A Frequency-Equivalent Scale-Free Derivation of the Neutron, Hydrogen Quanta, Planck Time, and a Black Hole from 2 and π; and Harmonic Fraction Power Laws

Donald Chakeres1, Richard Vento2, Vola Andrianarijaona3

1 Department of Radiology, the Ohio State University, Columbus, Ohio, USA

2 Department of Mathematics and Physics, Columbus State Community College, Columbus, Ohio, USA; Retired

3 Department of Physics and Engineering, Pacific Union College, Angwin, California, USA

**Abstract: **We find that π represents dual attributes. One is within the purely mathematical domain and can be derived for example, from infinite series, among several other methods. The other is within a 2D geometric-physical domain. This paper analyzes several physical constants from an analogous perspective where they are defined solely by mathematical and 2D geometric properties independent of any actual physical scaling data. The constants are evaluated as natural unit frequency equivalents of the neutron, electron, Bohr radius, Rydberg constant, Planck’s constant, Planck time, a Black hole with a Schwarzschild radius, the distance light travels in one time unit; and the fine structure constant. These constants are defined within two inter-related harmonic domains. In the linear domain, the ratios of the frequency equivalents of the Rydberg constant, Bohr radius, electron; and the fine structure constant are related to products of 2 and π. In the power law domain, their partial harmonic fraction powers, and the integer fraction powers of the fundamental frequency for Planck time are known. All of the constants are then derived at the point where a single fundamental frequency simultaneously fulfills both domains independent of any direct physical scale data. The derived values relative errors from the known values range from 10−3 to 10−1 supporting the concept and method.

**Keywords: **Fundamental Constants, Neutron, Black Hole, Planck Time, Computational Physics, Mathematical Physics, Hydrogen

## The Harmonic Neutron Hypothesis