Australia: The Land Where Time Began

A biography of the Australian continent 

Neutrino Oscillations – Violation of the Leggett-Garg Inequality

The Leggett-Garg inequality, which is an analogue of Bell’s inequality that involves correlations of measurements on a system at different times, is one of the hallmark tests of quantum mechanics against classical predictions. According to Formaggio et al. the phenomenon of neutrino oscillations should adhere to predictions of quantum-mechanics and provide an observable violation of the Leggett-Garg inequality. In this paper Formaggio et al. demonstrate how oscillation phenomena can be used to test for violations of the classical bound by carrying out measurements on neutrinos at distinct energies, instead of a single neutrino at distinct times. It is shown by a study of the data provided by the MINOS experiment that there is a greater than 6σ violation over a distance of 735 km, which represents the greatest distance over which either the Leggett-Garg inequality or Bell’s inequality has been tested.

The principle of superposition is possibly one of the counterintuitive aspects of quantum mechanics, which stipulates that an entity can exist in multiple different states simultaneously. It has been indicated by Bell and others how distinguishing between classical systems and those demonstrating quantum superposition could be shown experimentally (Bell, 1964; Kochen & Specker, 1967). Bell’s inequality concerns correlations among measurements on systems that are separated spatially. Analogous tests were developed by Leggett and Garg that concerns correlations among measurements that have been performed on a system at different times, and they extended the tests to apply to macroscopic entities (Leggett & Garg, 1985). The Leggett-Garg inequality (LGI), referred to sometimes as the “time-analogue” of Bell’s inequality, allows for a complementary test of quantum mechanics while potentially avoiding some of the difficulties that are involved in performing a test that is truly free of loop holes of Bell’s inequality (Hensen et al., 2015; Shalm et al., 2015; Giustina et al., 2015; Gallicchio, Friedman & Kaiser, 2014). See (Emary, Lambert & Nori, 2014) for a recent review.

Sources & Further reading

1. Formaggio, J.A., Kaiser, D.I., Mursky, M.M. & Weiss, T.E., 2016, Violation of Leggett- Garg Inequality in Neutrino Oscillations,  arXiv:1602.00041