Colloquium: A Century of Noether's Theorem
arxiv.org
arxiv.org
i.e. gravity can not be created or destroyed, it can only be moved (works just like Conservation of Charge).
And a Magnetic monopole can not be created unless you create both sides at the same time.
As for "no magnetic monopoles" - this one isn't actually a law, there's nothing in any of our physical theories that says you cannot have magnetic monopoles, it's just that experimentally nobody's ever found one (and we've looked pretty hard).
It's important to note about magnetic monopoles that the magnets we know are not made up of magnetic monopoles, they are made up of magnetic dipoles. No matter how small pieces you break a magnet into, even going down towards atom-sized bits, the pieces still have a north and a south pole.
The reason we have equation ∇·B=0 is due to empirical observation.
I don't. Say you suddenly open a wormhole and gravitational force pours though. This would violate conservation of gravity since now there is gravity when before there wasn't. i.e. such a wormhole would be impossible.
Or some kind of gravity shield that blocks any gravity from passing. Again, violates this rule. (It would have to deflect the gravity instead, so the total force doesn't change.)
> there's nothing in any of our physical theories that says you cannot have magnetic monopoles
It's not about having the monopole, it's about creating just one of them, and not creating both at once. I believe there is a conservation of magnetism law that would prevent that, analogous to conservation of charge (you can not create just one charge, both a plus and minus need to be created together).
Note that you can replace "open a wormhole" by "suddenly introduce a mass" and this statement is the same. In practice, both "introducing a mass" and "opening a wormhole" cannot be done instantly unless you violate conservation of energy, and as Einstein told us, energy also introduces gravitational force. So as you're turning the wormhole on, you would see the gravitational field increasing slowly and in accordance with conservation of mass and energy. There's no additional "conservation of gravity".
> It's not about having the monopole, it's about creating just one of them, and not creating both at once.
Ah, but this is conservation of magnetic charge. In a world where magnetic monopoles exist, this follows directly from the "full" Maxwell's equations, just like electric charge conservation does. See https://en.wikipedia.org/wiki/Maxwell's_equations#Charge_con...
But the point is, we can't even create two magnetic monopoles in a way that conserves total magnetic charge. We literally need a new fundamental particle for this to happen.