Magnetic Monopole: Are Maxwell's Equations Fallible?

[mezarashi]

While reading Serway's Physics for Scientists and Engineers, I found to my disbelief that he said:

There is some theoretical basis for speculating that magnetic monopoles - isolated north or south poles - may exist in nature, and attempts to detect them currently make up an active experimental field of investigation.

Then to contradict himself, in chapter 31 on Maxwell's equations (and this is accepted in many other texts as well), he quotes on the fourth equation - the divergence of the magnetic field is zero:

...which can be considered Gauss's law in magnetism, states that the magnetic flux through a closed surface is zero... This implies that the magnetic field lines cannot begin or end at any point. If they did, it would mean that isolated magnetic monopoles existed at those points.

So what's going on here? Are Maxwell's equations fallible afterall? Why would there be people researching in this field if not - oh and there apparently is credible research in monopoles, for example http://prola.aps.org/abstract/PRL/v35/i8/p487_1.

 

[marlon]

While reading Serway's Physics for Scientists and Engineers, I found to my disbelief that he said:

I refer to this thread for more info.

Bascally, we have NOT yet observed magnetic monopoles, though it would be a great thing if they existed. Magnetic monopoles are used in various areas of theoretical physics like cosmology and quantum chromo dynamics.

In the latter, it was Dirac who postulated the magnetic monopoles in order to achieve complete symmetry in the Maxwell equations (complete because up till than, there was no magnetic variant of the electric charge). Given this symmetry, you can jump from magnetic phenomena to electric phenomena and the other way around. They are just two different languages to say the same : E and B are DUAL.

This duality is used in the Dual Abelian Higgs model, which is a theoretical model to explain the quark confinement phenomenon. In this case, the quark (ie an electric charge) is replace by a dual quark : ie a magnetic monopole. These dual quarks then interact with each other via dual gluons or quanta of the dual color electric field.

I did my master thesis on this in college, so if you want to know more, please ask away

regards
marlon

 

[mezarashi]

So let me clarify your points. Dirac said that to make Maxwell's treatment complete, he would introduce a concept (the monopole) that would violate one of Maxwell's equation.

About the duality, I certainly have always fundamentally believed that the magnetic field is only secondary to the electric. That is, the electric field must be the prime mover. Although once the E field makes a B field, the B field can come back to move the E field. It's just totally new somehow to think of it differently.

And about the theoretical model you mention, how certain are we about it. I'm not clear on your comment on how two quarks (charges) could possibly make a monopole (dual quark). Would this be saying that the fundamentals of electromagnetics do not apply at the quantum level?

I refer to this thread for more info.
Bascally, we have NOT yet observed magnetic monopoles, though it would be a great thing if they existed.

What kind of experiments can we do or we wish we could do to look for them?

 

[marlon]

So let me clarify your points. Dirac said that to make Maxwell's treatment complete, he would introduce a concept (the monopole) that would violate one of Maxwell's equation.

The idea of Dirac was to make the Maxwell equations completely symmetrical when you replace E and B fields. This denotes the E/B-duality. This is done by adding an antisymmetric tensor field (the Dirac string) to the EM-field tensor. here is NO violation of the Maxwell equations what so ever , you need to look at it as an extension of the Maxwell equations.

http://hcs.harvard.edu/~jus/0302/song.pdf is a good undergraduate-level paper that explains what is going on.

This E/B-duality is used in the Abelian Higgs Model, but keep in mind that the magnetic monopoles are dual quarks here. The corresponding dual photons (well gluons to be exact) describe the dual COLOUR-electric fields !

About the duality, I certainly have always fundamentally believed that the magnetic field is only secondary to the electric. That is, the electric field must be the prime mover.

Not at all, this is exactly what Dirac is trying to bypass.

I'm not clear on your comment on how two quarks (charges) could possibly make a monopole (dual quark). Would this be saying that the fundamentals of electromagnetics do not apply at the quantum level?
What kind of experiments can we do or we wish we could do to look for them?

I have debated the Dual Abelian Higgs model many times here. Just look at the "elementary particles presented" thead. I have put a reference to a paper on this. Or do a search on this forum.

marlon

EDIT : Look at post nr 13

 

[mezarashi]

Ah, I'm starting to see the idea in a much clearer view now. The paper is great. Thanks, and really, good luck to all those who are looking for those poles >.< ( ... somehow santa claus came into the picture in that last statement )