Nonlinear, non-signaling Schrödinger equation
Abstract: 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.
- A similar conclusion within the Consistent Histories framework has been reached by R.B.Griffiths, arXiv:2303.13617v2
- I. Sbitnev, arXiv: 1307.6920.
- An alternative non-signaling criterion by B.S. Tsirelson (Hadronic Journal Supplement 8, 329-345 (1993)) seems to be valid but under too restricted conditions to cover the experimentally relevant situations.
- A. Bassi and K Hejazi. European Journal of Physics 36, 055027 (2015).
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