April issue of Discover magazine

[kyle_soule]

I have a question concerning the article, in the April issue of Discover magazine, on the varying speed of light [VSL] theory, theory being used very lightly.

My question is how João Magueijo got the dimensionless quantity

c/(ao/(hbar/Er)) = (8*л*eps o)/alpha

from using the Rydberg energy and Bohr radius to measure the speed of light.

My question is how he went from the Rydberg energy and Bohr radius to the dimensionless quantity, thanks for any help anybody has in clearing this up for me

http://xxx.lanl.gov/PS_cache/astro-ph/pdf/9811/9811018.pdf
is his paper, from which my question is asked. First figure, second page, first column.

 

[gtoguy97]

In his paper, Magueijo derives the dimensionless quantity by using a combination of the Rydberg energy, Bohr radius and Planck's constant. Specifically, he starts with the equation for the Rydberg energy: E_R = hcR/n^2 where h is Planck's constant, c is the speed of light, R is the Rydberg constant, and n is an integer. He then substitutes in the value of the Rydberg constant (R = me^4/8ϵο^2h^3) and the expression for the Bohr radius (a_0 = 4πϵοhbar^2/me^2), which gives him the equation: E_R = (mc^2/8)(4πϵο/me^2)(h/a_0) He then rearranges the equation to give him the dimensionless quantity: c/(a_0/(hbar/E_R)) = (8λϵο)/α where λ is the fine structure constant and α is the electromagnetic coupling constant.