The Quantum Condition and an Elastic Limit

Abstract

Charles-Augustin de Coulomb introduced his equations over two centuries ago. These equations quantified the force and the energy of interacting electrical charges. The electrical permittivity of free space was factored into Coulomb’s equations. A century later James Clear Maxwell showed that the velocity of light emerged as a consequence this permittivity. These constructs were a crowning achievement of classical physics. In spite of these accomplishments, the philosophy of classical Newtonian physics offered no causative explanation for the quantum condition. Planck’s empirical constant was interjected, ad-hoc, into a description of atomic scale phenomena. Coulomb’s equation was re-factored into the terms of an elastic constant and a wave number. Like Coulomb’s formulation, the new formulation quantified the force and the energy produced by the interaction of electrical charges. The Compton frequency of the electron, the energy levels of the atoms, the energy of the photon, the speed of the atomic electrons, and Planck’s constant, spontaneously emerged from the reformulation. The emergence of these quantities, from a classical analysis, extended the realm of classical physics into a domain that was considered to be exclusively that of the quantum.