Volume 16: Pages 504-529, 2003

Reverse‐Engineering the Vacuum: The Proton, the Neutron, and π⁰

Arne P. Olson

Argonne National Laboratory, Mail Stop NE‐362, 9700 S. Cass Ave., Argonne, IL 60439 U.S.A.

Heisenberg's uncertainty principle is extended to apply to three massless fields from which the internal components of the proton, neutron, and π⁰ are determined. The magnetic moment and charge radius of the proton and neutron are derived. The predicted proton magnetic moment is μ_p = {4α[1 − {m_e/(m_pw)}²]^1/2/3w}μ_N = 2.792 705μ_N, where μ_N is the nuclear magneton and α = 1/137.035 999 76 is the fine‐structure constant. The fraction of the proton's mass that is electromagnetic is w = 1 − [2(3)^½][ln (4/3)] = 0.003 440 07 or 3.2277 MeV, and m_e/m_p is the electron/proton mass ratio. This magnetic moment prediction is remarkably accurate: 0.0051% error versus measurement. The proton's predicted charge radius is 0.892 249 fm, in excellent agreement with experiment. The neutron's predicted magnetic moment is −1.913 036 7μ_N, versus −1.913 042 7 ± 0.000 000 5μ_N measured. The neutron's predicted mean square charge radius is −0.110 40 fm², versus (−0.1161 ± 0.0022) fm² measured. The neutron's predicted magnetic moment weighted radius is 0.825 23 fm, versus (0.83 ± 0.02) fm measured. The model predicts m(π⁰) = (1/2)m_p ln (4/3)[1 ± 2α²] = (134.976 390 ± 0.000 005) MeV, versus (134.9766 ± 0.0006) MeV measured. The proton is predicted to be stable, while the free neutron is not able to achieve hydrodynamic stability. A physical explanation for the origin of mass is obtained.

Keywords: proton and neutron structure, magnetic moments, uncertainty principle, vacuum fields, quantum clocks, quantum vortices, origin of mass

Received: June 19, 2003; Published online: December 15, 2008