The Vortex Electron and the Origin of the Bohr Radius and its Fine Structure Constant, and Pilot Waves

We relate the first Bohr radius to the radius of a finite sized vortex electron whose charge revolves at the speed of light speed in a Compton wavelength orbit and produces the Bohr magneton, identically. The revolving charge's impulses produce a spiraling electric field, or vortex, of Compton wavelets around the electron. A train of 43 Compton wavelets, n, emitted by the electron and reflected back from the nucleus, gives the Bohr radius $=$ (f*(0.75$+$n - re)/2 $+$ rp) $=$ 21.809394 Comptons. Here re $=$ 1/2$\pi $ and is the electron radius in Comptons and rp$=$ 0.001521 Comptons is the radius of the proton. This gives us 2$\pi $*a0 $=$ 137.0325 (26 ppm err). Here, f is a correction factor of 1.00057126 from the combined potential well and reduced mass correction. We also correct the distance for the distortion caused by the finite size of the electron, and then the resulting inverse fine structure constant is then 137.0306 ( a 39 ppm error). We also claim the Compton wavelets are equivalent to the pilot waves sought after by de Broglie and Bohm. -- References: www.tachyonmodel.com, Ernst Wall, The Physics of Tachyons, Hadronic Press (1995), Ernst L. Wall, Bull of APS \textbf{59}, E2.00005~ (2014).