The article doesn't mention, but also one of the million dollar Millennium Prizes is to do with exactly this.
Except for a few very special circumstances (high energy collisions), we can't get any real answers from Quantum Chromodynamics (QCD) about the nucleus that actually agree with reality - we can barely get any answers at all.
The problem is that these equations use what mathematicians, somewhat disdainfully, like to call "formal mathematics". That is to say that they are just a bunch of rules for manipulating symbols on paper that don't really make sense. More like numerology than real mathematics. No one knows if the rules make any sense at all. If you follow the rules in a different order, for example, you get different answers, and no one knows what it means. The "formal" equations are more based on physical understanding and not the usual solidly based "real" mathematics.
It is kind of like how people started using complex numbers before they understood why they worked. They knew the square root of minus 1 was nonsense, and yet you get the right answer, but no one knew why. Today it is a similar situation with QCD (except you can hardly get any answers at all).
So if you solve this problem (either in the positive or negative) you get 1 million dollars.
We really have to get more money into such prizes. The catering budget at CERN might cost more. Wordle just sold for more than a million. A tweet from some random influencer can cost a million. I read once that the human race spent more on ringtones in the 2000s than it did on fusion research. We need to better prioritize.
I'm relieved, at a presentation I did when I was an undergrad in the 90s I claimed that the QCD strong interaction boiled down to pion exchange at nuclear distance. It's good to see that I didn't mislead my classmates too badly.
How about this. What holds quarks together? Electrostatic force. Because charges in a line:
+2 -1 +2
Will be pulled together, not pushed apart. If coming from infinity they will reach the speed of light at some distance. Hand wave some relativity now because our Hadron just became a sort of black hole. Are they orbiting inside, outside, on on the event horizon. IDK but...
These orbiting charges create a magnetic field. What holds a nucleus together? Magnetism, along with some particular interaction of the quark charges similar to the above.
The quarks really do attract in that configuration. The question isn't "why don't they fly apart", but "how do they remain stable?" There are several hand wavy explanations possible.
Except for a few very special circumstances (high energy collisions), we can't get any real answers from Quantum Chromodynamics (QCD) about the nucleus that actually agree with reality - we can barely get any answers at all.
The problem is that these equations use what mathematicians, somewhat disdainfully, like to call "formal mathematics". That is to say that they are just a bunch of rules for manipulating symbols on paper that don't really make sense. More like numerology than real mathematics. No one knows if the rules make any sense at all. If you follow the rules in a different order, for example, you get different answers, and no one knows what it means. The "formal" equations are more based on physical understanding and not the usual solidly based "real" mathematics.
It is kind of like how people started using complex numbers before they understood why they worked. They knew the square root of minus 1 was nonsense, and yet you get the right answer, but no one knew why. Today it is a similar situation with QCD (except you can hardly get any answers at all).
So if you solve this problem (either in the positive or negative) you get 1 million dollars.