Spacetime physics with geometric algebra

This is an introduction to spacetime algebra (STA) as a unified mathematical language for physics. STA simplifies, extends, and integrates the mathematical methods of classical, relativistic, and quantum physics while elucidating geometric structure of the theory. For example, STA provides a single, matrix-free spinor method for rotational dynamics with applications from classical rigid body mechanics to relativistic quantum theory—thus significantly reducing the mathematical and conceptual barriers between classical and quantum mechanics. The entire physics curriculum can be unified and simplified by adopting STA as the standard mathematical language. This would enable early infusion of spacetime physics and give it the prominent place it deserves in the curriculum.