A Planck-Einstein-Dirac Wave Model of Electron

Abstract

The spherical model of electron cannot explain Bohr magneton, de Broglie wave, etc. To explain these properties physically, we propose that spin, one core concept of quantum theory, is a reality, and introduce this alternative solely based on experimental findings, Planck’s, Einstein’s, and Dirac’s insights, and follows classical laws, that an electron is an electrical wave with a literal $\frac{1}{2}$ spin (Dirac), i.e., spins two circles in one cycle, both angular momentum are ℏ. Its wavelength is determined by $E=h\nu_{m_0}=\frac{hc}{\lambda_{m_0}}=m_0c^2$ (Plank and Einstein), λ m 0 is the Compton wavelength. As E⃗ ⊥ c⃗ for a transverse wave, it has a net electricity due to the first spin, $f(E_q)=\frac{1}{2}E_0\left(1-\cos(2\omega_0t)\right)$, half of its cycle, i.e., the minimal meaningful unit as F = E q , is related with its charge, q = E q ϵ 0 . Moreover, an electron has a ring shape due to the second spin, 2 π R 0 = λ m 0 , λ m 0 is the electron-impact cross section. As $\hbar=\frac{h}{\lambda_{m_0}}\frac{\lambda_{m_0}}{2\pi}=m_0cR_0$, it has a quantized classical angular momentum, with a speed of c . The Bohr magneton, $\vec{\mu_B}=\vec{\frac{q}{2m_0}\hbar}$, g -factor is 2. Critically, the full Dirac’s equation of an electron with a constant velocity is $\vec{mc} = \vec{\hbar_\perp}+\vec{p_\perp } +\vec{\hbar_{//}} +\vec{p_{//}}$, and its electromagnetic properties due to charge are $\vec{f(E_q)} = \vec{f(E_q)\frac{\sqrt{c^2-v^{'2}}}{c}} + \vec{f(E_q) \frac{v\rq}{c}} = \vec{E_{net}^{//}} + \vec{E_q^\perp}$, $\vec{v\rq} // \vec{\hbar_\perp}$ or $\vec{v\rq} // \vec{\hbar_{//}}$, and $\vec{v\rq} // \vec{E_{net}}$. Assuming heavy charged particles have equivalent though shall not identical mechanisms, mathematically this model is equivalent to Special Relativity, and supports ALL its formulas, i.e., v < c , E = m c 2 , direction-insensitive m = γ m 0 and $t=\frac{t_0}{\gamma}$; Moreover, the net electricity $\vec{E_{net}^{//}}$ and Bohr magneton is orientation-quantized, direction-sensitive and follows Lorentz transformation, leading to Lorentz transformation of length contraction; while following Relativity, magnetism can be defined by $\vec{f(B)} =\vec{f(E_q)\frac{v\rq}{c^2}}$, which is not circularly symmetric and self-evidently does not follow Lorentz transformation. The temporospatial averaged magnetic intensity of a current is relativistic, $\bar{\vec{B}} =\sum\vec{{f(E_q)}\frac{\Delta v}{c^2 }}=\frac{\vec{I}}{2 \pi \epsilon_0 c^2}=\frac{\mu_0\vec{I}}{2\pi}$, and μ 0 ϵ 0 c 2 = 1, supporting Maxwell’s equations. Further implications include chirality therefore magnetic spatial quantization, de Broglie wave, etc. The spherical model should be just an observation due to orientation quantization of $\vec{E_{net}}$. We conclude this model of electron may provide one step further to the ultimate Quantum Theory in a nonrelativistic spacetime.