The Special Theory of Relativity

A Mathematical Approach
Author: Farook Rahaman
Publisher: Springer
ISBN: 8132220803
Category: Science
Page: 249
View: 8361

Continue Reading →

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.

Relativity

The Special and General Theory
Author: Albert Einstein,Robert W. Lawson
Publisher: Courier Corporation
ISBN: 9780486417141
Category: Science
Page: 168
View: 2155

Continue Reading →

This book contains the great physicist's own explanation of both the special and general theories of relativity. Written for readers interested in the theory but not conversant with the mathematical apparatus of theoretical physics, it presents the ideas in their simplest, most intelligible form.

Special Relativity for Beginners

A Textbook for Undergraduates
Author: Jrgen Freund
Publisher: World Scientific
ISBN: 981277159X
Category: Science
Page: 314
View: 9615

Continue Reading →

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: www.relativity.ch.

Special Relativity


Author: Nicholas M.J. Woodhouse
Publisher: Springer-Verlag
ISBN: 3540466762
Category: Science
Page: 88
View: 5621

Continue Reading →

Special Relativity

The Foundation of Macroscopic Physics
Author: W. G. Dixon
Publisher: CUP Archive
ISBN: 9780521272414
Category: Science
Page: 272
View: 3353

Continue Reading →

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

Discovering Relativity for Yourself


Author: Lilley
Publisher: CUP Archive
ISBN: 9780521297806
Category: Science
Page: 425
View: 4807

Continue Reading →

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: 4384

Continue Reading →

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: 6740

Continue Reading →

Solutions and hints to selected exercises

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: 8111

Continue Reading →

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.

Very Special Relativity

An Illustrated Guide
Author: Sander Bais
Publisher: Harvard University Press
ISBN: 9780674026117
Category: Mathematics
Page: 120
View: 4207

Continue Reading →

Using a series of easy-to-follow diagrams and elementary geometry, this visual guide to Einstein's Theory of Relativity explores fundamental concepts such as simultaneity, causality, and time dilation.

Differential Geometry and Relativity Theory

An Introduction
Author: RichardL. Faber
Publisher: Routledge
ISBN: 1351455141
Category: Mathematics
Page: 272
View: 6886

Continue Reading →

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

Vektoranalysis

Differentialformen in Analysis, Geometrie und Physik
Author: Ilka Agricola,Thomas Friedrich
Publisher: Springer-Verlag
ISBN: 3834896721
Category: Mathematics
Page: 313
View: 9459

Continue Reading →

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: 8193

Continue Reading →

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: 7725

Continue Reading →

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: 2952

Continue Reading →

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: 308

Continue Reading →

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: 4578

Continue Reading →

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.