  Henri Poincar\'e formulated the mathematics of Lorentz transformations, known
as the Poincar\'e group. He also formulated the Poincar\'e sphere for
polarization optics. It is shown that these two mathematical instruments can be
derived from the two-by-two representations of the Lorentz group. Wigner's
little groups for internal space-time symmetries are studied in detail. While
the particle mass is a Lorentz-invariant quantity, it is shown possible to
address its variations in terms of the decoherence mechanism in polarization
optics.
