A spinning top rotates, but its axis remains invisible. That's roughly how a muon behaves — a heavy cousin of the electron. Its spin (intrinsic rotation) changes direction, and the only way to infer this is by how the muon decays. In a new experiment, scientists tracked the spins of about 10 billion muons using data from the Muon g-2 facility at Fermilab.
They tested the Leggett-Garg inequality — a rule that holds for ordinary objects but is violated in the quantum world. If the muon behaved like a classical top, its spin at different times would obey this inequality. The measurements showed the opposite: the inequality is violated with a confidence of 5.5 sigma. It's as if a tossed coin, mid-flight, landed both heads and tails simultaneously.
The main challenge was to reconstruct hidden spin correlations from decay data. This is akin to reconstructing the trajectory of an invisible pendulum from the shadows it casts. The scientists built a simplified model of the detector and saw a clear violation signal. For now, precision is limited by systematic uncertainties, but future experiments could reduce them to the statistical level — about 0.1%. That would make this one of the most precise measurements of quantum correlations in time.
as written by the authors arXiv:2606.20788
We present the first study of Leggett-Garg inequality 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 Muon $$g-2$$ data corresponding to approximately $$10$$ billion muon decays. Using a simplified model of the detector acceptance and efficiency, the Leggett-Garg inequality is found to be violated with a single-bin significance of $$5.5\sigma$$, 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, $$\mathcal{O}(10^{-3})$$, potentially enabling one of the most precise measurements of temporal quantum correlations.
A muon lives only 2.2 microseconds, but in that time its spin manages to perform numerous quantum "somersaults," which the scientists captured.
In Carl Sagan's novel "Contact," muons are used to transmit hidden messages, exploiting their quantum properties.