Schr\"odinger--Newton equation with spontaneous wave function collapse

• URL: http://arxiv.org/abs/2210.15057v1
• Date: Wed, 26 Oct 2022 21:52:07 GMT
• Title: Schr\"odinger--Newton equation with spontaneous wave function collapse
• Authors: Lajos Di\'osi
• Abstract summary: Based on the assumption that the standard Schr"odinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals has survived from the nineteen-eighties. The Schr"odinger--Newton equation provides well-localized solitons for free macro-objects but lacks the mechanism how extended wave functions on solitons. We propose the Schr"odinger--Newton equation which contains the above two gravity-related modifications together.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Based on the assumption that the standard Schr\"odinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals has survived from the nineteen-eighties. The Schr\"odinger--Newton equation (1984) provides well-localized solitons for free macro-objects but lacks the mechanism how extended wave functions collapse on solitons. The gravity-related stochastic Schr\"odinger equation (1989) provides the spontaneous collapse but the resulting solitons undergo a tiny diffusion leading to an inconvenient steady increase of the kinetic energy. We propose the stochastic Schr\"odinger--Newton equation which contains the above two gravity-related modifications together. Then the wave functions of free macroscopic bodies will gradually and stochastically collapse to solitons which perform inertial motion without the momentum diffusion: conservation of momentum and energy is restored.

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