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.
Highlights
Bose et al [1] and Marletto and Vedral [2, 3] have proposed an ingenious idea to amplify and observe minuscule quantum gravitational effects in a table-top experiment
The Bose-Marletto-Vedral (BMV) effect is predicted by low energy perturbative quantum gravity, and by any approach to quantum gravity consistent with this low energy expansion, including string theory and loop quantum gravity
We point out that a refinement of the BMV effect could open a window on a quantum gravitational effect that would definitely not be accounted for by non-relativistic quantum physics: time discreteness
Summary
Bose et al [1] and Marletto and Vedral [2, 3] have proposed an ingenious idea to amplify and observe minuscule quantum gravitational effects in a table-top experiment. We point out that a refinement of the BMV effect could open a window on a quantum gravitational effect that would definitely not be accounted for by non-relativistic quantum physics: time discreteness The reason this is possible is that from the point of view of general relativity the BMV set up is a delicate interference apparatus that picks up a tiny difference δτ in proper time between two quantum branches, due to gravitationallyinduced time dilatation. By directly manipulating quantum superpositions of Planck mass particles, interference as a result of gravitational attraction we can indirectly probe time at the Planck scale. This is the key theoretical observation of this paper. A prospect of experimental access to the scale of the Planck time is so interesting to deserve full attention
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