It is well known from the Electromagnetic Theory that electrons traveling in a loop induce a magnetic field, and a surface confined by the loop behaves as a magnetic dipole surface. The magnetic dipole is a kind of a small magnet with 2 poles – north and south. The kind of dipoles formed by the current loop applies magnetic forces on another magnetic dipole, is called in physics “Axial Dipole”.
Another well-known dipole is that created by a pair of equal and opposite electric charges at a small distance from each other. This dipole is called a polar dipole. A careful study of electromagnetic forces acting between a pair of static charges as opposed to a pair of static dipoles, reveal the difference between charges and dipoles. The force between static charges passes through the straight line connecting them, whereas the force acting between 2 such dipoles does not necessarily coincide with that line. The force between dipoles may point in different directions, similar to the field lines of 2 magnets close to one another positioned in a certain orientation. In some cases, such as in Nuclear Physics, this force is called a Tensor force.
In addition to electric current loops, there is another magnetic dipole source: a particle’s spin. Charged particles with a non-zero spin, such as the electron and the proton, have a magnetic dipole moment as well. Some electrically neutral particles, such as the neutron, have a spin and a magnetic dipole moment.
Axial electric dipole
According to the Regular Charge-Monopole Theory developed by Comay, there is a full duality between magnetic and electric forces. The quarks carry magnetic monopole charges with equivalent properties to those of electric charges.
Therefore, just as an electrically charged, spin ½ electron creates an axial magnetic dipole, the magnetically charged spin ½ quark creates an axial electric dipole.
Based on the equations obtained by Comay, the quarks carrying the monopoles do not exert an electrical force directly on the electric charges, and the force applying is the force one axial electric dipole exerts on another axial electric dipole. That is to say, protons and neutrons can be considered as axial electric dipoles exerting forces one on the other.
Why does the Deuteron look like a Rugby ball?
The deuteron is a nucleus of a heavy Hydrogen atom containing a proton and a neutron. Had the Nuclear Force potential depended only on the distance between these proton and neutron, the deuteron’s geometry should have been spherical. However, it turns out that the deuteron’s shape looks more like an American football or a Rugby ball. This observation introduces an additional force acting inside the deuteron between the proton and the neutron, the lines of which are not necessarily directed toward the 2 nucleons, just like the force lines between two magnetic dipoles. Nuclear scientists call this force “The tensor component of the Nuclear Force”.
The first tentative to explain this phenomenon was related to the proton’s and neutron’s magnetic dipole moment. Quarks carry electric charges: u quarks carry a charge of 2/3 and the d quark -1/3. These quarks move within the nucleon – the proton or the neutron. Both their motion and their spin create magnetic moments, resulting in a magnetic dipole force between the proton and the neutron. But calculations showed that these forces are significantly weaker than the nuclear tensor force, and cannot explain the Rugby ball shape of the deuteron.
There is currently no consensus explanation for the origin of this phenomenon.
According to Comay’s model, quarks are magnetic monopoles, i.e., carrying magnetic charges. According to this model there is a duality between the magnetic and the electric fields, and the quarks, which carry a magnetic monopole charge and have a spin, create an axial electric dipole moment when moving within the nucleon’s space.
The forces we are dealing with here are much stronger: the square of the quarks’ magnetic monopole charge is about 100 times stronger than that of the electric charge of the electron. Therefore, the force induced by the axial electric dipoles of the proton and neutron is not negligible. Since all the quarks carry the same magnetic monopoles, the proton and neutron’s axial electric dipoles are very similar. Furthermore, the sign of the Nuclear Tensor Force is known from Nuclear Physics literature and is based on the rugby-ball shape of the deuteron. And it turns out that the sign of the nuclear tensor force coincides with the sign of the force between 2 equal axial dipoles.
The development of the Regular Charge-Monopole Theory is based on considerations which are totally independent of the specific geometrical structure of the deuteron. The fact that this theory accounts for both the existence of the Nuclear Tensor Force and its sign, provides an additional experimental proof for its validity and for its capacity to explain the Strong Interactions.
On Dirac’s Monopoles
In the 1960s, Schwinger examined the possibility that the quarks are magnetic monopoles. The monopole’s properties as Scwinger tested it were published in a 1931 article by Dirac. Measures showed that the upper limit to the neutron’s electric dipole moment tends to zero. However, if quarks carry magnetic monopoles, they should have a very large electric dipole moment. For this reason, the neutron, whose quantum state is composed of 3 quarks, is supposed to have a large electric dipole moment. It was on this very point that Schwinger stumbled upon in his attempt to describe the quarks as monopoles.
On the face of it, this experimental fact should have totally discredited Comay’s model as well.
But that’s not exactly so. As Comay discovered, a magnetic monopole doesn’t directly apply forces on electric charges, and this is the reason why the axial electric dipole associated with the monopoles does not exert a force on electric charges. Experiments measuring the neutron’s electric dipole, actually measured its interaction with electric charges, i.e., only the neutron’s polar electric dipole was measured, and was indeed found to be zero or tending to zero. This is how Comay’s model coincides with theses experimental measurements.