  Other than scattering problems where perturbation theory is applicable, there
are basically two ways to solve problems in physics. One is to reduce the
problem to harmonic oscillators, and the other is to formulate the problem in
terms of two-by-two matrices. If two oscillators are coupled, the problem
combines both two-by-two matrices and harmonic oscillators. This method then
becomes a powerful research tool to cover many different branches of physics.
Indeed, the concept and methodology in one branch of physics can be translated
into another through the common mathematical formalism. Coupled oscillators
provide clear illustrative examples for some of the current issues in physics,
including entanglement, decoherence, and Feynman's rest of the universe. In
addition, it is noted that the present form of quantum mechanics is largely a
physics of harmonic oscillators. Special relativity is the physics of the
Lorentz group which can be represented by the group of by two-by-two matrices
commonly called $SL(2,c)$. Thus the coupled harmonic oscillators can therefore
play the role of combining quantum mechanics with special relativity. Both Paul
A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while
they used different approaches to physical problems. Both were also keenly
interested in making quantum mechanics compatible with special relativity. It
is shown that the coupled harmonic oscillators can bridge these two different
approaches to physics.
