The Geometry of Special Relativity


Author: Tevian Dray
Publisher: CRC Press
ISBN: 1466510471
Category: Mathematics
Page: 150
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The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas. The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein’s general theory of relativity. The book also briefly describes the further steps leading to Einstein’s general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function.

The Geometry of Special Relativity - a Concise Course


Author: Norbert Dragon
Publisher: Springer Science & Business Media
ISBN: 3642283292
Category: Science
Page: 143
View: 6833

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In this concise primer it is shown that, with simple diagrams, the phenomena of time dilatation, length contraction and Lorentz transformations can be deduced from the fact that in a vacuum one cannot distinguish physically straight and uniform motion from rest, and that the speed of light does not depend on the speed of either the source or the observer. The text proceeds to derive the important results of relativistic physics and to resolve its apparent paradoxes. A short introduction into the covariant formulation of electrodynamics is also given. This publication addresses, in particular, students of physics and mathematics in their final undergraduate year.

The Geometry of Spacetime

An Introduction to Special and General Relativity
Author: James J. Callahan
Publisher: Springer Science & Business Media
ISBN: 1475767366
Category: Science
Page: 454
View: 3614

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Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

General Relativity Without Calculus

A Concise Introduction to the Geometry of Relativity
Author: Jose Natario
Publisher: Springer Science & Business Media
ISBN: 9783642214523
Category: Science
Page: 128
View: 7533

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“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.

The Geometry of Minkowski Spacetime

An Introduction to the Mathematics of the Special Theory of Relativity
Author: Gregory L. Naber
Publisher: Springer Science & Business Media
ISBN: 1441978380
Category: Mathematics
Page: 324
View: 2430

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This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: “... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993) “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993) “... his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993)

Special Relativity

From Einstein to Strings
Author: Patricia M. Schwarz,John H. Schwarz
Publisher: Cambridge University Press
ISBN: 9781139449502
Category: Science
Page: 376
View: 5634

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This book provides a thorough introduction to Einstein's special theory of relativity, suitable for anyone with a minimum of one year's university physics with calculus. It is divided into fundamental and advanced topics. The first section starts by recalling the Pythagorean rule and its relation to the geometry of space, then covers every aspect of special relativity, including the history. The second section covers the impact of relativity in quantum theory, with an introduction to relativistic quantum mechanics and quantum field theory. It also goes over the group theory of the Lorentz group, a simple introduction to supersymmetry, and ends with cutting-edge topics such as general relativity, the standard model of elementary particles and its extensions, superstring theory, and a survey of important unsolved problems. Each chapter comes with a set of exercises. The book is accompanied by a CD-ROM illustrating, through interactive animation, classic problems in relativity involving motion.

The Special Theory of Relativity


Author: Dennis Morris
Publisher: Stylus Publishing, LLC
ISBN: 1944534385
Category: Science
Page: 314
View: 6934

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This book concentrates on presenting the theory of special relativity as the geometry of space-time. The presentation is straightforward, complete and reader-friendly, with explanatory asides, that give historical context and links with other branches of physics and mathematics. The first four chapters give a complete description of the special theory and the nature of space and time, with the minimum use of mathematics. The mathematics necessary is introduced in the following five chapters, with the final fifteen chapters devoted to a comprehensive and detailed exposition of Einstein’s special relativity. Features: * Concentrates on presenting the theory of special relativity as the geometry of space-time * The presentation is straightforward, complete and reader-friendly, with explanatory asides, which give historical context and links with other branches of physics and mathematics

Differential Geometry and Relativity Theory

An Introduction
Author: Richard L. Faber
Publisher: CRC Press
ISBN: 9780824717490
Category: Mathematics
Page: 272
View: 7182

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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

Differential Forms and the Geometry of General Relativity


Author: Tevian Dray
Publisher: CRC Press
ISBN: 1466510005
Category: Mathematics
Page: 321
View: 4461

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Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.

Relativity

An Introduction to Spacetime Physics
Author: Steve Adams
Publisher: CRC Press
ISBN: 9780203018606
Category: Science
Page: 296
View: 4049

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Provides the essential principles and results of special relativity as required by undergraduates. The text uses a geometric interpretation of space-time so that a general theory is seen as a natural extension of the special theory. Although most results are derived from first principles, complex and distracting mathematics is avoided and all mathematical steps and formulae are fully explained and interpreted, often with explanatory diagrams.; The emphasis throughout the text is on understanding the physics of relativity. The structure of the book is designed to allow students of different courses to choose their own route through the short self-contained sections in each chapter. The latter part of the book shows how Einstein's theory of gravity is central to unraveling fundamental questions of cosmology.

Geometry of Minkowski Space-Time


Author: Francesco Catoni,Dino Boccaletti,Roberto Cannata,Vincenzo Catoni,Paolo Zampetti
Publisher: Springer Science & Business Media
ISBN: 9783642179778
Category: Science
Page: 116
View: 4882

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This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions. The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.

General Relativity


Author: N.M.J. Woodhouse
Publisher: Springer Science & Business Media
ISBN: 9781846284878
Category: Science
Page: 220
View: 9372

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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.

Analytic Hyperbolic Geometry and Albert Einstein's Special Theory of Relativity


Author: Abraham A. Ungar
Publisher: World Scientific
ISBN: 9812772308
Category: Mathematics
Page: 628
View: 428

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This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors . Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative . The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami-Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, MAbius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincar(r) ball model of hyperbolic geometry. In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. The novel relativistic resultant mass of the system, concentrated at the relativistic center of mass, dictates the validity of the dark matter and the dark energy that were introduced by cosmologists as ad hoc postulates to explain cosmological observations about missing gravitational force and late-time cosmic accelerated expansion. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry. Sample Chapter(s). Chapter 1: Introduction (145 KB). Contents: Gyrogroups; Gyrocommutative Gyrogroups; Gyrogroup Extension; Gyrovectors and Cogyrovectors; Gyrovector Spaces; Rudiments of Differential Geometry; Gyrotrigonometry; Bloch Gyrovector of Quantum Information and Computation; Special Theory of Relativity: The Analytic Hyperbolic Geometric Viewpoint; Relativistic Gyrotrigonometry; Stellar and Particle Aberration. Readership: Undergraduates, graduate students, researchers and academics in geometry, algebra, mathematical physics, theoretical physics and astronomy."

Die Relativitätstheorie Einsteins


Author: Max Born
Publisher: Springer-Verlag
ISBN: 3642554598
Category: Science
Page: 501
View: 356

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Dieses Buch ist bis heute eine der populärsten Darstellungen der Relativitätstheorie geblieben. In der vorliegenden Version haben J. Ehlers und M. Pössel vom Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) in Golm/Potsdam den Bornschen Text kommentiert und einen den anschaulichen, aber präzisen Stil Borns wahrendes, umfangreiches Ergänzungskapitel hinzugefügt, das die stürmische Entwicklung der Relativiatätstheorie bis hin zu unseren Tagen nachzeichnet. Eingegangen wird auf Gravitationswellen und Schwarze Löcher, auf neuere Entwicklungen der Kosmologie, auf Ansätze zu einer Theorie der Quantengravitation und auf die zahlreichen raffinierten Experimente, welche die Gültigkeit der Einsteinschen Theorie mit immer größerer Genauigkeit bestätigt haben. Damit bleibt dieses Buch nach wie vor einer der unmittelbarsten Zugänge zur Relativitätstheorie für alle die sich für eine über das rein populärwissenschaftliche hinausgehende Einführung interessieren.

Relativity

An Introduction to the Special Theory
Author: Asghar Qadir
Publisher: World Scientific
ISBN: 9789971506124
Category: Science
Page: 128
View: 7561

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The most important feature in this book is the simple presentation with details of calculations. It is very easy to follow. Fairly sophisticated calculations are developed very rapidly. The presentation is logical and the detailed coverage makes this book very readable and useful. The contents develop Relativity as a modern theory of motion, starting by placing it in historical perspective and proceeding to show its logical necessity. The development of the Lorentz transformation is given using only one assumption rather than two. Right away in Chapter 3, geometry as required in Special Relativity for extension to General Relativity is introduced. This enables the use of the four-vector formalism of Minkowski. By the end of Chapter 4, the general Lorentz transformations for three-dimensional motion and their relation to four-dimensional boosts have already been explained. In Chapter 5 applications of relevance in Physics are provided. After a brief introduction to elementary electromagnetic theory, it is reformulated as a theory in four-dimensions using tensors in Chapter 6. Finally in Chapter 7, the theory is extended to deal with accelerated motion as ?corrections? to Special Relativity.

Einstein's Theory of Relativity


Author: Max Born
Publisher: Courier Corporation
ISBN: 0486142124
Category: Science
Page: 400
View: 4042

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Semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, more) and of Einstein's theories of relativity.

Special Relativity

The Foundation of Macroscopic Physics
Author: W. G. Dixon
Publisher: CUP Archive
ISBN: 9780521272414
Category: Science
Page: 272
View: 2704

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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: 8389

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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.

Space, Time, and Spacetime


Author: Lawrence Sklar
Publisher: Univ of California Press
ISBN: 9780520031746
Category: Philosophy
Page: 423
View: 1658

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In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and time--problems that require for their resolution the resources of philosophy and of physics. The overall issues explored are our knowledge of the geometry of the world, the existence of spacetime as an entity over and above the material objects of the world, the relation between temporal order and causal order, and the problem of the direction of time. Without neglecting the most subtle philosophical points or the most advanced contributions of contemporary physics, the author has taken pains to make his explorations intelligible to the reader with no advanced training in physics, mathematics, or philosophy. The arguments are set forth step-by-step, beginning from first principles; and the philosophical discussions are supplemented in detail by nontechnical expositions of crucial features of physical theories.

Relativity in Rotating Frames

Relativistic Physics in Rotating Reference Frames
Author: G. Rizzi,M.L. Ruggiero
Publisher: Springer Science & Business Media
ISBN: 9401705283
Category: Science
Page: 456
View: 1295

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Even if the subject is a long-standing one, this is the first monograph on this field. On the one hand, this book is intended to give a rather wide review on this field, both in a historical and pedagogical perspective; on the other hand, it aims at critically re-examining and discussing the most controversial issues. For instance, according to some authors the celebrated Sagnac effect is a disproval of the theory of relativity applied to rotating frames; according to others, it is an astonishing experimental evidence of the relativistic theory. In order to give the reader a deeper insight into this research field, the contributing authors discuss their opinions on the main subjects in an enthralling virtual round table: in this way, the reader can get a direct comparison of the various viewpoints on the most controversial and interesting topics. This is particularly expedient, since the differences in the various approaches are often based upon subtleties that can be understood only by a direct comparison of the underlying hypotheses.