This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.

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.

This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.

Early in this century, it was shown that the new non-Newtonian physics -- known as Einstein's Special Theory of Relativity -- rested on a new, non-Euclidean geometry, which incorporated time and space into a unified "chronogeometric" structure. This high-level study elucidates the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phase of Relativity. After a discussion of Newtonian principles and 19th-century views on electrodynamics and the aether, the author offers illuminating expositions of Einstein's electrodynamics of moving bodies, Minkowski spacetime, Einstein's quest for a theory of gravity, gravitational geometry, the concept of simultaneity, time and causality and other topics. An important Appendix -- designed to define spacetime curvature -- considers differentiable manifolds, fiber bundles, linear connections and useful formulae. Relativity continues to be a major focus of interest for physicists, mathematicians and philosophers of science. This highly regarded work offers them a rich, "historico-critical" exposition -- emphasizing geometrical ideas -- of the elements of the Special and General Theory of Relativity.

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.

Einstein's Special Theory of Relativity, first published in 1905, radically changed our understanding of the world. Familiar notions of space and time and energy were turned on their head, and our struggle with Einstein's counterintuitive explanation of these concepts was under way. The task is no easier today than it was a hundred years ago, but in this book Sander Bais has found an original and uniquely effective way to convey the fundamental ideas of Einstein's Special Theory. Bais's previous book, The Equations, was widely read and roundly praised for its clear and commonsense explanation of the math in physics. Very Special Relativity brings the same accessible approach to Einstein's theory. Using a series of easy-to-follow diagrams and employing only elementary high school geometry, Bais conducts readers through the quirks and quandaries of such fundamental concepts as simultaneity, causality, and time dilation. The diagrams also illustrate the difference between the Newtonian view, in which time was universal, and the Einsteinian, in which the speed of light is universal. Following Bais's straightforward sequence of simple, commonsense arguments, readers can tinker with the theory and its great paradoxes and, finally, arrive at a truly deep understanding of Einstein's interpretation of space and time. An intellectual journey into the heart of the Special Theory, the book offers an intimate look at the terms and ideas that define our reality.

An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.

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

Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

“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.