Scaling Law Echoing Musical Harmony at the Frontier between Atomic and Subatomic Particles

Using the mass of neutron as unit of energy, we scaled some physical constants that include the charge of the electron, Bohr radius, and Rydberg constant into dimensionless quantities. These dimensionless physical constants lie down on a straight line in a log-log plot, suggesting that they are ruled by a power law. Further geometrical analysis of the plot shows that the power that corresponds to each of these constants is a partial harmonic number (1 ± 1/n). Thus, in the new unit of energy, these constants constitute the mathematical harmonic series 1/1, 1/2, 1/3, 1/4, ...1/n that rule numerous phenomena such as the musical octave notes. The harmonic pattern surprisingly applies to subatomic particles as well. We are presenting our results in this poster.