On the Possibility of Experimental Detection of the Discreteness of Time

Abstract

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 s) if the masses of the particles in the experiment approach the Planck mass (~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.