Consistency of Angles and the Fine-Structure Constant

The purpose of this work is to investigate how the assumption that angle is dimensionless has affected our expression and understanding of fundamental constants and equations in SI. The approach is to (i) define the radian and cycle as units of dimension angle related by cyc = 2π rad and (ii) attempt to reverse the implications and loss of information that have been introduced by previously setting rad = 1 and the unit hertz to s-1 rather than cyc/s. An important result is that the analysis indicates that the fine-structure constant is not dimensionless as universally accepted; rather it is an angle of approximately 0.4181°. Using the Bohr hydrogen model, this angle can be interpreted as the phase lag between the electric field seen at the center of the nucleus due to the electron and the field indicated by the electron's actual position. If the fine-structure constant is an angle as suggested, then it can be normalized to create new systems of natural units (with rad ≈ 137.04). In this class of natural units, Coulomb’s constant and the magnetic force constant are simple expressions of the von Klitzing constant and the speed of light, without the need for intermediate constants for the characteristic impedance of vacuum, vacuum permittivity, or vacuum permeability.