Classical-quantum scattering (2412.04839v1)

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 possibleclassical-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.

• The paper examines a framework coupling quantum matter to classical fields, finding simple classical-quantum scattering models inconsistent with observed gravitational phenomena like spacecraft slingshots.
• Using an influence functional approach, the framework preserves Lorentz symmetry but indicates a loss of energy-momentum conservation in $2 o 2$ scattering due to the classical field's stochastic interaction.
• The findings challenge simple semiclassical gravity models and suggest that more complex approaches, such as variable parameters or renormalization, might be needed to reconcile classical-quantum theories with observations.

Classical-Quantum Scattering: An Examination of the Intersection of Quantum Matter and Classical Fields

Daniel Carney and Akira Matsumura's paper, "Classical-Quantum Scattering," explores the theoretical framework developed by Oppenheim and collaborators to couple quantum fields to classical, relativistic fields. This research takes a step beyond the conventional approach, where gravitational fields are assumed to be quantum entities, and seeks to test hypotheses about how quantum matter might interact with classical gravitational fields.

Key Contributions and Methodology

Carney and Matsumura begin by contextualizing gravity's non-renormalizable nature under conditions where spacetime curvature is negligible relative to the Planck scale. They acknowledge the theoretical consistency of quantized gravity in non-extreme settings. However, they take a critical approach to exploring classical alternatives, especially as experimental capabilities advance to distinguish these paradigms.

The authors focus on a classical-quantum (CQ) Yukawa interaction model, which simplifies the gravitational analogy to a Yukawa field coupling with quantum matter. Utilizing a Feynman-Vernon influence functional approach, they derive equations of motion and scattering probabilities in this CQ framework. A notable outcome of this model is the ability to compute Lorentz-covariant scattering probabilities, consistent with Oppenheim et al.'s original proposal.

Numerical Results and Implications

In this work, Carney and Matsumura explore $2 \to 2$ scattering in both non-relativistic and relativistic schemes. Their analysis reveals inconsistencies with observed phenomena in scenarios like spacecraft trajectory alteration during slingshot maneuvers, given the assumptions of constant decoherence and diffusion parameters ($D_0$ and $D_2$). These results suggest that the simplest CQ gravity models contradict empirical gravitational interactions by predicting observable deviations that contradict standard physics.

The computations boldly indicate that while the CQ framework upholds Lorentz symmetry, it eschews traditional energy-momentum conservation due to its open-system nature. This can be attributed to the classical field's stochastic dynamics and interaction with quantum matter, implying that energy and momentum could be exchanged with the environment. This serves as a departure from unitary quantum theories that preserve such conservation laws.

Theoretical and Practical Speculations

The implications of this research extend beyond gravitational theories into broader domains where classical and quantum systems overlap. While the authors provide compelling evidence against constant $D_0$ and $D_2$ configurations in realistic classical-quantum gravity models, their findings open pathways for exploring variable functional dependences in these parameters.

The work challenges existing paradigms by indicating the potential pitfalls of semiclassical gravity models, particularly where stochastic elements could imply significant deviations from anticipated Newtonian results. It also posits a fundamentally open system as a plausible framework that accommodates the inherent information exchange with a classical, noisy field.

Future Directions

Carney and Matsumura advocate for further exploration into renormalization treatments within CQ models, suggesting that additional complexity, such as field-dependent decoherence-diffusion trade-offs, could reconcile theoretical predictions with real-world observations. Their paper poses essential questions about how classical fields could be represented or treated under different scales or configurations, encouraging a deeper investigation into the interplay of classical stochastic processes and quantum mechanics.

This research represents a substantial contribution to the ongoing discourse about the integration of quantum physics with classical descriptions, especially in contexts where traditionally separate paradigms begin to intersect due to experimental advancements.