Quantum Systems as results of Geometric Evolutions

TL;DR

This paper proposes a geometric evolution framework from Finsler to Riemann structures to model quantum states as equivalence classes, offering insights into quantum mechanics and cosmological issues.

Contribution

It introduces a novel geometric evolution mechanism that derives quantum states and dynamics from Finslerian models, connecting geometry with quantum theory.

Findings

Recoveries of standard quantum mechanics ingredients

A proposed solution to the cosmological constant problem

A mechanism explaining the absence of quantum interference at classical scales

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.