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Nonlinear, non-signaling Schr\"odinger equation
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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.
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Cited by 1 Pith paper
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Ruling out nonlinear modifications of quantum theory with contextuality
Nonlinear modifications of quantum theory, including Deutsch's map, Weinberg's model, and the Schrödinger-Newton equation, can convert contextuality into noncontextuality, enabling experimental falsification.
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