Quantum Systems as results of Geometric Evolutions

Abstract

In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to { M}$. Quantum states are equivalence classes, composed by the configurations that evolve through an internal dynamics drive by the above geometric evolution. Each equivalence class is conformed by the ontological states that evolve to the same final state. The existence of an hermitian scalar product in an associated linear space is discussed and related with the quantum pre-Hilbert space. This hermitian product emerges from geometric and statistical considerations. Our scheme recovers the main ingredients of the usual Quantum Mechanics. Several consequences are discussed and compared with the predictions of the standard Quantum Mechanics. A natural solution of the cosmological constant problems is proposed, as well as a mechanism for the absence of quantum interferences at classical scales.