If you move at high speed, time slows down, space squashes up and you get heavier. Travel fast enough and you could weigh as much as a jumbo jet, be flattened thinner than a CD without feeling a thing-and live forever As for the angles of a triangle, they do not always have to add up to 180 degrees. And then, of course, there are black holes. These are but a few of the extraordinary consequences of Einstein's theory of relativity. It is now over a hundred years since he made these discoveries, and yet the general public is still largely unaware of them. Filled with illuminating anecdotes and fascinating accounts of experiments, this book aims to introduce the interested lay person to the subject of relativity in a way which is accessible and engaging and at the same time scientifically rigorous. With relatively few mathematical equations--nothing more complicated than the Pythagoras's Theorem--this VSI packs a lot time into very little space, and for anyone who has felt intimidated by Einstein's groundbreaking theory, it offers the perfect place to start.
About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

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.

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.

This book is a considerable amplification and modernisation of the authors' earlier Essential Relativity. It aims to bring the challenge and excitement of modern relativity and cosmology at rigorous mathematical level within reach of advanced undergraduates and beginning graduates, while containing enough new material to interest the experienced lecturer.

... schon wieder ein neues Buch iiber die Spezielle Relativitatstheorie. Wozu? Es gibt doch wirklich genug gute Biicher zu diesem Thema. Das ist eigentlich auch unsere Ansicht; warum wir dann doch dieses Manuskript fertiggestellt haben, ist eine Verkettung eher ungewollter Umstande. 2uerst entstand, als Folge eines leichtsinnigen Versprechens, das ich H6rern meiner Vorlesung - nicht ahnend, wieviel Zeit die Ausarbeitung erfordern wiirde - gegeben hatte, eine Reinschrift der Vorlesungsvor- bereitung. Dieses Skript fand, wie man heute sagt., eine erstaunliche Akzeptanz, vermutlich, weil die modernen yom Fernsehen verw6hn- ten Studenten in Vorlesungen nicht mehr gerne mitschreiben, sondern Vorlesungen mehr als Unterhaltungsveranstaltungen ansehen wollen. Nachdem damit fUr uns dieser Punkt abgehakt war und die Leh- re wieder etwas hinter die Forschung zuriicktreten sollte, kam Herr Schwarz yom Verlag Vieweg und wollte das Skript als Lehrbuch her- ausbringen, was grundsatzlich natiirlich kein Problem gewesen ware, heutzutage ist ja alles cameraready im Computer. Aber Herr Schwarz, als moderner Physiker, meinte, ein heutiges Buch iiber spezielle Relati- vitatstheorie miiBte 'rf, ..v enthalten und nicht das zwar praktische, aber altmodische i von Minkowski. Da er damit im Prinzip recht hatte, ging die Formuliererei ab Kapitel 5 von neuem los.

Many people know that Einstein invented the theory of relativity, but only few have more than a superficial idea of its content. This book aims to explain the basic features of relativity in detail, emphasising the geometrical aspects by using a large number of diagrams, and assuming no knowledge of higher level mathematics.

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.

What happens when the country's greatest logician meets the century's greatest physicist? In the case of Kurt Godel and Albert Einstein the result in Godel's revolutioinary new model of the cosmos. In the 'Godel Universe' the philosophical fantasy of time travel becomes a scientific reality. For Godel, however, the reality of time travel signals the unreality of time. If Godel is right, the real meaning of the Einstein revolution had remained, for half a century, a secret. Now, half-century after Godel met Einstein, the real meaning of time travel in the Godel universe can be revealed.

The birth of a completely new branch of observational astronomy is a rare and exciting occurrence. For a long time, our theories about gravitational waves-proposed by Albert Einstein and others more than a hundred years ago-could never be fully proven, since we lacked the proper technology to do it. That all changed when, on September 14, 2015, instruments at the LIGO Observatory detected gravitational waves for the first time. This book explores the nature of gravitational waves-what they are, where they come from, why they are so significant and why nobody could prove they existed before now. Written in plain language and interspersed with additional explanatory tutorials, it will appeal to lay readers, science enthusiasts, physical science students, amateur astronomers and to professional scientists and astronomers.

CHOSEN AS A BOOK OF THE YEAR BY THE GUARDIAN, DAILY TELEGRAPH, NEW STATESMAN AND BBC SCIENCE FOCUS 'An intimate, unique, and inspiring perspective on the life and work of one of the greatest minds of our time. Filled with insight, humour, and never-before-told stories, it's a view of Stephen Hawking that few have seen and all will appreciate' James Clear, author of Atomic Habits An icon of the last fifty years, Stephen Hawking seems to encapsulate genius: not since Albert Einstein has a scientific figure held such a position in popular consciousness. In this enthralling memoir, writer and physicist Leonard Mlodinow tells the story of his friend and their collaboration, offering an intimate account of this giant of science. The two met in 2003, when Stephen asked Leonard if he would consider writing a book with him, the follow up to the bestselling A Brief History of Time. As they spent years working on a second book, The Grand Design, they forged a deep connection and Leonard gained a much better understanding of Stephen's daily life and struggles -- as well as his compassion and good humour. Together they obsessed over the perfect sentence, debated the physics, and occasionally punted on Cambridge's waterways with champagne and strawberries. In time, Leonard was able to finish Stephen's jokes, chide his sporadic mischief, and learn how the hardships of his illness helped forge that unique perspective on the universe. By weaving together their shared story with a clear-sighted portrayal of Hawking's scientific achievements, Mlodinow creates a beautiful portrait of Stephen Hawking as a brilliant, impish and generous man whose life was not only exceptional but also genuinely inspiring.

Basic to the entire theory and applications of black hole physics Global Aspects in Gravitation and Cosmology covers the topics needed to understand the current key issues in gravitation theory: cosmology and black holes. Emphasized is the basic theme that the very nature of the gravitational field is such that global features of space-time inevitably come into play whenever we try to understand and interpret this force in detail. After discussing the fundamental role played by global considerations in gravity and general relativity, Joshi points out the significant problems that remain. The key problem of which been the issue of quantum effects in strong gravity fields, an understanding of which is essential to formulate any quantum theory of gravity. This book will be beneficial to mathematicians and physicists.

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."

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.

Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and gravitational science.

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.

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.

The book is intended to serve as lecture material for courses on relativity at undergraduate level. Although there has been much written on special relativity the present book will emphasize the real applications of relativity. In addition, it will be physically designed with the use of box summaries so as to allow easy access of practical results. The book will be composed of eight chapters. Chapter 1 will give an introduction to special relativity that is the world without gravity. Implications will be presented with emphasis on time dilation and the Doppler shift as practical considerations. In Chapter 2, the four-vector representation of events will be introduced. The bulk of this chapter will deal with flat space dynamics. This will require the generalization of Newton's first and second laws. Some important astronomical applications will be discussed in Chapter 3 and in Chapter 4 some engineering applications of special relativity such as atomic clocks will be presented. Chapter 5 will be dedicated to the thorny question of gravity. The physical motivation of the theory must be examined and the geometrical interpretation presented. Chapter 6 will present astronomical applications of relativistic gravity. These include the usual solar system tests; light bending, time delay, gravitational red-shift, precession of Keplerian orbits. Chapter 7 will be dedicated to relativistic cosmology. Many of the standard cosmological concepts will be introduced, being mathematically simple but conceptually subtle. The concluding chapter will be largely dedicated to the global positioning system as an engineering problem that requires both inertial and gravitational relativity. The large interferometers designed as gravitational wave telescopes will be discussed here.