Quantum Backreaction on ``Classical'' Variables

TL;DR

This paper develops a consistent formalism for coupling classical and quantum variables via coupled Hamilton-Heisenberg equations, allowing the calculation of quantum backreaction on classical systems, with applications to gravity and matter interactions.

Contribution

It introduces a variational principle-based method to couple quasiclassical and quantum variables, enabling the study of backreaction effects in a unified framework.

Findings

Provides a formalism for quantum backreaction on classical variables.

Derives coupled Hamilton-Heisenberg equations from a variational principle.

Suggests a candidate theory of gravity coupled to quantized matter without quantizing gravity.

Abstract

A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become entangled with the quantum variables with the result that the value of the quasiclassical variables depends on the quantum state. This provides a formalism to compute the backreaction of any quantum system on a quasiclassical one. In particular, it leads to a natural candidate for a theory of gravity coupled to quantized matter in which the gravitational field is not quantized.