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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.

Qmechanic
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    Possible duplicates: https://physics.stackexchange.com/q/118825/2451 and links therein. – Qmechanic Dec 15 '18 at 19:40
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    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
  • @QCD. In fact they'd be weaker. Because if the force is constant they'd cancel out no matter the distance between them. The force would pretty much depend only on direction. Whereas in QED, because the force drops with distance the charges in an atom don't cancel out precisely. –  Dec 15 '18 at 20:19
  • @zooby Electric dipoles are induced because the electron and the proton are pulled in different directions, not because the force is dependent on distance (as proof of this, you can induce electric dipoles with a constant electric field, which is what is done in capacitors with a dielectric material between the plates). The net force on the atom is pretty much zero (exactly zero in the case of constant electric field), but the internal components are being pulled in different directions, which is what creates the dipole. What is preventing this effect in a much more strongly-coupled theory? – probably_someone Dec 15 '18 at 20:27
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    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
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    @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
  • So all that your saying about forces increasing with distance makes it even more implausible that separate quarks could exist. Which makes it even more of a mystery to me what the problem is here? –  Dec 15 '18 at 20:34
  • @zooby As I said before, the problem is not in understanding qualitatively and vaguely why confinement occurs, but rather in deriving that result in the low-energy limit, where everything is non-perturbative and so none of our usual tools work. Nobody is saying that confinement shouldn't occur; we just have no idea, at present, how to prove that QCD predicts it in the low-energy limit. – probably_someone Dec 15 '18 at 20:38
  • Interesting. So to disprove confinement you'd have to find a stable configuration in which quarks are unconfined? Or is it just the maths don't even know how to define such a thing. So basically is the problem of finding how to do QCD in a non-pertubative framework? –  Dec 15 '18 at 20:51
  • I am confused by your question. It's been a while but I don't think confinement is not a mystery or a "difficult problem". A static potential comes from QCD and can be used to describe quarkonium states. We understand confinement. All of QCD is difficult because it is a non-linear self-coupled theory and it is STRONG. The last point prevents us from using perturbation theory in general, except for deep inelastic scattering problems where the theory is asymptotically free... I think. –  Dec 15 '18 at 20:53
  • @zooby, last comment is on point. We cannot do perturbation theory easily in QCD except for certain cases. And the math prevents freedom of quarks. The nature of the non-abelian gauge theory does not allow it. And nature is in agreement. We were trying to describe the apparent "structure" of nucleons and the apparent fact that the pieces do not seem to be found in nature. –  Dec 15 '18 at 20:55
  • True, it still seems strange that people are trying to prove something mathematically that just seems self evident. But I guess, the point is that it is hoped the tools used in the proof will be useful for other things. –  Dec 15 '18 at 21:03
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    @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 01:45

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