  The main purpose of this paper is to review the progress that has taken place
so far in the search for a single unifying principle that harmonizes (i) the
wave and particle natures of matter and radiation, both at the quantum and the
classical levels, on the one hand and (ii) the classical and quantum theories
of matter and radiation on the other hand. The famous paradoxes of quantum
theory, the mysterious nature of measurements in quantum theory and the
principal no-go theorems for hidden variables are first briefly reviewed. The
Koopman-von Neumann Hilbert space theory based on complex wave functions
underlying particle trajectories in classical phase space, is an important step
forward in that direction. It provides a clear and beautiful harmony of
classical waves and particles. Sudarshan has given an alternative but
equivalent formulation that shows that classical mechanics can be regarded as a
quantum theory with essentially hidden non-commuting variables. An extension of
KvNS theory to classical electrodynamics provides a sound Hilbert space
foundation to it and satisfactorily accounts for entanglement and
Bell-CHSH-like violations already observed in classical polarization optics. An
important new insight that has been obtained through these developments is that
entanglement and Bell-like inequality violations are neither unique signatures
of quantumness nor of non-locality---they are rather signatures of
non-separability. Finally, Sudarshan's proposed solution to the measurement
problem using KvNS theory for the measuring apparatus is sketched to show to
what extent wave and particles can be harmonized in quantum theory.
