John De Pillis

Illustrated Special Relativity Through Its Paradoxes: a Fusion of Linear Algebra, Graphics, and Reality (Spectrum) John De Pillis

This illustrated, full-color work shows that linear algebra is a natural language for special relativity. Requiring a minimum of expertise beyond basic matrix theory, the authors use full-color illustrations to introduce inertial frames and Minkowski diagrams that explain the nature of simultaneity, why faster-than-light travel is impossible, and the proper way to add velocities. We resolve the twin paradox, the train-in-tunnel paradox, the pea-shooter paradox and the lesser-known accommodating universe paradox and the bug-rivet paradox that shows how rigidity is incompatible with special relativity. Since Einstein, in his seminal 1905 paper introducing the theory of special relativity, acknowledged his debt to Clerk Maxwell, we fully develop Maxwell's four equations that unify the theories of electricity, optics, and magnetism. These equations also lead to a simple calculation for the frame-independent speed of electromagnetic waves in a vacuum. (Maxwell himself was unaware that light was a special case of electromagnetic waves.) Using relativistic properties of speeds, a straightforward proof of E=mc2 is given. Several chapters are devoted to early experiments of Roemer, Fizeau, and de Sitter in their efforts to measure the speed of light along with the Michelson-Morley experiment abolishing the necessity of a universal aether. The exposition is thorough, but not overly technical, and bountifully illustrated by cartoons. Supplemental interactive animations are found at Special-Relativity-Illustrated.com. This book is be suitable for a one-semester general-education introduction to special relativity. It is especially well-suited to self-study by interested laypersons or use as a supplement to a more traditional text.