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One of those is the so-called $$g$$ factor of the electron, related to the ratio of the spin and orbital contributions to the magnetic moment. Relativistic theory (i.e., the Dirac equation) shows that $$g=2$$. The measured value differs from 2 by a little bit, a fact well accounted for in QED. $\begin{array}{ll} {\rm experiment} &g/2 = 1.001 159 652 41 (20)\\ {\rm Theory} &g/2 = 1.001 159 652 38 (26)\\ \end{array}$ Some of the errors in the theory are related to our knowledge of constants such as $$\hbar$$, and require better input. It is also clear that at some scale QCD (the theory of strong interactions) will start playing a rôle. We are approaching that limit.