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arXiv · 2610.03501

Born rule in Schroedinger-Newton scenarios of semiclassical gravity

Tanguy Fontana·Axelle Coulon·Giovanni Manfredi
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Abstract

We investigate dynamical relaxation to the Born rule in a semiclassical gravity model described by the Schrödinger-Newton equations. Using a Gaussian variational solution for the self-gravitating wave packet, combined with Nelson's stochastic representation of quantum dynamics, we track the evolution of particle ensembles whose initial probability distribution differs from $|Ψ|^2$. Relaxation to the Born rule ("quantum equilibrium") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].

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Tanguy Fontana, Axelle Coulon, Giovanni Manfredi. 2026-10-02. Born rule in Schroedinger-Newton scenarios of semiclassical gravity. https://arxiv.org/abs/2610.03501

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