Classical-quantum scattering

TL;DR

This paper examines a framework for modeling quantum fields coupled to classical stochastic fields, demonstrating Lorentz-covariant scattering calculations and revealing inconsistencies with classical gravity predictions in a simplified model.

Contribution

It provides a detailed analysis of a proposed classical-quantum scattering framework, showing its Lorentz covariance and probability conservation at tree level, and evaluates its implications for gravity coupling.

Findings

Scattering probabilities are Lorentz-covariant and probability-conserving at tree level.

Classical-quantum gravity predictions are inconsistent with observed gravitational phenomena.

The framework offers insights into coupling quantum matter with classical gravity models.

Abstract

We analyze the framework recently proposed by Oppenheim et al. to model relativistic quantum fields coupled to relativistic, classical, stochastic fields (in particular, as a model of quantum matter coupled to ``classical gravity''). Perhaps surprisingly, we find that we can define and calculate scattering probabilities which are Lorentz-covariant and conserve total probability, at least at tree level. As a concrete example, we analyze $2 \to 2$ scattering of quantum matter mediated by a classical Yukawa field. Mapping this to a gravitational coupling in the non-relativistic limit, and assuming that we can treat large objects as point masses, we find that the simplest possible ``classical-quantum'' gravity theory constructed this way gives predictions for $2 \to 2$ gravitational scattering which are inconsistent with simple observations of, e.g., spacecraft undergoing slingshot maneuvers. We comment on lessons learned for attempts to couple quantum matter to ``non-quantum'' gravity, or more generally, for attempts to couple relativistic quantum and classical systems.