At low energy, the fine structure constant is 1/137.03... Dirac called the search for an explanation a big problem and so far nobody knows where the value comes from.
But surely, there must be some conjectures on what determines the number? Is the number due to some hidden structure of electric charges? Is it due to some hidden structure of photons? Is it due to some hidden process details during photon emission or absorption?
Are there any ideas that are serious (non-numerological!) on its origin? Google scholar does not yield much. Are there any ideas that circulate only from mouth to mouth?