Classical-quantum gravity as quantum gravity in disguise

TL;DR

This paper explores whether classical-quantum hybrid theories of gravity can be embedded into fully quantum frameworks, revealing potential inconsistencies like violation of angular momentum conservation.

Contribution

It demonstrates that classical-quantum gravity models based on completely positive dynamics can be embedded into a fully quantum theory, highlighting fundamental issues.

Findings

Hybrid models can be embedded into quantum theories on larger Hilbert spaces.

A classical-quantum system can violate angular momentum conservation despite symmetry.

The study questions the fundamental consistency of classical-quantum hybrid approaches.

Abstract

Whether gravity must be quantized remains one of the biggest open problems in fundamental physics. Classical-quantum hybrid theories have recently attracted attention as a possible framework in which gravity is treated classically yet interacts consistently with quantum matter. Schemes based on completely positive dynamics satisfy most formal consistency requirements and enable a systematic treatment of quantum backreaction, but they also invite the question of whether the hybrid description is fundamental or instead an effective sector of a larger quantum theory. Here, we demonstrate that classical-quantum gravity based on completely positive dynamics admits an embedding into a fully quantum theory on an enlarged Hilbert space. As a complementary illustration, we consider a qubit interacting with a classical particle and demonstrate that the corresponding hybrid system violates angular momentum conservation despite rotational symmetry of the underlying equations of motion. This provides an explicit example of a fully closed, rotationally invariant classical-quantum system with completely positive dynamics that violates a conservation law.