  The distribution of noncollinear magnetism in an electronic system provides
information about the kinetic energy as well as some kinetic energy densities.
Two different everywhere-positive kinetic densities related to the
Schr\"odinger--Pauli Hamiltonian are considered. For one-electron systems
described by a single Pauli spinor, the electron density, spin density and
current density completely determines these kinetic energy densities. For
many-electron systems, lower bounds on the kinetic energy densities are proved.
These results generalize a lower bound due to von Weizs\"acker, which is based
on the electron density alone and plays an important role in density functional
theory. The results have applications in extensions of density functional
theory that incorporate noncollinear spin densities and current densities.
