On the Possibility of Experimental Detection of the Discreteness of Time - Christodoulou, Marios; Rovelli, Carlo (Frontiers in Physics, 2020)
The Bose-Marletto-Vedral (BMV) experiment tests a quantum gravitational effect predicted by low energy perturbative quantum gravity. It has received attention because it may soon be within observational reach in the lab. We point out that: (i) in relativistic language, the experiment tests an interference effect between proper-time intervals; (ii) the feasibility study by Bose et al. suggests that current technology could allow to probe differences of such proper-time intervals of the order of $10^{-38}$ seconds, about twenty orders of magnitude beyond the current resolution of the best atomic clocks; (iii) the difference of proper times approaches Planck time ($10^{-44}$ seconds) if the masses of the particles in the experiment approach the Planck mass ($\sim$micrograms). This implies that the experiment might open a window on the structure of time at the Planck scale. We show that if time differences are discrete at the Planck scale ---as research in quantum gravity may suggest--- the Planckian discreteness of time would appear as quantum levels of an in principle measurable entanglement entropy.