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.

On Albert Einstein's seventy-sixth and final birthday, a friend gave him a simple toy made from a broomstick, a brass ball attached to a length of string, and a weak spring. Einstein was delighted: the toy worked on a principle he had conceived fifty years earlier when he was working on his revolutionary theory of gravitya principle whose implications are still confounding physicists today.

Starting with this winning anecdote, Anthony Zee begins his animated discussion of phenomena ranging from the emergence of galaxies to the curvature of space-time, evidence for the existence of gravity waves, and the shape of the universe in the first nanoseconds of creation and today. Making complex ideas accessible without oversimplifying, Zee leads the reader through the implications of Einstein's theory and its influence on modern physics. His playful and lucid style conveys the excitement of some of the latest developments in physics, and his new Afterword brings things even further up-to-date.

Das Lehrbuch soll Studierende mit Interesse an den theoretischen Naturwissenschaften, deren Kenntnisse im wesentlichen aus einem Grundkurs der Differential- und Integralrechnung wie etwa fur Ingenieurfacher bestehen, in die klassische Feldtheorie mit modernen mathematischen Methoden einfuhren. Dementsprechend sind die Tensoranalysis und die Differentialgeometrie die mathematischen Themen, die Geometrie der Raum-Zeit und das Prinzip der Relativitat im Zusammenhang mit den Grundgesetzen der Elektrodynamik und der Gravitation die physikalischen. Mit Rucksicht auf die Mathematik der Relativitatstheorie, aber auch aus didaktischen Erwagungen, gliedert sich der Text in zwei Teile. Um den Leser unter einfacheren Anforderungen an das Vorstellungsvermogen mit der Methodik vertraut zu machen, wird zunachst der affine und euklidische Raum den mathematischen Objekten zugrundegelegt, um verallgemeinernd zur komplexeren Geometrie auf Mannigfaltigkeiten und Riemannschen Raumen hinuberfuhren zu konnen. Die Tensoranalysis in ebenen und gekrummten Raumen wird durch eine Einfuhrung in die spezielle und allgemeine Relativitatstheorie erganzt und abgeschlossen, wobei die Geometrie der Raum-Zeit und die Formulierung der Grundgesetze sowie mathematische Folgerungen zur Sprache kommen.

Gitter messen, wenn WH dafUr ausschlieBlich geometrische Gebilde verwenden, wel che in diesem Gitter auch physikalisch existieren? Physikalische Objekte, die dafUr in Frage kommen, sind Versetzungen, welche in jedem Kristall in einer ungeheuer groBen Zahl vorhanden sind. Wir suchen dann einmal nach solchen, physikalisch stabilen Formen dieser Versetzungen, die geeignet sind, uns ein MaB fUr eine Lange zu liefern, sowie Ferner nach physikalisch stabilen, schwingenden Versetzungen, die uns eine Schwingungsdauer fUr eine Uhr hergeben. Dies gelingt mit einer sehr ge nau untersuchten Gleichung fUr Versetzungen in Kristallen, mit der sog. sine Gordon - Gleichung, fUr die wir eine denkbar einfache physikalische BegrUndung angeben konnen. Darauf aufbauend werden wir dann einen relativistischen Effekt nach dem andern entdecken, am Ende auch das Prinzip von der universellen Konstanz einer ausgezeichneten Signalgeschwindigkeit, welche hier auf dem Gitter definiert ist: Die Kontinuumsnaherung eines Kristallgitters wird als Modell einer relativistischen Raum - Zeit erkennbar. Die Grundidee, die zu dieser Reduktion der relativistischen Phanomene auf be grifflich leichter faBbare Aussagen fuhrt, laBt sich kurz so formulieren: FUr die physikalischen Konstituenten eines idealen Raumgitters postulieren wir die Axio matik der Newtonschen Mechanik. Aber erst die auf diesem Gitter existierenden, lokalen Abweichungen von der idealen Struktur (Konfigurationen von Versetzun gen im KristaII) besitzen in bezug auf dieses Gitter diejenigen tragen Massen, deren Bewegung wir beobachten und fUr deren Bewegung wir dann - innerhalb relativ leicht Uberschaubarer GUltigkeitsgrenzen - die Gesetze der SpezieIIen Relativitats theorie finden."

Enjoy Our Universe is a guide for an enjoyable visit to the Universe. The "Universe" refers to all "observable things," ranging in size from the entire cosmos to elementary particles. This small tome on fundamental physics, cosmology, Higgs bosons, time travel and all that, is unlike any other analogous book. Its scientific statements are correct or, at least, they coincide with the opinions held by the vast majority of experts. It establishes clear distinctions between things we know for sure - in the sense of having strong observational support for them - and things that we know that we do not know, or we do not understand. In this sense, it is scientifically honest. In descriptions of our Universe and of the way it functions, beauty is a recurring word. In an attempt to portray its beauty from the eyes of the beholder, the book is profusely illustrated. Its offbeat, tongue-in-cheek illustrations greatly enhance its readability, particularly in those chapters whose understanding, admittedly, requires a little extra effort. This book's idiosyncracies remind us of our own smallness and eccentricities even as we read about the logic, function and magnificence of the Universe.

This book is an introduction to gravitational waves and related astrophysics. It provides a bridge across the range of astronomy, physics and cosmology that comes into play when trying to understand the gravitational-wave sky. Starting with Einstein's theory of gravity, chapters develop the key ideas step by step, leading up to the technology that finally caught these faint whispers from the distant universe. The second part of the book makes a direct connection with current research, introducing the relevant language and making the involved concepts less mysterious. The book is intended to work as a platform, low enough that anyone with an elementary understanding of gravitational waves can scramble onto it, but at the same time high enough to connect readers with active research - and the many exciting discoveries that are happening right now. The first part of the book introduces the key ideas, following a general overview chapter and including a brief reminder of Einstein's theory. This part can be taught as a self-contained one semester course. The second part of the book is written to work as a collection of "set pieces" with core material that can be adapted to specific lectures and additional material that provide context and depth. A range of readers may find this book useful, including graduate students, astronomers looking for basic understanding of the gravitational-wave window to the universe, researchers analysing data from gravitational-wave detectors, and nuclear and particle physicists.

This text is more conceptually and mathematically than experimentally orientated, elaborating on the underlying logic and dwelling on the subtleties and apparent paradoxes. In this updated edition additional examples and problems have been included.

Die Sprache und die Methoden der modernen Differentialgeometrie sind in der vergangenen Dekade immer mehr in die theoretische Physik eingedrungen. Was vor 15 Jahren, als das Buch zuerst als Vorlesungsskriptum herauskam, noch extravagant erschien, ist heute ein Gemeinplatz. Dies hat mich in der Ansicht gestarkt, dass die Studenten der theoretischen Physik diese Sprache lernen mussen, je eher desto besser. Schliesslich werden sie die Professoren des 21. Jahrhunderts sein und es ware absurd, wurden sie dann die Mathematik des 19. Jahrhunderts lehren. Daher habe ich in der neuen Auflage auf dieser Symbolik beharrt, einige Fehler korrigiert und ein Kapi- tel uber Eichtheorien hinzugefugt. Da es sich gezeigt hat, dass sie die fundamentalen Wechselwirkungen beschreiben und ihre Struktur zumindest auf dem klassischen Ni- veau hinreichend klar ist, scheinen sie mir zur Minimalausrustung zu gehoeren, uber die jeder Theoretiker verfugen muss. Mit Bedauern musste ich davon Abstand nehmen, die neueren Entwicklungen der Kosmologie und Kaluza-Klein-artige Theorien aufzu- nehmen, aber ich fuhlte mich an mein ursprungliches Versprechen gebunden, den Studenten keine theoretischen Spekulationen aufzuburden, fur die es keine sichere experimentelle Evidenz gibt. Vielen Physikern bin ich fur Hinweise bezuglich dieses Bandes sehr verpflichtet. Insbesondere P. Aichelburg, H. Rumpf und vor allem H. Urbantke haben zahlreiche Korrekturen und Verbesserungen angebracht. I. Dahl-Jensen sei dafur gedankt, dass sie manche nach Gefuhl angefertigte Zeichnungen mit dem Computer ins richtige Lot gebracht hat.

In den letzten Dekaden hat das Gebiet der klassischen dynamischen Systeme eine beachtliche Renaissance erlebt, und manches, was beim erst en Erscheinen dieses Kur- ses als mathematisch zu hochgestochen erschien, ist heute Gemeingut der aktiven Physiker geworden. Das Ziel der Neuauflage ist es, . dieser Entwicklung zu dienen, indem ich versucht habe, das Buch leserfreundlicher zu gestalten und Fehler auszu- merzen. Da schon die erste Auflage ffir eine einsemestrige Vorlesung reichlich beladen war, wurde neues Material nur in dem Mafie aufgenommen, als anderes weggelassen oder vereinfacht werden konnte. Eine Erweiterung muf3te jedoch das Kapitel mit dem Be- weis des KAM-Satzes erfahren, urn dem neuen Trend in der Physik Rechnung zu tragen. Dieser besteht nicht nur in der Verwendung feinerer mathematischer Hilfs- mittel, sondern auch in einer Neubewertung des Wortes "fundamental". Was frfiher als Schmutzeffekt abgetan wurde, erscheint heute als Folge eines tieferen Prinzips. Ja so- gar diese Keplerschen Gesetze, welche die Radien der Planetenbahnen bestimmen und die man als mystischen Unsinn gerne verschwieg, scheinen in Richtung einer Wahrheit zu deuten, die sich oberflachlicher Betrachtung verschlief3t: SchachteluI). g vollkomme- ner platonischer Korper ffihrt zu Verhaltnissen von Radien, die irrational sind, aber algebraischen Gleichungen niederer Ordnung genfigen. Gerade solche Irrationalzahlen lassen sich am schlechtesten durch rationale approximieren, und Bahnen mit diesem Radiusverhaltnis sind gegenfiber gegenseitigen Storungen am robustesten, da sie am wenigsten unter Resonanzeffekten leiden. In letzter Zeit wurden einige fiberraschende Resultate fiber chaotische Systeme gefunden, doch hat ten deren Beweise leider den Rahmen dieses Buches gesprengt und muf3ten unterbleiben.

"Oh, what a delightful book This is the clearest explanation of relativity available--and the most fun. It's great to have it available again. Whether or not you're a scientist, you will relish this book."--Walter Isaacson, author of "Einstein: His Life and Universe" "A clear and vivid exposition of the essential ideas and methods of the theory of relativity . . . can be warmly recommended especially to those who cannot spend too much time on the subject."--Albert Einstein "If you know high-school math, are not afraid of equations, and want to find out what Einstein really said, read Lillian Lieber's book. She will lead you through special and general relativity, helping you at every step to understand the essential equations, including tensors, with amazing clarity and conciseness. This uniquely charming book remains as vivid as ever and even more helpful, thanks to the excellent new foreward and notes by David Derbes and Robert Jantzen."--Peter Pesic, author of "Abel's Proof: An Essay on the Sources" "and Meaning of Mathmatical Unsolvability" and "Sky in a Bottle" "Does the nature of time fascinate you? Does gravity seem a mysterious subject? Are you interested in learning just what it is that Einstein actually did that made him so famous? Then this wonderful book is just the thing. I read the original 1945 edition when I was a high-school student in the 1950s, and it had a tremendous impact on me. I predict the same experience for you, or perhaps a young friend, with this new, updated edition."--Paul J. Nahin, author of "Time Machines," "Oliver Heaviside," and "Dr. Euler's Fabulous Formula"

Using "just enough mathematics to help and not to hinder the lay reader," Lillian R. Lieber provides a thorough explanation of Albert Einstein's theory of relativity. Her delightful style, in combination with her husband's charming illustrations, makes for an interesting and accessible read about one of the most celebrated ideas of all times.

Lillian R. Lieber was a professor and head of the Department of Mathematics at Long Island University. She wrote a series of lighthearted (and well-respected) math books, many of them illustrated by her husband, Hugh Gray Lieber.

David Derbes teaches physics at the University of Chicago Laboratory Schools.

Robert Jantzen is a professor of mathematics at Villanova University.

Classical electromagnetism - one of the fundamental pillars of physics - is an important topic for all types of physicists from the theoretical to the applied. The subject is widely recognized to be one of the most challenging areas of the physics curriculum, both for students to learn and for lecturers to teach. Although textbooks on electromagnetism are plentiful, hardly any are written in the question-and-answer style format adopted in this book. It contains nearly 300 worked questions and solutions in classical electromagnetism, and is based on material usually encountered during the course of a standard university physics degree. Topics covered include some of the background mathematical techniques, electrostatics, magnetostatics, elementary circuit theory, electrodynamics, electromagnetic waves and electromagnetic radiation. For the most part the book deals with the microscopic theory, although we also introduce the important subject of macroscopic electromagnetism as well. Nearly all questions end with a series of comments whose purpose is to stimulate inductive reasoning and reach various important conclusions arising from the problem. Occasionally, points of historical interest are also mentioned. Both analytical and numerical techniques are used in obtaining and analyzing solutions. All computer calculations are performed with MathematicaCO (R) and the relevant code is provided in a notebook; either in the solution or the comments.

E=mc2 is the world's most famous equation. Discover the thought process and physics behind general relativity and Einstein's contribution to science, in this authorized edition. In this collection of his seven most important essays on physics, Einstein guides his reader step-by-step through the many layers of scientific theory that formed a starting point for his discoveries. By both supporting and refuting the theories and scientific efforts of his predecessors, Einstein reveals in a clear voice the origins and meaning of such significant topics as physics and reality, the fundamentals of theoretical physics, the common language of science, the laws of science and of ethics, and an elementary derivation of the equivalence of mass and energy. This remarkable collection allows the general reader to understand not only the significance of Einstein's masterpiece, but also the brilliant mind behind it. This authorized book features a new introduction by Neil Berger and an illustrated biography of Albert Einstein, which includes rare photos and never-before-seen documents from the Albert Einstein Archives at the Hebrew University of Jerusalem.

This volume presents Einstein's writings from the final period of his work in Switzerland. Most of the material in Volume 4 documents Einstein's search for a relativistic theory of gravitation, a search that ended in Berlin in the fall of 1915 with the completion of the general theory of relativity.

Three scientific manuscripts, printed here for the first time, provide insight into Einstein's efforts to generalize his original relativity theory into a theory of gravitation. The first is a review article on the special theory of relativity. The second consists of notes that document Einstein's research on gravitation. The third manuscript contains calculations on the problem of the motion of the perihelion of Mercury. The explanation of the observed anomaly of this motion was to become one of the classical tests of general relativity. The existence of such a manuscript has not been known before now. All three of these manuscripts, along with other material in this volume, add significantly to our understanding of the creation of general relativity.

This supplementary paperback volue presents only the English translations of non-English materials and is not intended for use without the original-language documentary edition.

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.

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

Somewhere near the heart of existence, shimmers the ethereal beauty of the mystery of Time. Though seemingly familiar to us all, time harbours secrets that penetrate the very deepest levels of reality, and though we feel certain in our conviction that we're swept forth upon the crest of its never-ending flow, with Einstein's discovery of relativity came what is perhaps the most stunning realisation in the entire history of scientific thought - the wondrously breathtaking revelation that in reality, there's actually no such thing as the passage of time... How can this extraordinary truth be reconciled with the reality we so surely suppose to experience? What does it mean for the very human concerns of life and death, free will, identity, and self? What should it mean for our philosophy? And how should it inform our world view? The search for answers leads through the fantastical realm of quantum physics, and the strange parallel worlds it describes, as we discover that the answers which such questions provoke, are perhaps even more profound than the questions themselves. Buried deep within the riddle of time, lies the staggering beauty of the world. As we peel back the layers to try and sneak a glimpse into eternity, we find a light shining not only upon the nature of reality, but on the nature of ourselves...