  A CP violating kinematic structure is presented. The essential physical input
is to question the textbook wisdom, ``Now when a particle is at rest, one
cannot define its spin as either left- or right-handed, so phi_R(0) =
phi_L(0),'' as found, e.g., in Lewis Ryder's Quantum Field Theory, and in many
other books on the representations of the Lorentz group. It is suggested that
this equality is true only up to a phase. The demand of C, P, and T
covariances, separately, fixes this phase to be pm 1. If these conditions are
relaxed, a natural CP-violating kinematic structure emerges. Having established
a CP-violating kinematic structure, we then discuss how Planck scale physics
necessarily invokes non-commutative space-time and that such changes in the
structure of space-time will force upon us additional violations/deformations
of the CPT structure of space-time, and a violation of the principle of
equivalence via a violation of the Lorentz symmetries. The latter may carry
significant consequences for understanding the data on ultra high energy cosmic
rays.
