version of this book
A fully discrete model cannot be completely symmetric as a continuous model can be. There are ways around this like using a random lattice but such models implicitly assume a continuous manifold. In a fully discrete model there must be an absolute frame of reference and preferred directions in that frame related to the graininess of the lattice that defines the space time manifold. One would expect experimental affects from this absolute frame of reference and perhaps such affects have already been observed. It is conceivable that the symmetry breaking that has been observed in weak interactions is a result of our absolute motion against this manifold and not a break down of parity.