Einstein's energy-momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is 'Lorentz-covariant.' As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees of freedom. The aim of this book is to present one Lorentz-covariant picture of these two different space-time symmetries. Using the same mathematical tool, it is possible to give a Lorentz-covariant picture of Gell-Mann's quark model for the proton at rest and Feynman's parton model for the fast-moving proton. The mathematical formalism for these aspects of the Lorentz covariance is based on two-by-two matrices and harmonic oscillators which serve as two basic scientific languages for many different branches of physics. It is pointed out that the formalism presented in this book is applicable to various aspects of optical sciences of current interest.

cB) 114 7. 8 Constant electric and magnetic fields at right angles (8,

Since the first French edition of the book emphasized rather the solid facts of Cosmology than the detailed discussions of controversial results, relatively few revisions were necessary for the English edition. They were made early in 1979 and affected about 5% of the text. The main revisions referred to the distance scale, the dlstribution of galaxies, the X-ray observations of clusters, the cosmic time evolution of quasars and radiogalaxies and the 3 K radiation. A new short bibliography presents the recent articles and the latest proceedings of Symposia; from these the reader can easily trace a more complete list of refer ences. I am happy to thank Professor Beiglbock for suggestions he made to improve Part lIon Spaces of Constant Curvature, and Drs. S. and J. Mitton for translating the manuscript into English. I also thank with pleasure Marie-Ange Sevin for correcting the final version. J. Heidmann March 1980, Meudon, France Preface The aim of this book is to present the fundamentals of cosmology. Its subject is the study of the universe on a grand scale: - on a grand distance scale, since from the start, we shall be escaping the con fines of our own Galaxy to explore space as far as the limits of the observable universe, some ten thousand million light years away; - and on a grand time scale, as we shall look back into the past to the very first moments of the initial expansion, about twelve thousand million years ago."

A brief introduction to gravity through Einstein's general theory of relativity Of the four fundamental forces of nature, gravity might be the least understood and yet the one with which we are most intimate. From the months each of us spent suspended in the womb anticipating birth to the moments when we wait for sleep to transport us to other realities, we are always aware of gravity. In On Gravity, physicist A. Zee combines profound depth with incisive accessibility to take us on an original and compelling tour of Einstein's general theory of relativity. Inspired by Einstein's audacious suggestion that spacetime could ripple, Zee begins with the stunning discovery of gravity waves. He goes on to explain how gravity can be understood in comparison to other classical field theories, presents the idea of curved spacetime and the action principle, and explores cutting-edge topics, including black holes and Hawking radiation. Zee travels as far as the theory reaches, leaving us with tantalizing hints of the utterly unknown, from the intransigence of quantum gravity to the mysteries of dark matter and energy. Concise and precise, and infused with Zee's signature warmth and freshness of style, On Gravity opens a unique pathway to comprehending relativity and gaining deep insight into gravity, spacetime, and the workings of the universe.

As we navigate through life we instinctively model time as having a flowing present that divides a fixed past from open future. This model develops in childhood and is deeply saturated within our language, thought and behavior, affecting our conceptions of the universe, freedom and the self. Yet as central as it is to our lives, physics seems to have no room for this flowing present. What Makes Time Special? demonstrates this claim in detail and then turns to two novel positive tasks. First, by looking at the world "sideways" - in the spatial directions - it shows that physics is not "spatializing time" as is commonly alleged. Even relativity theory makes significant distinctions between the spacelike and timelike directions, often with surprising consequences. Second, if the flowing present is an illusion, it is a deep one worthy of explanation. The author develops a picture whereby the temporal flow arises as an interaction effect between an observer and the physics of the world. Using insights from philosophy, cognitive science, biology, psychology and physics, the theory claims that the flowing present model of time is the natural reaction to the perceptual and evolutionary challenges thrown at us. Modeling time as flowing makes sense even if it misrepresents it.

This book is an elaboration of lecture notes for the graduate course on General Rela tivity given by the author at Boston University in the spring semester of 1972. It is an introduction to the subject only, as the time available for the course was limited. The author of an introduction to General Relativity is faced from the beginning with the difficult task of choosing which material to include. A general criterion as sisting in this choice is provided by the didactic character of the book: Those chapters have to be included in priority, which will be most useful to the reader in enabling him to understand the methods used in General Relativity, the results obtained so far and possibly the problems still to be solved. This criterion is not sufficient to ensure a unique choice. General Relativity has developed to such a degree, that it is impossible to include in an introductory textbook of a reasonable length even a very condensed treatment of all important problems which have been discussed until now and the author is obliged to decide, in a more or less subjective manner, which of the more recent developments to omit. The following lines indicate by means of some examples the kind of choice made in this book."

BY W. H. MCCREA, F. R. S. 'THE only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy. ' So Einstein writes on page 2 of this book. Most present-day physicists would agree, and many before Einstein must have held the same opinion. Einstein, however, put the opinion into practice to better purpose than any physicist before him. And for Einstein it evidently meant what it means for most of us today: a theory is the construction of a theoretical model of the world of physics; all the mathematical discussion applies to the model; the model embodies the 'system of concepts', and it serves 'to represent the complex of our experiences' if the experience of the theoretical observer in the theoretical model can be put into satisfactory correspondence with the experi- ence of the actual observer in the actual physical world. Classical mechanics and classical electromagnetism pro- vide models that are good representations of two sets of actual experiences. As Einstein was the first fully to appreciate, however, it is not possible to combine these into a single self-consistent model. The construction of the simplest possible self-consistent model is the achieve- ment of Einstein's theory of special relativity. The theory is found, in particular, to give a satisfactory representation of the electromagnetic interaction between charged particles through its use of the concept of the electromagnetic field.

On their 100th anniversary, the story of the extraordinary scientific expeditions that ushered in the era of relativity In 1919, British scientists led extraordinary expeditions to Brazil and Africa to test Albert Einstein's revolutionary new theory of general relativity in what became the century's most celebrated scientific experiment. The result ushered in a new era and made Einstein a global celebrity by confirming his dramatic prediction that the path of light rays would be bent by gravity. Today, Einstein's theory is scientific fact. Yet the effort to "weigh light" by measuring the gravitational deflection of starlight during the May 29, 1919, solar eclipse has become clouded by myth and skepticism. Could Arthur Eddington and Frank Dyson have gotten the results they claimed? Did the pacifist Eddington falsify evidence to foster peace after a horrific war by validating the theory of a German antiwar campaigner? In No Shadow of a Doubt, Daniel Kennefick provides definitive answers by offering the most comprehensive and authoritative account of how expedition scientists overcame war, bad weather, and equipment problems to make the experiment a triumphant success. The reader follows Eddington on his voyage to Africa through his letters home, and delves with Dyson into how the complex experiment was accomplished, through his notes. Other characters include Howard Grubb, the brilliant Irishman who made the instruments; William Campbell, the American astronomer who confirmed the result; and Erwin Findlay-Freundlich, the German whose attempts to perform the test in Crimea were foiled by clouds and his arrest. By chronicling the expeditions and their enormous impact in greater detail than ever before, No Shadow of a Doubt reveals a story that is even richer and more exciting than previously known.

There is little doubt that Einstein's theory of relativity captures the imagination. Not only has it radically altered the way we view the universe, but the theory also has a considerable number of surprises in store. This is especially so in the three main topics of current interest that this book reaches, namely: black holes, gravitational waves, and cosmology. The main aim of this textbook is to provide students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject. Indeed, the book follows Einstein in that it introduces the theory very much from a physical point of view. After introducing the special theory of relativity, the basic field equations of gravitation are derived and discussed carefully as a prelude to first solving them in simple cases and then exploring the three main areas of application. This new edition contains a substantial extension content that considers new and updated developments in the field. Topics include coverage of the advancement of observational cosmology, the detection of gravitational waves from colliding black holes and neutron stars, and advancements in modern cosmology. Einstein's theory of relativity is undoubtedly one of the greatest achievements of the human mind. Yet, in this book, the author makes it possible for students with a wide range of abilities to deal confidently with the subject. Based on both authors' experience teaching the subject this is achieved by breaking down the main arguments into a series of simple logical steps. Full details are provided in the text and the numerous exercises while additional insight is provided through the numerous diagrams. As a result this book makes an excellent course for any reader coming to the subject for the first time while providing a thorough understanding for any student wanting to go on to study the subject in depth

A beloved introductory physics textbook, now including exercises and an answer key, explains the concepts essential for thorough scientific understanding In this concise book, R. Shankar, a well-known physicist and contagiously enthusiastic educator, explains the essential concepts of Newtonian mechanics, special relativity, waves, fluids, thermodynamics, and statistical mechanics. Now in an expanded edition-complete with problem sets and answers for course use or self-study-this work provides an ideal introduction for college-level students of physics, chemistry, and engineering; for AP Physics students; and for general readers interested in advances in the sciences. The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics.

Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books! The beginning of the 20th century heralded a scientific revolution: what a few brilliant minds uncovered about our reality in the first twenty years has shaped the history of our species. And one of them in particular stands out: Einstein, with his celebrated E=mc2. In this remarkable and insightful book, Christophe Galfard describes how E=mc2 is a direct consequence of the Theory of Special Relativity, the theory of how objects move and behave, at speeds close to the speed of light. He considers Einstein's legacy in the light of the 21st century, with fresh hindsight, and considers its impact on our vision of reality. The reader will discover that far from being just a formula, it is a brand new understanding of the nature of space and time. Some of the greatest scientific breakthroughs in the history of science have been made by geniuses who managed to merge and unite hitherto separated domains of knowledge. Galfard explores two unifications with Einstein's theories, and looks at the even bigger picture of how E=mc2 has changed our world, and what it entails for the future. Throughout, Galfard takes the reader on an extremely entertaining journey, using simple, jargon-free language to help the reader gain a deeper understanding of science. With humour and patience, he guides us through the world of particles, anti-matter and much more to bring us closer to an ultimate understanding of reality as we understand it today.

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

Applications of quantum field theoretical methods to gravitational physics, both in the semiclassical and the full quantum frameworks, require a careful formulation of the fundamental basis of quantum theory, with special attention to such important issues as renormalization, quantum theory of gauge theories, and especially effective action formalism. The first part of this graduate textbook provides both a conceptual and technical introduction to the theory of quantum fields. The presentation is consistent, starting from elements of group theory, classical fields, and moving on to the effective action formalism in general gauge theories. Compared to other existing books, the general formalism of renormalization in described in more detail, and special attention paid to gauge theories. This part can serve as a textbook for a one-semester introductory course in quantum field theory. In the second part, we discuss basic aspects of quantum field theory in curved space, and perturbative quantum gravity. More than half of Part II is written with a full exposition of details, and includes elaborated examples of simplest calculations. All chapters include exercises ranging from very simple ones to those requiring small original investigations. The selection of material of the second part is done using the "must-know" principle. This means we included detailed expositions of relatively simple techniques and calculations, expecting that the interested reader will be able to learn more advanced issues independently after working through the basic material, and completing the exercises.

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.

As we navigate through life we instinctively model time as having a flowing present that divides a fixed past from open future. This model develops in childhood and is deeply saturated within our language, thought and behavior, affecting our conceptions of the universe, freedom and the self. Yet as central as it is to our lives, physics seems to have no room for this flowing present. What Makes Time Special? demonstrates this claim in detail and then turns to two novel positive tasks. First, by looking at the world "sideways" - in the spatial directions - it shows that physics is not "spatializing time" as is commonly alleged. Even relativity theory makes significant distinctions between the spacelike and timelike directions, often with surprising consequences. Second, if the flowing present is an illusion, it is a deep one worthy of explanation. The author develops a picture whereby the temporal flow arises as an interaction effect between an observer and the physics of the world. Using insights from philosophy, cognitive science, biology, psychology and physics, the theory claims that the flowing present model of time is the natural reaction to the perceptual and evolutionary challenges thrown at us. Modeling time as flowing makes sense even if it misrepresents it.

Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects, from primordial inflation and cosmic microwave anisotropy to the dark energy that propels an accelerating universe.
The author presents the subject with an emphasis on physical examples and simple applications without the full tensor apparatus. The reader first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation, cosmic microwave anisotropy to the "dark energy" that propels an accelerating universe.
Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.

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