Science behind magnetic monopoles in any depth?

In summary, magnetic monopoles would be a phenomenon that could explain quantization of charge, and also make the Maxwell equations more symmetrical. They would become (in Gaussian units) \vec{J}_m- \frac{\partial \vec{B}}{\partial t}.
  • #1
Just some guy
69
1
Hi,

Just wondering, does anybody know of any texts or websites that go into the science behind magnetic monopoles in any depth? I'm thinking of writing a report on them as part of my A2 course but I can't find much information about them! (apart from the fact that nobody's detected them and people think they might not exist, but what the heck :biggrin: )
 
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  • #2
The existence of magnetic monopoe would be very fun because it would explain quantization of charge (i.e. why charges come in integer multiples of e) and also because it would make the Maxwell equations more symetrical. They would become (in Gaussian units)

[tex]\nabla \cdot \vec{E} = \rho_e[/tex]
[tex]\nabla \cdot \vec{B} = \rho_m[/tex]
[tex]\nabla \times \vec{E} = -\vec{J}_m- \frac{\partial \vec{B}}{\partial t}[/tex]
[tex]\nabla \times \vec{B} = \vec{J}_e+\frac{\partial \vec{E}}{\partial t}[/tex]


Read the wiki page if you haven't: http://en.wikipedia.org/wiki/Magnetic_monopoles
 
  • #3
Yes, I've read the wiki article, but it isn't really enough to base a 4000 word report on...
 
  • #4
4000 words that's a lot, I'll agree.

And the equations I wrote are probably wrong in the units area; there should be a bunch of 4pi and c I think... sorry bout that.
 
  • #5
Study the maxwell's generalised equations. Look up duality transformations, look up one-forms, hodge duals. Believe me there's way more than 4000 words to write on this. However a lot of this stuff might be tough for A2; are you doing the Advancing Physics (IoP) course?
 
  • #6
quasar987 said:
And the equations I wrote are probably wrong in the units area; there should be a bunch of 4pi and c I think... sorry bout that.

If we have the electric current density 4-vector [itex]\rho^e=(-\rho^e/c, j_x^e, j_y^e, j_z^e)[/itex] (sorry about the bad notation), then the magnetic current density 4-vector would be (I think) [itex]\rho^m=(\rho^m, j^m_x/c, j^m_y/c, j^m_z/c)[/itex] (where both are written as covariant vectors).

Could someone correct me if I'm wrong? (I suppose I should just check the units...)
 
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  • #7
masudr said:
Study the maxwell's generalised equations. Look up duality transformations, look up one-forms, hodge duals. Believe me there's way more than 4000 words to write on this. However a lot of this stuff might be tough for A2; are you doing the Advancing Physics (IoP) course?

Yes I am. I know it might be a bit beyond me but I want to do something exceptional and I'm willing to try some of the more advanced stuff. Thanks for the advice:smile:
 
  • #8
Just some guy said:
Yes I am. I know it might be a bit beyond me but I want to do something exceptional and I'm willing to try some of the more advanced stuff.

OK, TRY THESE;

1. DIRAC, THE MONOPOLE CONCEPT, INTR.JOUR.THRO.PHYS,V17,No4(1978)
2. KAZAMA, ELECTRON-MONOPOLE SYSTEM, AS ABOVE PP249-265
3. BRANDT & PRIMACK, DYONS, AS ABOVE,PP267-273
4. MARCIANO, NON-ABELIAN MONOPOLES, AS ABOVE,PP275-286
5. NAMBU, TOPOLOGICAL CONFIG IN GAUGE THEORIES, AS ABOVE,PP287-292
6. FREUND, MONOPOLES,TOPOLOGY,SYMMETRY, AS ABOVE,PP301-308.
7.RAJARAMAN, SOLITONS & INSTANTONS, NORTH HOLLAND PRESS.1982
REFERENCE No7 IS A 400 PAGE BOOK.



REGARDS

sam
 
  • #9
Just some guy said:
Yes I am. I know it might be a bit beyond me but I want to do something exceptional and I'm willing to try some of the more advanced stuff. Thanks for the advice:smile:

I did the same A-Level course as you in the years 2002-2004. For my A2 research report, I zoomed over the 3 problems that classical mech + electrodynamics could not explain, I did a brief review on the mathematics of linear vector spaces (and operators defined on them), and then went on to the postulates of quantum mechanics, a list of some operators in position representation, and as an example I solved the particle in a 1D box problem.

Obviously I was about 2 years ahead in terms of when people normally learn QM, and so undoubtedly there were some oversights (or errors if you like) in my work, but it did not fit in very well the criteria on the mark scheme, since I did not have many diagrams etc; in fact apart from the graphs of the wavefunctions I had no diagrams! So my teacher could not give me any more than 32/40 marks (which was an A) but I felt it perhaps deserved more.

While monopoles are interesting, the best way to look at them would be in covariant equations, and that requires learning about tensors, component notation, lorentz transformations as a (1, 1) tensor, and 4-vectors and such like. While you probably could learn it all, I don't think you'd have the time. I recommend you find a more well-documented phenomenon, especially one that can have a lot of good pictures etc. I think that examinations are ridiculous, and are designed to get you to jump through hoops. It's slightly different here as an undergrad at Oxford, but A-Levels (and much more so GCSEs) are a lot to do with hoop-jumping.

Hope this helps.
 
  • #10
samalkhaiat said:
Just some guy said:
OK, TRY THESE;
1. DIRAC, THE MONOPOLE CONCEPT, INTR.JOUR.THRO.PHYS,V17,No4(1978)
2. KAZAMA, ELECTRON-MONOPOLE SYSTEM, AS ABOVE PP249-265
3. BRANDT & PRIMACK, DYONS, AS ABOVE,PP267-273
4. MARCIANO, NON-ABELIAN MONOPOLES, AS ABOVE,PP275-286
5. NAMBU, TOPOLOGICAL CONFIG IN GAUGE THEORIES, AS ABOVE,PP287-292
6. FREUND, MONOPOLES,TOPOLOGY,SYMMETRY, AS ABOVE,PP301-308.
7.RAJARAMAN, SOLITONS & INSTANTONS, NORTH HOLLAND PRESS.1982
REFERENCE No7 IS A 400 PAGE BOOK.
REGARDS
sam

Hmm, I can't find 'the monopole concept' anywhere - is it still in print and if so where can I get it from?
 
  • #11
Just some guy said:
Hmm, I can't find 'the monopole concept' anywhere - is it still in print and if so where can I get it from?

It's a journal, not a book. Look in a big academic library, or look up the journal online.
 

1. What are magnetic monopoles?

Magnetic monopoles are hypothetical particles that have a single magnetic pole, either north or south, instead of the traditional dipole with both north and south poles. They are considered to be the magnetic equivalent of electric charges.

2. Can magnetic monopoles be found in nature?

Currently, there is no evidence of the existence of magnetic monopoles in nature. However, several theories in particle physics and cosmology suggest that they may have existed in the early universe or could be created in high-energy experiments.

3. What is the science behind magnetic monopoles?

The science behind magnetic monopoles is complex and still being researched. According to Maxwell's equations, any magnetic field must have both a north and south pole, but the existence of magnetic monopoles would violate these equations. Theories such as gauge field theories and topological defects attempt to explain how magnetic monopoles could exist.

4. How are magnetic monopoles related to electricity?

Magnetic monopoles are related to electricity through the unification of the electromagnetic force. In theories such as Grand Unified Theories (GUTs) and supersymmetric theories, magnetic monopoles and electric charges are seen as two aspects of the same fundamental force.

5. What are the potential applications of magnetic monopoles?

If magnetic monopoles are ever discovered and harnessed, they could have significant technological applications. They could potentially be used in new types of motors, generators, and other devices that rely on magnetic fields. They could also provide new insights into the fundamental laws of the universe and the unification of forces.

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