Emmy Noether was also recently the subject of In Our Time, a fantastic BBC roundtable discussion program. She seems to have had a remarkable skill for invariants and finding symmetries in complex math, perhaps even some kind of intuition that allowed her to make incredible leaps in different academic areas around the topic. She played a crucial part in helping Einstein and Hilbert lay the groundwork for the theory of general relativity, as well as making significant advances in abstract algebra. The scope of her contributions is only recently starting to be truly appreciated and I would highly recommend listening to the show.

Emmy Noether's story is an interesting perspective on the sociology of the scientific establishment a hundred years ago. But (in case the reader doesn't appreciate the importance of the ideas) it's also worth focusing on what is a fantastic and profound result regarding symmetries and how they make problem-solving easy (in a very concrete operational sense). The ideas are so deep that they're not only applicable when there are exact symmetries, but degrade gracefully to also give approximate answers when symmetries are approximate.

I think everyone wants to know the answer to this as it would literally be the grand unified field theory. But since we’re here, my two cents is on conservation of space-time with the corresponding symmetry rule being the relationship between zero and infinity. Manifested physically as a relationship between the gravitational constant and the Hubble constant. The cosmological constant being a happy accident as result of hybrid geometry combining a Riemann Manifold and Anti-de Sitter space the other forces emerging as result of space-time expansion/flow in this geometry through kinks in Space-time caused by energy concentrations in the form of particles calculated with the good ol’ Bernoulli equation. With the number of dimensions being exactly 4 (modifying the exponents of Einstein’s equations from ^3 to ^4). I can go on at the risk of sounding more like a crackpot but alas to quote Michel de Montaigne “Que sais-je?”

I don't understand what you mean by conservation of gravity. Do you mean conservation of mass? There is literally nothing else than mass and some universal constants that determine the gravitational force.

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.

> I don't understand what you mean by conservation of gravity. Do you mean conservation of mass?

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).

> 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.

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.

Isn't divB=0 one of Maxwell's equations? That seems to be "one of our physical theories" claiming the impossibility of magnetic monopoles.

Ah, but this is indeed just us saying "hey, we don't see any monopoles anywhere, so let's simplify the equations to divB=0". The "full" equations have a divB={stuff that's perfectly symmetric to divE RHS}, and also a modified curlE term to make the "full" set of equations completely symmetric for electricity and magnetism. You can see these equations at

Interesting! I guess I've never learned much physics more recent than 1904.

It’s perfectly possible to modify Maxwell’s equations to include magnetic monopoles. Doing so makes Maxwell’s equations more symmetric between electric and magnetic fields.

The reason we have equation ∇·B=0 is due to empirical observation.

A bit off topic, but anyone know what the symmetries for Conservation of Gravity and Conservation of Magnetic charge are?

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.