The elementary charge value might be determined by Hamiltonian dynamics

Abstract With the electron’s discovery in 1897, it became recognized that each electron has exactly the same electric charge quantum, known as the elementary charge value. In natural units, the elementary charge value is the square root of the electromagnetic fine structure constant, which yields the ground state electron speed in the hydrogen atom. The origin of these fundamental constants has been a long-standing mystery ever since the electron’s discovery. We propose that the elementary charge value may be calculable via a Hamiltonian dynamics based method. Hamiltonian dynamics applies to the electron’s quantum mechanical wave aspect and also to its Zitterbewegung oscillation aspect, together yielding its wave-particle property. We start by investigating the dimensionality of the electron phase space, in which its electromagnetic oscillations evolve. We then apply the Kolmogorov-Arnold-Moser theorem to show the existence of quasiperiodic orbits in the electron’s phase space, and demonstrate that the elementary charge value may correspond to Feigenbaum’s superstable orbits.