# Dynamical determination of the basic Planck units

Vladan Pankovic

Arxiv ID: 0912.5455•Last updated: 5/26/2021

In this work we consider determination of the basic Planck units (mass,
length and charge) using two dynamical principles. First one is definition of
the (reduced) Compton length of the physical system (which, as it is
well-known, can be considered as the critical parameter that characterizes
necessity for application of the quantum field theoretical formalism). Second
one is definition of the classical dimension of a physical system (that can be
considered as a generalization of the concept of the classical radius of the
electron) by equivalence of the system rest energy and potential energy for
corresponding length. For electrostatic Coulomb potential energy it implies
Planck charge, but without any explicit expression for system mass or (reduced)
Compton length. For Newtonian gravitational potential energy it implies Planck
mass and Planck length. It is shown that analogous results follow when second
dynamical principle is changed by new dynamical principles in which Planck
length corresponds to geometrical mean value between (reduced) Compton
wavelength and Schwarzschild radius for arbitrary physical system. More
generally, it is shown that basic Planck units can be obtained by analogous
relations between three characteristic length parameters determined by general
relativity dynamics for Kerr-Newman black hole with angular momentum equivalent
to reduced Planck constant.

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