Born rule in Schroedinger-Newton scenarios of semiclassical gravity
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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BibTeX
@misc{fontana2026born,
title = {{Born rule in Schroedinger-Newton scenarios of semiclassical gravity}},
author = {Tanguy Fontana and Axelle Coulon and Giovanni Manfredi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03501},
eprint = {2610.03501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03501},
}
RIS
TY - UNPB
TI - Born rule in Schroedinger-Newton scenarios of semiclassical gravity
AU - Tanguy Fontana
AU - Axelle Coulon
AU - Giovanni Manfredi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03501
UR - https://arxiv.org/abs/2610.03501
AB - 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)].
ER -