ELI5: What is Yang-Mills Existence and Mass Gap?
Imagine you have a bunch of tiny, tiny particles, like the ones that make up everything in the universe. These particles are like little kids playing in a playground. They run around, bump into each other, and interact in different ways.
Now, imagine that there are some rules that these "kid particles" have to follow. These rules are like the laws of physics, and they are described by a special theory called "Yang-Mills theory". This theory is like a rulebook for how the particles play together.
The first part of the problem, "Yang-Mills Existence", is about proving that this rulebook is a good rulebook. It's like asking: "Does this rulebook make sense? Can we use it to describe a playground that actually exists?" Mathematicians believe the answer is yes, but they haven't been able to prove it yet.
The second part of the problem, "Mass Gap", is about the particles themselves. It's like asking: "Are the kid particles always moving, or can they be at rest?"
Some particles, like the ones that carry light (photons), can have very little energy, so they are always moving. But other particles, like the ones that make up the center of atoms (protons and neutrons), have a lot of energy, even when they are not moving. This energy is what we call "mass".
The "mass gap" is the idea that there's a minimum amount of energy a particle must have, just like there's a minimum height you have to be to ride a roller coaster. If a particle doesn't have enough energy, it can't exist.
The problem is to prove that this "mass gap" is real, and that the particles described by Yang-Mills theory have this minimum amount of energy.
Why is this important? Because Yang-Mills theory is a big part of how we understand the universe. Proving that it's a good theory and that it explains why particles have mass would be a huge step in understanding how everything works.
