A Finslerian version of 't Hooft Deterministic Quantum Models

TL;DR

This paper develops a Finsler geometric framework for deterministic quantum models at the Planck scale, deriving Hamiltonians from geometric data and exploring symmetry breaking that challenges Bell's inequalities.

Contribution

It introduces a Finslerian approach to deterministic quantum models, linking geometric structures to Hamiltonians and analyzing symmetry breaking effects.

Findings

Existence of maximal acceleration and speed in Finslerian models

Spontaneous symmetry breaking of SO(6N) symmetry

Implication for Bell's inequalities in spin systems

Abstract

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.