I think your point is the current Maxwell equations explain physics so well that if we change them to accommodate magnetic monopoles they would have to be worse. If I understand you right, it overlooks that we can add terms[0] to Maxwell's equations that don't affect predictions in a world free of magnetic monopoles:
∇⋅E = ρ(electric) / ϵ0
∇⋅B = μ0 * ρ(magnetic)
∇⨯E = -μ0 * J(magnetic) - ∂B/∂t
∇⨯B = μ0 * J(electric) + (μ0)(ϵ0)(∂E/∂t)
We could switch every physics textbook to using the above today, and the only difference would be setting ρ(magnetic) and J(magnetic) to zero when there are no monopoles in the problem.
[0] Griffiths Introduction to Electrodynamics 3E, Section 7.3.4
If anything it's frustrating that there aren't monopoles, because if there were, we could make the E and B equations symmetrical under interchange of the fields. It would be a lot prettier, and I think it would be easier to teach to undergrads.
I mean you could just do that and tell the students that the magnetic charge and current densities are always zero unless we eventually discover monopoles.
Comments
I think your point is the current Maxwell equations explain physics so well that if we change them to accommodate magnetic monopoles they would have to be worse. If I understand you right, it overlooks that we can add terms[0] to Maxwell's equations that don't affect predictions in a world free of magnetic monopoles:
∇⋅E = ρ(electric) / ϵ0
∇⋅B = μ0 * ρ(magnetic)
∇⨯E = -μ0 * J(magnetic) - ∂B/∂t
∇⨯B = μ0 * J(electric) + (μ0)(ϵ0)(∂E/∂t)
We could switch every physics textbook to using the above today, and the only difference would be setting ρ(magnetic) and J(magnetic) to zero when there are no monopoles in the problem.
[0] Griffiths Introduction to Electrodynamics 3E, Section 7.3.4
If anything it's frustrating that there aren't monopoles, because if there were, we could make the E and B equations symmetrical under interchange of the fields. It would be a lot prettier, and I think it would be easier to teach to undergrads.
How about a single equation instead ?
http://www.av8n.com/physics/maxwell-ga.htm
(or even just equations (3), which make symmetries more apparent)
I mean you could just do that and tell the students that the magnetic charge and current densities are always zero unless we eventually discover monopoles.