The Mass, Radius, and Magnetic Moment of Electrons and Protons

The electron-proton scattering experiment by the PRad (proton radius) team at Jefferson Lab measured the root mean square (rms) charge radius of the proton as rp = 0.831 ± 0.007(stat) ± 0.012(syst) fm. We offer a theoretical explanation of the new measurement based on a ring current model of a proton. This model further builds on older ring current and/or Zitterbewegung models for an electron and, hence, we will also highlight those results when relevant. We obtain a theoretical radius that is equal to four times the range parameter (ħ/mc) in Yukawa’s formula: r = 4ħ/mc = 0.841 fm. The 1/4 factor stems from the energy equipartition theorem: using Wheeler’s ‘mass without mass’ idea, we effectively assume half of the energy of a proton is explained by the electromagnetic, while the other half is attributed to the strong force, which we do not model but isolate from the analysis using the energy equipartition theorem. As for the small difference between the theoretical and measured radius, we attribute this to the mathematical idealizations that underpin ring current models. While useful and necessary as a concept, we think pointlike electric charges with zero rest mass and/or zero dimension that, therefore, move at light-speed, do not exist: they must have some (very) small dimension which explains the anomaly. We think mathematical idealization also explains the anomalous magnetic moment of an electron. We think the calculations may offer a model of matter-particles in general.