Violation of the Leggett-Garg inequality in photon-graviton conversion

TL;DR

The paper addresses whether gravity can exhibit quantum behavior by examining temporal correlations in a photon–graviton system driven by a background magnetic field. It develops a quantum-mechanical framework in which a photon converts into a graviton through magnetic-field–induced mixing, and computes two-time LGI correlations to test macroscopic realism and noninvasive measurability. The analysis reveals LGI violations (K3 > 1) with a maximal value of 3/2, demonstrating nonclassical dynamics; however, the predicted effect is extremely small for realistic parameters, posing a substantial experimental challenge. The work provides a novel avenue to probe the quantum nature of gravity and motivates further studies with squeezed states or ensemble measurement strategies to improve feasibility.

Abstract

The Leggett-Garg inequality (LGI) is a temporal analogue of Bell's inequality and provides a quantitative test of the nonclassicality of a system through its violation. We analytically investigate the violation of the LGI in the context of photon-graviton conversion in a magnetic field background, motivated by its potential applications to testing the nonclassicality of gravity. When gravitational perturbations are quantized as gravitons, the conversion of an initial single photon state gives rise to a superposition of photon and graviton states. We show that the temporal correlations obtained from successive projective measurements on the photon-graviton system violate the LGI. Observation of such a violation would provide a novel avenue for probing the quantum nature of gravity.

Figures (1)

• Figure 1: The quantity $K_3$ is plotted as a function of the dimensionless parameter $\lambda \,\Delta t$, where $\lambda=\sqrt{2}B/M_{\rm P}$. The black curve shows the function $K_3$, while the red horizontal line indicates the classical upper bound $K_3=1$ imposed by the LGI. Hence, in the regions where the black curve exceeds the red line ($K_3>1$), the LGI is violated.