Why would the ratio of the strong nuclear force to electromagnetism be about 137 to 1? What does the fine structure constant have to do with it? [closed]

Question

Is it just another weird coincidence that the strong force is approximately 137 times as strong (at appropriate distances) as the EM force?

Also, when comparing the four fundamental forces and their strengths, are we talking about the strong force between quarks or the residual force between protons and neutrons?

P.S.: I have been asked to edit this...

I could not find a specific site or book or article or paper about the fine structure constant that mentioned its relation to the ratio of the EM force to the strong interaction... Or vice versa....

THAT is why I posted this....

(Wikipedia's article on the Fine Structure Constant used to have one very long equation(s) that showed every possible derivation; every connection to other physical constants... But again, nothing about the relation to the Strong Force...)

Answer 1

They are called coupling constants:

In attributing a relative strength to the four fundamental forces, it has proved useful to quote the strength in terms of a coupling constant. The coupling constant for each force is a dimensionless constant.

These constants have been determined from fits to the data at the level where quantum mechanics has to be used, where expansions in series of the solution have powers of these constants as diminishing power. Electromagnetism with its 1/137 gives non exploding terms to the series. The strong force with 1 means that the series cannot converge, and other methods have to be found to calculate strong interactions with predictive accuracy.(QCD on the lattice for example)

So it is not a coincidence, it is a mathematical fit to the measurements that gives 1/137 for EM, and the inability to converge and fit gives 1 to the strong coupling.

Answer 2

These couplings are free parameters in the standard model, their values to be determined by experiment. Their values might be determined by physics beyond the standard model.

An example of how this might work: We suppose that there is a "grand unified force", combining all forces except gravity, whose coupling at the Planck scale is about 1/24. We also suppose that this grand unified force is divided into two forces, strong and electroweak, by a superheavy Higgs field, and then the electroweak force is divided into electromagnetic and weak forces by the Higgs field whose residual boson was observed in 2012.

The strength of force couplings actually varies with energy scale. This running of couplings is described by "beta functions" derived from the "renormalization group equations" of a theory. Given all this, it should be possible to derive the observed values of strong, weak, and electromagnetic forces, by using the beta functions of our grand unified theory, given that the unified coupling is 1/24 at the Planck scale, that the superheavy Higgs mechanism happens below the grand unification scale of 10^15 GeV, and that the electroweak Higgs mechanism happens below the Fermi scale of 246 GeV. (Each time there is a Higgsing, a unified force is broken into two forces with different couplings that run differently.)

A theory like this can then explain why the observed couplings are what they are, using these inputs of 1/24, 10^15 GeV, and 246 GeV. Presumably those numbers (along with other details like the symmetry group of the unified force, and the charges and degrees of freedom of the matter fields), would come from an even more fundamental theory like string theory.