Strength of strong force and electromagnetic force In this link, it is claimed that the strength of the strong force w.r.t. the E&M force is about 137 times larger. Does this have anything to do with the fine structure constant?
 A: The E&M and the strong force are described by a quantum field theory, more precisely by a gauge theory (i.e. QED and QCD). In case of QED the coupling (vertex) between a photon and a (anti)matter particle, i.e. electron (positron), is related to the electric charge $e$.
Generally, the strength of a quantum field theory, denoted as $\alpha$, is usually expressed by a square of the charge because at least two vertices are necessary to describe a "minimal" interaction between them. For QED this means $\alpha_{\rm QED} \propto e^2$ which yields (with appropriate constants) the dimensionless Sommerfeld fine structure "constant" $\alpha_{\rm QED} \sim \frac{1}{137}$. Remarkably, this number is independent of the system of units used.
A similar but more involved procedure yields a corresponding strength of the strong interaction which is of the order of one, i.e. $\alpha_{\rm QCD} \sim 1$.
At first glance, a comparison reveals now that the strong force is about 137 times "stronger" than the electromagnetic force.
Unfortunately, the situation is not so simple because the strength of a gauge coupling, described by the "fine structure constant" $\alpha$, is not a constant but depend on the (resolution) energy $Q$, i.e., $\alpha = \alpha(Q)$. In other words, the strengths of both forces change with the distance (since $Q \sim 1/\text{distance}$, think of Heisenberg relation)! For the QCD the strength decreases with energy while for QED the strength increases with energy.
