If the color force has infinite range, why should the scale matter?
This is not really how QCD works, from what I understand it is much, much more complex, but here’s a really simple model to show why distance can still matter even when the force between any two particles is (effectively) independent of distance:
Imagine a meson made up of a quark with red color charge and an antiquark of anti-red color charges also present is lone quark of red color charge. The lone quark will feel an attractive force of 10,000 N from the antiquark in the meson and a repulsive force also of approximately 10,000 N from the quark in the meson. If the distance between the meson and the lone quark is 10 m, which is many, many times greater than distance between the two quarks in the meson, the attractive and repulsive forces will be coming from the same direction and therefore cancel out leading to a net force of zero.
At the other end of the scale if the lone quark is so close to the meson that it is effectively in between the quark and the antiquark, it will feel an attractive force of 10,000 N from one direction and a repulsive force of 10,000 N in the opposite direction, leading to a net force of 20,000 N attracting it to the antiquark.
The total attraction will depend on the angle between the quark and the antiquark in the meson, which falls off rapidly with distance.
Like I say this is just a toy model of a force that doesn’t change with distance and shouldn’t be taken too seriously.
Except is it color charge that is responsible or the gluonic field? Here is the excerpt from wikipediaon color confinement which seems to indicate that it is indeed something of a mystery.
Like I said don’t take my previous post too seriously, there’s so much wrong with it. It’s just to show that distance can matter even when the force between any two individual particles doesn’t change with distance.
Fair enough, I just want to highlight one part of that quote though: “no analytic proof exists that quantum chromodynamics should be confining”
Indeed, they are different forces with different properties. I just wanted to point out that the idea that the force can get very strong for certain configurations isn’t unique.
No, the strong force is the actual force. I didn’t offer a refutation to this claim earlier in the thread, but perhaps I should have as I see it might have caused confusion. In my post, when I said “strong force” I meant the actual fundamental force mediated by gluon exchange. This is standard usage.
This is correct. To expand: QCD is applied in practice in terms of the momenta involved rather than the distances involved, but the former language can loosely be converted into the latter by invoking the de Broglie relationship between momentum and wavelenth. In any case, in the more natural momentum language, the strength of the strong force varies quite dramatically at different momentum scales. Of note, QCD exhibits something called asymptotic freedom, namely that the strength of the interaction decreases toward zero at very high momentum scales. (By “momentum scale” here I mean how much momentum is exchanged between two interacting particles. “Very high momentum scale” thus means that two high-momentum particles interact and exchange much of their momenta.) Translating this to a spatial language has pitfalls, but doing so anyway implies that the strong force has zero strength at zero distance.
This is a less interesting statement than it might seem at first. It’s a statement about the calculational difficulties of QCD. For the other forces, you can turn the calculations into an infinite sum where the terms gets less and less important, allowing you to calculate just the first couple of terms and estimate how big the tiny amount that’s left over can be. This doesn’t work at all for QCD, and unless you include an infinite number of terms, you won’t get close to the answer. Folks have made significant mathematical progress toward showing confinement analytically, but it has been demonstrated through other means and isn’t a major open question or anything. In particular, confinement has been well-studied through numerical calculations (“lattice QCD”).
I would quibble with the “at all”, since you can still use perturbative expansions for very high-momentum problems. It’s still no good for most problems, though.
The problem at hand was confinement, and I had a line talking how QCD is particularly non-perturbative for this problem, but I took it out as TMI. But, yes, for other questions QCD can be handled perturbatively.
This explanation from Duke University seems to contradict that.
As for lattice QCD, although I have to admit I don’t have the background to understand it, it seems like it is a special instantiation of the theory designed specifically to avoid some of the issues we’ve been discussing.
Your statement is also contradicted in this chart from CERN
Most physical situations are simply not amenable to exact analytic solutions and the ones that are tend to very simple situations or situations which are simplified by a high degree of symmetry. The fact that analytic solutions are often not available is a feature of all the different regimes in physics: e.g. Newtonian physics, quantum physics and general relativity.
When analytic methods are not available, usually peturbation theory -where you take situation for which an analytic solution does exist and describe other situations as series of peturbations from that solution, is the preferred method of calculation. Peturbation theory is used extensively in quantum physics (it’s also used in Newtonian physics and general relativity); sometimes peturbation theory can be used to obtain exact answers, but often it is useful as a way of obtaining numerical answers. Sometimes though even peturbation theory is ineffective. Even in QED, where nearly all practical calculations are done peturbatively, peturbation theory has problems, but physicists use what some consider a bit of a fudge called renormalization to fix those problems. Even if is a fudge though it does work as answers in extremely close agreement with experiment are obtained (in peturbative quantum gravity even renormalization fails though for example). In QCD however peturbation theory is only of use in a limited set of situations, so a different method know as the lattice model is used more often. In the lattice model spacetime is broken down in to discrete chunks, again this has a particular advantage of being useful to obtain numerical solutions.
I don’t see anything in your cites that contradicts what I said. Which claim are you taking issue with? Perhaps you are misinterpreting the word “residual”. When these cites say “residual strong interaction”, they aren’t defining “strong interactions” as the residual force. On the contrary, the strong interaction is binding the quarks together, and the resulting entity is neutral except for a residual effect. This residual effect of the strong force is what they are referring to by “residual strong force”, but the important semantic feature is that the naked phrase “strong force” does not imply the residual force, which is what was claimed in post #13. Your cites employ the standard usage of “strong force”.
I don’t see what your objection is here. The strong force usually means the fundamental force as opposed to the residual strong force. Sometimes the residual strong force is simply know as the strong force, which isn’t necessarily a huge contradiction as it is a direct result of the strong force.
It’s real QCD, just approximated numerically as opposed to via perturbation theory. For an analogy, consider finding the area under a curve. (I’m assuming you know calculus, but if not, this analogy won’t be very helpful.) The area can be found by taking an integral, which itself can be analytically evaluated by noting how limits work and taking the appropriate ones. If none of that were possible (say the mathematics of limits hadn’t been invented yet or were somehow disallowed), you could recast the problem from an integral into a sum of areas of rectangles (Riemann sum). If the Riemann sum is too hard to do by hand, you might use a computer. In the extreme case of an infinite number of rectangles, you recover the continuum behavior of calculus. But you can still draw mathematically meaningful conclusions from the approximate, numerical method.
This seems to be the best answer I’ve found so far. The force is “residual” in the sense that it is mediated by pions or other particles which are exchanged between nucleons. Since those have limited range, it explains why the color force is confined.
Just to make sure it’s clear: color confinement isn’t a consequence of the finite range of a pion mediator. Rather, color confinement is present from the start in QCD. Because of confinement, if you want to model nucleon-nucleon strong interactions in terms of particle exchange, the exchanged particle needs to be colorless but also needs to carry color internally. The pion is the lightest candidate for this.
In other words, confinement isn’t caused by pion exchange having a limited range. Rather, one is stuck exchanging these massive pions due to confinement.
Also just to be sure (it might be already) : pion exchange isn’t considered fundamental. It’s a descriptive model that bears fruit and that also had tremendous historical relevance, but underlying it still the fundamental gluon-mediated strong force.
Fortunately, this man has the answer as to the proton’s size.
http://www.sciencedomain.org/abstract.php?iid=224&id=4&aid=1298#.Ucwyrtj2uSq
Read the full article and prepare to be amazed…
Band name!!
I tried to find out what I could about the publication and author. Rational Wiki has this:
He doesn’t have any academic credentials that I could find though. Also I think it’s interesting that one of the reviewers for the article said the following:
So how it went from that to being worthy of publication might be more interesting than the paper.