Die bewegte Uhr und eine Uhr im Gravitationsfeld gehen nach. Das beruhmte Paradoxon von den Zwillingen, die sich erst voneinander entfernen und dann wieder zusammenkommen, untersuchen wir zunachst im speziell-relativistischen Gedankenexperiment, also ohne Gravitation. Der Zwilling, der seinen Bruder mit einer hoeheren Geschwindigkeit wieder einholt, bleibt am Ende der jungere, was sich mit der sog. Zwillingsungleichung einfach verifizieren lasst.Die Gravitation kann prinzipiell nicht abgeschirmt werden. Ihren Einfluss auf den Gang einer Uhr verstehen wir mit einem Gedankenexperiment von V. Muller. Wahrend die Zwillinge betragsmassig immer dieselbe Geschwindigkeit zueinander besitzen, gelangen sie aber bei ihrer Bewegung durch den Raum in die Nahe verschiedener Massen, so dass sie unterschiedlicher Gravitation ausgesetzt sind. Das kann dazu fuhren, dass am Ende der zuruckkehrende Zwilling sogar der altere ist.

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.

Mit diesem Buch taucht der Leser ein in die exotische Welt der kompakten Sterne. Der Autor ermoeglicht eine verstandliche UEbersicht uber die Entstehung, Eigenschaften und die Physik hinter astrophysikalischen Objekten wie Weisse Zwergen, Neutronensternen oder Schwarzen Loechern. Nach einer Einfuhrung zur Klassifizierung und Entwicklung von Sternen werden die notwendigen Grundlagen von Einsteins Allgemeiner Relativitatstheorie erlautert, die zum Verstandnis benoetigt werden. Anhand von konkreten astrophysikalischen Objekten wird der Leser anschliessend in die Geheimnisse der Gravitation und Physik kompakter Objekte eingefuhrt. Abgerundet wird das Thema mit einem Kapitel zur Entstehung und Detektion von Gravitationswellen, die zurzeit mit advLIGO, advVIRGO und KAGRA sehr erfolgreich detektiert werden. Der Leser erhalt Antworten auf spannende Fragen wie: Wie sollen wir uns einen Weissen Zwerg oder gar ein Schwarzes Loch vorstellen? Was bedeutet die Chandrasekhar Masse? Gibt es Schwarze Loecher wirklich in unserem Universum? Welche Bedeutung hat die Relativitatstheorie auf diesem Gebiet? Was sind Gravitationswellen? Wie entstehen Gravitationswellen beim Verschmelzen von kompakten Objekten? Wie kann man diese Wellen nachweisen? Dieses Buch eignet sich durch seine Verknupfung von Astronomie und Physik sehr gut fur Bachelor- und Masterausbildung in Physik und Astronomie, aber auch interessierte Laien koennen hier einen Einstieg in das Thema finden. Mit diesem Buch soll auch ein Beitrag zur Wurdigung der Leistung Albert Einsteins vor uber 100 Jahren geleistet werden, ohne dessen Allgemeine Relativitatstheorie das Verstandnis von kompakten Objekten nicht moeglich gewesen ware.

Gamma-ray bursts (GRBs) are the most luminous explosions in the universe, which within seconds release energy comparable to what the Sun releases in its entire lifetime. The field of GRBs has developed rapidly and matured over the past decades. Written by a leading researcher, this text presents a thorough treatment of every aspect of the physics of GRBs. It starts with an overview of the field and an introduction to GRB phenomenology. After laying out the basics of relativity, relativistic shocks, and leptonic and hadronic radiation processes, the volume covers all topics related to GRBs, including a general theoretical framework, afterglow and prompt emission models, progenitor, central engine, multi-messenger aspects (cosmic rays, neutrinos, and gravitational waves), cosmological connections, and broader impacts on fundamental physics and astrobiology. It is suitable for advanced undergraduates, graduate students, and experienced researchers in the field of GRBs and high-energy astrophysics in general.

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism (the view that reality is limited to the present) than with the B-Theory (the view that time is just another dimension like space through which things are spread out). The Moving Spotlight view, on this picture, agrees with Presentism that everything is the way it is now, it simply thinks that non-present beings are amongst the things that are now some way. Cameron argues that the Moving Spotlight theory provides the best account of truthmakers for claims about what was or will be the case, and he defends the view against a number of objections, including McTaggart's argument that the A-Theory is inconsistent, and the charge that if the A-Theory is true but presentism false then we could not know that we are present. The Moving Spotlight defends an account of the open future-that what will happen is, as yet, undetermined-Land argues that this is a better account than that available to the Growing Block theory.

Was sind die Einsteingleichungen? Kann man sie verstehen, ohne Physik studiert zu haben? Dieses Buch gibt die Antwort: Behutsam und detailreich gibt der Autor naturwissenschaftlich Interessierten einen verstandlichen Zugang zu Einsteins Relativitatstheorien. An Vorkenntnissen wird nur das vorausgesetzt, was man in der Oberstufe im Gymnasium lernt. Leser setzen sich mit den physikalischen Phanomenen und mathematischen Techniken auseinander, damit sie Einsteins Gravitationstheorie auch quantitativ verstehen koennen. Leser nahern sich somit Antworten auf Fragen rund um die Allgemeine Relativitatstheorie: Was unterscheidet Einsteins und Newtons Gravitationstheorie? Wie kann man gravitative Anziehung geometrisch beschreiben? Wie kann ein Schwarzes Loch Licht "verschlucken"?

This monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jeremie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes-or Schwarzschild spacetimes-under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.

Have you ever wondered about Time: what it is or how to discuss it? If you have, then you may have been bewildered by the many different views and opinions in many diverse fields to be found, such as physics, mathematics, philosophy, religion, history, and science fiction novels and films. This book will help you unravel fact from fiction. It provides a broad survey of many of these views, these images of time, covering historical, cultural, philosophical, biological, mathematical and physical images of time, including classical and quantum mechanics, special and general relativity and cosmology. This book gives you more than just a review of such images. It provides the reader a basis for judging the scientific soundness of these various images. It develops the reader's critical ability to distinguish Images of Time in terms of its contextual completeness. Differentiating between metaphysical images (which cannot be scientifically validated) and those that could, in principle, be put to empirical test. Showing that mathematical and classical mechanical images are more complete, and genuine quantum mechanics based images have the greatest degree of contextual completeness. Through the use of a simple algorithm, the reader can decide the classification of any of the images of time discussed in this book. These distinctions are of particular importance in this day and age, when we are flooded by a plethora of competing Images of Time. Many of these have no scientific basis or empirical support or content. This book will be of value not only to philosophers, scientists and students, but also to the general reader interested in this fundamental topic, because it introduces a method of distinguishing between science fiction and science fact.

Dieses Buch bietet eine Einfuhrung in die spezielle und allgemeine Relativitatstheorie fur Physiker, Ingenieure und andere Naturwissenschaftler, die einen Einstieg in das Thema suchen, ohne sich in zu viel neue Mathematik einzuarbeiten. Einsteins grundlegende Gleichungen werden so ohne die Hilfe von Tensoren das erste Mal nur mit Hilfe der Matrizenalgebra hergeleitet. Im 1. Kapitel wird die spezielle und im 2. Kapitel die allgemeine Relativitatstheorie behandelt. Die Schwarzschildloesung fur eine kugelfoermige Masse wird im 3. Kapitel angegeben, sowie "Schwarze Loecher" vorgestellt und untersucht. Noch erforderliche Mathematik wird entweder direkt oder im Anhang zur Verfugung gestellt.

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

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism (the view that reality is limited to the present) than with the B-Theory (the view that time is just another dimension like space through which things are spread out). The Moving Spotlight view, on this picture, agrees with Presentism that everything is the way it is now, it simply thinks that non-present beings are amongst the things that are now some way. Cameron argues that the Moving Spotlight theory provides the best account of truthmakers for claims about what was or will be the case, and he defends the view against a number of objections, including McTaggart's argument that the A-Theory is inconsistent, and the charge that if the A-Theory is true but presentism false then we could not know that we are present. The Moving Spotlight defends an account of the open future-that what will happen is, as yet, undetermined-and argues that this is a better account than that available to the Growing Block theory.

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself.

These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large.

Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.

These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole. In the first case, the singularity in our past. A discussion of the Cauchy problem for General Relativity is also included in the book.

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.

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge theory in three dimensions which describes knot and three-manifold invariants, to topological string theory, which is deeply related to Gromov-Witten invariants. This has led to some surprising relations between three-manifold geometry and enumerative geometry. This book gives the first coherent presentation of this and other related topics. After an introduction to matrix models and Chern-Simons theory, the book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implications of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory. It is written in a pedagogical style and will be useful reading for graduate students and researchers in both mathematics and physics willing to learn about these developments.

With this reader-friendly book, it doesn't take an Einstein to understand the theory of relativity and its remarkable consequences.

In clear, understandable terms, physicist Richard Wolfson explores the ideas at the heart of relativity and shows how they lead to such seeming absurdities as time travel, curved space, black holes, and new meaning for the idea of past and future. Drawing from years of teaching modern physics to nonscientists, Wolfson explains in a lively, conversational style the simple principles underlying Einstein's theory.

Relativity, Wolfson shows, gave us a new view of space and time, opening the door to questions about their flexible nature: Is the universe finite or infinite? Will it expand forever or eventually collapse in a "big crunch"? Is time travel possible? What goes on inside a black hole? How does gravity really work? These questions at the forefront of twenty-first-century physics are all rooted in the profound and sweeping vision of Albert Einstein's early twentieth-century theory. Wolfson leads his readers on an intellectual journey that culminates in a universe made almost unimaginably rich by the principles that Einstein first discovered.

"Wolfson takes the fear out of Einstein's relativity theory in this brisk piece of pop-science."—Publishers Weekly

"In a clear style, [Wolfson] spreads before his readers the historical and conceptual background of [relativity] theory, emphasizing its simplicity at every opportunity. He also offers beautifully clear explanations of such classic puzzles as the Twin Paradox. A strong overview for the lay reader."—Library Journal

"Wolfson explains in a lively, conversational style the simple priciples underlying Einstein's theory."—Astronomical Society of the Pacific

"Wolfson's account is head and shoulders above most, and is a good place to start out."—New Scientist

"With straightforward language and clear examples, Wolfson proves you don't have to be an Einstein to understand his great ideas."—Science News

"Wolfson leads the reader gently and irresistibly down the logical path that Einstein followed to arrive at his theories."—Washington Post Book World

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.

"Die Quantenheilung basiert auf den Erkenntnissen der Quantenphysik", heisst es in Internetseiten, Buchern und Broschuren zahlreicher Alternativmediziner. Hypnotiseure und Reiki-Meister folgern aus E = mc(2), dass Materie aus der Energie der Gedanken entsteht. "Alles ist vorstellbar", folgt in einem Buch uber Schamanismus aus der Quantenmechanik. Der "Relative Quantenquark" raumt mit der Vorstellung auf, dass esoterische und alternativmedizinische Konzepte mit der Relativitatstheorie und Quantenphysik zu begrunden waren. Um zwischen Grenzgebieten der Physik und Quantenunsinn unterscheiden zu koennen, nimmt das Buch die Leser mit auf eine Reise durch die Grundlagen der Quantenphysik und Relativitatstheorie und erklart, welche Hurden diese Theorien nehmen mussten, um als wissenschaftlich anerkannt zu werden. "Quarkstuckchen" zeigen reale Beispiele fur Kurioses und Unwissenschaftliches, das den Anschein erweckt, sich auf Quantenphysik und Relativitatstheorie zu stutzen. In der Neuauflage nimmt der Autor u.a. Pseudophysik, Quantenphilosophie und missgluckte Wissenschaftskommunikation unter die Lupe. Wer sich auf Einstein, Heisenberg oder Schroedinger beruft, beansprucht wissenschaftliche Seriositat und schreckt unangenehme Fragen ab. Was aber steckt wirklich hinter den Theorien der modernen Physik? Holm Hummler erlautert die wichtigsten Konzepte und zeigt auf, wo Wissenschaft nur falsch verstanden und wo sie in Scheinargumenten missbraucht wird.

This thesis describes the use of the angular distributions of the most energetic dijets in data recorded by the ATLAS experiment, at CERN's Large Hadron Collider (LHC), the goal of which is to search for phenomena beyond what the current theory of Particle Physics (the Standard Model) can describe. It also describes the deployment of the method used in ATLAS to correct for the distortions in jet energy measurements caused by additional proton-proton interactions. The thesis provides a detailed introduction to understanding jets and dijet searches at the LHC. The experiments were carried out at two record collider centre-of-mass energies (8 and 13 TeV), probing smaller distances than ever before. Across a broad momentum transfer range, the proton constituents (quarks and gluons) display the same kinematical behaviour, and thus still appear to be point-like. Data are compared to predictions corrected for next-to-leading order quantum chromodynamics (NLO QCD) as well as electroweak effects, demonstrating excellent agreement. The results are subsequently used to set limits on parameters of suggested theoretical extensions to the Standard Model (SM), including the effective coupling and mass of a Dark Matter mediator.

Das vorliegende Buch bietet eine gut verstandliche Einfuhrung in die spezielle und allgemeine Relativitatstheorie und zeigt einen Weg auf, wie beide Themen standardmassig in das Bachelorstudium der Physik integriert werden koennen. Damit richtet es sich in erster Linie an Studenten beziehungsweise Dozenten der Physik einschliesslich des Physik-Lehramtes. Dank der zahlreichen UEbungsaufgaben mit ausfuhrlich dargestellten Loesungen ist es auch zum Selbststudium geeignet, wobei lediglich Grundkenntnisse der klassischen Mechanik und der Elektrodynamik sowie der zugehoerigen mathematischen Hilfsmittel vorausgesetzt werden. Die ersten beiden Teile dieses Buches basieren auf der Vorlesung zur Relativitatstheorie, die der Autor seit 2007 regelmassig und mit grossem Erfolg fur Bachelorstudenten der Physik in Jena anbietet. Darin werden die Grundlagen der SRT (Lorentz-Transformationen, Vierervektoren, relativistische Punktmechanik) und der ART (Krummung der Raumzeit, Einstein'sche Feldgleichungen, Schwarzschild-Loesung) behandelt. Im dritten Abschnitt werden als "Erganzungen fur Fortgeschrittene" mathematische Methoden dargestellt, die unter anderem eine systematische Loesung des Randwertproblems der Einstein-Maxwell-Gleichungen fur ein stationares Schwarzes Loch gestatten. Auf diese Weise wird - erstmals in einem Lehrbuch - eine physikalische Herleitung der beruhmten Kerr-Newman-Loesung gegeben. Fur die vorliegende zweite Auflage wurde der Abschnitt uber Gravitationswellen aktualisiert und erweitert sowie eine Reihe kleiner Verbesserungen vorgenommen.

The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic. After imposing this assumption, the only freedom left, as far as the geometry is concerned, is the choice of one out of three permissible spatial geometries, and one scalar function of time. Combining the cosmological principle with an appropriate description of the matter leads to the standard models. It is worth noting that these models yield quite a successful description of our universe. However, even though the universe may, or may not, be almost spatially homogeneous and isotropic, it is clear that the cosmological principle is not exactly satisfied. This leads to several questions. The most natural one concerns stability: given initial data corresponding to an expanding model of the standard type, do small perturbations give rise to solutions that are similar to the future? Another question concerns the shape of the universe: what are the restrictions if we only assume the universe to appear almost spatially homogeneous and isotropic to every observer? The main purpose of the book is to address these questions. However, to begin with, it is necessary to develop the general theory of the Cauchy problem for the Einstein-Vlasov equations. In order to to make the results accessible to researchers who are not mathematicians, but who are familiar with general relativity, the book contains an extensive prologue putting the results into a more general context.