# Magnetic Monopoles detected? Mayhaps

I told you so!

MathematicalPhysicist
Gold Member
btw isnt it meaningless to say: "north or south magnetic pole" because there is only one pole and it's not relative to other pole as for example a simple magnetic is.

I'm not sure how they would classify monopoles, unless they expose it to a known magnetic dipole and observe what it behaves as, but other than that, I can't provide any further answer to how they could classify a monopole as north or south.

Hurkyl
Staff Emeritus
Gold Member
"north" and "south" are just synonyms for positive and negative. (not necessarily in that order)

Quote from the magnetic monopoles article:

"The researchers also measured the transverse optical conductivity of a thin film of the crystal using a technique known as high-resolution Kerr microscopy and found a sharp peak at low energies. According to Tokura and co-workers, this peak can only be explained by the presence of monopoles in the band structure of the crystal."

Anybody care to explain what a Kerr microscopse is?

Monopoles are supposed to have arisen from inflation, according to Alan Guth. Why monopoles? What type of electric circuit corresponds to a monopole? Might they occur as virtual entities, with +/- separate only within the bounds of the HUP?

Loop Quantum Gravity: By saying "I told you so" to Brad_Ad23, I did not mean that I had previously said that they'd been found, but that I had previously said that I think they exist (and not yet found [to my knowledge] until now.)

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Yeah that did confuse me a bit as well.

Anywho, I had a post for a few posts up, but couldn't post it, but here it is:

First off, monopoles are the magnetic equivalent to a pure positive or
pure minus electric charge. You may be familiar that the electric force
and magnetic force are combined into the electromagnetic force. Yet, they
appear to exhibit a bizzare asymmetry. We can easily get single charges,
but never single magnetic poles. Plus always comes with minus. To
isolate a single monopole would be quite an achievement and verify several

As for Kerr Microscopy:

http://physics.nist.gov/Divisions/Div841/Gp3/Facilities/kerr.html [Broken]

http://www.boulder.nist.gov/magtech/kerrscop.htm [Broken]

Those should tell you what Kerr Microscopy and what a Kerr Microscope are
respectively.

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There can be no monopoles.

Since more than 50 years it is known that, what we call magnetism, is in fact a relativistic side effect of the electric field. So there can only be apparent dipoles.

This was exactly mathematically proven by e.g. Rosser, Electromagnetism by Special Relativity, Butterworth, London.

Experiment rules over mathematical proof, except in this case where the experiment is not conclusive, then it is up for speculation, so therefore, one can't outright say they do/don't exist. Keep in mind that absence of evidence is not evidence of absence.

Hurkyl
Staff Emeritus
Gold Member
Claims of mathematical proof are highly suspect as well because theories permitting monopoles (such as Dirac's symmetrized Maxwell equations, for an elementary example) exist.

In fact, in Dirac's symmetrized Maxwell equations, if nonzero magnetic and electric charges have the right relationship, the theory is physically indistingusihable from the ordinary Maxwell equations, so no such proof can exist.

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Experiment rules over mathematical proof
That is true! However from the Maxwell theory together with the Lorentz transformation it follows that magnetic monopoles cannot exist. (Refer to the book of Rosser mentioned above).

So, if magnetic monopoles are found it has severe consequences:
- Either the Maxwell theory is wrong
- Or Special Relativity is wrong

In both cases we will have to re-think main areas of physics.

Or, neither are wrong. If other theories which are consistent to exist that incorperate both Maxwell and hence SR, and have monopoles, such as the aforementioned Dirac equations, then what do we have? Why it looks like different formulae for the same phenomenon, only each looking at certain conditions maybe? I would say that is more accurate. In physics, mathematical proof is merely an interesting footnote, albeit an important footnote.

Evaluation of the Lorentz transformation shows that the magnetic field is a relativistic side effect of the electric field. If we would have magnetic monopoles in addition then we would have two independent causes of magnetism.

The Lorentz transformation fully explains the magnetic phenomena as given by Maxwell. If we now have an additional source of magnetism which would give an additional contribution to the magnetic field, the Maxwell equations can no longer be correct.

But then how can the Dirac version even exist? And as an aside, I am curious if the math you speak of takes into account any quantum effects. IIRC, monopoles arise on a quantum level.

The relativistic requirement of Lorentz invariance requires that derivatives in space in time all appear to the same order, since all four coordinates must be treated on equal footing. The K-G equation illustrates that an expression which satisfies this condition but is non-linear in the space and time derivatives gives rise to anomalous results. Dirac set out to find an equation which was first order in space and time derivatives. The result of his efforts, the Dirac equation, is difficult to motivate, impossible to prove, and far more complicated that the non-relativistic analog, but it has been shown to work, and satisfies all the requirements of special relativity and quantum mechanics.

So what does Dirac have to do with Monopoles is my question!?

Staff Emeritus
Gold Member
Dearly Missed
Check out this Wikipedia definition. Dirac showed that if there was even one magnetic monopole in the universe, then electric charge would have to be quantized. Which it is, of course and which ordinary quantum theory does not explain.

Dirac showed that if there was even one magnetic monopole in the universe, then electric charge would have to be quantized.
Is the reverse conclusion correct? That means if the electric charge is quantized then there must be magnetic monopoles?

It is a property of the magnetic field that, if we notice to be in a field and we move with an appropriate velocity into an appropriate direction, the magnetic field will disappear.

Now assume that you are at the side of a magnetic monopole. Then you will also be able to move in a specific direction so that you will not notice the field any longer. So you see a magnetic monopole which has no magnetic field.

Tom Mattson
Staff Emeritus
Gold Member
Originally posted by Albrecht
If we would have magnetic monopoles in addition then we would have two independent causes of magnetism.

So what?

The Lorentz transformation fully explains the magnetic phenomena as given by Maxwell. If we now have an additional source of magnetism which would give an additional contribution to the magnetic field, the Maxwell equations can no longer be correct.

No, Maxwell's theory can be correct in regions free of magnetic charge, just as [nab].E=0 is true in regions free of electric charge.

Your arguments fail on four grounds.

First, as has been noted, no equation can rule out the existence of anything physical.

Second, and what is related to the first, we must accept or reject the existence of monopoles strictly on the basis of experimental findings, not on the basis of the consequences of what they might do to our neat, tidy theory. It just so happens that photons also throw a monkey wrench into the Maxwell theory. Should we disbelieve them, too? Of course not; we simply adopt a new theory (QED) which contains the old one as a special case.

Third, rejecting monopoles on the basis that SR applied to a charge yields all observed magnetic effects "as given by Maxwell" is a circular argument. If you apply the Lorentz transform to a moving charge (and so tacitly assume that moving charges are the only sources of the EM field), then of course you are going to reproduce the "no monopoles" statement of the Maxwell theory.

Fourth, it is not true that the existence of monopoles would force a massive overhaul of the Maxwell theory. Dirac produced an elegant generalized EM theory that does in fact contain the Maxwell theory as a special case.

edit: fixed color bracket

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I agree 100%!

you are going to reproduce the "no monopoles" statement of the Maxwell theory
Is there in fact such a statement? Was it given by Maxwell?

Dirac produced an elegant generalized EM theory
Can you please give us a reference to the corresponding paper of Dirac?

Again my question: What is about the magnetic monopole which disappears when the observer is in an appropriate motion state. Can this happen?

Tom Mattson
Staff Emeritus
Gold Member
Originally posted by Albrecht
Is there in fact such a statement? Was it given by Maxwell?

Yes, it is [nab].B=0.

Can you please give us a reference to the corresponding paper of Dirac?

I don't have that reference, but the theory is nicely presented in section 1.4 of this book:

http://www.plasma.uu.se/CED/Book/EMFT_Book.pdf

Again my question: What is about the magnetic monopole which disappears when the observer is in an appropriate motion state. Can this happen?

The monopole will not disappear, because it is a permanent source of the B field, just as electric charges are permanent sources of the E field. In the Dirac theory, the B field can only disappear under Lorentz transformations if it arises from electric currents. Similarly, In the Dirac theory monopole currents can give rise to E fields that disappear under Lorentz transformations.

The symmetrization of Maxwell's equations introduces a "Coulomb's law" for magnetic fields and a "Biot-Savart law" for electric fields.

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http://www.plasma.uu.se/CED/Book/EMFT_Book.pdf[/QUOTE]
Thanks for this reference to the EMFT book of Bo Thide.

It is an interesting intellectual exercise to build a complementary pairing of electricity and magnetism, in which the charge is called magnetic and the relativistic side effect is called electric.

It has very surprising logical consequences if we generalise this assumption of complementary charges.

We have to keep in mind that every polar force (so, assumably also the strong force) has it's own "magnetism", as relativity, which is the cause of magnetism, is valid for every force. Should we now assume that also in the case of the strong interaction there is not only this relativistic side effect, i.e. this related kind of a "magnetism" but that there are also monopoles of this related magnetism? If this is generalised, very force has to have besides it's original charge a kind of complementary charge corresponding to the magnetic monopole we are talking about.

Or do we have to assume that the electric force is special compared to the other forces? Do we know a reason why it should be that way?

On the other hand, do we know whether this "magnetic force" of the magnetic monopole, which would (if existing) be additional to the normal magnetic field, would interact with our existing electromagnetic world? Before we investigate this monopole charge by an experiment, we cannot know. To be serious we have initially to assume that it is some kind of a new "fifth force" if it should exist.

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