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.

## 9 thoughts on “More about Magnetic Monopoles”

1. Eliyahu Comay says:

Dear Neil,
Below I refer to two points mentioned in your last Comment.
1. Now I understand that the notion of a core should be defined explicitly. Thus, the core consists of all baryonic elements, except the three valence quarks and the additional quark-antiquark pair(s). There is a good evidence showing that the core contains closed quark shells of the u,d flavor. Obviously, these quarks carry the same monopole charge as the valence quarks. At the baryonic center there should be a non-quark object that carries magnetic monopole of the opposite sign. This system is analogous to an atom where electrons are bound to a nucleus. It means that the first statement in your last Comment is incorrect.
2. I’ve been told that the theory presented in my internet site is still unsuitable for Wikipedia. I’ll be happy to know that this unsuitability is removed.
Cheers, Eli

2. Neil says:

Dear Eli
When I’m reading through your pages, I don’t find any details on the core that attracts the three valance quarks of the proton. If all quarks carry the same magnetic monpole, does it mean that new particles or at least one new particle have to be found at the core? I’m pretty sure anti quarks can’t be the answer. So according to your theory what particles are sitting at the core?
Cheers, Neil

• Eliyahu Comay says:

Dear Neil,
In my opinion, an answer to your question can be found in two different ways. In principle, one may find a solid theoretical argument that restricts the form of the baryonic core. I do not see how this course can be accomplished and I do not devote time to this purpose. The second course is based on an examination of well established experimental data. As of today, this course already yields the following properties of the core:
1. You are right. The core is not made of antiquarks because quark-antiquark may annihilate each other and undermine the proton’s stability.
2. The core carries three positive monopole units. This property explains the residual nature of the nuclear force and its similarity to the force between neutral molecules. (Obviously, the sign of the quark/core monopole can be reversed. Here it is chosen in order to keep an analogy with the sign of the nucleus/electron electric charge.)
3. The core is electrically neutral. This property is inferred from the strong decrease of the elastic electron-proton cross section in very high energy. An electrically charged core should yield Mott elastic events for the electron-core interaction (see [1], pp. 192, 196, eqs. (6.23), (6.28)). The Mott cross section decreases much slower.
4. The core contains closed shells of quarks. This property is inferred from the increase of the proton-proton elastic (and total) cross section in very high energy (see [2], p. 12). The closed shells enter the interaction only if the interaction energy is high enough (like in the Franck-Hertz experiment).
5. An examination of the presently available experimental data indicates that the inner closed shells are made of u,d quarks. This (intuitively agreeable) property is derived from a comparison of the proton’s mass and radius and the pion’s value of these quantities. A comparison of the mass of the Sigma baryon and that of the K meson indicates that it is not affected by an inner closed shell of strange quarks.
[1] D. H. Perkins, Introduction to High Energy Physics (Addison-Wesley, Menlo Park CA, 1987).
[2] http://pdg.lbl.gov/2011/reviews/rpp2011-rev-cross-section-plots.pdf

• Neil says:

Dear Eli
Since a u valence quark has a negative magnetic monopole and a u core quark has a positive magnetic monopole it means, that the sign of the magnetic monopole of quarks can either be changed or there are two kinds of u and d quarks. Which one is it?
Thank you very much for taking the time and answering my questions.
You mentioned wikipedia, and I saw that there is no article for your Regular Charge-Monopole Theory. I think it might be a good way to bring your ideas more into the open, because it is unlikely to stumble across your homepage whereas in wikipedia I find myself very often browsing through links and ending up at interesting articles that were not my initial topic of search. I would like to write it , but unfortunately I’m nowhere near considering myself “a good enough expert” on particle physics, and I surely don’t want to write anything wrong about your theory. Thank you for the recommended books. I already have them on my shelf, but the math certainly makes them not a too easy read-especially for a beginner like me.
Cheers, Neil

3. Neil says:

Hello Eliyahu Comay
Best regards, Neil

• Eliyahu Comay says:

Dear Neil,
I agree with your opinion on how interaction between physicists should be organized. The veracity of any idea that does not negate experimental data should be discussed and the examination should be unbiased. Personally, I try to adhere to this principle.
In the following points I refer to specific physical issues mentioned in your comment and describe some aspects of my hadronic model. I hope that they clarify matters.
1. Quarks carry two different kinds of electromagnetic-like charges. One kind is the ordinary electric charge whose value (in units of the electron’s charge) is either +2/3 or -1/3, respectively. The second kind of charge is a (negative) unit of magnetic monopole. All quarks carry the same monopole unit and the baryonic core carries three (positive) monopole units. Hence, the sum of monopole units of a baryon vanishes. The same is true for mesons which are made of a quark-antiquark pair. The 1/r law that holds for the electromagnetic potential entails the well known screening effect of electrodynamics. In the case of baryons, this law should be applied separately to the electric charges and the magnetic monopoles of each particle.
2. Thus, at points that are far enough from a baryon, monopole effects fade away because the sum of monopole charge of a baryon’s components is zero. The same property holds for effects of the neutron’s electric charge, whereas the proton is “seen” as a positively charge particle.
3. Polar dipole should vanish in systems whose state is determined by forces that conserve parity. However, a vanishing effect does not hold for axial dipoles. Thus, due to the quarks’ electric charge, hadrons whose angular momentum does not vanish have an axial magnetic dipole associated with the quarks’ motion and their spin. This effect is seen in the proton and in the neutron. By the same token, a monopole related axial electric dipole should exist in baryons. This axial electric dipole is the underlying reason for the nuclear tensor force.
4. It is important to note the Regular Charge-Monopole theory that explains why there is no direct interaction between charges and monopoles and that both kinds of charges interact with the same electromagnetic radiation. See http://www.tau.ac.il/~elicomay/OVERVIEW.html
5. For reading a short description of an important theoretical element that has been overlooked in the process of QCD construction, see http://www.tau.ac.il/~elicomay/part_phy.html
Cheers, Eli

• Neil says:

Thank you for the quick answer-it cleared things up. It was a little misunderstanding on my part, because I thought that in your theory quarks wouldn’t have any ordinary electric charge. But since they do my question is immediately answered.
Cheers, Neil

4. John Carroll says:

What is the theoretical magnetic charge of a magnetic mopnopole? Even though it has never been measured, I assume there is a theoretical prediction of its value?

• Eliyahu Comay says:

Hello John,

The Regular Charge Monopole Theory (RCMT) begins with an analysis of a classical system [1]. This regular theory conserves duality relations between a theory of charges without monopoles and a theory of monopoles without charges. As a classical theory, it says nothing about the strength of the elementary monopole unit. Hence, this quantity is a free parameter and the theory is relieved from the burden of the gigantic and extremely unphysical elementary unit of 137/4.

It turns out that this theory is useful for describing strong interactions [2]. Strong interaction data indicate that the elementary monopole unit is not much less than unity.

In short – the elementary monopole unit is a free parameter. Its size stems from an analysis of experimental measurements.

Remark: this theory and its consequences are different from Dirac’s monopole theory. As stated by Dirac himself, in spite of a very long search, the Dirac monopole theory has no experimental support [3].

[1] E. Comay, Nuovo Cimento, 80B, 159 (1984).
[2] E. Comay, published in “Has the Last Word Been Said on Classical Electrodynamics?” Editors: A. Chubykalo, V. Onoochin, A. Espinoza, and R. Smirnov-Rueda (Rinton Press, Paramus, NJ, 2004). (The article’s title is “A Regular Theory of Magnetic Monopoles and Its Implications”. See:
http://www.tau.ac.il/~elicomay/LastWord.pdf
[3] P. A. M. Dirac, A letter to A. Salam, published in “Monopoles in Quantum Field Theory”. Ed. N. S. Craigie, P. Goddard and W. Nahm (World Scientific, Singapore, 1982).