Why could magnetic monopoles exist?

[Ahsan Khan]

TL;DR Summary

I am looking for reasons/ways of how can a magnetic monopole could exist even theoretically.

Hi all,

In textbooks and all other places they are saying that in principle magnetic monopoles can exist but yet have not been found (isolated). My pain increases further when I see a theoretical physicst say statements like, "We do not know of any theoretical reason why magnetic monopoles, magnet with a single North Pole or a single South Pole could not exist." The very reason of my pain with statements (facts) like these is my understanding (which is know must have some flaw) of magnetism.
My understanding begins with the fact that magnetism arrises as result of moving charges or current (it can also be their due to a time varying electric field). I learn that movement of charge, for instance the movement of electrons, orbiting around give rise to magnetic field in atoms/matter. They also say their is intrinsic magnetic field of electrons and protons (and even neutrons) due to something what they call spin. Obviously their will be current loops due to electron orbital motion. As a rule of thumb the side where current is clockwise we have south Pole of magnet there and at the side where current is counter-clockwise we have north Pole there.

I see that in any current loop I have, if their one side is having clockwise current then their must be other side and that other side must have a counter-clockwise current. It means if I have South Pole I can't get rid of North Pole on the other side. It's even theoretically impossible to have just a South Pole or just North Pole. It is impossible as per my understanding. They theoretical physicsts however believe something else though they too agree that no monopoles have yet been found,but problem is they believe in the possibility of existence of monopoles. There are even many researches like SQUID going on to create magnetic monopoles. I wonder if you can't have clockwise current (as seen from one side) without having counter-clockwise current (from other side) why you believe that north and south magnetic poles can exist separately.

Regards!
Thanks a bunch :)

 

[PeterDonis]

Your reasoning about why magnetic monopoles can't exist is correct for classical electrodynamics. However, the physicists you refer to, who say there is no theoretical reason why magnetic monopoles can't exist, are not talking about classical electrodynamics, or even quantum electrodynamics by itself. They are talking about quantum field theories in general, and in particular the kinds of quantum field theories that they view as candidates for a "theory of everything"--one that could unify all of the particles and interactions we know of. All such quantum field theories contain monopoles.

Such theories will reduce to quantum electrodynamics under particular conditions, and under those conditions, monopoles can't form; but there are other conditions under which, according to such theories, they can, and such conditions (very high temperature and density) would have been present in the very early universe. So many physicists believe that there should be monopoles in the universe, we just haven't found them yet.

 

[Ahsan Khan]

Your reasoning about why magnetic monopoles can't exist is correct for classical electrodynamics. However, the physicists you refer to, who say there is no theoretical reason why magnetic monopoles can't exist, are not talking about classical electrodynamics, or even quantum electrodynamics by itself. They are talking about quantum field theories in general, and in particular the kinds of quantum field theories that they view as candidates for a "theory of everything"--one that could unify all of the particles and interactions we know of. All such quantum field theories contain monopoles.

Such theories will reduce to quantum electrodynamics under particular conditions, and under those conditions, monopoles can't form; but there are other conditions under which, according to such theories, they can, and such conditions (very high temperature and density) would have been present in the very early universe. So many physicists believe that there should be monopoles in the universe, we just haven't found them yet.

Thank you so much PeterDonis, an excellent reply. I got it that the existence and non-existance of monopole(or anything) should be better understood by using modern theories(Quantum field theories) and for me it means the classical electrodynamics is true only in its own limited range. This was the very reason why by having the knowledge of just classical electrodynamics I was seeing the existence of magnetic monopoles as, even a theoretical impossibility.

The classical picture tells me that you have to have a current loop and then you will eventually have on one side of the loop, South Pole and on the other, the North Pole, that is you get a magnetic dipole. So the source of magnetic field (magnetic dipole) is current. It will be an additional favour if you give me the following details about a magnetic monopole.

(1) What could be the source of magnetism in a magnetic monopole; electric current which is also the source of magnetism in a magnetic dipole or the property of magnetism in magnetic monopole has to be intrinsic just as the property of electric charge, as they believe?

(2) The very dense matter in the early universe must have a good number of magnetic monopoles, with changing conditions monopoles disappears, as you hinted. So do they believe, out of those many magnetic monopoles present in the early universe, which had very high density and temperature, some of those monopoles may still be at some location of the earth, they hope to be possible? If that's the case they may be working to find these hidden monopoles. They could be going at different locations of Earth and in the mud/sand or in mines for example, searching any magnetic monopole. Are they really hopping to discover a magnetic monopole of the early universe?

Regards!

 

[Ahsan Khan]

Your reasoning about why magnetic monopoles can't exist is correct for classical electrodynamics. However, the physicists you refer to, who say there is no theoretical reason why magnetic monopoles can't exist, are not talking about classical electrodynamics, or even quantum electrodynamics by itself. They are talking about quantum field theories in general, and in particular the kinds of quantum field theories that they view as candidates for a "theory of everything"--one that could unify all of the particles and interactions we know of. All such quantum field theories contain monopoles.

Oops! I found a piece of information (not sure of reliability) and in that they say even bout classical electrodynamics that nothing in classical electrodynamics prohibits magnetic monopoles.

Attaching the screenshot and if possible the pdf file too.

 

[snorkack]

Summary:: I am looking for reasons/ways of how can a magnetic monopole could exist even theoretically.

Hi all,

In textbooks and all other places they are saying that in principle magnetic monopoles can exist but yet have not been found (isolated). My pain increases further when I see a theoretical physicst say statements like, "We do not know of any theoretical reason why magnetic monopoles, magnet with a single North Pole or a single South Pole could not exist." The very reason of my pain with statements (facts) like these is my understanding (which is know must have some flaw) of magnetism.
My understanding begins with the fact that magnetism arrises as result of moving charges or current (it can also be their due to a time varying electric field).

That second is the key.
Look at the Maxwell equations:
∇⋅E=ρ/ε₀
∇⋅B=0
∇×E=δB/δt*(-1)
∇×B=δE/δt*(μ₀ε₀)+J*μ₀

Pay attention that the Maxwell equations where both ρ and J are 0, describing propagation of electromagnetic waves in vacuum away from charges and currents, are basically symmetric for interchange of electric and magnetic fields!
This is the grounds for speculation about magnetic monopoles. The guess is that the absence/scarcity of magnetic monopoles near us is merely accidental, and we might encounter a locality where both magnetic and electric monopole charges are around.

 

[hutchphd]

However, the physicists you refer to, who say there is no theoretical reason why magnetic monopoles can't exist, are not talking about classical electrodynamics, or even quantum electrodynamics by itself.

I do not understand this statement. Is there a theoretical reason why classical electrodynamics could not be formulated including magnetic monopoles? Please flesh this out a little.

 

[vela]

My understanding begins with the fact that magnetism arises as result of moving charges or current (it can also be their due to a time varying electric field).

I see that in any current loop I have, if their one side is having clockwise current then their must be other side and that other side must have a counter-clockwise current. It means if I have South Pole I can't get rid of North Pole on the other side. It's even theoretically impossible to have just a South Pole or just North Pole.

You're thinking about a magnetic field produced by moving electric charges. Indeed, when a magnetic field is produced by an electric current loop, a north pole comes with a south pole.

With a magnetic monopole, it would have an associated magnetic field, much like electric charges come with an electric field. A magnetic current loop would produce a dipole electric field. From one side, it would look like there's a positive charge end, and from the other, a negative charge. Just like magnetic poles come in pairs when a magnetic field is produced by an electric current loop, electric charges would appear to come in pairs when an electric field is produced by a magnetic current loop. It would be incorrect to conclude, however, that electric monopoles (charges) can't exist. Likewise, you shouldn't conclude a magnetic monopole can't exist because of the field produced by an electric current loop.

 

[PeterDonis]

they say even bout classical electrodynamics that nothing in classical electrodynamics prohibits magnetic monopoles.

What they mean is that there is nothing mathematically inconsistent about a theory that changes classical electrodynamics so that magnetic monopoles are possible. But such a theory would not be the same classical electrodynamics that we currently have; it would contradict at least one Maxwell Equation (the equation $\nabla \cdot B = 0$ since magnetic monopoles would appear as a nonzero "magnetic charge" on the RHS of that equation).

Is there a theoretical reason why classical electrodynamics could not be formulated including magnetic monopoles?

Yes, that classical electrodynamics says $\nabla \cdot B = 0$, which, as noted above, is inconsistent with magnetic monopoles. You could change classical electrodynamics to allow monopoles, but then it would be a different theory from the classical electrodynamics we currently have.

 

[Ahsan Khan]

What they mean is that there is nothing mathematically inconsistent about a theory that changes classical electrodynamics so that magnetic monopoles are possible. But such a theory would not be the same classical electrodynamics that we currently have; it would contradict at least one Maxwell Equation (the equation $\nabla \cdot B = 0$ since magnetic monopoles would appear as a nonzero "magnetic charge" on the RHS of that equation).Yes, that classical electrodynamics says $\nabla \cdot B = 0$, which, as noted above, is inconsistent with magnetic monopoles. You could change classical electrodynamics to allow monopoles, but then it would be a different theory from the classical electrodynamics we currently have.

This clears my every confusion. Thank you and everyone else who attempts to answer

 

[Ahsan Khan]

(1) What could be the source of magnetism in a magnetic monopole; electric current which is also the source of magnetism in a magnetic dipole or the property of magnetism in magnetic monopole has to be intrinsic just as the property of electric charge, as they believe?

(2) The very dense matter in the early universe must have a good number of magnetic monopoles, with changing conditions monopoles disappears, as you hinted. So do they believe, out of those many magnetic monopoles present in the early universe, which had very high density and temperature, some of those monopoles may still be at some location of the earth, they hope to be possible? If that's the case they may be working to find these hidden monopoles. They could be going at different locations of Earth and in the mud/sand or in mines for example, searching any magnetic monopole. Are they really hopping to discover a magnetic monopole of the early universe?

Regards!

But I still need answer to these two questions. Thanks a lot to PeterDonis for the marvellous mentoring.
Regards!

 

[PeterDonis]

I still need answer to these two questions.

(1) In an altered electrodynamics that allows magnetic monopoles, the source of the magnetism in a monopole is magnetic charge, just as the source of electricity in an electric monopole (like a charged particle) is electric charge. In other words, in this altered theory, there are two kinds of electromagnetic charges, not one. The second kind of charge (and its associated current) is the new aspect of this theory.

In the various quantum field theories that have monopoles, there is an underlying mechanism behind the magnetic charge that would probably require an "A" level discussion to explain. But at the macroscopic level, it ends up looking like the magnetic charge in the altered version of classical electrodynamics that I described above.

(2) Physicists who think magnetic monopoles might exist generally seem to believe that they were created in the early universe, but I'm not sure whether they would still exist in a place like the Earth. They might only exist in regions of space not occupied by solar systems and stars and planets.

 

[Ahsan Khan]

Understood, thanks and regards! :)

 

[vanhees71]

I'd also say, the puzzle is, why there's no observational sign of any magnetic monopoles. Neither in classical nor quantum electrodynamics/QFTs there's any argument against their existence. To the contrary, electromagnetism would get much more symmetric with magnetic monopoles, and as the famous work by Dirac shows, it would be a possible explanation, why the electric charge of observable particles are all integer multiples of the elementary charge $e$, because for this discreteness there's also no deeper explanation within contemporary physics, although there are some constraints of the possible "charge patterns" in the Standard Model from the necessity to avoid the anomalous breaking of the electroweak gauge symmetry. This socalled anomaly, i.e., the breaking of a symmetry present in a classical field theory when quantizing this symmetry, is avoided in the Standard Model by precisely having the particle content with its electric charges, i.e., two flavors of quarks with $-e/3$ and $+2e/3$ charge, each coming in 3 "colors", and a negatively charged lepton + a neutral neutrino in each "family", but even this is not the only "charge pattern" that avoids the anomalous breaking of the electroweak gauge symmetry.