  The fundamental equation that describes polarization mode dispersion does not
have a mathematically correct and convincing proof. This problem stems from the
fact that Poincare's sphere, where Stokes vectors are represented, is just a
manifold (a representation space) devoid of metric. In this "space" orthogonal
vectors are antiparallel and, therefore, it is hard to justify the use of a
Euclidean metric. However, if one realizes that in Poincare's sphere only
three-dimensional rotations are represented, a Euclidean pseudo-scalar product
can be defined and a mathematically correct proof for the polarization mode
dispersion can be given.
