Steve Agnew,
Quoting you, "The gyromagnetic ratio in simple QM is 2.0. The measured gyromagnetic ratio with a cyclotron is ge = 2.0023193042617(15) and the difference between the measurement and the simple 2.0 is called the anomalous gyromagnetic ratio, ga". This much I agree.
Again quoting you, "This is a measured constant". Here I differ. How can ga be a measured constant? It is just the difference between theoretical value and measured value; it is not directly measured. Is it directly measured? Either you got it wrong or I am unaware of the direct measurement of the ga.
Again quoting, "that is due to the electron self energy of quantum electrodynamics, QED". You say that ga is due to electron self energy. Maybe. However that is just an explanation and so I do not agree with it.
I do fully agree with the mathematical relation between Fine Structure Constant and ga. The relation exists because Fine structure constant, in my opinion, is a packing constant (a ratio between diameter and mass both expressed in terms of the number of constituents). However I have not derived the relation.
Why fight QED, you ask me. As a theoretical model, QED is incomplete. It is just an offshoot of QM, which itself is incomplete. If QM gives an overall model covering the particles and the large-scale structures, then we can say it is a 'complete model', even if it does not explain everything. But unfortunately, it can explain only things at quantum level. My theory, on the other hand, gives an overall picture, and so is a complete theory. The opposition to QM comes from this fact.
Jose P Koshy