You've got this backward. Alpha is the fundamental physical constant: c, e and \hbar are the derived quantities. I'll quote part of another comment that I left

You've got this backward. Alpha is the fundamental physical constant: c, e and \hbar are the derived quantities. I'll quote part of another comment that I left on this thread: > 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-Rosenband-1808-12.pdf http://phys.columbia.edu/~millis/1900/readings/Science-2008-...