GA2015 – Lecture 5

Spacetime Algebra

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.