Geometric Algebra For Physicists Page

of quantum mechanics wasn't a mystery anymore. In Arthur’s equations,

"One equation," Arthur breathed. "The entire light of the heavens in one line." Geometric Algebra for Physicists

He picked up a dusty, slim volume he’d found in a London bookstall: Die Ausdehnungslehre by Hermann Grassmann, a 19th-century schoolmaster ignored by his peers. Beside it lay the works of William Kingdon Clifford. of quantum mechanics wasn't a mystery anymore

The year was 1964, and the corridors of Princeton were hushed, save for the rhythmic scratching of chalk against slate. Dr. Arthur Penhaligon sat slumped in his office, surrounded by the debris of modern physics: scattered tensors, sprawling matrices, and the jagged indices of differential forms. Beside it lay the works of William Kingdon Clifford

"Why," he whispered to the empty room, "does the universe need three different grammars to say one sentence?"

The result wasn't a number. It wasn't a vector. It was a —a directed segment of a plane.

As the sun dipped below the horizon, Arthur’s chalk began to fly. He realized that by simply adding these different types of objects together—scalars, vectors, and bivectors—he created a . This was the "Geometric Algebra" Clifford had dreamed of. Suddenly, the "imaginary"