Five- and eight-vector extensions of relativistic quantum theory: The preferred reference frame

Abstract

The complex quaternion approach to relativistic quantum theory is extended to include time, in the preferred cosmic reference frame, as a fifth dimension. Particle mass appears as an eigenvalue of this invariant operator. Closing the extended algebra also suggests three additional space-time components, possibly related to microscopic rotational degrees of freedom and the scale setting fundamental length. The Dirac, Klein-Gordon, Maxwell, and Einstein equations are generalized to accommodate 5- and 8-vector space-time, including gravitational curvature. The usual conserved probability density is shown to harbor fundamental difficulties.