  It is proposed that the paradox of wave-particle duality in quantum mechanics
may be resolved using a physical picture analogous to magnetic domains. Within
this picture, a quantum particle represents a coherent region of a quantum wave
with characteristic total energy, momentum, and spin. The dynamics of such a
state are described by the usual linear quantum wave equations. But the
coherence is maintained by a nonlinear self-interaction term that is evident
only during transitions from one quantum state to another. This is analogous to
the self-organizing property of domains in a ferromagnetic material, in which a
single domain may appear as a stable macro-particle, but with rapid transitions
between different domain configurations also possible. For the quantum case,
this implies that the "collapse of the wave function" is a real dynamical
physical process that occurs continuously in spacetime. This picture may also
permit the resolution of apparent paradoxes associated with quantum measurement
and entangled states.
