Decoding Spacetime

Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject. Three major applications of general relativity are then discussed: black holes, perturbation theory and gravitational waves, and cosmology. Students will learn the origin of how spacetime curves (the Einstein equation) and how matter moves through it (the geodesic equation). They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe. A brief introduction to quantum field theory in curved spacetime is also included. A student familiar with this book will be ready to tackle research-level problems in gravitational physics.

Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.

The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with

The book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein's field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.

The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern p

Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear and concise introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the

This book is an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of spacetime and those which play a role in the Penrose–Hawking singularity theorems. Indeed, the author's prime purpose is to give a rigorous proof of the simplest of these theorems yet one which is representative of the whole. No previous exposure either to relativity theory or differential geometry is required to the reader, as necessary concepts are developed when needed, though in order to keep the presentation reasonably accessible, some restrictions are imposed on the types of space considered. Each chapter is liberally supplied with exercises and examples. The book will therefore be attractive to senior undergraduate and first year graduate students of mathematics and physics for independent study or courses preparatory to more advanced works.

General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminat

This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, and examines what they imply for a realistic theory of quantum gravity. General relativity in three spacetime dimensions has become a popular arena in which to explore the ramifications of quantum gravity. As a diffeomorphism-invariant theory of spacetime structure, this model shares many of the conceptual problems of realistic quantum gravity. But it is also simple enough that many programs of quantization can be carried out explicitly. After analysing the space of classical solutions, this book introduces some fifteen approaches to quantum gravity - from canonical quantization in York's 'extrinsic time' to Chern-Simons quantization, from the loop representation to covariant path integration to lattice methods. Relationships among quant

Houses are not just assemblages of individual rooms but intricate patterns of organised space, governed by rules and conventions about the size and configuration of rooms, which domestic activities go together, how the interior should be decorated and furnished and what kinds of household object are appropriate in each setting, how family members relate to one another in different spaces, and how and where guests should be received and entertained in the home. Decoding Homes and Houses introduces new, computer-based techniques designed to retrieve and interpret this wealth of social and symbolic information. The various representations and measures show how domestic space provides a shared framework for everyday life, how social meanings are constructed in the home and how different sub-groups within society differentiate themselves through their patterns of domestic space and lifestyles.

This is a revised and updated edition of Graham Nerlich's classic book The Shape of Space. It develops a metaphysical account of space which treats it as a real and concrete entity. In particular, it shows that the shape of space plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument, and, using a number of novel examples, investigates how different spaces would affect perception differently. This leads naturally to conventionalism as a non-realist metaphysics of space, an account which Professor Nerlich criticises, rejecting its Kantian and positivistic roots along with Reichenbach's famous claim that even the topology of space is conventional. He concludes that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, and offers an extensive discussion of the relativity of motion.

This is a revised and updated edition of Graham Nerlich's classic book The Shape of Space. It develops a metaphysical account of space which treats it as a real and concrete entity. In particular, it shows that the shape of space plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument, and, using a number of novel examples, investigates how different spaces would affect perception differently. This leads naturally to conventionalism as a non-realist metaphysics of space, an account which Professor Nerlich criticises, rejecting its Kantian and positivistic roots along with Reichenbach's famous claim that even the topology of space is conventional. He concludes that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, and offers an extensive discussion of the relativity of motion.

This book gets to the heart of science by asking a fundamental question about its essence: what is the true nature of space and time? Both defy modern physics and scientists find themselves continually searching for answers. This unique volume brings together world leaders in cosmology, particle physics, quantum gravity, mathematics, philosophy and theology, to provide fresh insights into the deep structure of space and time. In an attempt to understand the question, subjects ranging from dark matter to the philosophical and theological implications of spacetime are covered, ensuring that the issue is thoroughly explored. Interesting and thought-provoking answers provide a well-rounded read.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

Dispositionalism is the view that causal powers are among the irreducible properties of nature. It has long been among the core competing positions in the metaphysics of laws, but its potential implications for other key debates within metaphysics and the philosophy of science have remained under-explored. Travis Dumsday fills this major gap in the literature by establishing new connections between dispositionalism and such topics as substance ontology, ontic structural realism, material composition, emergentism, natural-kind essentialism, perdurantism, time travel, and spacetime substantivalism. He also puts forward a novel view concerning the precise relationship between causal powers and the fundamental laws of nature. His rich and accessible study will appeal to readers interested in contemporary analytic metaphysics and philosophy of science.

After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.

One of the greatest challenges in fundamental physics is to reconcile quantum mechanics and general relativity in a theory of quantum gravity. A successful theory would have profound consequences for our understanding of space, time, and matter. This collection of essays written by eminent physicists and philosophers discusses these consequences and examines the most important conceptual questions among philosophers and physicists in their search for a quantum theory of gravity. Comprising three parts, the book explores the emergence of classical spacetime, the nature of time, and important questions of the interpretation, metaphysics, and epistemology of quantum gravity. These essays will appeal to both physicists and philosophers of science working on problems in foundational physics, specifically that of quantum gravity.

Dispositionalism is the view that causal powers are among the irreducible properties of nature. It has long been among the core competing positions in the metaphysics of laws, but its potential implications for other key debates within metaphysics and the philosophy of science have remained under-explored. Travis Dumsday fills this major gap in the literature by establishing new connections between dispositionalism and such topics as substance ontology, ontic structural realism, material composition, emergentism, natural-kind essentialism, perdurantism, time travel, and spacetime substantivalism. He also puts forward a novel view concerning the precise relationship between causal powers and the fundamental laws of nature. His rich and accessible study will appeal to readers interested in contemporary analytic metaphysics and philosophy of science.

During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and gradua

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory.

Uniting the usually distinct areas of particle physics and quantum field theory, gravity and general relativity, this expansive and comprehensive textbook of fundamental and theoretical physics describes the quest to consolidate the basic building blocks of nature, by journeying through contemporary discoveries in the field, and analysing elementary particles and their interactions. Designed for advanced undergraduates and graduate students and abounding in worked examples and detailed derivations, as well as including historical anecdotes and philosophical and methodological perspectives, this textbook provides students with a unified understanding of all matter at the fundamental level. Topics range from gauge principles, particle decay and scattering cross-sections, the Higgs mechanism and mass generation, to spacetime geometries and supersymmetry. By combining historically separate areas of study and presenting them in a logically consistent manner, students will appreciate the und

Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the framework allows discussion of strings and branes directly at the quantum level. Written by internationally renowned experts, this comprehensive introduction to boundary conformal field theory reaches from theoretical foundations to recent developments, with an emphasis on the algebraic treatment of string backgrounds. Topics covered include basic concepts in conformal field theory with and without boundaries, the mathematical description of strings and D-branes, and the geometry of strongly curved spacetime. The book offers insights into string geometry that go beyond classical notions. Describing the theory from basic concepts, and providing numerous worked examples from conformal field theory and string theory, this reference is of interest

Supergravity, together with string theory, is one of the most significant developments in theoretical physics. Written by two of the most respected workers in the field, this is the first-ever authoritative and systematic account of supergravity. The book starts by reviewing aspects of relativistic field theory in Minkowski spacetime. After introducing the relevant ingredients of differential geometry and gravity, some basic supergravity theories (D=4 and D=11) and the main gauge theory tools are explained. In the second half of the book, complex geometry and N=1 and N=2 supergravity theories are covered. Classical solutions and a chapter on AdS/CFT complete the book. Numerous exercises and examples make it ideal for Ph.D. students, and with applications to model building, cosmology and solutions of supergravity theories, it is also invaluable to researchers. A website hosted by the authors, featuring solutions to some exercises and additional reading material, can be found at www.camb

Black holes and gravitational radiation are two of the most dramatic predictions of general relativity. The quest for rotating black holes - discovered by Roy P. Kerr as exact solutions to the Einstein equations - is one of the most exciting challenges facing physicists and astronomers. Gravitational Radiation, Luminous Black Holes and Gamma-Ray Burst Supernovae takes the reader through the theory of gravitational radiation and rotating black holes, and the phenomenology of GRB-supernovae. Topics covered include Kerr black holes and the frame-dragging of spacetime, luminous black holes, compact tori around black holes, and black-hole spin interactions. It concludes with a discussion of prospects for gravitational-wave detections of a long-duration burst in gravitational-waves as a method of choice for identifying Kerr black holes in the Universe. This book is ideal for a special topics graduate course on gravitational-wave astronomy and as an introduction to those interested in this co

Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers in all areas of theoretical physics. The 'Foundation' section develops the formalism in six chapters, and uses it in the next four chapters to discuss four key applications - spherical spacetimes, black holes, gravitational waves and cosmology. The six chapters in the 'Frontier' section describe cosmological perturbation theory, quantum fields in curved spacetime, and the Hamiltonian structure of general relativity, among several other advanced topics, some of which are covered in-depth for the first time in a textbook. The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 200 exercises are included to test and develop the reader's understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research.

Based on lectures given in honour of Stephen Hawking's sixtieth birthday, this book comprises contributions from some of the world's leading theoretical physicists. It begins with a section containing chapters by successful scientific popularisers, bringing to life both Hawking's work and other exciting developments in physics. The book then goes on to provide a critical evaluation of advanced subjects in modern cosmology and theoretical physics. Topics covered include the origin of the universe, warped spacetime, cosmological singularities, quantum gravity, black holes, string theory, quantum cosmology and inflation. As well as providing a fascinating overview of the wide variety of subject areas to which Stephen Hawking has contributed, this book represents an important assessment of prospects for the future of fundamental physics and cosmology.

The theory of quantum gravity promises a revolutionary new understanding of gravity and spacetime, valid from microscopic to cosmological distances. Research in this field involves an exciting blend of rigorous mathematics and bold speculations, foundational questions and technical issues. Containing contributions from leading researchers in this field, this book presents the fundamental issues involved in the construction of a quantum theory of gravity and building up a quantum picture of space and time. It introduces the most current approaches to this problem, and reviews their main achievements. Each part ends in questions and answers, in which the contributors explore the merits and problems of the various approaches. This book provides a complete overview of this field from the frontiers of theoretical physics research for graduate students and researchers.

This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.

This book, first published in 2007, is an introductory textbook on quantum field theory in gravitational backgrounds intended for undergraduate and beginning graduate students in the fields of theoretical astrophysics, cosmology, particle physics, and string theory. The book covers the basic (but essential) material of quantization of fields in an expanding universe and quantum fluctuations in inflationary spacetime. It also contains a detailed explanation of the Casimir, Unruh, and Hawking effects, and introduces the method of effective action used for calculating the back-reaction of quantum systems on a classical external gravitational field. The broad scope of the material covered will provide the reader with a thorough perspective of the subject. Every major result is derived from first principles and thoroughly explained. The book is self-contained and assumes only a basic knowledge of general relativity. Exercises with detailed solutions are provided throughout the book.

Black holes and gravitational radiation are two of the most dramatic predictions of general relativity. The quest for rotating black holes - discovered by Roy P. Kerr as exact solutions to the Einstein equations - is one of the most exciting challenges facing physicists and astronomers. Gravitational Radiation, Luminous Black Holes and Gamma-Ray Burst Supernovae takes the reader through the theory of gravitational radiation and rotating black holes, and the phenomenology of GRB-supernovae. Topics covered include Kerr black holes and the frame-dragging of spacetime, luminous black holes, compact tori around black holes, and black-hole spin interactions. It concludes with a discussion of prospects for gravitational-wave detections of a long-duration burst in gravitational-waves as a method of choice for identifying Kerr black holes in the Universe. This book is ideal for a special topics graduate course on gravitational-wave astronomy and as an introduction to those interested in this co

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.

These two volumes are the proceedings of a major International Symposium on General Relativity held at the University of Maryland 27 to 29 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 their subjects developed and offer individual insights in their search for new directions.

String Theory, first published in 1998, comprises two volumes which provide a comprehensive and pedagogic account of the subject. Volume 2 begins with an introduction to supersymmetric string theories and presents the important advances of recent years. The first three chapters introduce the type I, type II, and heterototic superstring theories and their interactions. The next two chapters present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy. The final chapters are concerned with four-dimensional string theories, showing how some of the simplest string models connect with previous ideas for unifying the Standard Model. They collect many important results on world-sheet and spacetime symmetries. An appendix summarizes the necessary background on fermions and supersymmetry. An essential text and reference for graduate students and researchers i

This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.

Based on lectures given in honour of Stephen Hawking's sixtieth birthday, this book comprises contributions from some of the world's leading theoretical physicists. It begins with a section containing chapters by successful scientific popularisers, bringing to life both Hawking's work and other exciting developments in physics. The book then goes on to provide a critical evaluation of advanced subjects in modern cosmology and theoretical physics. Topics covered include the origin of the universe, warped spacetime, cosmological singularities, quantum gravity, black holes, string theory, quantum cosmology and inflation. As well as providing a fascinating overview of the wide variety of subject areas to which Stephen Hawking has contributed, this book represents an important assessment of prospects for the future of fundamental physics and cosmology.

The greatest challenge in fundamental physics is how quantum mechanics and general relativity can be reconciled in a theory of 'quantum gravity'. The project suggests a profound revision of our notions of space, time and matter, and so 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 all the issues. This volume contains accessible introductions to the main and less well 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.

The greatest challenge in fundamental physics is how quantum mechanics and general relativity can be reconciled in a theory of 'quantum gravity'. The project suggests a profound revision of our notions of space, time and matter, and so 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 all the issues. This volume contains accessible introductions to the main and less well 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.

String Theory, first published in 1998, comprises two volumes which provide a comprehensive and pedagogic account of the subject. Volume 2 begins with an introduction to supersymmetric string theories and presents the important advances of recent years. The first three chapters introduce the type I, type II, and heterototic superstring theories and their interactions. The next two chapters present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy. The final chapters are concerned with four-dimensional string theories, showing how some of the simplest string models connect with previous ideas for unifying the Standard Model. They collect many important results on world-sheet and spacetime symmetries. An appendix summarizes the necessary background on fermions and supersymmetry. An essential text and reference for graduate students and researchers i

This book presents the first, comprehensive exposition of the interpretation of quantum mechanics pioneered by Louis de Broglie and David Bohm. The purpose is to explain how quantum processes may be visualized without ambiguity or confusion, in terms of a simple physical model. Developing the theme that a material system, such as an electron, is a particle guided by a surrounding quantum wave, an examination of the classic phenomena of quantum theory is presented to show how the spacetime orbits of an ensemble of particles can reproduce the statistical quantum predictions. The mathematical and conceptual aspects of this theory are developed carefully from first principles. The book thus provides a comprehensive overview of an approach which brings clarity to a subject notorious for its conceptual difficulties. It will, therefore, appeal to all physicists with an interest in the foundations of their subject.