An experiment to detect the Discreteness of time

Abstract

To this date no empirical evidence contradicts general relativity. In particular, there is no experimental proof a quantum theory of gravity is needed. Surprisingly, it appears likely that the first such evidence would come from experiments that involve non relativistic matter and extremely weak gravitational fields. The conceptual key for this is the Planck mass, a mesoscopic mass scale, and how it relates with what remains of general relativity in the Newtonian limit: time dilation. Indeed, current technological capabilities can amplify differences in time dilation superposition that are much smaller than the smallest time interval that can be measured by an atomic clock. Inspired from recent proposals to detect non--classicality of the gravitational field, we devise and examine the feasibility of an experiment that could detect a granularity of time at the Planck scale.