> Now for a piece that's more interesting. The fine-structure constant (alpha) is the coupling constant that sets the strength of electromagnetism. This means that its value is the thing that matters in the equation: e^2/\hbar c. Each of the other values is a derived quantity. Further, to speak a bit loosely, only changes in alpha matter -- in the sense that if the speed of light (c) changes, but the other constants (e and \hbar) change in a way that keeps alpha the same, then you wouldn't be able to tell with an experiment that anything has changed.
> Contrast this situation w/ a change in alpha -- a table-top experiment would be able to detect the change (given that it's large enough, and we have methods of measuring changes on year-time scales that are a few parts in ~10^-18 (Rosenband, 2008)), as it would mean that physics has changed in a fundamental way.
> http://phys.columbia.edu/~millis/1900/readings/Science-2008-...
Alpha could be different in different galaxies. It will not vary in a galaxy but maybe vary between galaxies. This is not clear, most likely not. It has much to do with the early stages of galaxy crystallization which could be the same for all galaxies.
It has a geometrical underlying principle in BSM-SG. c is also derived, e more or less, not so sure with h, guess you could.
Most of the 'constants' from the standard model are derived in BSM-SG, there are only very few underlying constants.