  A long-standing quantum-mechanical puzzle is whether the collapse of the wave
function is a real physical process or simply an epiphenomenon. This puzzle
lies at the heart of the measurement problem. One way to choose between the
alternatives is to assume that one or the other is correct and attempt to draw
physical, observable consequences which then could be empirically verified or
ruled out. As a working hypothesis, we propose simple models of collapse as a
real physical process for direct binary symmetric measurements made on one
particle. This allows one to construct irreversible unstable Schr\"odinger
equations capable of describing continuously the process of collapse induced by
the interaction of the quantum system with the measuring device. Due to unknown
initial conditions the collapse outcome remains unpredictable so no
contradictions with quantum mechanics arise. Our theoretical framework predicts
a finite time-scale of the collapse and links with experiment. Sensitive probes
of the collapse dynamics could be done using Bose-Einstein condensates,
ultracold neutrons or ultrafast optics. If confirmed, the formulation could be
relevant to the transition from quantum fluctuations to classical
inhomogeneities in early cosmology and to establishing the ultimate limits on
the speed of quantum computation and information processing.
