On Wednesday, January 9, 2019 at 12:29:52 PM UTC-6, John Clark wrote:
> I agree with Lawrence Crowell it would be wise to stick with dimensionless 
> units. They're not many non integer constants in physics without a 
> obvious purely mathematical definition such as PI and e have but the Fine 
> Structure Constant is one of that rare breed of pure dimensionless numbers 
> that mathematicians have never found anything special about but 
> physicists have. 
> If you place 2 electrons a distance d apart they will repel each other 
> because they will both have a negative charge; call the energy needed to 
> overcome that repulsion Er and let's call the energy in one photon of 
> light with a wavelength of  (2PI)*d  Er.  Er/Ep is the Fine Structure 
> Constant (FSC), the ratio of 2 energies is obviously a pure number and is 
> very close to 1/137 but not exactly so, the reciprocal of the FSC obtained 
> experimentally is  137.035999139 plus or minus 31 in the last two digits. 
> It can also be calculated theoretically using Feynman Diagrams and the 
> result is 137.035999173  plus or minus 35 in the last two digits. Another 
> physical interpretation is the ratio of the velocity of a electron in the 
> innermost orbit of the Bohr model of the Hydrogen atom to the velocity of 
> light in a vacuum.  
> Is the Fine Structure Constant a rational number? Is it a algebraic 
> number? Is it a transcendental number? Nobody knows.
>  John K Clark

Is it computable at least?

- pt 

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