Leggett-Garg Inequalities for testing quantum mechanics of neutrino oscillations

This project examines the quantum mechanical nature of neutrino oscillations through the Leggett-Garg Inequality (LGI), a test for temporal correlations that distinguishes quantum mechanics from classical hidden-variable theories. Using data from the MINOS experiment, which measures neutrino survival probabilities across a 735 km baseline, two methods were employed to calculate LGI violations: a conventional approach and an overlap method. While both are valid, the overlap method is theoretically more accurate as it incorporates uncertainties in energy. The conventional method identified 80 triplets with 62 LGI violations, while the overlap method identified 780 triplets with an average of 528 LGI violations. These results demonstrate significant LGI violations, affirming quantum coherence in neutrino oscillations and challenging classical macrorealism. This study advances our understanding of quantum behavior in macroscopic systems, offering robust evidence for the quantum mechanical framework of neutrino physics.