Proving Symmetry of Modified Maxwell Equations

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Discussion Overview

The discussion centers on the modification of Maxwell's equations to include magnetic monopoles, specifically focusing on the proposed forms of the equations and the mathematical proof of their correctness. The scope includes theoretical exploration and mathematical reasoning related to symmetry in physics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes modified Maxwell equations that include magnetic monopoles, questioning how to prove their correctness mathematically.
  • Another participant argues that deriving the equations theoretically without considering symmetry may not be sufficient, suggesting that Maxwell's equations are based on experimental laws.
  • A third participant states that the divergence of the magnetic field equation defines "magnetic charge," implying a foundational aspect of the proposed modifications.
  • A later reply specifies the term "magnetic charge density" in relation to the curl of the electric field equation, indicating a more precise understanding of the concepts involved.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of symmetry in deriving the modified equations, indicating that there is no consensus on the approach to proving their correctness.

Contextual Notes

The discussion does not resolve the mathematical steps required to prove the modified equations, nor does it clarify the definitions and assumptions related to magnetic charge and its implications.

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If there were magnetic monopole, the Maxwell equations should be modified as

[tex] \nabla\cdot\vec{B} = \mu_0\rho_m[/tex]

[tex] \nabla\times\vec{E} = - \frac{\partial \vec{B}}{\partial t} - \mu\vec{J}_m[/tex]

and plus the other two.

I wonder how to prove these two modified equations are of correct form? Someone told me they should be of those form because of symmetry. I would like to prove that mathematically but have no way to start ...
 
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Em,I think it's not possible by just derive theoretically and do not use the idea of symmetry,because Maxwell equations themselves are mathematical summaries of experimental laws,right?
 
The divB equation is the definition of "magnetic charge".
The curl E follows from the continuity equation for magnetic charge.
 
"magnetic charge density", to be exact.
 

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