Leggett-Garg inequalities and decays of unstable systems

Abstract

We apply the Leggett-Garg inequalities (LGIs) to the cases of classical and quantum unstable systems. For classical systems the two assumptions of macroscopic realism and noninvasive measurements imply that the three-measurement string ${K}_{3}$ is identically equal to 1. Also, for quantum-mechanical systems, for which the two assumptions are, in general, not valid, we find that ${K}_{3}=1$ for purely exponential decays (${K}_{3}\ensuremath{\le}1$ is the general LGI). On the other hand, the necessary deviations from the exponential decay law at short and long times predicted by quantum mechanics lead to values of ${K}_{3}\ensuremath{\ne}1$. Moreover, a strict violation ${K}_{3}>1$ typically occurs at short times. Thus, we conclude that experiments in which such deviations from the exponential decay law have been observed should also have in their data violations of the LGIs.