  Using the Finsler structure living in the phase space associated to the
tangent bundle of the configuration manifold, deterministic models at the
Planck scale are obtained. The Hamiltonian function are constructed directly
from the geometric data and some assumptions concerning time inversion
symmetry. The existence of a maximal acceleration and speed is proved for
Finslerian deterministic models. We investigate the spontaneous symmetry
breaking of the orthogonal symmetry SO(6N) of the Hamiltonian of a
deterministic system. This symmetry break implies the non-validity of the
argument used to obtain Bell's inequalities for spin states. It is introduced
and motivated in the context of Randers spaces an example of simple 't Hooft
model with interactions.
