advanced issues independently after working through the basic material, and completing the exercises.

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.

Das vorliegende Tutorium ART ist die ideale Hilfe und Begleitung zur Vorlesung Allgemeine Relativitatstheorie! Dieses Lehrbuch richtet sich an Studierende, die eine Vorlesung zur ART hoeren, und an alle, die genau wissen wollen, wie die Physik das Zwillingsparadoxon, Schwarze Loecher und die Krummung der Raumzeit beschreibt. Die physikalischen Konzepte der ART, wie Raumzeit oder das AEquivalenzprinzip, werden grundlich motiviert und anschaulich eingefuhrt. Die grundlegenden Begriffe der Differenzialgeometrie, die die mathematische Grundlage der ART darstellen, werden sauber erklart, und mit vielen Beispielen wird dafur gesorgt, dass man mit ihnen sicher und routiniert umgehen kann. Mit diesen Werkzeugen werden dann spannende physikalische Phanomene behandelt: Was passiert, wenn man in ein schwarzes Loch fallt? Was genau passiert mit mir, wenn eine Gravitationswelle durch mich hindurchgeht? Und woher wissen wir, dass es einen Urknall gegeben haben muss? All diese Fragen beantwortet dieses Buch. Das Buch kann als begleitende Lernhilfe parallel zu einer Vorlesung benutzt werden, funktioniert aber auch als Lehrbuch, aus dem man selbststandig die Grundlagen der ART lernen kann. Dabei werden die Lerninhalte nicht nur anschaulich und reich bebildert dargestellt, der Stoff wird auch mit vielen UEbungsaufgaben inklusive ausfuhrlicher Loesungen verfestigt. Der Inhalt Newtonsche Mechanik - Spezielle Relativitatstheorie - Mathematische Grundlagen der SRT - Das AEquivalenzprinzip - Tensorkalkul auf Mannigfaltigkeiten - Geometrie: Metriken und kovariante Ableitungen - Geometrie: Krummung - Die Einsteingleichungen - Symmetrien und Erhaltungssatze - Die Schwarzschildmetrik - Kosmologie - Gravitationswellen

With this reader-friendly book, it doesn't take an Einstein to understand the theory of relativity and its remarkable consequences.

In clear, understandable terms, physicist Richard Wolfson explores the ideas at the heart of relativity and shows how they lead to such seeming absurdities as time travel, curved space, black holes, and new meaning for the idea of past and future. Drawing from years of teaching modern physics to nonscientists, Wolfson explains in a lively, conversational style the simple principles underlying Einstein's theory.

Relativity, Wolfson shows, gave us a new view of space and time, opening the door to questions about their flexible nature: Is the universe finite or infinite? Will it expand forever or eventually collapse in a "big crunch"? Is time travel possible? What goes on inside a black hole? How does gravity really work? These questions at the forefront of twenty-first-century physics are all rooted in the profound and sweeping vision of Albert Einstein's early twentieth-century theory. Wolfson leads his readers on an intellectual journey that culminates in a universe made almost unimaginably rich by the principles that Einstein first discovered.

"Wolfson takes the fear out of Einstein's relativity theory in this brisk piece of pop-science."—Publishers Weekly

"In a clear style, [Wolfson] spreads before his readers the historical and conceptual background of [relativity] theory, emphasizing its simplicity at every opportunity. He also offers beautifully clear explanations of such classic puzzles as the Twin Paradox. A strong overview for the lay reader."—Library Journal

"Wolfson explains in a lively, conversational style the simple priciples underlying Einstein's theory."—Astronomical Society of the Pacific

"Wolfson's account is head and shoulders above most, and is a good place to start out."—New Scientist

"With straightforward language and clear examples, Wolfson proves you don't have to be an Einstein to understand his great ideas."—Science News

"Wolfson leads the reader gently and irresistibly down the logical path that Einstein followed to arrive at his theories."—Washington Post Book World

Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books! The beginning of the 20th century heralded a scientific revolution: what a few brilliant minds uncovered about our reality in the first twenty years has shaped the history of our species. And one of them in particular stands out: Einstein, with his celebrated E=mc2. In this remarkable and insightful book, Christophe Galfard describes how E=mc2 is a direct consequence of the Theory of Special Relativity, the theory of how objects move and behave, at speeds close to the speed of light. He considers Einstein's legacy in the light of the 21st century, with fresh hindsight, and considers its impact on our vision of reality. The reader will discover that far from being just a formula, it is a brand new understanding of the nature of space and time. Some of the greatest scientific breakthroughs in the history of science have been made by geniuses who managed to merge and unite hitherto separated domains of knowledge. Galfard explores two unifications with Einstein's theories, and looks at the even bigger picture of how E=mc2 has changed our world, and what it entails for the future. Throughout, Galfard takes the reader on an extremely entertaining journey, using simple, jargon-free language to help the reader gain a deeper understanding of science. With humour and patience, he guides us through the world of particles, anti-matter and much more to bring us closer to an ultimate understanding of reality as we understand it today.

Rather than focusing on the contributions of theoretical physicists to the understanding of the subatomic world and of the beginning of the universe - as most popular science books on particle physics do - this book is different in that, firstly, the main focus is on machine inventors and builders and, secondly, particle accelerators are not only described as discovery tools but also for their contributions to tumour diagnosis and therapy. The characters of well-known (e.g. Ernest Lawrence) and mostly unknown actors (e.g. Nicholas Christofilos) are outlined, including many colourful quotations. The overall picture supports the author's motto: "Physics is beautiful and useful". Advance appraisal: "Accelerators go all the way from the unique and gargantuan Large Hadron Collider to thousands of smaller versions in hospitals and industry. Ugo Amaldi has experience across the range. He has worked at CERN and has for many years been driving the application of accelerators in medicine. This is a must-read introduction to this frontier of modern technology, written beautifully by a world expert." Frank Close, Professor of Physics at Oxford University author of "The Infinity Puzzle" "This book should be read by school teachers and all those interested in the exploration of the microcosm and its relation to cosmology, and in the use of accelerators for medical applications. With a light hand and without formulae the autho r easily explains complicated matters, spicing up the text with amusing historical anecdotes. His reputation as an outstanding scientist in all the fields treated guarantees high standards." Herwig Schopper, former CERN Director General author of "LEP - The Lord of the Collider Rings at CERN" "This book tells the story of modern physics with an unusual emphasis on the machine-builders who made it all possible, and their machines. Learning to accelerate particles has enabled physicists to probe the subatomic world and gain a deeper understanding of the cosmos. It has also brought numerous benefits to medicine, from the primitive X-ray machines of over a century ago to today's developments in hadron therapy for cancer. Amaldi tells this story in a most fascinating way." Edward Witten, Professor of Mathematical Physics at the Institute for Advanced Study in Princeton; Fields Medal (1990)