Proton size is presently estimated by measurements of proton charge radius of approximately 0.84 fm. In contrast, based on binary mechanics postulates and equations [1], reported proton radius is about 1.34 fm. This substantial size discrepency may be resolved by data indicating that the proton charge radius may underestimate proton size because three parts of proton structure contain concentrations of positive fractional charges.
Proton (Hadron) Structure and Cycle. Discovery of the proton (hadron) cycle in 2011 revealed a 42 component structure in which energy quanta rotate in a clockwise direction in the perspective shown in Fig. 1 [2] [3]. Each component is a quantized location in 0-state (empty) or 1-state (energy quanta). Thus, the proton cycle has 242 possible configurations, accounting for a wide range of particles and particle states.
In Fig. 1, two types of location and associated energy quanta have been defined: M and L. M-type locations exhibit a fractional 1/3 charge attribute (+ or -) when in the 1-state. L-type locations exhibit a directional property (orange arrows) indicating 1-state motion direction due to electrostatic or magnetic potentials. The proton cycle exhibits a structure with three groups (black arrows) of positive fractional charges located at 90 degree angles to each other: upward, lower-left and lower-right.
Non-Spherical Proton Shape. Integer coordinates may be assigned to the quantized locations shown in Fig. 1. The proton cycle locations are asymmetrically distributed in this space [4]. Fig. 2 shows two x-ray views (Y,X and Y,Z) illustrating a non-spherical proton shape. Considering a third X,Z view, proton structure features a non-spherical shape.
Work by G. A. Miller [5] has suggested that observed non-spherical proton shape may be a "deformation" of a spherical "ground-state" shape. In contrast to Miller and conventional quantum chromodynamics, analysis by the author cited above suggests that a non-spherical shape is a fundamental property of proton structure even at the lowest energy levels.
Proton Size. Using the coordinate system in Fig. 2 for the centers of each location, the average location position or "center of gravity" is {2,2,2} in quantized length units. Location radius is its distance from the center of gravity. Average radius is 2 length units. With the Keene Scale primary length constant of approx. 0.67 fm [6], the average location radius in Fig. 1 is approx. 1.34 fm.
Proton location radii varied from 0.95 fm for the inner loci to 1.65 fm and 2.02 fm for each group of three outer loci arranged at 90 degree angles to each other (Fig. 1, black arrows).
Proton Electric Dipole Moment. As reported by Binary Mechanics Lab (BML), proton structure contains 21 positive and negative fractional charges. The net fractional charge is +3, consistent with the observed proton charge of +1. Fig. 3 shows two views (Y,X and Y,Z) of the distribution of fractional charges in the proton structure volume [7]. This density and charge sign distribution establishes a non-zero proton electric dipole moment (EDM) in agreement with Olive et al [8]. Considering a third X,Z view, the data exhibits three regions within proton structure at 90 degree angles to each other where positive fractional charges are concentrated.
BML calculated proton EDM equals 8.534265E-32 ecm with one quanta in the proton cycle up to 8.534265E-31 ecm with 10 quanta. These BML results are consistent with upper limits for proton EDM estimated using Hg-199 atoms, placing the constraint at less than 7.9E-25 ecm or 2.0E-25 ecm.
Discussion
Another Proton Radius Puzzle. The 1.34 fm proton radius based on the proton cycle is substantially greater than reported 0.84 fm proton radius based on proton charge radius measurements. The 0.84 fm estimate may be an artifact of the measurement method based on charge interaction events. In other words, the 0.84 fm result for proton size may be consistent with measurement of one of the three fractional charge groups at the proton structure periphery (Fig.1, black arrows). In sum, the 0.84 fm result may represent parts of the complete proton structure.
In support of this interpretation, an approx. 0.82 fm electron radius was reported in the BML derivation of Planck's constant h entirely from first principles [9]. The 0.82 fm electron size is close to the size of just one of the three fractional charge groups in the overall proton structure.
The Blind Men and the Elephant. This report may illustrate the familiar fable about the blind men and elephant. That story shows that researchers may tend to believe a limited experience (proton size based on proton charge distribution) and ignore other valid perspectives (proton size based on the proton cycle discovery).
References
[1] Keene, J. J. "Binary mechanics postulates" JBinMech November, 2020.
[2] Keene, J. J. "Proton and electron bit cycles" JBinMech April, 2015.
[3] Keene, J. J. "Proton structure 3D animation" JBinMech May, 2020.
[4] Keene, J. J. "Non-spherical proton shape" JBinMech February, 2015.
[5] Miller, G. A. "Colloquium: The Shape of Hadrons." Rev. Mod. Phys. 84, 1231 (2012)
[6] Keene, J. J. "How to derive the primary and secondary physical constants" JBinMech March, 2025.
[7] Keene, J. J. "Non-zero proton electric dipole moment" JBinMech February, 2015.
[8] Olive, K.A. et al. (Partical Data Group) Chin. Phys. C 38, 090001, 2014.
[9] Keene, J. J. "Intrinsic proton spin derivation" JBinMech December, 2018.
© 2026 James J Keene
