Schrödinger--Newton equation with spontaneous wave function collapse

Abstract

Based on the assumption that the standard Schrödinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals has survived from the nineteen-eighties. The Schrödinger--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 Schrödinger 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 Schrödinger--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.

7pp

References in corpus (4)

• Underground test of gravity-related wave function collapse
• Notes on Certain Newton Gravity Mechanisms of Wave Function Localisation and Decoherence
• Stochastic extensions of the regularized Schrödinger-Newton equation
• Three little paradoxes: making sense of semiclassical gravity

Cited by in corpus (2)

• Probing the Schroedinger-Newton equation in a Stern-Gerlach interferometer
• Spontaneous wave function collapse from non-local gravitational self-energy