E-Book Overview
<STRONG>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.
E-Book Content
Dray
“Clear, beautiful, crystalline. Relativity is about hyperbolas in spacetime! The mathematically inclined will savor Tevian Dray’s friendly primer.” —Rudy Rucker, author of Geometry, Relativity, and the Fourth Dimension “This book is essentially a grown-up version of the masterful Spacetime Physics by Taylor and Wheeler. Anyone who teaches or intends to teach special relativity needs to own a copy.” —Niall O’Murchadha, Department of Physics, National University of Ireland
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.
K14782
Mathematics/Physics
The Geometry of Special Relativity
“This book is very clearly and simply written. The treatment is mathematically and physically sound. The diagrams are especially good. Though there are many introductory books on special relativity, this book is unique in its emphasis on hyperbolic functions and geometry. The book can stand alone as an elementary introduction to relativity. Or it can serve well as a supplement to other books, on relativity or electrodynamics. I strongly endorse it.” —David Hestenes, Professor Emeritus, Department of Physics, Arizona State University
The Geometry of Special Relativity Tevian Dray
THE GEOMETRY OF SPECIAL RELATIVITY
THE GEOMETRY OF SPECIAL RELATIVITY TEVIAN DRAY
Cover photo: Shukhov radio tower in Moscow, Russia. Designed by Vladimir Shukhov, it is a 138-meterhigh hyperboloid s