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I have similar difficulty with the supposition that the strong force does not follow the inverse-square law. This law reflects the relation between a distance and the area of a sphere which has that distance for a radius. Fairly obvious considerations of conservation support inverse-square reductions in force.

Can anybody offer an "explanation" for what the distance law is for the strong force?

Simply, the geometrical argument behind the inverse square law for gravity and electromagnetism is predicated upon two facts: the carrier particles are massless, and they don't interact. In the case of QCD (the modern theory of the strong force), the carrier particles are massless, but they interact via the strong force. In other words, the force is self-coupled. The result is that the force is proportional to distance.

[Geek alert: In the old Yukawa theory of the strong force, the carrier particles are massive, which leads to a force that drops off exponentially. This is the inter-hadron force that binds nuclei together. The carrier particle for this force is the pion, which can be envisioned as a quark-antiquark pair. The reason that this very real force isn't typically mentioned in discussions of the Standard Model is because it isn't a fundamental force. It is analogous to the Van der Waals force in electromagnetism.]

You can envision the force this way. As you pull two quarks apart, they exchange gluons, which are coupled to the color charges of the quarks. Each gluon also carries a color charge and an anticolor charge, so the exchanged gluons will also exchange gluons between them, and thus will be drawn together. The farther this "color flux tube" between the quarks is drawn out, the more gluons will be exchanged by the gluons mediating the quark-quark force, and the more tightly they will be bound. The flux tube thus acts like a spring. If you pull the quarks far enough apart, you will put enough energy into the flux tube to create a new quark-antiquark pair, which will "screen" the separating quarks from each other (i.e., snap the long flux tube into two short ones). It's rather like trying to separate a north pole from a south pole by cutting a magnet in half; all you get is two short magnets. The color charges are thus "confined" to the hadrons, which have a net color charge of zero.

Physicist said: The flux tube thus acts like a spring. If you pull the quarks far enough apart, you will put enough energy into the flux tube to create a new quark-antiquark pair, which will "screen" the separating quarks from each other (i.e., snap the long flux tube into two short ones).

Thanks. I get it. I think.

Physicist said: In other words, the force is self-coupled. The result is that the force is proportional to distance."

I don't get it. Do you have a simpler way to explain what the term "self-coupled" means in this context. What are the alternatives to being "self-coupled"? Did you mean to say that the force is constant with distance or proportional to distance. The former was the case I thought applied. Is the strong force proportional to distance?