  We study a single quantum particle in discrete spacetime evolving in a causal
way. We see that in the continuum limit any massless particle with a two
dimensional internal degree of freedom obeys the Weyl equation, provided that
we perform a simple relabeling of the coordinate axes or demand rotational
symmetry in the continuum limit. It is surprising that this occurs regardless
of the specific details of the evolution: it would be natural to assume that
discrete evolutions giving rise to relativistic dynamics in the continuum limit
would be very special cases. We also see that the same is not true for
particles with larger internal degrees of freedom, by looking at an example
with a three dimensional internal degree of freedom that is not relativistic in
the continuum limit. In the process we give a formula for the Hamiltonian
arising from the continuum limit of massless and massive particles in discrete
spacetime.
