On the Planck scale and properties of matter
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.
scientific article; zbMATH DE number 5603168