Neutrino Oscillations as a Probe of Macrorealism

The correlations between successive measurements of a quantum system can violate a family of Leggett-Garg Inequalities (LGIs) that are analogous to the violation of Bell’s inequalities of measurements performed on spatially separated quantum systems. These LGIs follow from a macrorealistic point of view, imposing that a classical system is at all times in a definite state and that a measurement can, at least in principle, leave this state undisturbed. Violations of LGIs can be probed by neutrino flavour oscillations if the correlators of consecutive flavour measurements are approximately stationary. We discuss here several improvements of the methodology used in previous analyses based on accelerator and reactor neutrino data. We argue that the strong claims of LGI violations made in previous studies are based on an unsuitable modelling of macrorealistic systems in statistical hypothesis tests. We illustrate our improved methodology via the example of the MINOS muon-neutrino survival data, where we find revised statistical evidence for violations of LGIs at the $(2-3)σ$ level, depending on macrorealistic background models.

💡 Research Summary

This paper revisits the use of neutrino flavour oscillations as a probe of macrorealism through the violation of Leggett‑Garg inequalities (LGIs). LGIs are temporal analogues of Bell inequalities, derived under three macrorealist postulates: a system possesses a definite state at all times, measurements can be performed non‑invasively, and the system’s evolution is fully determined by its initial condition. Previous neutrino analyses employed the standard LG string Kₙ = Σ_{i=1}^{n‑1} C_{i,i+1} – C_{1n}, where C_{ij}=⟨Q_i Q_j⟩ are two‑time correlators, and tested violations by counting phase‑matched combinations of L/E data. The authors argue that this approach is statistically flawed because the “classical” LG string used in earlier works never violates the LGI for physically admissible correlators; apparent violations arise only from unphysical values (|C|>1) caused by experimental uncertainties.

To overcome these shortcomings, the authors introduce two methodological improvements. First, they generalize the LG string by allowing arbitrary sign assignments σ_i = ±1, defining Kₙ(σ)=∑{i=1}^{n} σ_i C{i,i+1} and then taking K_maxₙ = max_σ Kₙ(σ). This yields the strongest possible violation for any given set of correlators. Second, they exploit the stationarity of neutrino oscillation correlators—under vacuum or uniform‑matter propagation the correlator depends only on the time (or L/E) difference: C(τ)=2P_{++}(τ)−1. They construct sequences s of time‑differences τ_i that can be split into two disjoint subsets s_a and s_b whose summed intervals match within a small tolerance ε. Each admissible sequence defines a candidate LG string; the fraction of sequences that produce K_max(s) > n−2 quantifies the LGI violation.

A critical part of the analysis is the definition of realistic macrorealistic background hypotheses. The authors replace the earlier “classical” model with two physically motivated Markovian backgrounds: (a) a fully correlated system with C(τ)=1 (Γ=0) and (b) a decorrelating system with exponential decay C(τ)=e^{−Γτ}, where Γ is fitted to the data. For each background they generate pseudo‑data sets with the same statistical uncertainties as the MINOS muon‑neutrino survival measurements, compute K_max for each set, and build the null‑distribution of LGI violations. Comparing the actual MINOS data to these distributions yields p‑values corresponding to 2–3σ evidence of LGI violation, depending on the chosen background model. Notably, the optimized sign‑assignment and the inclusion of both “1+3” and “2+2” matching schemes uncover violations that were invisible to the earlier fixed‑order analysis.

The paper concludes that earlier claims of strong LGI violations in neutrino experiments were overstated due to inappropriate statistical modeling. The new framework provides a robust, physically consistent test of macrorealism that can be applied to current and future long‑baseline experiments (e.g., DUNE, Hyper‑K). It also opens avenues for extending the method to three‑flavour oscillations and to scenarios with non‑stationary Hamiltonians. Overall, the work establishes a more reliable bridge between neutrino phenomenology and foundational questions about the quantum‑classical boundary.