Amplification of Nonlocal Effects in Nonlinear Quantum Mechanics by Extreme Localization

TL;DR

This paper explores how nonlinear quantum mechanics, especially the Doebner-Goldin nonlinearity, amplifies nonlocal effects under extreme localization, potentially impacting our understanding of Planck-scale physics.

Contribution

It demonstrates that nonlinear quantum effects can be significantly amplified at extreme localization, offering new insights into quantum geometry and Planck-scale phenomena.

Findings

Nonlocal signaling effects are amplified by the Doebner-Goldin nonlinearity.

Amplification occurs under extreme localization conditions.

Implications for quantum geometry and Planck-scale physics.

Abstract

Due to its connection to the diffeomorphism group, nonlinear quantum mechanics may play an important role in quantum geometry. The Doebner-Goldin nonlinearity (arising from representations of the diffeomorphism group) amplifies nonlocal signaling effects under extreme localization, suggesting that even if greatly suppressed at low energies, such effects may be significant at the Planck scale. This offers new perspectives on Planck-scale physics.