This is a comprehensive textbook for advanced undergraduates and beginning graduate students in physics or astrophysics, developing both the formalism and the physical ideas of special and general relativity in a logical and coherent way. The book is in two parts. Part one focuses on the special theory and begins with the study of relativistic kinematics from three points of view: the physical (the classic gedanken experiments), the algebraic (the Lorentz transformations), and the graphic (the Minkowski diagrams). Part one concludes with chapters on relativistic dynamics and electrodynamics. Part two begins with a chapter introducing differential geometry to set the mathematical background for general relativity. The physical basis for the theory is begun in the chapter on uniform accelerations. Subsequent chapters cover rotation, the electromagnetic field, and material media. A second chapter on differential geometry provides the background for Einstein's gravitational-field equation and Schwarzschild's solution. The physical significance of this solution is examined together with the challenges to the theory that have been successfully met inside the solar system. Other applications follow in the final chapters on astronomy and cosmology: These include black holes, quasars, and gravity waves as well as the relativistic features of an expanding universe ¿ including a section on the inflationary model.

Evidence that Einstein's addition is regulated by the Thomas precession has come to light, turning the notorious Thomas precession, previously considered the ugly duckling of special relativity theory, into the beautiful swan of gyrogroup and gyrovector space theory, where it has been extended by abstraction into an automorphism generator, called the "Thomas gyration." The Thomas gyration, in turn, allows the introduction of vectors into hyperbolic geometry, where they are called "gyrovectors," in such a way that Einstein's velocity additions turns out to be a gyrovector addition. Einstein's addition thus becomes a gyrocommutative, gyroassociative gyrogroup operation in the same way that ordinary vector addition is a commutative, associative group operation. Some gyrogroups of gyrovectors admit scalar multiplication, giving rise to gyrovector spaces in the same way that some groups of vectors that admit scalar multiplication give rise to vector spaces. Furthermore, gyrovector spaces form the setting for hyperbolic geometry in the same way that vector spaces form the setting for Euclidean geometry. In particular, the gyrovector space with gyrovector addition given by Einstein's (Mobius') addition forms the setting for the Beltrami (Poincare) ball model of hyperbolic geometry.
The gyrogroup-theoretic techniques developed in this book for use in relativity physics and in hyperbolic geometry allow one to solve old and new important problems in relativity physics. A case in point is Einstein's 1905 view of the Lorentz length contraction, which was contradicted in 1959 by Penrose, Terrell and others. The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein."

This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions. First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized. Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kahler manifolds. This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.

A survey of the most recent developments in general relativity and in the theory of the unification of Fundamental Interactions is presented in this book. The theoretical results, the cosmological and astrophysical aspects, the experimental and observational programs are shown in 26 general talks by renowned scientists active in this field.

Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of "time machines," spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett interpretation, and the recent important approach known as "decoherence." A big problem, as I see it, is that various people thoroughly investigate their narrow field without being aware of certain very close relations to other fields of research. What we need now is not only to see the trees but also the forest. In the present book I intend to do just that: to carry out a first approximation to a synthesis of the related fundamental theories of physics. I sincerely hope that such a book will be useful to physicists. From a certain viewpoint the book could be considered as a course in the oretical physics in which the foundations of all those relevant fundamental theories and concepts are attempted to be thoroughly reviewed. Unsolved problems and paradoxes are pointed out. I show that most of those ap proaches have a common basis in the theory of unconstrained membranes. The very interesting and important concept of membrane space, the tensor calculus in and functional transformations in are discussed.

Cosmic Origins tells the story of how physicists and astronomers have struggled for more than a century to understand the beginnings of our universe, from its origins in the Big Bang to the modern day. The book will introduce the science as a narrative, by telling the story of the scientists who made each major discovery. It will also address and explain aspects of our theories that some cosmologists are still hesitant to accept, as well as gaps in our knowledge and even apparent inconsistencies in our measurements. Clearly written by a master of scientific exposition, this book will fascinate the curious general reader as well as providing essential background reading for college-level courses on physics and astronomy.

The 13th Italian Conference on General Relativity and Gravitational Physics was held in Cala Corvino-Monopoli (Bari) from September 21to September 25, 1998. The Conference, which is held every other year in different Italian locations, has brought together, as in the earlier conferences in this series, those scientists who are interested and actively work in all aspects of general relativity, from both the mathematical and the physical points of view: from classical theories of gravitation to quantum gravity, from relativistic astrophysics and cosmology to experiments in gravitation. About 70 participants came from Departments of Astronomy and Astrophysics, Departments of Mathematics and Departments of Experimental and Theoretical Physics from all over the Country; in addition a few Italian scientists working abroad kindly accepted invitations from the Scientific Committee. The good wishes of the University and of the Politecnico di Bari were conveyed by the director of Diparti mento Interuniversitario di Matematica, Prof. Franco Altomare. These proceedings contain the contributions of the two winners of the SIGRAV prizes, the invited talks presented at the Conference and most of the contributed talks. We thank all of our colleagues, who did their best to prepare their manuscripts. The pleasant atmosphere induced by the beauty of the place was greatlyenhanced not only by the participation of so many colleagues, who had lively discussions about science well beyond Conference hours, but also by the feeling of hospitalityextended to the participants by the staff of the Cala Corvino Hotel, where the Conference was held."

"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."--S. Chandrasekhar
"A "tour de force" lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."--L. P. Hughston, "Times Higher Education Supplement"
"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."--James W. York, "Physics Today"

The greatest challenge in fundamental physics attempts to reconcile quantum mechanics and general relativity in a theory of "quantum gravity." The project suggests a profound revision of the notions of space, time and matter. It has become a key topic of debate and collaboration between physicists and philosophers. This volume collects classic and original contributions from leading experts in both fields for a provocative discussion of the issues. It contains accessible introductions to the main and less-well-known known approaches to quantum gravity. It includes exciting topics such as the fate of spacetime in various theories, the so-called "problem of time" in canonical quantum gravity, black hole thermodynamics, and the relationship between the interpretation of quantum theory and quantum gravity. This book will be essential reading for anyone interested in the profound implications of trying to marry the two most important theories in physics.

This textbook attempts to bridge the gap that exists between the two levels on which relativistic symmetry is usually presented - the level of introductory courses on mechanics and electrodynamics and the level of application in high energy physics and quantum field theory: in both cases, too many other topics are more important and hardly leave time for a deepening of the idea of relativistic symmetry. So after explaining the postulates that lead to the Lorentz transformation and after going through the main points special relativity has to make in classical mechanics and electrodynamics, the authors gradually lead the reader up to a more abstract point of view on relativistic symmetry - always illustrating it by physical examples - until finally motivating and developing Wigner's classification of the unitary irreducible representations of the inhomogeneous Lorentz group. Numerous historical and mathematical asides contribute to conceptual clarification.

Einstein's Revolution is a textbook on relativity written from a historical-methodological point of view. It can be used as an account of Einstein's physical theory even if the reader has no sympathy with the author's philosophical standpoint, or it can be read for the author's philosophical argument, without the reader having to follow all the details of the physics. The work challenges a distinction made by the Vienna Circle an still influential today: the distinction between "the context of discovery" and "the context of justification." According to the traditional view, the context of discovery calls for no rational reconstruction and belongs, in effect, to psychology, while only latter is subject to a proper logic of appraisal. Against these theses, Zahar shows that there is a logic of discovery and that it plays an important role in the appraisal of theories.

Gauge theory of elementary particle physics was first published in 1984 and has become a standard textbook in the subject. This companion volume provides graduate students with problems and solutions, enabling them to learn the calculational techniques necessary to understand the research literature. Several new topics are also included and the presentation is self-contained, making the book suitable even for those not familiar with the main book.

It is not an exaggeration to say that one of the most exciting predictions of Einstein's theory of gravitation is that there may exist "black holes" putative objects whose gravitational fields are so strong that no physical bodies or signals can break free of their pull and escape. The proof that black holes do exist, and an analysis of their properties, would have a significance going far beyond astrophysics. Indeed, what is involved is not just the discovery of yet another even if extremely remarkable, astro physical object, but a test of the correctness of our understanding of the properties of space and time in extremely strong gravitational fields. Theoretical research into the properties of black holes, and into the possible corol laries of the hypothesis that they exist, has been carried out with special vigor since the beginning of the 1970's. In addition to those specific features of black holes that are important for the interpretation of their possible astrophysical manifestations, the theory has revealed a number of unexpected characteristics of physical interactions involving black holes. By the middle of the 1980's a fairly detailed understanding had been achieved of the properties of the black holes, their possible astrophysical manifestations, and the specifics of the various physical processes involved. Even though a completely reliable detection of a black hole had not yet been made at that time, several objects among those scrutinized by astrophysicists were considered as strong candidates to be confirmed as being black holes."

If the laws of nature are fine-tuned for life, can we infer other universes with different laws? How could we even test such a theory without empirical access to those distant places? Can we believe in the multiverse of the Everett interpretation of quantum theory or in the reality of other possible worlds, as advocated by philosopher David Lewis? At the intersection of physics and philosophy of science, this book outlines the philosophical challenge to theoretical physics in a measured, well-grounded manner. The origin of multiverse theories are explored within the context of the fine-tuning problem and a systematic comparison between the various different multiverse models are included. Cosmologists, high energy physicists, and philosophers including graduate students and researchers will find a systematic exploration of such questions in this important book.

An analysis of one of the three great papers Einstein published in 1905, each of which was to alter forever the field it dealt with. The second of these papers, "On the Electrodynamics of Moving Bodies", established what Einstein sometimes referred to as the "so-called Theory of Relativity". Miller uses the paper to provide a window on the intense intellectual struggles of physicists in the first decade of the 20th century: the interplay between physical theory and empirical data; the fiercely held notions that could not be articulated clearly or verified experimentally; the great intellectual investment in existing theories, data, and interpretations - and associated intellectual inertia - and the drive to the long-sought-for unification of the sciences. Since its original publication, this book has become a standard reference and sourcebook for the history and philosophy of science; however, it can equally well serve as a text on twentieth-century philosophy.

EDWIN TURNER AND RACHEL WEBSTER Co-Chairs, Scientific Organizing Committee lAU Symposium 173, Astrophysical Applications of Gravitational Lenses, was held in Melbourne, Australia from July 9-14, 1995. The Symposium was sponsored by lAU Commissions 47 and 40. With the discovery by Walsh and collaborators of the first instance of a gravitational lens, the multiply imaged quasar 0957+561, the area of grav itational lensing moved from speculative theory to a major astrophysical tool. Since that time, there have been regular, approximately biennial in ternational meetings both in Europe and in North America, which have specifically focussed on gravitational lensing. On this occasion, with the blessing of the lA U, the meeting was held at the University of Melbourne in Australia. It was the first international astronomical meeting to be held at the University of Melbourne, and hope fully has given the astronomical community some enthusiasm for trekking half-way round the globe to Australia to discuss their latest work.

Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms of the Minkowski vector space and the flat spacetime manifold. Then it discusses the kinematics of special relativity in terms of Lorentz tranformations, and treats the group structure of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of spinor (vector) space can induce a proper, orthochronous Lorentz mapping on the Minkowski vector space. The second part begins with a discussion of relativistic particle mechanics from both the Lagrangian and Hamiltonian points of view. The book then turns to the relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, Dirac, and non-abelian gauge fields. The final chapter deals with recent work on classical fields in an eight-dimensional covariant phase space.

Man kann ohne Obertreibung sagen, daE es die Astronomie seit tiber fUnftausend J ahren als exakte Wissenschaft gibt. In dieser ganzen Zeit beriihrte sie die letzten Fragen der Mensch- heit. Ihre Geschichte niederzuschreiben stellt uns vor zahlIose Probleme. Wir beginnen mit einer Zeit, die wir weitgehend durch Schlu&folgerungen kennen; wir gehen dann zu Zeiten tiber, von denen wir wissen, da& das meiste Indizienmaterial verlorengegangen ist; und wir enden bei den letzten Dekaden eines Jahrhunderts, das den Astronomen Beachtung und wirtschaftliche Mittel in nie dagewesenem Umfang beschert hat. Aus einem typischen Jahrhundert der hellenistischen Ara, einem goldenen Zeitalter der Astronomie, mogen wir eine Handvoll Texte haben. 1m Gegensatz dazu werden heute jedes Jahr mehr als zwanzig- tausend astronomische Artikel veroffentlicht, und, tiber fUnfJahre genommen, ist die Zahl der Astronomen, unter deren Namen diese erscheinen, von der Ordnung vierzigtausend. Wenn diese Geschichte also am Anfang wie eine Skizze anmutet, ist sie notwendiger- weise am Schlu& eine Silhouette, die den Gegenstand ebenso durch das definiert, was sie ausla&t, als dadurch, was sie enthalt. Sie schreitet in einem solchen Ma& immer schneller voran, daE der Raum, der einem Dutzend hochstwichtiger neuer Bticher gewidmet wird, ein kleiner Bruchteil davon ist, was am Anfang einer heute ganz trivial erscheinenden Aussage eingeraumt wird. Das ist kein Zufall.

After Physics presents ambitious new essays about some of the deepest questions at the foundations of physics, by the physicist and philosopher David Albert. The book's title alludes to the close connections between physics and metaphysics, much in evidence throughout these essays. It also alludes to the work of imagining what it would be like for the project of physical science-considered as an investigation into the fundamental laws of nature-to be complete. Albert argues that the difference between the past and the future-traditionally regarded as a matter for metaphysical or conceptual or linguistic or phenomenological analysis-can be understood as a mechanical phenomenon of nature. In another essay he contends that all versions of quantum mechanics that are compatible with the special theory of relativity make it impossible, even in principle, to present the entirety of what can be said about the world as a narrative sequence of "befores" and "afters." Any sensible and realistic way of solving the quantum-mechanical measurement problem, Albert claims in yet another essay, is ultimately going to force us to think of particles and fields, and even the very space of the standard scientific conception of the world, as approximate and emergent. Novel discussions of the problem of deriving principled limits on what can be known, measured, or communicated from our fundamental physical theories, along with a sweeping critique of the main attempts at making sense of probabilities in many-worlds interpretations of quantum mechanics, round out the collection.

Introduction to Special Relativity By Robert Resnick, Rensselaer Polytechnic Institute This book gives an excellent introduction to the theory of special relativity. Professor Resnick presents a fundamental and unified development of the subject with unusually clear discussions of the aspects that usually trouble beginners. He includes, for example, a section on the common sense of relativity. His presentation is lively and interspersed with historical, philosophical and special topics (such as the twin paradox) that will arouse and hold the reader' s interest. You' ll find many unique features that help you grasp the material, such as worked-out examples, summary tables, thought questions and a wealth of excellent problems. The emphasis throughout the book is physical. The experimental background, experimental confirmation of predictions, and the physical interpretation of principles are stressed. The book treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and contains special appendices on the geometric representation of space-time and on general relativity. Its organization permits an instructor to vary the length and depth of his treatment and to use the book either with or following classical physics. These features make it an ideal companion for introductory courses.

Dieses Buch ist bis heute eine der popularsten Darstellungen der Relativitatstheorie geblieben. In der vorliegenden Version haben J. Ehlers und M. Poessel vom Max-Planck-Institut fur Gravitationsphysik (Albert-Einstein-Institut) in Golm/Potsdam den Bornschen Text kommentiert und einen den anschaulichen, aber prazisen Stil Borns wahrendes, umfangreiches Erganzungskapitel hinzugefugt, das die sturmische Entwicklung der Relativiatatstheorie bis hin zu unseren Tagen nachzeichnet. Eingegangen wird auf Gravitationswellen und Schwarze Loecher, auf neuere Entwicklungen der Kosmologie, auf Ansatze zu einer Theorie der Quantengravitation und auf die zahlreichen raffinierten Experimente, welche die Gultigkeit der Einsteinschen Theorie mit immer groesserer Genauigkeit bestatigt haben. Damit bleibt dieses Buch nach wie vor einer der unmittelbarsten Zugange zur Relativitatstheorie fur alle die sich fur eine uber das rein popularwissenschaftliche hinausgehende Einfuhrung interessieren.

CHOICE Highly Recommended Title, August 2019 Expertly guided by renowned cosmologist Dr. David Lyth, learn about the pioneering scientists whose work provided the foundation for Einstein's formulation of his theories of relativity, and about Einstein's groundbreaking life and work as well. This highly readable and accessible panorama of the field delicately balances history and science as it takes the reader on an adventure through the centuries. Without complex mathematics or scientific formulae, this book will be of interest to all, even those without a scientific background, who are intrigued to find out more about what paved the way for one of our most famous physicists to push the boundaries of physics to new lengths. Features: Written by an internationally renowned physicist and cosmologist Describes the life and times of Einstein and his important predecessors Focuses on one of the most famous areas of science, Einstein's Relativity Theory

From the international bestselling author of Physics of the Impossible and Physics of the Future.

This is the story of a quest: to find a Theory of Everything. Einstein dedicated his life to seeking this elusive Holy Grail, a single, revolutionary 'god equation' which would tie all the forces in the universe together, yet never found it. Some of the greatest minds in physics took up the search, from Stephen Hawking to Brian Greene. None have yet succeeded.

In The God Equation, renowned theoretical physicist Michio Kaku takes the reader on a mind-bending ride through the twists and turns of this epic journey: a mystery that has fascinated him for most of his life. He guides us through the key debates in modern physics, from Newton's law of gravity via relativity and quantum mechanics to the latest developments in string theory. It is a tale of dazzling breakthroughs and crushing dead ends, illuminated by Kaku's clarity, storytelling flair and infectious enthusiasm.

The object of the quest is now within sight: we are closer than ever to achieving the most ambitious undertaking in the history of science. If successful, the Theory of Everything could simultaneously unlock the deepest mysteries of space and time, and fulfil that most ancient and basic of human desires - to understand the meaning of our lives.

The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.