Smaller Proton Confirmed

Robert Oldershaw
2 min readSep 7, 2019

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In 1987 Discrete Scale Relativity predicted that the radius of the proton would be approximately 0.81 x 10^–13 cm, i.e., 0.81 fermi, on the basis of a Schwarzschild metric [Astrophysical Journal 322, 34–36, 1987]. Subsequently a more realistic Kerr-Newman metric yielded a refined DSR prediction of 0.8144 fermi. DSR’s prediction can be compared with the predicted radius of the proton of approximately 0.88 fermi produced by the Quantum Electrodynamics (QED) sector of the Standard Model (SM) of particle physics.

Much to the surprise of theoretical physicists, recent and repeated determinations of the proton radius have yielded a value of approximately 0.8418 fermi for the proton’s charge radius, which deviates from the SM/QED prediction at the 5-sigma level of confidence [Pohl et al, Nature 466, 213–216, 8 July 2010 and Antognini et al, Science 339, 417–420, 25 Jan 2013]. A newer 2017 measurement appears to reduce the proton radius estimate further to 0.83 fermi [Beyer, et al., Science, Oct 5, 2017]. Experimental determinations of the proton’s magnetic radius have ranged from 0.777 fermi to 0.863 fermi.

In the Sept. 6, 2019 issue of Science a new experiment confirms the “surprising discrepancy” (5%!) between the “textbook value” for the proton radius and experimental results. Bezginov et al find a proton radius of 0.833 fermi, with an uncertainty of 0.010 fermi.

The full range of proton radius determinations is roughly 0.75 fermi to 0.88 fermi [see Carroll et al, http://arxiv.org/abs/1108.5785 , Figure 1, 2011]. The median value for this range of proton radius estimates is about 0.815 fermi, which is reasonably close to DSR’s prediction of 0.8144 fermi. Discrete Scale Relativity’s prediction is still below the recently measured values, but it appears to be more accurate than the Standard Model/QED prediction. The empirical results clearly favor a significantly more compact proton.

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