  Generic arguments lead to the idea that quantum gravity has a minimal length
scale. A possible observational signal of such a minimal length scale is that
photons should exhibit dispersion. In 2009 the observation of a short gamma ray
burst seemed to bound the minimal length scale to distances smaller than the
Planck length, implying that spacetime appeared continuous to distances below
the Planck length. This poses a challenge for such minimal distance models.
Here we propose a modification of the position and momentum operators, ${\hat
x}$ and ${\hat p}$, which lead to a minimal length scale, but preserve the
photon energy-momentum relationship $E = p c$. In this way there is no
dispersion of photons with different energies. This can be accomplished without
modifying the commutation relationship $[{\hat x}, {\hat p}] = i \hbar$.
