  The quantum state of a particle can be completely specified by a position at
one instant of time. This implies a lack of information, hence a symmetry, as
to where the particle will move. We here study the consequences for free
particles of spin 0 and spin 1/2. On a cubic spatial lattice a hopping equation
is derived, and the continuum limit taken. Spin 0 leads to the Schroedinger
equation, and spin 1/2 to the Weyl equation. Both Hamiltonians are hermitian
automatically, if time-reversal symmetry is assumed. Hopping amplitudes with a
"slight" inhomogeneity lead to the Weyl equation in a metric-affine space-time.
