In this lecture we introduce the geometric algebra of Minkowski spacetime, or spacetime algebra. Historically spacetime algebra drove much of the early interest in geometric algebra, and this importance was recently celebrated in a new edition of David Hestenes’ book of the same name, first published 50 years ago.
Spacetime algebra simplifies many of the calculations and concepts associated with special relativity. It provides a clean definition of relative velocity, and quickly derives results for velocity addition and red-shift. Lorentz transformations are generated by rotors, and the rotor dynamics framework introduced for rigid body mechanics provides a simple equation for motion in an electromagnetic field.