Reading the daily by arxiv today I cannot overlook a quite interesting paper that will appear soon on Physical Review Letters. This paper (see here), written by Saurya Das and Elias Vagenas, presents some relevant conclusions about the effects of gravity in quite common quantum mechanical systems. The authors rely their conclusions on an acquired result, due mostly to string theory, that a fundamental length must exist and this fundamental length modifies in a well defined way the indeterminacy principle. So, one can quantify this effect on whatever quantum mechanical system through a correcting Hamiltonian term and evaluating the effect of gravity on this system. In this way one can obtain an estimation on how relevant is the effect and how far can be an experimental measurement of this. The conclusions the authors reached are quite interesting. Of course, all of the cases imply a too small effect to be in the reach of a laboratory observation but, the most not trivial conclusion is that could exist an intermediate fundamental length that could be observed e.g. at LHC. This intermediate length should be placed between the electroweak and the Planck scale.
It is the first time that I see such estimations on quite simple quantum mechanical models and I would expect more extended analysis on a similar line. Surely, it would be striking to see in laboratory such a tiny effect correcting the Lamb shift. But, working in quantum optics, I learned that progress experimentalists are able to put out can be very impressive in a very short time. So, I would not be surprised if in some years Physical Review Letters should publish some experimental letter about this matter being the first evidence of a quantum gravity effect in a laboratory.