It is known that two coupled harmonic oscillators can support the symmetry
group as rich as O(3,3) which corresponds to the Lorentz group applicable to
three space-like and three time-like coordinates. This group contains many
subgroups, including O(3), O(3,2), O(2,1) which are already familiar to us. In
this report, we discuss the symmetry of O(1,1) which plays pivotal roles in
quantum optics and particle physics. For this one-parameter group, a
full-fledged group theory is not necessary, and we can start the discussion
from the Hamiltonian of the coupled oscillator system. It is shown first that,
from the group theoretical point of view, the squeeze state of light is a
representation of this O(1,1) group. It is then shown that the same
mathematical device supports three seemingly different ideas of Feynman, namely
the parton model, the relativistic quark model for hadrons, and the ``rest of
the universe'' in connection with the density matrix. If these three theories
are combined, they produce a covariant picture of Feynman's parton model with a
built-in decoherence mechanism.