Non-Singular Potential and Nuclear Physics

Pharis E Williams
15247 W Domingo Ln
Sun City West, AZ 85375
Phone: (623) 322-9783
email: willres@sdc.org

Historically the Maxwell electromagnetic field equations arose as a distillation of empirical laws such as Coulomb’s law. However, to recover Coulomb’s law from Maxwell’s equations requires the integration of a non-physical Dirac function to get the electrostatic potential. By reversing the approach this problem may be avoided, quantum mechanics derived, and new insights to nuclear physics obtained at the same time. In 1918 Weyl introduced his geometrical description of electromagnetism wherein his scale factor led to the gauge function and Einstein argued against it. In 1926 London showed that if Weyl’s scale factor was required to be fixed at unity and one was given an electrostatic potential the only paths allowed were those satisfying Schrödinger’s wave equation. This showed that quantum mechanics was required for a unity scale factor. The requirement of a unity scale factor and the five dimensions given by the first law of thermodynamics may be used to derive an electrostatic potential for a particle whose gauge characteristics are independent of where and when they exist. Two interesting features of this electrostatic potential are that they must have a quantized electric charge and that they must be non-singular. A quantized charge is not new as all known charged particles come with their charge quantized. The non-singular feature is new from the point of view that the electrostatic potential determined from Maxwell’s equations is a singular potential that varies as the inverse of the distance from the particle. The non-singular potential has a long range inverse relation to the separation, but there is a short range maximum absolute value and a return to zero as the separation vanishes. This non-singular potential produces a force between particles that changes its changes its long range character when separations go below the separation of the maximum value separation. This change in character leads to nuclear physics. The non-singular character of the potential leads to the development of two- and three-particle Schrödinger and Dirac quantum mechanics that produces a new model of nuclear physics. The two-particle Dirac equation leads to the fields contained in the Yang-Mills equations while the three-particle fields satisfy the SU-3 group relations. The resulting nuclear model predicts the low-Z nuclear masses much more accurately than does the semi-empirical nuclear mass formula. The non-singular potential in the two-particle system also predicts the half life of the neutron. In addition to the non-singular character of the potential there are two other features that, while they do not influence the nuclear model much, they play a larger role in gravitational physics. One feature is that the gravitational field is time dependent and the other feature is that the electric field depends upon the mass. The time dependence shows up in red shifts and dark matter/energy. However, the only thing that the mass dependence is known to appear in to date is the ratio of the electromagnetic to the gravitational force where the ratio is established by the time and mass dependences. The value of the ratio of the electrostatic to gravitational force is another aspect of the inductive coupling between the electromagnetic and the gravitational fields.