  It is supposed that at very small scales a quantum field is an infinite
homogeneous quantum computer. On a quantum computer the information cannot
propagate faster than $c=a/\tau$, $a$ and $\tau$ being the minimum space and
time distances between gates, respectively. It is shown that the information
flow satisfies a Dirac equation, with speed $v=\zeta c$ and $\zeta=\zeta(m)$
mass-dependent. For $a/\tau=c$ the speed of light $\zeta^{-1}$ is a vacuum
refraction index increasing monotonically from $\zeta^{-1}(0)=1$ to
$\zeta^{-1}(M)=\infty$, $M$ being the Planck mass for $2a$ the Planck length.
