Conservation Laws and the Non-Classicality of Gravity

Abstract

We analyze the interaction between quantum matter and classical objects through a general effective channel for hybrid dynamics, subject to the fundamental constraint that no quantum correlations can be generated between the classical and quantum sectors from any initially separable state. We demonstrate that, within this hybrid framework, imposing an additive conserved observable $\langle O_{QC} \rangle = \langle O_Q \rangle + \langle O_C \rangle$ strictly forbids a classical system from altering the local observable $\langle O_Q \rangle$ of its quantum counterpart. Applying this no-go theorem to gravity, under the assumption of such hybrid dynamics, we show that if global momentum or energy is conserved, a strictly classical gravitational field cannot induce momentum or energy transfers in a quantum system. In contrast, a quantum gravitational field naturally facilitates such back-action. Drawing upon the fundamental relationship between conservation laws and the quantum properties of objects, our analysis provides a novel perspective for interpreting existing experimental observations, such as free fall, as potential indicators of the non-classicality of gravity.