The spherical model of electron should be incorrect as it cannot explain Bohr magneton, de Broglie wave, etc. To explain these properties physically, here we introduce an alternative based on Planck, Einstein, and Dirac’s insights, and classical conservation laws, that an electron is an electrical wave (magnetism is just electricity, Einstein) with a literal ${2}$ spin, i.e., spins two circles in one cycle, its wavelength is determined by $E=h={}=m_0c^2$ (Plank and Einstein), λm₀ is the Compton wavelength. As $ \perp $ for a transverse wave, it has a net electricity due to the first spin, $E_q={2}E_0\left(1-\cos(2\omega_0t)\right)$ that related with charge, Fig.1. Moreover, an electron has a ring shape due to the second spin, 2πR₀ = λm₀, i.e., the electron-impact cross section. As $\hbar={}}{2\pi}=m_0cR_0$, it has a quantized classical angular momentum, with a speed of c. Therefore,its _g_-factor is 2; the Bohr magneton, $={2m_0}\hbar}$. Furthermore, assuming heavy charged particles have an equivalent though shall not identical mechanism, mathematically this model is equivalent to Special Relativity, and supports ALL its formulas, i.e., v < c; and $m={}m_0=\gamma m_0$, E = mc², $t={\gamma}$, that are direction-insensitive and determined by its speed, v; Critically, both spins are quantized, ℏ, Fig.3A&C; the complete Dirac’s equation of an electron is $ = +} ++ $, e.g., in an external electrical field, $|E_q|=\left|_{\perp}}}+_{//}\right| = |}{c}} + {c}}| $, $ {//}}$, Fig. 3D; therefore; $}$ is direction-sensitive and determined by its relative speed, and follows Lorentz transformation, leading to Lorentz transformation of Length; and magnetism is just electricity due to speed, a concept also applies to Bohr magneton; therefore supporting the basic Maxwell’s equations. Implications also include chirality, strong force, de Broglie wave, Fig.4, etc. The spherical model should be just an observation, as the electrical force between an electron and a proton tends to be maximized due to spins, and the electrical dipole moment, determined by the moment of inertia, $I_m=m_0R_0^2=\hbar{c}$, is nearly undetectable. We conclude this model of electron is the realization of Dirac’s insights, the only possible model that can physically explain Bohr magneton and de Broglie wavelength of an electron, and provides one step further to the ultimate Quantum Theory.
