On the Planck scale and properties of matter
type: Item
instance of: scholarly article
title: On the Planck scale and properties of matter
zbMATH Open document ID: 1178.85003
author: Ari Lehto
published in: Nonlinear Dynamics
publication date: 2009-09-11T00:00:00Z
review text: Invariant and long-lived physical properties and structures of matter are modeled by intrinsic rotations in three and four degrees of freedom. The rotations are quantized starting from the Planck scale by using a nonlinear \(1/r\) potential and periodic doubling - a common property of nonlinear dynamical systems. Because the time cannot be used for modeling time-independent phenomena, the period of revolution \(\tau\) is used instead. A second-order differential equation is derived, which has the form of the equation describing a harmonic oscillator with \(1/\tau^2\)-dependence of the spring constant. The differential equation has solutions, which allow volumetric doubling and velocity quantization in three and four degrees of freedom. It is found that the absolute values given by the scale-independent model fit closely with observations in a wide range of scales. A comparison is made between the values calculated from the model and the properties of the basic elementary particles, particle processes, planetary systems, and other physical phenomena. It is obtained that the model values fit better to observed values in the field of elementary particles and quantized galaxy redshifts, and are less accurate for planetary systems. The model also shows that the perceived forces can be divided into two categories: (1) the force is always attractive, like in gravitation and (2) the force is attractive or repulsive, like in electrostatics.
reviewed by: Claudia-Veronika Meister
Mathematics Subject Classification ID: 85A05
Mathematics Subject Classification ID: 82C32
Mathematics Subject Classification ID: 81V25
Mathematics Subject Classification ID: 81V35
zbMATH DE Number: 5603168
zbMATH Keywords: structure of matter
zbMATH Keywords: Planck scale
zbMATH Keywords: periodic doubling
zbMATH Keywords: electric charge
zbMATH Keywords: magnetic moment
zbMATH Keywords: elementary particle
zbMATH Keywords: solar system
zbMATH Keywords: 55 Cancri
zbMATH Keywords: exoplanets
zbMATH Keywords: galaxy redshift
MaRDI profile type: Publication
full work available at URL: s11071-008-9357-z
OpenAlex ID: W4241337015
cites work: Q3035768
cites work: CODATA recommended values of the fundamental physical constants: 1998
cites work: Scale relativity and fractal space-time: applications to quantum physics, cosmology and chaotic systems.
cites work: On the origin of the gravitational quantization: the Titius-Bode law
cites work: Q4778998
DOI: 10.1007/S11071-008-9357-Z
description: scientific article; zbMATH DE number 5603168