  We use a recent formalism of quantum geodesics in noncommutative geometry to
construct geodesic flow on the infinite chain
$\cdots\bullet$--$\bullet$--$\bullet\cdots$. We find that noncommutative
effects due to the discretisation of the line cause an initially real geodesic
flow amplitude $\psi$ (for which the density is $|\psi|^2$) to become complex.
This has been noted also for other quantum geometries and suggests that the
complex nature of the wave function in quantum mechanics (and the interference
effects that follow) may have its origin in a quantum/discrete nature of
spacetime at the Planck scale.
