Gravitationally induced wave-function collapse from dynamical bifurcation

TL;DR

This paper introduces a nonlinear Schrödinger framework where gravity causes wave-function collapse through a bifurcation, leading to stable localized states without stochastic noise or environmental effects.

Contribution

It presents a deterministic, gravity-induced collapse model with a bifurcation mechanism, extending Schrödinger-Newton models while avoiding their short-distance issues.

Findings

Extended quantum states become unstable beyond a critical mass.

Collapse corresponds to the dynamical selection of localized attractors.

The model predicts gravity-driven localization without stochastic noise.

Abstract

We propose an effective non-relativistic framework in which wave-function collapse emerges as a deterministic dynamical instability induced by gravitational self-interaction and regulated by short-distance repulsion. The dynamics is described by a nonlinear Schr\"odinger equation supplemented by a phenomenological repulsive sector ensuring regularity at high densities. Using a variational Gaussian ansatz, we derive an explicit effective energy functional and show that extended quantum states lose stability beyond a critical mass scale. This loss of stability is associated with a bifurcation in the reduced dynamical system governing the wave-function width, leading to the emergence of stable localized configurations. Within this picture, collapse corresponds to the dynamical selection of one of these localized attractors, driven by infinitesimal asymmetries in the initial state and occurring without stochastic noise or environmental coupling. The mechanism provides a controlled and quantitative realization of gravity-induced localization, extending Schr\"odinger--Newton-type models while avoiding their pathological short-distance behavior. Possible implications for mesoscopic systems probing the quantum-to-classical transition are briefly discussed.