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.

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

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.

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"?

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.

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.

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.

Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the first time these topics have been gathered into a single place and presented with an advanced graduate student audience in mind; several dozen exercises are also included. The main prerequisite for this book is a working understanding of Riemannian geometry and basic knowledge of elliptic linear partial differential equations, with only minimal prior knowledge of physics required. The second part of the book includes a short crash course on general relativity, which provides background for the study of asymptotically flat initial data sets satisfying the dominant energy condition.

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.

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.

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

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

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.

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.

"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 book describes the basic concepts of supersymmetric theories. It is aimed at theorists, experimentalists and cosmologists interested in supersymmetry, and its content is correspondingly divided into three distinct tracks of study. The topics covered include a discussion of the motivation for supersymmetry in fundamental physics, a description of the minimal supersymmetric model as well as models of grand unification and string models, a presentation of the main scenarios for supersymmetry breaking, including the concepts and results of dynamical breaking. On the astrophysics/cosmology side, the book includes discussions of supersymmetric dark matter candidates, inflation, dark energy, and the cosmological constant problem. Some very basic knowledge of quantum field theory is needed and extensive appendices (in particular an introduction to the Standard Model of fundamental interactions) allow the reader to refresh and complete their notions.

Ongoing studies in mathematical depth, and inferences from helioseismological' observations of the internal solar rotation have shown up the limitations in our knowledge of the solar interior and of our understanding of the solar dynamo, manifested in particular by the sunspot cycle, the Maunder minimum, and solar flares. This second edition retains the identical overall structure as the first edition, but is designed so as to be self-contained with the early chapters presenting the basic physics and mathematics underlying cosmical magnetohydrodynamics, followed by studies of the specific applications appropriate for a book devoted to a central area in astrophysics.
New to this edition:
Chapter 6 gives an account of the present state of dynamo theory in general, and Chapter 8 the applications to the Sun and to other Late-Type' stars with differing rotation rates -- the Solar-Stellar Connection'. The minority of the more massive Early-Type' stars that are observably magnetic are well described by theoblique rotator' model, with a quasi-steady, fossil' magnetic structure frozen' into the highly conducting, non-turbulent envelope. Chapter 9 deals with the considerable progress on the associated theoretical problems.
Chapter 7 contains new material, relevant to both Late- and Early-Type Main Sequence stars, to the evolved Red Giants, and also to contracting pre-Main Sequence stars (Chapter 10}, which show the highest degree of magnetic activity (the magneto-rotational instability, and the magneto-centrifugal winds emitted by the surrounding accretion disk'). In the earlier phases of star formation in molecular clouds (Chapters 11-12), magneto-turbulence' is emerging as the appropriate scenario for the prediction of the mass spectrum of proto-stars, and the associated formation of planetary satellites. Chapter 14 describes developments in the study of the magnetosphere of a pulsar' -- a magnetized neutron star -- consisting of spontaneously generated electron-positron pairs.

Our understanding of the physical universe underwent a revolution in the early twentieth century - evolving from the classical physics of Newton, Galileo, and Maxwell to the modern physics of relativity and quantum mechanics. The dominant figure in this revolutionary change was Albert Einstein. In a single year, 1905, Einstein produced breakthrough works in three areas of physics: on the size and the effects of atoms; on the quantization of the electromagnetic field; and on the special theory of relativity. In 1916 he produced a fourth breakthrough work, the general theory of relativity. A Student's Guide to Einstein's Major Papers focuses on Einstein's contributions, setting his major works into their historical context, and then takes the reader through the details of each paper, including the mathematics. This book helps the reader appreciate the simplicity and insightfulness of Einstein's ideas and how revolutionary his work was, and locate it in the evolution of scientific thought begun by the ancient Greek natural philosophers.

This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.
To request a copy of the Solutions Manual, visit: http: //global.oup.com/uk/academic/physics/admin/solutions

Special relativity provides the foundations of our knowledge of space and time. Without it, our understanding of the world, and its place in the universe, would be unthinkable. This book gives a concise, elementary, yet exceptionally modern, introduction to special relativity. It is a gentle yet serious 'first encounter', in that it conveys a true understanding rather than purely reports the basic facts. Only very elementary mathematical knowledge is needed to master it (basic high-school maths), yet it will leave the reader with a sound understanding of the subject. Special Relativity: A First Encounter starts with a broad historical introduction and motivation of the basic notions. The central chapters are dedicated to special relativity, mainly following Einstein's historical route. Later chapters turn to various applications in all parts of physics and everyday life. Unlike other books on the subject, the current status of the experimental foundations of special relativity is accurately reported and the experiments explained. This book will appeal to anyone wanting a introduction to the subject, as well as being background reading for students beginning a course in physics.