The Special Theory of Relativity

A Mathematical Approach

Author: Farook Rahaman

Publisher: Springer

ISBN: 8132220803

Category: Science

Page: 249

View: 3907

The book expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the book discusses the relativistic effect on photons. Using a mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 14 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the book provides numerous relevant worked examples in every chapter. The book’s mathematical approach helps students in their independent study and motivates them to research the topic further.

Special Relativity for Beginners

A Textbook for Undergraduates

Author: Jrgen Freund

Publisher: World Scientific

ISBN: 981277159X

Category: Science

Page: 314

View: 9166

This book, first appearing in German in 2004 under the title Spezielle Relativit„tstheorie fr Studienanf„nger, offers access to the special theory of relativity for readers with a background in mathematics and physics comparable to a high school honors degree. All mathematical and physical competence required beyond that level is gradually developed through the book, as more advanced topics are introduced. The full tensor formalism, however, is dispensed with as it would only be a burden for the problems to be dealt with. Eventually, a substantial and comprehensive treatise on special relativity emerges which, with its gray-shaded formulary, is an invaluable reference manual for students and scientists alike.Some crucial results are derived more than once with different approaches: the Lorentz transformation in one spatial direction three times, the Doppler formula four times, the Lorentz transformation in two directions twice; also twice the unification of electric and magnetic forces, the velocity addition formula, as well as the aberration formula. Beginners will be grateful to find several routes to the goal; moreover, for a theory like relativity, it is of fundamental importance to demonstrate that it is self-contained and without contradictions.Author's website:

Special Relativity

The Foundation of Macroscopic Physics

Author: W. G. Dixon

Publisher: CUP Archive

ISBN: 9780521272414

Category: Science

Page: 272

View: 6017

The book aims to illuminate the importance of special relativity in the examination of dynamics, thermodynamics and electromagnetism.

Spezielle Relativitätstheorie für Studienanfänger

Author: Jürgen Freund

Publisher: vdf Hochschulverlag AG

ISBN: 3825228843

Category: Science

Page: 252

View: 4471

Die Spezielle Relativitätstheorie ist nichts Schwieriges und Geheimnisvolles! Studienanfänger der Natur- und Technikwissenschaften können sie mit ihren Kenntnissen der Mathematik und der Physik in vollem Umfang und bis ins Detail verstehen, wenn sie sich die Mühe machen, sich durch dieses Lehrbuch durchzuarbeiten. Zahlreiche, z.T. auch kompliziertere Problemstellungen, bis hin zum Energie-Impuls-Vierervektor und zum elektromagnetischen Feld, werden ausführlich behandelt und zeigen dem Anfänger, wie relativistische Rechnungen anzupacken sind. Auch die bekannten Paradoxa und Paradoxien werden umfassend erklärt. Für den Wissenschaftler, der mit diesem Gebiet schon vertraut ist, ist dieses Lehrbuch wegen seiner umfangreichen Formelauflistungen nicht minder wertvoll. Kurz nach dem einhundertsten Jahrestag der Speziellen Relativitätstheorie liegt hiermit ein Kompendium vor, das dieses Teilgebiet der Physik entzaubert und in die elementare Grundlagenphysik einreiht.

Discovering Relativity for Yourself

Author: Lilley

Publisher: CUP Archive

ISBN: 9780521297806

Category: Science

Page: 425

View: 6186

Discovering Relativity for yourself explains Einstein's Theory of Relativity to readers who are daunted by the standard mathematical approach to that profound theory. For twenty years Sam Lilley taught this subject to adults with no science background. Now he has written an explanation of the theory that demands no prior knowledge of mathematics or physics beyond an ability to do simple arithmetic. The first quarter of the book uses no more than arithmetic and a little simple geometry to introduce some of the main concepts of the theory, as well as discussing an impressive experimental test, which comes down strongly in its favour. When eventually further progress demands use of algebra and other mathematical techniques, these are carefully explained in a way that makes them accessible to absolute beginners, using many new and unorthodox methods.

Hyperbolic Triangle Centers

The Special Relativistic Approach

Author: A.A. Ungar

Publisher: Springer Science & Business Media

ISBN: 9789048186372

Category: Science

Page: 319

View: 5179

After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein’s special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einstein’s relativistic mass hence meshes up extraordinarily well with Minkowski’s four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperbolic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing to its novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in geometry, abstract algebra, theoretical physics and astronomy. For a fruitful reading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einstein’s special relativity in terms of its underlying hyperbolic geometry. Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in the velocity space of cosmology.

General Relativity

A Geometric Approach

Author: Malcolm Ludvigsen

Publisher: Cambridge University Press

ISBN: 9780521639767

Category: Mathematics

Page: 217

View: 8879

Solutions and hints to selected exercises

Differential Geometry and Relativity Theory

An Introduction

Author: RichardL. Faber

Publisher: Routledge

ISBN: 1351455141

Category: Mathematics

Page: 272

View: 1643

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity

Einstein's General Theory of Relativity

With Modern Applications in Cosmology

Author: Øyvind Grøn,Sigbjorn Hervik

Publisher: Springer Science & Business Media

ISBN: 0387692002

Category: Science

Page: 538

View: 5285

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.


The Special and the General Theory

Author: Albert Einstein,Robert W. Lawson,Amit Hagar

Publisher: Barnes & Noble Publishing

ISBN: 9780760759219

Category: Science

Page: 125

View: 6590

Albert Einstein's Relativity: The Special and the General Theory (1920) is a cornerstone of modern physics. Einstein intended this book for "those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus." Indeed, within the vast literature on the philosophy of space and time, Einstein's Relativity shall remain an illuminable and intelligible exposition, highly quotable as one of the most lucid presentations of the subject matter, and a launching pad for any further inquiry on the fascinating features of our universe.


Differentialformen in Analysis, Geometrie und Physik

Author: Ilka Agricola,Thomas Friedrich

Publisher: Springer-Verlag

ISBN: 3834896721

Category: Mathematics

Page: 313

View: 7273

Dieses Lehrbuch eignet sich als Fortsetzungskurs in Analysis nach den Grundvorlesungen im ersten Studienjahr. Die Vektoranalysis ist ein klassisches Teilgebiet der Mathematik mit vielfältigen Anwendungen, zum Beispiel in der Physik. Das Buch führt die Studierenden in die Welt der Differentialformen und Analysis auf Untermannigfaltigkeiten des Rn ein. Teile des Buches können auch sehr gut für Vorlesungen in Differentialgeometrie oder Mathematischer Physik verwendet werden. Der Text enthält viele ausführliche Beispiele mit vollständigem Lösungsweg, die zur Übung hilfreich sind. Zahlreiche Abbildungen veranschaulichen den Text. Am Ende jedes Kapitels befinden sich weitere Übungsaufgaben. In der ersten Auflage erschien das Buch unter dem Titel "Globale Analysis". Der Text wurde an vielen Stellen überarbeitet. Fast alle Bilder wurden neu erstellt. Inhaltliche Ergänzungen wurden u. a. in der Differentialgeometrie sowie der Elektrodynamik vorgenommen.

The General Theory of Relativity

A Mathematical Exposition

Author: Anadijiban Das,Andrew DeBenedictis

Publisher: Springer Science & Business Media

ISBN: 1461436583

Category: Science

Page: 678

View: 3769

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupled Einstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.

A Gyrovector Space Approach to Hyperbolic Geometry

Author: Abraham A. Ungar

Publisher: Morgan & Claypool Publishers

ISBN: 1598298224

Category: Mathematics

Page: 182

View: 8929

The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that is extensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry

General Relativity

Author: N.M.J. Woodhouse

Publisher: Springer Science & Business Media

ISBN: 9781846284878

Category: Science

Page: 220

View: 9897

Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.

Inside Relativity

Author: Delo E. Mook,Thomas Vargish

Publisher: Princeton University Press

ISBN: 9780691025209

Category: Science

Page: 320

View: 6894

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

Special Relativity

Author: N.M.J. Woodhouse

Publisher: Springer Science & Business Media

ISBN: 9781852334260

Category: Mathematics

Page: 196

View: 5442

This book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.

Was ist die Relativitätstheorie?

Author: Juri B. Rumer

Publisher: Vieweg+Teubner Verlag

ISBN: 9783322004451

Category: Science

Page: 64

View: 1650

Seit Albert Einstein die Relativitatstheorie geschaffen hat. sind mehr als 60 Jahre vergangen. 1m Laufe der Zeit hat sich diese Theorie. die damals vielen nur als ein paradoxes Spiel des Verstandes erschien. zu einem Eckpfeiler der Physik entwickelt. Die moderne Physik ware ohne die Relativitatstheorie fast eben so undenkbar wie ohne die Vorstellung uber Atome und Mole kule. Es ist schwierig. aile physikalischen Erscheinungen auch nur aufzuzahlen. die ohne die Relativitatstheorie nicht erklart werden konnten. Auf dieser Theorie beruhen die Konstruktion solch komplizierter Gerate wie der Beschleuniger fUr Elementar teilchen. die Berechnung von Kernreaktionen usw. Leider aber ist die Relativitatstheorie auBerhalb eines recht engen Kreises von Spezialisten sehr wenig bekannt. Sie gehort allerdings auch zu den "schwierigsten Theorien", und man kann yom Nichtphysiker den Umgang mit ihrem komplizierten ma thematischen Apparat nicht verlangen. Dessenungeachtet glauben wir aber. daB man die Grundbe griffe und Ideen dieser Theorien in einer solchen Form darstellen kann, daB sie einem genugend groBen Kreis von Lesern ver standlich werden. Wir hoffen, daB der Leser nach der Lekture unseres Buches nicht zu der Meinung kommt. die Relativitatstheorie behaupte, "alles in der Welt sei relativ". 1m Gegenteil, er wird sehen, daB' die Relativitatstheorie, wie auch jede andere echte physikalische Theorie, eine Lehre uber die objektive Wirklichkeit ist. die nicht von den Wunschen und dem Geschmack eines einzelnen abhangt. Indem man sich von den alten Vorstellungen uber Raum, Zeit und Masse befreit, wird man einen tiefen Einblick in den wirk lichen Aufbau der Welt gewinnen.