Quantum-like Chaos in Prime Number Distribution and in Turbulent Fluid Flows

TL;DR

This paper explores the intriguing connection between prime number distributions, quantum mechanics, and turbulent fluid flows, proposing that prime numbers exhibit quantum-like spectral properties within turbulent systems.

Contribution

It introduces a model linking prime number spectra to quantum-like laws in turbulent fluid flows, highlighting the fractal spacetime structure of dynamical systems.

Findings

Prime number spectra follow quantum-like laws.

Turbulent flows exhibit prime number structures.

Fractal spacetime underpins dynamical systems.

Abstract

Recent studies indicate a close association between the distribution of prime numbers and quantum mechanical laws governing the subatomic dynamics of quantum systems such as the electron or the photon. Number theoretical concepts are intrinsically related to the quantitative description of dynamical systems of all scales ranging from the microscopic subatomic dynamics to macroscale turbulent fluid flows such as the atmospheric flows. It is now recognised that Cantorian fractal spacetime characterise all dynamical systems in nature. A cell dynamical system model developed by the author shows that the continuum dynamics of turbulent fluid flows consist of a broadband continuum spectrum of eddies which follow quantumlike mechanical laws. The model concepts enable to show that the continuum real number field contains unique structures, namely prime numbers which are analogous to the dominant eddies in the eddy continuum in turbulent fluid flows. In this paper it is shown that the prime number frequency spectrum follows quantumlike mechanical laws.