  A nonlinear extension of Schr\"odinger's wave equation is proposed that
ensures non-signaling by keeping linear the evolution of
\textit{coordinate-diagonal} elements of the density matrix. The equation
contains a negative kinetic energy term that turns spreading of wave packets
into its opposite: collapsing, as some effective mass $M$ grows beyond a
universal critical mass, estimated to be about $\mu = 2\cdot10^{-23}~$kg; then
linear quantum kinetic energy gets negligible, which marks the
quantum-classical border. Interference of large molecules is suggested for an
experimental check of the proposed framework.
