Ari Lehto, PERIOD DOUBLING PHENOMENON AS THE ORIGIN OF ELECTRON PROPERTIES
Abstract: In the Standard Model of elementary particles, the rest mass, magnetic
moment and electric charge of the electron are considered to be natural
constants. In this article, it is proposed that these properties can be
calculated in a simple way from the corresponding Planck units using
the well-known period doubling phenomenon in nonlinear dynamical
systems. Periods corresponding to the values of the electron and
positron properties belong to a subset of stable periods. The periodic
structures of the rest energy and magnetic moment consist of three
internal degrees of freedom, whereas the Coulomb energy of the electric
charge consists of four. The number of period doublings for the
elementary charge determines the value of the fine structure constant
Ari Lehto, On the Planck Scale and Structures of Matter,
NPA Conference, Storrs, University of Connecticut, May 25-29, 2009
Abstract: Invariant properties and structures of matter are modeled by internal period-like degrees of freedom. Invariance then means periods, which remain unaltered over time. Period doubling is a phenomenon common to nonlinear dynamical systems. In this model the doubling process is generalized into multiple dimensions and utilized to bring about sub-harmonic frequencies, which generate decreasing energies and increasing sizes. It is assumed that period doubling takes place at the Planck scale, and therefore the Planck units are used as reference. The sub-harmonics can be converted into several other physical quantities by well known physical relations. A certain class of sub-harmonics is stable and the elementary electric charge (squared), rest energies and magnetic moments of the electron-positron and proton-antiproton pairs are shown to belong to this class. It is suggested that the structure of the Solar system results from period doubling, too.
Ari Lehto, On the Planck Scale and Properties of Matter, Nonlin. Dyn. 55, 279-298 (2009)
Abstract: 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 period doubling - a common property of nonlinear dynamical systems. 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. The model also shows that the perceived forces can be divided into two categories: (1) force is always attractive, like in gravitation and (2) force is attractive or repulsive, like in electrostatics.
Ari Lehto, Periodic Time and the Stationary Properties of Matter,
Chin. J. Phys., Vol. 28, no. 3, June 1990
Ari Lehto, On (3+3)-Dimensional Discrete Space-Time
University of Helsinki, Report Series in Physics, HU-P-236 (1984).