Rydberg formula simplification, a new elementary charge, and the elimination of the fine structure constant: Results of a theoretical demand for formula beautification

In physics, the term “beauty” is synonymous with the qualities of simplicity and efficiency, and there are historical precedents for its interconnection with highly accurate equations. This paper presents a novel and rigorous approach to formula beautification that begins with mandating theorems of fundamental constant reduction and nonfundamental constant elimination from certain classic equations, with the initial focus on the Rydberg formula. Reducing fundamental constants and removing all nonfundamental elements from the Rydberg constant expression begin with changing its mass component. A comparison of the Rydberg and the Compton equations suggests that a smaller mass is needed to replace the electron rest mass in the Rydberg constant formula. This substitution, in conjunction with formula beautification, results in an equivalent but more elegant formulation, and unveils a new elementary charge determination. The new elementary charge value mathematically interacts with the speed of light and the Planck constant in different ways to produce the electric constant, magnetic constant, and the impedance of free space. Additionally, when substituted into equations for Millikan's charge quantity, it integrates more concisely with fundamental constants, generates formulas with greater simplicity and beauty, and eliminates the fine structure constant. Also, it can be derived from fundamental constants exclusively, whereas the Millikan value cannot. The Millikan number requires the fine structure constant and an integer of 2, to mathematically integrate with other fundamental constants. A convincing proposition is made that the fine structure constant is simply a by-product of Millikan's inaccurate elementary charge introduction. It acts as an algebraic correcting factor to allow the Millikan value to meld with other fundamental constants. This assertion is strengthened when all of the fine structure definitions are shown to have coulomb unit imbalances, making them mathematically inoperable. It is confirmed when the new elementary charge, which replaces the Millikan value, equilibrates every fine structure definition and eliminates the fine structure constant. Therefore, the fine structure constant and all related entities such as the anomalous magnetic moment and the electron and proton g-factors are extinguished with the implementation of the new elementary charge. Restoring unit balance within the fine structure definitions reveals that the formula beautification approach, in addition to fundamental constant reduction and nonfundamental constant elimination, must also include unit-less number removal and cycle and radian unit separation, completing a blueprint for fundamental formula creation and modification. The execution of the new elementary charge substitution for the Millikan charge, the fine structure constant removal, and the blueprint implementation for equation modification results in several fundamental constants being redefined and many physics inconsistencies being resolved. The inconsistencies that are remedied include the equivalency of the classical electron radius, Compton wavelength and the Bohr radius, the Bohr magneton and the electron magnetic moment, the nuclear magneton and the proton magnetic moment, the electron gyromagnetic ratio and the electron charge-to-mass ratio, and the proton gyromagnetic ratio and the proton charge-to-mass ratio. The fundamental constants that are redefined but maintain the same value are the coulomb, ampere, electron charge-to-mass ratio, and the proton charge-to-mass ratio. The fundamental constants redefined with a new quantity are the electron and proton masses, Avogadro constant, unified atomic mass unit, electron volt, Bohr radius, classical electron radius, Compton wavelength, proton and electron magnetic moments, Bohr and nuclear magnetons, and the electron and proton gyromagnetic ratios.