Violation of the Leggett-Garg Inequality in Neutrino Oscillations

TL;DR

This paper demonstrates a significant violation of the Leggett-Garg inequality using neutrino oscillation data from the MINOS experiment, providing strong evidence of quantum behavior over long distances.

Contribution

It introduces a novel method of testing the Leggett-Garg inequality through neutrino oscillations at different energies, extending the experimental verification over unprecedented distances.

Findings

Over 6σ violation of the Leggett-Garg inequality observed

Longest distance tested for Leggett-Garg violation (735 km)

Supports quantum mechanics predictions in neutrino behavior

Abstract

The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than $6{\sigma}$ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.