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 $c=a/τ$, $a$ and $τ$ being the minimum space and time distances between gates, respectively. It is shown that the information flow satisfies a Dirac equation, with speed $v=ζc$ and $ζ=ζ(m)$ mass-dependent. For $a/τ=c$ the speed of light $ζ^{-1}$ is a vacuum refraction index increasing monotonically from $ζ^{-1}(0)=1$ to $ζ^{-1}(M)=\infty$, $M$ being the Planck mass for $2a$ the Planck length.

4 PRL-style pages with 4 eps figures