The Fisher's information and quantum-classical field theory: classical statistics similarity

TL;DR

This paper demonstrates the fundamental differences between classical and quantum mechanics using Fisher information and proposes a new field theory framework that unifies quantum and classical field theories.

Contribution

It introduces a novel approach using Fisher information to construct a self-consistent field theory linking quantum and classical physics.

Findings

Classical statistics cannot derive quantum mechanics.

Fisher information is effective for unifying quantum and classical theories.

A new self-consistent field theory framework is proposed.

Abstract

The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed.