Quantum Gravity can be considered as the "Holy Grail" of modern
physics.  Gravity was the first force to be discovered and formalized
by Newton but it is the latest to be quantized. Up to now there is no
theory of quantum gravity. Strings, supergravity, loop quantum gravity
are only sketches of the basic fluctuations of space and time
occurring down to the Planck scale with the aim of paving the way for
the unification of the fundamental forces.

One phenomenological approach is that of determining the magnitude of
space and time quantum fluctuations to set the basis for a future
quantization.  Here we estimate the upper limit of quantum gravity
fluctuations from the analysis of the energy fluctuations of photons
from the farthest quasars imaged by HST. We find no appreciable
fluctuations due to quantum gravity.  Most of quantum gravity models,
based on the so-called holographic scenario and random walk models are
ruled out.