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

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.

Covariant Physics: From Classical Mechanics to General Relativity and Beyond endeavours to provide undergraduate students as well as self-learners with training in the fundamentals of the modern theories of spacetime, most notably the general theory of relativity as well as physics in curved spacetime backgrounds in general. This text does so with the barest of mathematical preparation. In fact, very little beyond multivariable calculus and a bit of linear algebra is assumed. Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance. The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers.

Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding. The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology. This new third edition has been updated to take account of fresh observational evidence and experiments.

This textbook gradually introduces the reader to several topics related to black hole physics with a didactic approach. It starts with the most basic black hole solution, the Schwarzschild metric, and discusses the basic classical properties of black hole solutions as seen by different probes. Then it reviews various theorems about black hole properties as solutions to Einstein gravity coupled to matter fields, conserved charges associated with black holes, and laws of black hole thermodynamics. Next, it elucidates semiclassical and quantum aspects of black holes, which are relevant in ongoing and future research. The book is enriched with many exercises and solutions to assist in the learning. The textbook is designed for physics graduate students who want to start their research career in the field of black holes; postdocs who recently changed their research focus towards black holes and want to get up-to-date on recent and current research topics; advanced researchers intending to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. Besides general relativity, the reader needs to be familiar with standard undergraduate physics, like thermodynamics, quantum mechanics, and statistical mechanics. Moreover, familiarity with basic quantum field theory in Minkowski space is assumed. The book covers the rest of the needed background material in the main text or the appendices.

It would be hard to imagine a better guide to this difficult subject. -- Scientific American In Three Roads to Quantum Gravity, Lee Smolin provides an accessible overview of the attempts to build a final theory of everything. He explains in simple terms what scientists are talking about when they say the world is made from exotic entities such as loops, strings, and black holes and tells the fascinating stories behind these discoveries: the rivalries, epiphanies, and intrigues he witnessed firsthand. Provocative, original, and unsettling. -- The New York Review of Books An excellent writer, a creative thinker. -- Nature

Einstein's standard and battle-tested geometric theory of gravity--spacetime tells mass how to move and mass tells spacetime how to curve--is expounded in this book by Ignazio Ciufolini and John Wheeler. They give special attention to the theory's observational checks and to two of its consequences: the predicted existence of gravitomagnetism and the origin of inertia (local inertial frames) in Einstein's general relativity: inertia "here" arises from mass "there."

The authors explain the modern understanding of the link between gravitation and inertia in Einstein's theory, from the origin of inertia in some cosmological models of the universe, to the interpretation of the initial value formulation of Einstein's standard geometrodynamics; and from the devices and the methods used to determine the local inertial frames of reference, to the experiments used to detect and measure the "dragging of inertial frames of reference." In this book, Ciufolini and Wheeler emphasize present, past, and proposed tests of gravitational interaction, metric theories, and general relativity. They describe the numerous confirmations of the foundations of geometrodynamics and some proposed experiments, including space missions, to test some of its fundamental predictions--in particular gravitomagnetic field or "dragging of inertial frames" and gravitational waves.

Every document in "The Collected Papers of Albert Einstein" appears in the language in which it was written, and supplementary paperback volumes present the English translations if all non-English materials. For those desiring a supplement to Volume 5, for instance, this paperback includes translations of correspondence that give a much richer picture of Einstein in his twenties and thirties than we ever had. In addition to illuminating the personal aspects of his life, the letters document his scientific activity: his concentration for years on the unfathomable problems of quanta and radiation, his extensive knowledge of experimental physics, his many fruitful interactions with experimentalists, and finally his long struggle to generalize the 1905 theory of relativity to include gravitation and accelerated frames of reference. This paperback translation does not include notes or annotation of the documentary volume and is not intended for use without the original language documentary edition, which provides the extensive editorial commentary necessary for a full historical and scientific understanding of the documents.

Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.

Albert Einstein, one of the most prolific scientists of the twentieth century, developed the theory of relativity which was crucial for the advancement of modern physics. Young Einstein identified a paradox between Newtonian Mechanics and Maxwell's equations which pointed to a flawed understanding of space and time by the scientists of the day. In Relativity, Einstein presents his findings using a minimal amount of mathematical language, but the text can still be challenging for readers who lack an extensive scientific background. The Routledge Guidebook to Einstein's Relativity expands on and supplements this seminal text, by exploring: the historical context of Einstein's work and the background to his breakthroughs details of experimental verification of special and general relativity the enduring legacy of Einstein's theories and their implications for future scientific breakthroughs. This is an essential introduction for students of physics, philosophy and history in understanding the key elements of the work and the importance of this classic text to society today.

Here a physicist and a professor of literature guide general readers through the ideas that revolutionized our conception of the physical universe.

A superlative, fascinating graphic account of Albert Einstein's strange world and how his legacy has been built upon since. It is now more than a century since Einstein's theories of Special and General Relativity began to revolutionise our view of the universe. Beginning near the speed of light and proceeding to explorations of space-time and curved spaces, Introducing Relativity plots a visually accessible course through the thought experiments that have given shape to contemporary physics. Scientists from Isaac Newton to Stephen Hawking add their unique contributions to this story, as we encounter Einstein's astounding vision of gravity as the curvature of space-time and arrive at the breathtakingly beautiful field equations. Einstein's legacy is reviewed in the most advanced frontiers of physics today - black holes, gravitational waves, the accelerating universe and string theory.

This advanced undergraduate text introduces Einstein's general theory of relativity. The topics covered include geometric formulation of special relativity, the principle of equivalence, Einstein's field equation and its spherical-symmetric solution, as well as cosmology. An emphasis is placed on physical examples and simple applications without the full tensor apparatus. It begins by examining the physics of the equivalence principle and looks at how it inspired Einstein's idea of curved spacetime as the gravitational field. At a more mathematically accessible level, it provides a metric description of a warped space, allowing the reader to study many interesting phenomena such as gravitational time dilation, GPS operation, light deflection, precession of Mercury's perihelion, and black holes. Numerous modern topics in cosmology are discussed from primordial inflation and cosmic microwave background to the dark energy that propels an accelerating universe. Building on Cheng's previous book, 'Relativity, Gravitation and Cosmology: A Basic Introduction', this text has been tailored to the advanced student. It concentrates on the core elements of the subject making it suitable for a one-semester course at the undergraduate level. It can also serve as an accessible introduction of general relativity and cosmology for those readers who want to study the subject on their own. The proper tensor formulation of Einstein's field equation is presented in an appendix chapter for those wishing to glimpse further at the mathematical details.

What does the passage of time consist in? There are some suggestive metaphors. aEvents approach us, pass us, and recede from us, like sticks and leaves floating on the river of time.a aWe are moving from the past into the future, like ships sailing into an unknown ocean.a There is surely something right and deep about these metaphors. But how close are they to the literal truth? In this book Bradford Skow argues that they are far from the literal truth. Skowas argument takes the form of a defense of the block universe theory of time, a theory that, in many ways, treats time as a dimension of reality that closely resembles the three dimensions of space. Opposed to the block universe theory of time are theories that take the metaphors more seriously: presentism, the moving spotlight theory, the growing block theory, and the branching time theory. These are theories of arobusta passage of time, or aobjective becoming.a Skow argues that the best of these theories, the block universe theoryas most worthy opponent, is the moving spotlight theory, the theory that says that apresentnessa moves along the series of times from the past into the future. Skow defends the moving spotlight theory against the objection that it is inconsistent, and the objection that it cannot answer the question of how fast time passes. He also defends it against the objection that it is incompatible with Einsteinas theory of relativity. Skow proposes several ways in which the moving spotlight theory may be made compatible with the theory of relativity. Still, this book is ultimately a defense of the block universe theory, not of the moving spotlight theory. Skow holds that the best arguments against the block universe theory, and for the moving spotlight theory, start from the idea that, somehow, the passage of time is given to us in experience. Skow discusses several different arguments that start from this idea, and argues that they all fail.

DROPOUT. PACIFIST. PHYSICIST. CASANOVA. REFUGEE. REBEL. GENIUS. THINK YOU KNOW EINSTEIN? THINK AGAIN His face is instantly recognisable. His name is shorthand for genius. Today, he's a figurehead as much as a man, symbolic of things larger than himself: of scientific progress, of the human mind, even of the age. But who was Einstein really? The Nobel Prize-winning physicist who discovered relativity, black holes and E = mc2, dined with Charlie Chaplin in Hollywood and was the inspiration for (highly radioactive) element 99, Albert Einstein was also a high school dropout with an FBI file 1,400 pages long. In this book, Samuel Graydon brings history's most famous scientist back to life. From his lost daughter to escaping the Nazis, from his love letters to unlikely inventions, from telling jokes to cheer up his sad parrot Bibo to refusing the Presidency of Israel, through the discoveries and thought experiments that changed science, Einstein in Time and Space tells 99 unforgettable stories of the man who redefined how we view our universe and our place within it.

This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.
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Bradford Skow presents an original defense of the 'block universe' theory of time, often said to be a theory according to which time does not pass. Along the way, he provides in-depth discussions of alternative theories of time, including those in which there is 'robust passage' of time or 'objective becoming': presentism, the moving spotlight theory of time, the growing block theory of time, and the 'branching time' theory of time. Skow explains why the moving spotlight theory is the best of these arguments, and rebuts several popular arguments against the thesis that time passes. He surveys the problems that the special theory of relativity has been thought to raise for objective becoming, and suggests ways in which fans of objective becoming may reconcile their view with relativistic physics. The last third of the book aims to clarify and evaluate the argument that we should believe that time passes because, somehow, the passage of time is given to us in experience. He isolates three separate arguments this idea suggests, and explains why they fail.

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. Among the new developments that occurred during this period was the introduction of a particular notion of 'quasi-local mass-momentum and angular momentum', the topic of Penrose's Royal Society paper. Many encouraging results were initially obtained but, later, difficulties began to emerge and remain today. Also, an extensive paper (with Eastwood and Wells) gives a thorough account of the relation between twistor cohomology and massless fields. This volume witnesses Penrose's increasing conviction that the puzzling issue of quantum measurement could only be resolved by the appropriate unification of quantum mechanics with general relativity, where that union must involve an actual change in the rules of quantum mechanics as well as in space-time structure. Penrose's first incursions into a possible relation between consciousness and quantum state reduction are also covered here.

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. This sixth volume describes an actual experiment to measure the length of time that a quantum superposition might last (developing the Diosi-Penrose proposal). It also discusses the significant progress made in relation to incorporating the 'googly' information for a gravitational field into the structure of a curved twistor space. Penrose also covers such things as the geometry of light rays in relation to twistor-space structures, the utility of complex numbers in drawing three-dimensional shapes, and the geometrical representation of different types of musical scales. The turn of the millennium was also an opportunity to reflect on progress in many areas up until that point.

Based on the author's own work and results obtained by renowned cosmologists, this short book provides a concise introduction to the relatively new research field of cosmological thermodynamics. Starting with a brief overview of basic cosmology and thermodynamics, the text gives an interesting account of the application of horizon thermodynamics to the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model, the inhomogeneous (Lemaitre-Tolman-Bondi) LTB model, and the gravitationally induced adiabatic particle creation scenario which is considered to be a viable alternative to the concordance Lambda-CDM model of the Universe. Both seasoned and new researchers in this field will appreciate the lucid presentation and the rich bibliography.

This excellent, semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, and more) and coverage of Einstein's special and general theories of relativity, discussing the concept of simultaneity, kinematics, Einstein's mechanics and dynamics, and more.

Relativity has much to offer for a well-rounded education. Yet books on relativity either assume a strong background in physics and math, aimed at advanced physics students, or, alternatively, offer a broad description with little intellectual challenge. This book bridges the gap. It aims at readers with essentially no physics or math background, who still find it rewarding to think rigorously. The book takes a "thinking tools" approach, by first making readers comfortable with a new thinking tool and then applying it to learn more about how nature works. By the end of the book, readers will have collected a versatile toolbox and will be comfortable using the tools to think about and really understand the intriguing phenomena they may have only heard about, including the twin paradox, black holes, and time travel. End-of-chapter exercises span a range of difficulty, allowing adventurous readers to stretch their understanding further as desired. Students who have studied, or are studying, relativity at a more mathematical level will also find the book useful for a more conceptual understanding.

A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology.

Ryan Wasserman presents a wide-ranging exploration of puzzles raised by the possibility of time travel, including the grandfather paradox, the bootstrapping paradox, and the twin paradox of special relativity. He draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology. The Paradoxes of Time Travel is written in an accessible style, and filled with entertaining examples from physics, science fiction, and popular culture.