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"Physical, measurable particles are not points but have extension. By definition, an electron without extension would be described exactly by the 1-particle Dirac equation, which has a degenerate spectrum. But the real electron is described by a modified Dirac equation, in which the so-called form factors figure. These are computable from QED, resulting in an anomalous magnetic moment and a nonzero Lamb shift removing the degeneracy of the spectrum. Both are measurable to high accuracy, and are not present for point particles, which by definition satisfy the Dirac equation exactly."

I presume having extension means that the mass of a physical electron is not considered to be concentrated at a single point?