Causality violation of Schrödinger-Newton equation: direct test on the horizon?

Abstract

We quote a definitive simple proof that neither classical stochastic dynamics nor quantum dynamics can be nonlinear if we stick to their standard statistical interpretations. A recently proposed optomechanical test of gravity's classicality versus quantumness is based on the nonlinear Schrödinger-Newton equation (SNE) which is the nonrelativistic limit of standard semiclassical gravity. While in typical cosmological applications of semiclassical gravity the predicted violation of causality is ignored, it cannot be disregarded in applications of the SNE in high sensitive laboratory tests hoped for the coming years. We reveal that, in a recently designed experiment, quantum optical monitoring of massive probes predicts fake action-at-a-distance (acausality) on a single probe already. The proposed experiment might first include the direct test of this acausality.

5pp, to appear in Journal of Physics: Conference Series (2025), proceedings of DICE2024

References in corpus (2)

• Notes on Certain Newton Gravity Mechanisms of Wave Function Localisation and Decoherence
• Semi-classical gravity phenomenology under the causal-conditional quantum measurement prescription