The Moxness Bump

Looking further at Moxness' work, thanks to his helpful blog post of yesterday, I think we can make sense of it. First, let us select a natural length unit $L$ based on both the Compton wavelength $\lambda$ of the electron and the fine structure constant,

$L = \frac{2 \lambda}{\alpha} = \frac{\alpha}{R_{\infty}} = 6.650 \times 10^{-10}$m.

The ansatz is that a natural system of units in a varying constant cosmology should account for quantum mass, Bohr radii and charge. Next we define a natural time unit $T$ using a Riofrio law

$L = \alpha^{8} cT$

where the large power of alpha reflects the dimensionality of an internal space in the M Theory context. Then $T = 0.276$s. Finally, a natural mass unit $M$ is given by the rule

$M = \frac{\hbar}{cL} = 5.290 \times 10^{-34}$kg.

Moxness then predicts the characteristic central mass scale $m_{\textrm{EW}}$ with the definition

$m_{\textrm{EW}} = \sqrt{2 \alpha^{-8}} M = 147.99$ GeV.

The numbers work. The role of M Theory here is rather unclear, but it would be nice to get rid of fairy fields in this spectacular fashion.