  Students encounter harmonic-oscillator models in many aspects of basic
physics, within widely-varying theoretical contexts. Here we highlight the
interconnections and varying points of view. We start with the classical
mechanics of masses coupled by springs and trace how the same essential systems
are reanalyzed in the unretarded van der Waals interactions between dipole
oscillators within classical and quantum theories. We note how classical
mechanical ideas from kinetic theory lead to energy equipartition which
determines the high-temperature van der Waals forces of atoms and molecules
modeled as dipole oscillators. In this case, colliding heat-bath particles can
be regarded as providing local hidden variables for the statistical mechanical
behavior of the oscillators. Next we note how relativistic classical
electrodynamical ideas conflict with the assumptions of nonrelativistic
classical statistical mechanics. Classical electrodynamics which includes
classical zero-point radiation leads to van der Waals forces between dipole
oscillators, and these classical forces agree at all temperatures with the
forces derived from quantum theory. However, the classical theory providing
this agreement is not a local theory, but rather a non-local hidden-variables
theory. The classical theory can be regarded as involving hidden variables in
the random phases of the plane waves spreading throughout space which provide
the source-free random radiation.
