[db48x]

Except that if the divergence of the magnetic field were anything other than zero, the laws as presently written wouldn’t successfully predict electromagnetic effects. Because the laws as currently written _do_ make predictions, and exquisitely precise predictions at that, the divergence must be zero with no monopoles at all or so close to zero that monopoles would be extraordinarily weak if they did exist. Their effects would be so slight that they would be useless for any practical purpose except possibly impressing the Nobel committee.

[rnhmjoj]

The fact that standard EM theory with zero magnetic charge works well only proves that normally there aren't lots of magnetic monopoles floating around: they could be very short-lived particles or strange phase of the matter, but still real and Maxwell's equations don't say anything about this.

As far as I know there's no mathematical or physical reason to outright forbid magnetic monopoles. On the contrary, there is a well-known argument by Dirac that says that if they would exist then charge is quantised, which we know it is. This is one of the reasons people are still looking for magnetic monopoles.

[eigenket]

I don't really understand your point here. If we do discover magnetic monopoles (which would not necessarily be very weak but instead very rare) then we would take the equation

Div(B) = 0

And update it to say

Div(B) = sigma

Where sigma is a field describing the monopole density. Theres a ready "gap" in Gauss' law for magnetism where you can easily stick monopoles. Of course the divergence would be zero in the absence of monopoles, just as the divergence of the electric field is zero in the absence of electric monopoles, but decidedly non-zero when there's an electron around.

[shric]

It looks like this is already a polarizing topic

[data_maan]

+1 ;)

Not too many got the joke it seems :D

[shric]

Well I wasn't sure if it would be downvoted due to low effort, but it got 17 points, so thanks :p

[ryan-duve]

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

[xmcqdpt2]

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.

[BlueTemplar]

How about a single equation instead ?

http://www.av8n.com/physics/maxwell-ga.htm

(or even just equations (3), which make symmetries more apparent)

[danbruc]

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.

[elashri]

This is incorrect, you can put non-zero divergence of magnetic field and all the equations and predictions stays the same. Better it would make Maxwell's equations symmetric under exchange of fields and sources. \

> so close to zero that monopoles would be extraordinarily weak if they did exist

Why? I can't think of a reason why would this be the case? You are not solving Maxwell's equation for the universe. You can have divergence of electric field closed to zero because you have very low density (the field source) in the region you are studying.