Scale relativistic formulation of non-differentiable mechanics II: The Schroedinger picture

TL;DR

This paper reformulates Schrödinger's equation within the Scale Relativistic framework, linking non-differentiable geometries to quantum mechanics and suggesting macroscopic chaotic systems as potential quantum-like structures.

Contribution

It demonstrates that Schrödinger's equation can be derived from non-differentiable Newtonian dynamics, offering a new interpretation of quantum axioms within the Scale Relativistic approach.

Findings

Schrödinger's equation is a reformulation of non-differentiable Newtonian dynamics.

Macroscopic chaotic systems may exhibit quantum-like behavior at large time scales.

The approach provides a coherent reinterpretation of quantum mechanics axioms.

Abstract

This article is the second in a series of two presenting the Scale Relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. Here, we show Schroedinger's equation to be a reformulation of Newton's fundamental relation of dynamics as generalized to non-differentiable geometries in the first paper \cite{paper1}. It motivates an alternative interpretation of the other axioms of standard quantum mechanics in a coherent picture. This exercise validates the Scale Relativistic approach and, at the same time, it allows to identify macroscopic chaotic systems considered at time scales exceeding their horizon of predictability as candidates in which to search for quantum-like structuring or behavior.