A Finslerian version of 't Hooft deterministic quantum models

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 functions 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 nonvalidity 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 a simple ’t Hooft model with interactions.