Dirac's magnetic charge generalization of maxwell's equations?

In summary, Dirac said that the magnetic charge density explained charge quantization. However, I'm not familiar with the equations, and it's unclear whether this is still a theoretical idea or if there is now experimental data to support it.
  • #1
Peeter
305
3
I've seen two references to magnetic charge density as something that Dirac said would explain charge quantization. The first is in Schwartz's "Principles of Electrodyanamics" (Dover) where the author comments how it is unaesthetic that the two maxwell's equations aren't symmetric in form:

[tex]
\partial_{\mu}F_{\mu\nu} = -4\pi j_v
[/tex]

[tex]
\partial_{\mu}G_{\mu\nu} = 0
[/tex]

This book (1972), gives the idea mention, saying it would be nice to be able to write the second tensor equation as:

[tex]
\partial_{\mu}G_{\mu\nu} = 4 \pi j_{\nu}^{(m)}
[/tex]

but procedes without it after such a mention "since no monopoles have as yet been seen".

Another reference was in:

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

This is an online book "Electromagnetic field theory", by Bo Thide where it's given more than just a passing reference. However, reading this I'm unclear whether it's just a theoretical idea. Is there now experimental data that the Dirac symmetrized Maxwells' equations explains (perhaps more than just the monopole idea) that the standard form doesn't?

In more advanced (quantum electrodynamics?) or more modern treatments of electrodynamics does this idea have any place?
 
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  • #2
Peeter said:
... However, reading this I'm unclear whether it's just a theoretical idea. Is there now experimental data that the Dirac symmetrized Maxwells' equations explains (perhaps more than just the monopole idea) that the standard form doesn't?


Not farmiliar with the eqns., but I thought Dirac condition for the magnetic monopole doesn't symmetrize the charges but only quantizes,the Dirac condition being ...

eg = hc/4pi ...where g = magnetic charge


Creator :smile:
 
  • #3
The equations I was referring to are: 1.50a-d from EMFT_Book.pdf here:

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


[tex]
\nabla \cdot E = \rho^e/\epsilon_0
[/tex]

[tex]
\nabla \times E = -\frac{\partial B}{\partial t} - \mu_0 j^m
[/tex]

[tex]
\nabla \cdot B = \mu_0 \rho^m
[/tex]

[tex]
\nabla \times B = \epsilon_0 \mu_0 \frac{\partial E}{\partial t} + \mu_0 j^e
[/tex]
 
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What is Dirac's magnetic charge generalization of Maxwell's equations?

Dirac's magnetic charge generalization of Maxwell's equations is a theoretical extension of James Clerk Maxwell's famous equations, which describe the fundamental laws of electricity and magnetism. The generalization adds a term that accounts for the existence of magnetic monopoles, or isolated magnetic charges, which have not yet been observed in nature.

Why did Paul Dirac propose this generalization?

Dirac proposed this generalization in 1931 in an attempt to reconcile the existence of electric charges with the symmetry between electric and magnetic fields. He believed that the existence of magnetic monopoles would balance out the asymmetry and provide a more elegant solution to the equations.

What are the implications of Dirac's magnetic charge generalization?

If magnetic monopoles were to exist and be described by Dirac's generalization, it would have significant implications for our understanding of fundamental physics. It would also affect our understanding of how magnetic fields are generated and how they interact with electric fields.

Has Dirac's magnetic charge generalization been verified?

As of now, there is no experimental evidence to support the existence of magnetic monopoles or to confirm Dirac's generalization. However, there have been theoretical studies and experiments that have attempted to detect or create magnetic monopoles, but none have been successful to date.

Are there any current applications of Dirac's magnetic charge generalization?

Although Dirac's generalization has not been verified and has not found practical applications, it has been a source of inspiration for theoretical studies and has sparked interest in the search for magnetic monopoles. It also serves as a reminder of the ongoing pursuit to understand the fundamental laws of the universe.

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