Nonlinear, non-signaling Schr\"odinger equation

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.