one can ask whether an expected consequence of Quantum Gravity, the quantum nature of spacetime at the Planck scale, might leave observable traces.

Indeed Quantum Spacetime [@DFR] would explain some aspects, as the horizon problem [@DMP], usually explained by inflation, without having to make that hypothesis; but are there effects which $only$ QST would explain?

Free classical electromagnetism on Quantum Spacetime would be no longer free: the electromagnetic field and potential $F, A$ would fulfill $$\partial_\mu F^{\mu \nu}  -i [A_{\mu}, F^{\mu \nu}]  =  0,$$ where the commutator would not vanish due to the quantum nature of spacetime.

This fact was noticed [@DF] at the very beginning of searches on Quantum Spacetime, as well as its first consequence: plane waves would be still solutions, but their superpositions would not in general, they would loose energy in favor of mysterious massive modes (see also [@Z]).

A naive computation showed that, by that mechanism, a monochromatic wave train passing through a partially reflecting mirror should loose, in favor of those ghost modes, a fraction of its energy - a very small fraction, unfortunately, of the order of one part in $10^{-130}$ [@DF]. This looked too small to be worth a more accurate computation.

