Doing physics with quaternions

Sweetser D.

It has been said that one reason physics succeeds is because all the terms in an equation are tensors of the same rank. This work challenges that assumption, proposing instead an integrated set of equations which are all based on the same 4-dimensional mathematical field of quaternions. Mostly this document shows in cookbook style how quaternion equations are equivalent to approaches already in use. As Feynman pointed out, “whatever we are allowed to imagine in science must be consistent with everything else we know. Fresh perspectives arise because, in essence, tensors of different rank can mix within the same equation. The four Maxwell equations become one nonhomogeneous quaternion wave equation, and the Klein-Gordon equation is part of a quaternion simple harmonic oscillator. There is hope of integrating general relativity with the rest of physics because the affine parameter naturally arises when thinking about lengths of intervals where the origin moves. Since all of the tools used are woven from the same mathematical fabric, the interrelationships become more clear to my eye. Hope you enjoy.