In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.

The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale's scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale's scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck's law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.

Yet over the past few decades, physicists have discovered a phenomenon that operates outside the confines of space and time: nonlocality - the ability of two particles to act in harmony no matter how far apart they may be. If space isn't what we thought it was, then what is it? In Spooky Action at a Distance, the award-winning journalist George Musser sets out to answer that question. He guides us on an epic journey into the lives of experimental physicists observing particles acting in tandem, astronomers finding galaxies that look statistically identical, and cosmologists hoping to unravel the paradoxes surrounding the big bang. He traces the contentious debates over nonlocality through major discoveries and disruptions of the twentieth century and shows how scientists faced with the same undisputed experimental evidence develop wildly different explanations for that evidence. Their conclusions challenge our understanding of the origins of the universe - and they suggest a new grand unified theory of physics.

Monte Carlo methods are a class of computational algorithms for simulating the behavior of a wide range of various physical and mathematical systems (with many variables). Their utility has increased with general availability of fast computers, and new applications are continually forthcoming. The basic concepts of Monte Carlo are both simple and straightforward and rooted in statistics and probability theory, their defining characteristic being that the methodology relies on random or pseudo-random sequences of numbers. It is a technique of numerical analysis based on the approximate solution of a problem using repeated sampling experiments and observing the proportion of times a given property is satisfied.
The term Monte Carlo was first used to describe calculational methods based on chance in the 1940s, but the methods themselves preceded the term by as much as a century. Quantum Monte Carlo (QMC) first appeared in 1982 and similarly was preceded by development of the related calculational methodology. The success of QMC methods over the past few decades has been remarkable, and this book will clearly demonstrate that success in its discussion of applications. For isolated molecules, the basic material of chemistry, QMC methods have produced exact solutions of the Schroedinger equation for very small systems and the most accurate solutions available for very large systems. The range of applications is impressive: folding of protein molecules, interactions in liquids, structure modeling in crystals and enzymes, quantum dots, designing heat shields and aerodynamic forms, architecture, design, business and economics, and even cinema and video games (3D modeling).
This booktakes a similar approach to Henry Schaefers classic book Quantum Chemistry (OUP, 1984 now a Dover edition), collecting summaries of some of the most important papers in the quantum Monte Carlo literature, tying everything together with analysis and discussion of applications. Quantum Monte Carlo is a reference book for quantum Monte Carlo applications, belonging near the desk of every quantum chemist, physicist, and a wide range of scientists and engineers across many disciplines, destined to become a classic.

The nature of space and time is one of the most fascinating and fundamental philosophical issues which presently engages at the deepest level with physics. During the last thirty years this notion has been object of an intense critical review in the light of new scientific theories which try to combine the principles of both general relativity and quantum theory-called theories of quantum gravity. This book considers the way string theory shapes its own account of spacetime disappearance from the fundamental level.

'Everything you wanted to know about physics but were afraid to ask' Priyamvada Natarajan, author of Mapping the Heavens __________________________ When leading theoretical physicist Professor Michael Dine was asked where you could find an accessible book that would teach you about the Big Bang, Dark Matter, the Higgs boson and the cutting edge of physics now, he had nothing he could recommend. So he wrote it himself. In This Way to the Universe, Dine takes us on a fascinating tour through the history of modern physics - from Newtonian mechanics to quantum, from particle to nuclear physics - delving into the wonders of our universe at its largest, smallest, and within our daily lives. If you are looking for the one book to help you understand physics, written in language anyone can follow, this is it. __________________________ 'An extraordinary journey into what we know, what we hope to know, and what we don't know, about the universe and the laws that govern it' Leonard Susskind, author of The Theoretical Minimum series 'This book is a rare event . . . presented by someone who is a true master' Sean Carroll, author of From Eternity to Here 'Dine's enthusiastic storytelling makes the read worth it for those who want to finally wrap their mind around string theory or the Higgs boson' Tess Joosse, Scientific American

This thoroughly revised 5th edition of Zeh's classic text investigates irreversible phenomena and their foundation in classical, quantum and cosmological settings. It includes new sections on the meaning of probabilities in a cosmological context, irreversible aspects of quantum computers, and various consequences of the expansion of the Universe. In particular, the book offers an analysis of the physical concept of time.

The hydrogen Lyman-alpha line is of utmost importance to many fields of astrophysics. This UV line being conveniently redshifted with distance to the visible and even near infrared wavelength ranges, it is observable from the ground, and provides the main observational window on the formation and evolution of high redshift galaxies. Absorbing systems that would otherwise go unnoticed are revealed through the Lyman-alpha forest, Lyman-limit, and damped Lyman-alpha systems, tracing the distribution of baryonic matter on large scales, and its chemical enrichment. We are living an exciting epoch with the advent of new instruments and facilities, on board of satellites and on the ground. Wide field and very sensitive integral field spectrographs are becoming available on the ground, such as MUSE at the ESO VLT. The giant E-ELT and TMT telescopes will foster a quantum leap in sensitivity and both spatial and spectroscopic resolution, to the point of being able, perhaps, to measure directly the acceleration of the Hubble flow. In space, the JWST will open new possibilities to study the Lyman-alpha emission of primordial galaxies in the near infrared. As long as the Hubble Space Telescope will remain available, the UV-restframe properties of nearby galaxies will be accessible to our knowledge. Therefore, this Saas-Fee course appears very timely and should meet the interest of many young researchers.

In recent years, the study of neutron stars and black holes has become increasingly important, and rigorous mathematical analysis needs to be applied in order to understand their basic physics. This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It presents basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics, and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge.org/9780521863834.

A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research. This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research. This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

The aim of this two-volume title is to give a comprehensive review of one hundred years of development of general relativity and its scientific influences. This unique title provides a broad introduction and review to the fascinating and profound subject of general relativity, its historical development, its important theoretical consequences, gravitational wave detection and applications to astrophysics and cosmology. The series focuses on five aspects of the theory: The first three topics are covered in Volume 1 and the remaining two are covered in Volume 2. While this is a two-volume title, it is designed so that each volume can be a standalone reference volume for the related topic.

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes-regions of space in which space and time are distorted in such a way that nothing, not even light, can escape-as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars.

Written by a former Olympiad student, Wang Jinhui, and a Physics Olympiad national trainer, Bernard Ricardo, Competitive Physics delves into the art of solving challenging physics puzzles. This book not only expounds a multitude of physics topics from the basics but also illustrates how these theories can be applied to problems, often in an elegant fashion. With worked examples that depict various problem-solving sleights of hand and interesting exercises to enhance the mastery of such techniques, readers will hopefully be able to develop their own insights and be better prepared for physics competitions. Ultimately, problem-solving is a craft that requires much intuition. Yet this intuition, perhaps, can only be honed by trudging through an arduous but fulfilling journey of enigmas.This is the second part of a two-volume series and will mainly analyze thermodynamics, electromagnetism and special relativity. A brief overview of geometrical optics is also included.

The aim of this two-volume title is to give a comprehensive review of one hundred years of development of general relativity and its scientific influences. This unique title provides a broad introduction and review to the fascinating and profound subject of general relativity, its historical development, its important theoretical consequences, gravitational wave detection and applications to astrophysics and cosmology. The series focuses on five aspects of the theory: The first three topics are covered in Volume 1 and the remaining two are covered in Volume 2. While this is a two-volume title, it is designed so that each volume can be a standalone reference volume for the related topic.

This volume gathers the content of the courses held at the Third IDPASC School, which took place in San Martino Pinario, Hospederia and Seminario Maior, in the city of Santiago de Compostela, Galiza, Spain, from January 21st to February 2nd, 2013. This school is the annual joint program of the International Doctorate Network in Particle Physics, Astrophysics, and Cosmology (IDPASC). The purpose of the school series is to present doctoral students from different universities and laboratories in Europe and beyond with a broad range of the latest results and current state of the art in the fields of Particle Physics, Astrophysics, and Cosmology, and to further introduce them to both the questions now posed by the potentials of physics and to challenges connected with current and future experiments - in particular, with the newly available energy ranges. Following these guidelines, the content of this third edition of the IDPASC School was jointly planned by the Academic Council and by the network's International Committee, whose members ensure every year its timely formulation, keeping up with the constant evolution of these fields. The program covers a balanced range of the latest developments in these fields worldwide, with courses offered by internationally acknowledged physicists on the Basic Features of Hadronic Processes, Quantum Chromodynamics, Physics and Technology of ALICE, LHCb Physics-Parity Violation, the Higgs System in and beyond the Standard Model, Higgs Searches at the LHC, Theory and Experiments with Cosmic Rays, Numerical Methods and Data Analysis in Particle Physics, Theoretical Cosmology, and AdS/CFT Correspondence. Most of these courses were complemented by practical and discussion sessions.

'Outstanding Academic Title for 2014' by CHOICEEinstein Relatively Simple brings together for the first time an exceptionally clear explanation of both special and general relativity. It is for people who always wanted to understand Einstein's ideas but never thought they could.Told with humor, enthusiasm, and rare clarity, this entertaining book reveals how a former high school drop-out revolutionized our understanding of space and time. From E=mc2 and everyday time travel to black holes and the big bang, Einstein Relatively Simple takes us all, regardless of our scientific backgrounds, on a mind-boggling journey through the depths of Einstein's universe. Along the way, we track Einstein through the perils and triumphs of his life - follow his thinking, his logic, and his insights - and chronicle the audacity, imagination, and sheer genius of the man recognized as the greatest scientist of the modern era.In Part I on special relativity we learn how time slows and space shrinks with motion, and how mass and energy are equivalent. Part II on general relativity reveals a cosmos where black holes trap light and stop time, where wormholes form gravitational time machines, where space itself is continually expanding, and where some 13.7 billion years ago our universe was born in the ultimate cosmic event - the Big Bang.

'Outstanding Academic Title for 2014' by CHOICEEinstein Relatively Simple brings together for the first time an exceptionally clear explanation of both special and general relativity. It is for people who always wanted to understand Einstein's ideas but never thought they could.Told with humor, enthusiasm, and rare clarity, this entertaining book reveals how a former high school drop-out revolutionized our understanding of space and time. From E=mc2 and everyday time travel to black holes and the big bang, Einstein Relatively Simple takes us all, regardless of our scientific backgrounds, on a mind-boggling journey through the depths of Einstein's universe. Along the way, we track Einstein through the perils and triumphs of his life - follow his thinking, his logic, and his insights - and chronicle the audacity, imagination, and sheer genius of the man recognized as the greatest scientist of the modern era.In Part I on special relativity we learn how time slows and space shrinks with motion, and how mass and energy are equivalent. Part II on general relativity reveals a cosmos where black holes trap light and stop time, where wormholes form gravitational time machines, where space itself is continually expanding, and where some 13.7 billion years ago our universe was born in the ultimate cosmic event - the Big Bang.

A new title in the Manchester Physics Series, this introductory text emphasises physical principles behind classical mechanics and relativity. It assumes little in the way of prior knowledge, introducing relevant mathematics and carefully developing it within a physics context. Designed to provide a logical development of the subject, the book is divided into four sections, introductory material on dynamics, and special relativity, which is then followed by more advanced coverage of dynamics and special relativity. Each chapter includes problems ranging in difficulty from simple to challenging with solutions for solving problems. Includes solutions for solving problems Numerous worked examples included throughout the book Mathematics is carefully explained and developed within a physics environment Sensitive to topics that can appear daunting or confusing

This book provides a number of combinatorial tools that allow a systematic study of very general discrete spaces involved in the context of discrete quantum gravity. In any dimension D, we can discretize Euclidean gravity in the absence of matter over random discrete spaces obtained by gluing families of polytopes together in all possible ways. These spaces are then classified according to their curvature. In D=2, it results in a theory of random discrete spheres, which converge in the continuum limit towards the Brownian sphere, a random fractal space interpreted as a quantum random space-time. In this limit, the continuous Liouville theory of D=2 quantum gravity is recovered. Previous results in higher dimension regarded triangulations, converging towards a continuum random tree, or gluings of simple building blocks of small sizes, for which multi-trace matrix model results are recovered in any even dimension. In this book, the author develops a bijection with stacked two-dimensional discrete surfaces for the most general colored building blocks, and details how it can be used to classify colored discrete spaces according to their curvature. The way in which this combinatorial problem arrises in discrete quantum gravity and random tensor models is discussed in detail.

This book is the second edition of an excellent undergraduate-level overview of classical and modern physics, intended for students of physics and related subjects, and also perfectly suited for the education of physics teachers. The twelve-chapter book begins with Newton's laws of motion and subsequently covers topics such as thermodynamics and statistical physics, electrodynamics, special and general relativity, quantum mechanics and cosmology , the standard model and quantum chromodynamics. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with standard mathematics. An important addition in this second edition is a set of exercises and problems, distributed throughout the book. Some of the problems aim to complement the text, others to provide readers with additional useful tools for tackling new or more advanced topics. Furthermore, new topics have been added in several chapters; for example, the discovery of extra-solar planets from the wobble of their mother stars, a discussion of the Landauer principle relating information erasure to an increase of entropy, quantum logic, first order quantum corrections to the ideal gas equation of state due to the Fermi-Dirac and Bose-Einstein statistics. Both gravitational lensing and the time-correction in geo-positioning satellites are explained as theoretical applications of special and general relativity. The discovery of gravitational waves, one of the most important achievements of physical sciences, is presented as well. Professional scientists, teachers, and researchers will also want to have this book on their bookshelves, as it provides an excellent refresher on a wide range of topics and serves as an ideal starting point for expanding one's knowledge of new or unfamiliar fields. Readers of this book will not only learn much about physics, they will also learn to love it.

This textbook provides an introduction to gravitational lensing, which has become an invaluable tool in modern astrophysics, with applications that range from finding planets orbiting distant stars to understanding how dark matter and dark energy conspired to form the cosmic structures we see today. Principles of Gravitational Lensing begins with Einstein's prediction that gravity bends light, and shows how that fundamental idea has spawned a rich field of study over the past century. The gravitational deflection of light was first detected by Eddington during a solar eclipse in May 1919, launching Einstein and his theory of relativity into public view. Yet the possibility of using the phenomenon to unlock mysteries of the Universe seemed remote, given the technology of the day. Theoretical work was carried out sporadically over the next six decades, but only with the discovery of the system Q0957+561 in 1979 was gravitational lensing transformed from a curiosity of general relativity into a practical observational tool. This book describes how the three subfields known as strong lensing, weak lensing, and microlensing have grown independently but become increasingly intertwined. Drawing on their research experience, Congdon and Keeton begin with the basic physics of light bending, then present the mathematical foundations of gravitational lensing, building up to current research topics in a clear and systematic way. Relevant background material from physics and mathematics is included, making the book self-contained. The derivations and explanations are supplemented by exercises designed to help students master the theoretical concepts as well as the methods that drive current research. An extensive bibliography guides those wishing to delve more deeply into particular areas of interest. Principles of Gravitational Lensing is ideal for advanced students and seasoned researchers looking to penetrate this thriving subject and even contribute research of their own.

This textbook is suitable for a one-semester introduction to General Relativity for advanced undergraduates in physics and engineering. The book is concise so that the entire material can be covered in the one-semester time frame. Besides, the readers are introduced to the subject easily without the need for advanced mathematics. Though concise, the theory development is lucid and the readers are exposed to possible analytic calculations. Full solutions to some important problems are provided, and the experimental evidence is discussed in detail.Resources are provided to instructors who adopt this textbook for their courses. Adopting instructors can print and copy portions of these resources solely for their teaching needs. All instructional resources are furnished for informational use only, and are subject to change without notice.

Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics.