Special relativity is the basis of many fields in modern physics: particle physics, quantum field theory, high-energy astrophysics, etc. This theory is presented here by adopting a four-dimensional point of view from the start. An outstanding feature of the book is that it doesn't restrict itself to inertial frames but considers accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus and relativistic hydrodynamics are addressed. In the last, brief chapter the author gives a preview of gravity and shows where it becomes incompatible with Minkowsky spacetime. Well illustrated and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra. The book is suitable for students in the third year of a physics degree or on a masters course, as well as researchers and any reader interested in relativity. Thanks to the geometric approach adopted, this book should also be beneficial for the study of general relativity. "A modern presentation of special relativity must put forward its essential structures, before illustrating them using concrete applications to specific dynamical problems. Such is the challenge (so successfully met!) of the beautiful book by Eric Gourgoulhon." (excerpt from the Foreword by Thibault Damour)

These two volumes are the proceedings of a major International Symposium on General Relativity held at the University of Maryland in March 1993 to celebrate the sixtieth birthdays of Professor Charles Misner and Professor Dieter Brill. The volumes cover classical general relativity, quantum gravity and quantum cosmology, canonical formulation and the initial value problem, topology and geometry of spacetime and fields, mathematical and physical cosmology, and black hole physics and astrophysics. As invited articles, the papers in these volumes have an aim which goes beyond that of a standard conference proceedings. Not only do the authors discuss the most recent research results in their fields, but many also provide historical perspectives on how the subjects have developed and offer individual insights in their search for new directions.

This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard's theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book will also prove useful for researchers. The prerequisites for this text have intentionally been kept to a minimum so that undergraduate students can also benefit from it. It is a cherished conviction that "mathematical proofs are the core of all mathematical joy," a standpoint this book vividly reflects.

Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another. This book introduces a framework for studying random geometries in any dimensions. Building on the resounding success of random matrices as theories of random two dimensional surfaces, random tensors are their natural generalization to theories of random geometry in arbitrary dimension. This book shows that many of the celebrated results in random matrices, most notably 't Hooft's 1/N expansion, can be generalized to higher dimensions. It provides a complete and self-contained derivation of the key results on random tensors.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Developing ideas sketched in the first volume, twistor theory is now applied to genuine issues of physics, and there are the beginnings of twistor diagram theory (an analogue of Feynman Diagrams). This collection includes joint papers with Stephen Hawking, and uncovers certain properties of black holes. The idea of cosmic censorship is also first proposed. Along completely different lines, the first methods of aperiodic tiling for the Euclidean plane that come to be known as Penrose tiles are described. This volume also contains Penrose's three prize-winning essays for the Gravity Foundation (two second places with both Ezra Newman and Steven Hawking, and a solo first place for 'The Non-linear graviton').

I first had a quick look, then I started reading it. I couldn't stop. -Gerard 't Hooft (Nobel Prize, in Physics 1999) This is a book about the mathematical nature of our Universe. Armed with no more than basic high school mathematics, Dr. Joel L. Schiff takes you on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, determining the size of the Earth with a stick in the ground and the age of the Solar System from meteorites, understanding how the Theory of Relativity makes your everyday GPS system possible, and so much more. These topics are easily accessible to anyone who has ever brushed up against the Pythagorean Theorem and the symbol , with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and extraordinary mathematical beauty of our Universe.

Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.

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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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.

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 1983. 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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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 1982. 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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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.

The quantum and relativity theories of physics are considered to underpin all of science in an absolute sense. This monograph argues against this proposition primarily on the basis of the two theories' incompatibility and of some untenable philosophical implications of the quantum model. Elementary matter is assumed in both theories to occur as zero-dimensional point particles. In relativity theory this requires the space-like region of the underlying Minkowski space-time to be rejected as unphysical, despite its precise mathematical characterization. In quantum theory it leads to an incomprehensible interpretation of the wave nature of matter in terms of a probability function and the equally obscure concept of wave-particle duality. The most worrisome aspect about quantum mechanics as a theory of chemistry is its total inability, despite unsubstantiated claims to the contrary, to account for the fundamental concepts of electron spin, molecular structure, and the periodic table of the elements. A remedy of all these defects by reformulation of both theories as nonlinear wave models in four-dimensional space-time is described.

This is the sixth volume in a series of books on the general topics of supersymmetry, supergravity, black holes and the attractor mechanism. The present volume is based upon lectures held in May 2011 at the INFN-Laboratori Nazionali di Frascati School on Black Objects in Supergravity (BOSS2011), directed by Stefano Bellucci, with the participation of prestigious lecturers, including G. Lopes Cardoso, W. Chemissany, T. Ortin, J. Perz, O. Vaughan, D. Turton, L. Lusanna and S. Ferrara. All lectures were at a pedagogical, introductory level, a feature which is reflected in the specific "flavor" of this volume, which also benefited greatly from extensive discussions and related reworking of the various contributions.

This book, now in a revised and updated second edition, explains the theory of special and general relativity in detail without approaching Einstein's life or the historical background. The text is formulated in such a way that the reader will be able to understand the essence intuitively, and new sections have been added on time machines, the twin paradoxes, and tensors. The first part of the book focuses on the essentials of special relativity. It explains the famous equivalence between mass and energy and tells why Einstein was able to use the theory of electrodynamics as a template for his "electrodynamics of moving bodies". General relativity is then addressed, mainly with the help of thought experiments. Reference is made to the previously introduced special relativity and the equivalence principle and, using many figures, it is explained how space-time is bending under gravity. The climax of the book is the Einstein equation of gravity, which describes the way in which matter bends space-time. The reader is shown how to obtain the famous Schwarzschild solution. Moreover, the book presents a numerically correct and yet intuitive explanation of the classic effects such as light bending and the advance of the perihelion. The book concludes by explaining the Friedmann model of the big bang and why the theory of gravity does not fit with quantum theory.

A self-contained introduction to general relativity that is based on the homogeneity and isotropy of the local universe. Emphasis is placed on estimations of the densities of matter and vacuum energy, and on investigations of the primordial density fluctuations and the nature of dark matter.

This book reflects the resurgence of interest in the quantum properties of black holes, culminating most recently in controversial discussions about firewalls. On the thermodynamic side, it describes how new developments allowed the inclusion of pressure/volume terms in the first law, leading to a new understanding of black holes as chemical systems, experiencing novel phenomena such as triple points and reentrant phase transitions. On the quantum-information side, the reader learns how basic arguments undergirding quantum complementarity have been shown to be flawed; and how this suggests that a black hole may surround itself with a firewall: a violent and chaotic region of highly excited states. In this thorough and pedagogical treatment, Robert Mann traces these new developments from their roots to our present-day understanding, highlighting their relationships and the challenges they present for quantum gravity.

This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.

Today, Relativity is becoming an integrated aspect of engineering fields. Its application to the Global Positioning System (GPS), extends in usage from smart watches to the navigation of cars, airplanes (drones) and even autonomous tractors. In rather expensive particle accelerators, physicists are everyday 'playing' with Relativistic Billiards, common to the betatrons of cancer therapy using electrons. Computer programs, such as 'ray tracing' methods, are enhanced to simulate objects in relativistic motion, which now offer us relativistic visualizations of accretion disks around compact, astrophysical objects like Black Holes.Against the backdrop of the applications explained throughout the chapters, this book takes on a practical and intuitive approach in introducing the Lorentz invariance of light propagation and space-time concepts. The book begins with simple mathematics, like the classical Pythagoras formula for energy-momentum 'triangles'. Later, readers will find the intuitive vector calculus reemerging in the expansion of full relativistic expressions. Prepared with instructive diagrams of recent experiments, even the layperson can grasp the essential study of Relativity and marvel at its applications within this book.

This book provides a completely revised and expanded version of the previous classic edition 'General Relativity and Relativistic Astrophysics'. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars - our best laboratories for general relativity - are studied in considerable detail. An introduction to gravitational lensing theory is included as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten's proof of the positive energy theorem, which is presented in detail, together with the required tools on spin structures and spinor analysis. In Part III, all of the differential geometric tools required are developed in detail. A great deal of effort went into refining and improving the text for the new edition. New material has been added, including a chapter on cosmology. The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It utilizes a very well structured approach, which should help it continue to be a standard work for a modern treatment of gravitational physics. The clear presentation of differential geometry also makes it useful for work on string theory and other fields of physics, classical as well as quantum.

'Gravity, a Geometrical Course' presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book, divided in two volumes, is a rich resource for graduate students and those who wish to gain a deep knowledge of the subject without an instructor. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differentiable manifolds, fibre-bundles, differential forms, and the theory of connections are covered, with a sketchy introduction to homology and cohomology. (Pseudo)-Riemannian geometry is presented both in the metric and in the vielbein approach. Physical applications include the motions in a Schwarzschild field leading to the classical tests of GR (light-ray bending and periastron advance) discussion of relativistic stellar equilibrium, white dwarfs, Chandrasekhar mass limit and polytropes. An entire chapter is devoted to tests of GR and to the indirect evidence of gravitational wave emission. The formal structure of gravitational theory is at all stages compared with that of non gravitational gauge theories, as a preparation to its modern extension, namely supergravity, discussed in the second volume. Pietro Fre is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, "Supergravity and Superstrings" and "The N=2 Wonderland", He is also the author of a popular science book on cosmology and two novels, in Italian.

This book gathers the lecture notes of the 100th Les Houches Summer School, which was held in July 2013. These lectures represent a comprehensive pedagogical survey of the frontier of theoretical and observational cosmology just after the release of the first cosmological results of the Planck mission. The Cosmic Microwave Background is discussed as a possible window on the still unknown laws of physics at very high energy and as a backlight for studying the late-time Universe. Other lectures highlight connections of fundamental physics with other areas of cosmology and astrophysics, the successes and fundamental puzzles of the inflationary paradigm of cosmic beginning, the themes of dark energy and dark matter, and the theoretical developments and observational probes that will shed light on these cosmic conundrums in the years to come.

Today many scientists recognize plasma as the key element to understanding new observations in near-Earth, interplanetary, interstellar, and intergalactic space; in stars, galaxies, and clusters of galaxies, and throughout the observable universe. Physics of the Plasma Universe, 2nd Edition is an update of observations made across the entire cosmic electromagnetic spectrum over the two decades since the publication of the first edition. It addresses paradigm changing discoveries made by telescopes, planetary probes, satellites, and radio and space telescopes. The contents are the result of the author's 37 years research at Livermore and Los Alamos National Laboratories, and the U.S. Department of Energy. This book covers topics such as the large-scale structure and the filamentary universe; the formation of magnetic fields and galaxies, active galactic nuclei and quasars, the origin and abundance of light elements, star formation and the evolution of solar systems, and cosmic rays. Chapters 8 and 9 are based on the research of Professor Gerrit Verschuur, and reinvestigation of the manifestation of interstellar neutral hydrogen filaments from radio astronomical observations are given. Using data from the Green Bank 100-m telescope (GBT) of the National Radio Astronomy Observatory (NRAO), detailed information is presented for a non-cosmological origin for the cosmic microwave background quadruple moment. This volume is aimed at graduate students and researchers active in the areas of cosmic plasmas and space science. The supercomputer and experimental work was carried out within university, National laboratory, Department of Energy, and supporting NASA facilities.

The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity (perihelion precession of Mercury, and light deflection by the sun). ------ Textbook features: detailed figures, worked examples, problems and solutions, boxed inserts, highlighted special topics, highlighted important math etc., helpful summaries, appendix, index.

The 2011 Nobel Prize in Physics was awarded for the discovery of cosmic acceleration due to dark energy, a discovery that is all the more perplexing as nobody knows what dark energy actually is. We put the modern concept of cosmological vacuum energy into historical context and show how it grew out of disparate roots in quantum mechanics (zero-point energy) and relativity theory (the cosmological constant, Einstein's "greatest blunder"). These two influences have remained strangely aloof and still co-exist in an uneasy alliance that is at the heart of the greatest crisis in theoretical physics, the cosmological-constant problem.