  Using complex quantum Hamilton-Jacobi formulation, a new kind of non-linear
equations is proposed that have almost classical structure and extend the
Schroedinger equation to describe the collapse of the wave function as a
finite-time process. Experimental bounds on the collapse time are reported (of
order 0.1 ms to 0.1 ps) and its convenient dimensionless measure is introduced.
This parameter helps to identify the areas where sensitive probes of the
possible collapse dynamics can be done. Examples are experiments with
Bose-Einstein condensates, ultracold neutrons or ultrafast optics.
