  The space-time metric is widely believed to be subject to stochastic
fluctuations induced by quantum gravity at the Planck scale. This work is based
on two different phenomenological approaches being currently made to this
topic, and theoretical models which describe this phenomenon are not dealt with
here. By using the idea developed in one of these two approaches in the
framework of the other one, it is shown that the constraints on the nature of
Planck scale space-time fluctuations already set by the observation of
electrons and gamma-rays with energies above 15 TeV are much stronger than have
been shown so far. It is concluded that for the kind of Planck scale
fluctuations implied by several models, including the most naive one, to be
consistent with the observations, the transformation laws between different
reference frames must be modified in order to let the Planck scale be
observer-independent.
