# Why is color confinement a difficult problem?

Assuming color force follows a constant rule of force instead of an inverse square rule of force. And that red, green and blue are all attracted to each other.

Why is color confinement considered a mystery?

Any particles which are unconfined will feel a force towards other unconfined particles along great distances making it very difficult for unconfined particles to exist.

(Unconfined electric charges would do the same except the force weakens over distances meaning electric charges could exist separately if far enough space between them.)

This seems almost self-evident. So what is the mystery that people are trying to solve here?

It's even simple enough to run some simulations on a computer with classical particles of color charges and see that they group in colour-less groups.

• Possible duplicates: physics.stackexchange.com/q/118825/2451 and links therein. – Qmechanic Dec 15 '18 at 19:40
• The issue is not, as you seem to assume, about developing a qualitative understanding of confinement. The main difficulty is quantifying that intuition and showing that we get confinement from first principles in QCD. Also, your reasoning doesn't actually work; for instance, why does association with nearby color charges prevent a color charge from feeling that long-range force? In electromagnetism, bound net-neutral charge distributions definitely feel long-range forces from other charges (giving rise to induced electric dipoles); by your logic, this effect should be much stronger in QCD. – probably_someone Dec 15 '18 at 20:12
• A constant force rule would not result in QCD-like behavior. The QCD force actually increases with distance of separation. Furthermore, when colored quarks are seperated they instantaneously drag quark/antiquark pairs from the vacuum and rearrange to form color neutral hadrons. This is a relativistic quantum phenomenon and no classical analogy could explain it. – Lewis Miller Dec 15 '18 at 20:28
• @zooby In any case, the constant-force characterization of the interaction between color charges is an approximate result from perturbative QCD, which is only valid in the weak-coupling, high-energy limit. The energies at which confinement occurs are much lower, which means that non-perturbative QCD applies, and your characterization no longer describes reality. – probably_someone Dec 15 '18 at 20:29
• @zooby Not everything that seems self-evident actually is self-evident. Most of formal mathematics and a lot of theoretical physics exists for precisely that reason. A great example is the development of non-Euclidean geometry, which arose directly from hundreds of years of unsuccessful efforts to prove Euclid's fifth postulate ("there is only one line that is parallel to a given line and passes through a given point"), which until the early 19th century seemed like a self-evident consequence of Euclid's other postulates. – probably_someone Dec 16 '18 at 1:45