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arXiv:2606.20788 · Reports on Progress in Physics

Leggett–Garg inequality violation in muon g –2 experiments

Brian Batell, Morgan E. Cassidy, Kun Cheng

Published Oct 1, 2026• 0 citations
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Abstract

We present the first study of Leggett-Garg inequality (LGI) violation in polarized muon spin precession. We formulate a procedure to reconstruct temporal correlators of the longitudinal muon polarization from measured time-dependent muon decay spectra and apply it to publicly available Fermilab Muondata corresponding to approximatelybillion muon decays. Using a simplified model of the detector acceptance and efficiency, the LGI is found to be violated with a single-bin significance of, while combining neighboring bins further increases the significance. While our analysis is limited by systematic uncertainties associated with the detector modeling, a dedicated experimental analysis could reduce these uncertainties toward the statistical level,, potentially enabling one of the most precise measurements of temporal quantum correlations.

DOI
10.1088/1361-6633/aeb43f

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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.
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