This is a follow-up especially aimed at those non-experts who got really excited by my recent posts on the internal structure of the proton (here, here and here), in which I described the proton as being a lot more complicated than just two up quarks and a down quark, emphasizing the presence of many gluons and of many quark/anti-quark pairs in addition to those three quarks that everyone talks about.
Following those posts, I got a lot of very good questions. I’ve been absorbing them and thinking about how to answer them effectively. I had taken you as far as I knew how to go without hitting technical barriers. You probably noticed I was very careful to address certain issues and not others — answering certain questions and avoiding others. And many of you, intelligently, asked the questions I didn’t answer. So now you get to find out why I didn’t answer them in the first place. [You asked!] You’ll also note there are no pictures. In a couple of cases, that’s due to lack of time. But mostly, it’s because we’re going beyond where pictures can convey the reality.
So fasten your belts, and be prepared for the possibility that you may not entirely like the answers.
In most cases the answer to the questions you’ve been asking involves coming to grips with something weird about quantum mechanics. Describing reality becomes a lot harder when we are forced to come face-to-face with the fact that our reality is quantum in nature. Even those of us who do know quantum mechanics very well cannot form a clear intuitive picture of it. We can only learn how to calculate what quantum mechanical systems do, and how to get intuition for how quantum mechanical systems will work. But why they work that way? Sorry. Our minds just don’t form a picture of the world that corresponds to how the world really behaves. To quote Richard Feynman: “I think I can safely say that nobody understands quantum mechanics.”
Some of the questions you asked don’t make sense in a quantum world. They have no answers; you are simply not able to ask them, any more than you can ask, say, how much does a the sound of a piano weigh? On top of that, protons are sufficiently complicated that even for some of the questions that we should be able to answer, the answers are either not known or are so complicated that I don’t have a good answer for you.
Anyway, here are some of the questions you asked, and some of the answers, as best as I can give you. We’ll start with two simpler ones before it gets murky.
Why don’t the quarks or gluons hit each other inside the proton and make a Higgs particle sometimes?
They don’t have enough energy, relative to one another. You need a collision that has a lot of energy to make a Higgs particle: 125 GeV or so. The typical energies of the objects inside a proton are a small fraction of a proton’s mass-energy, about 1 GeV, so when they hit each other the total energy in that collision is far less than the mass-energy of a Higgs particle. Only by accelerating two protons and having them hit each other head on can you arrange that the energy of a collision of a gluon from one proton with a gluon in the other proton has energy far above 1 GeV, and potentially enough to make a Higgs particle. You can’t do it within one proton.
It’s very roughly the same reason that two cars that hit head on will make a horrible mess of each other, but a single car can’t just do that to itself.
Given that a proton is a big mess of quarks, anti-quarks and gluons, is a nucleus, made from protons and neutrons, really to be thought of as a simple collection of protons and neutrons? or is it just as big a mess of quarks and antiquarks and gluons as protons are?
You can think of it as protons and neutrons. While the quarks and gluons and anti-quarks are tightly bound inside protons and neutrons, and rush furiously about, the atomic nucleus is a much more fragile object, made from protons and neutrons loosely bound together. The protons and neutrons inside a nucleus remain largely distinguishable. This loose binding is why nuclear fission occurs so easily with some nuclei: it just takes a rather low-energy neutron to break a nucleus apart, much like a pile of beach balls stuck together with cheap glue could be broken apart by another beach ball crashing into them.
Another hint that this is the case is that the radius of a nucleus grows roughly as the one-third power of the number A of protons and neutrons that it contains. That is just you would expect if you tried to gather A beach balls into a somewhat spherical shape without deforming them very much.
That said, it’s not entirely boring in the nucleus. The process proton + neutron → neutron + proton, in which an up quark moves from a proton to a neutron while a down quark simultaneously moves from a neutron to a proton (or a down antiquark moves from the proton to the neutron, which is basically indistinguishable), happens regularly, and is indeed one of the processes that generates the forces that helps keep a nucleus together. This process is central in explaining why neutrons are necessary to make a stable nucleus. In fact, it’s not an accident that roughly equal numbers of neutrons and protons give you something relatively stable. And these forces that hold the protons and neutrons together have to be moderately strong, since ordinary electric forces (which are rather weak, by comparison with the strong nuclear force) are trying their best to push the protons away from each other and blow the nucleus apart.
This last point helps explain why for larger nuclei the number of neutrons is bigger than the number of protons. Without the proton’s electric charge the ideal situation would be to have equal numbers of each, but given that the proton does have an electric charge, the energy cost of putting another proton into an already electrically-charged nucleus is high, so on average it turns out to be less costly, if you want to make a bigger nucleus, to put a neutron in instead.
How many quark and antiquark pairs are there in a proton?
You notice that I did not attempt to address this in my articles. That’s because this number cannot be specified. First, the number is constantly changing [or, in quantum mechanics language, constantly fluctuating — meaning that if you were to measure it many times, you would get a different answer each time]. And second, even the average number of pairs will depend on exactly what question you ask.
Is the large number of quarks and antiquarks fixed, or does it vary from baryon to baryon?
[A baryon is any hadron like a proton, in that it contains three quarks, many gluons, and many quark/anti-quark pairs. But there are many types of baryons. In general the three extra quarks may be of different types from those found in the proton, and the whole system may have its energy distributed differently than is the case for a proton.]
Well, the answer depends on exactly what you meant by your question.
The number of quarks and anti-quarks is always changing — and also hard to define clearly — yet however you choose to define it, the average number of quarks and antiquarks of any particular type, and the degree to which that number fluctuates, is the same in every proton. All protons are exactly identical in any measurable intrinsic property.
One baryon which is extremely similar to a proton is a neutron; they’re almost twins, except for the exchange of an up quark for a down quark.
If by other baryons you want to include, say, the Omega baryon, or the Lambda baryon, or one of the many others, then no, the properties of the quark/anti-quark pairs are not exactly the same as for the proton, though they don’t differ very much. The basic processes which lead to the existence of those quark and anti-quark pairs are always the same, but the details of what makes the baryon a Sigma or an Omega rather than a proton do affect the details of the quark/anti-quark pairs.
What about the hadrons that have equal numbers of quarks and anti-quarks, such as the neutral pion? How can we tell the difference between a neutral pion and the vacuum of empty space? Or between a pion and another such hadron, say, the eta, which also has equal numbers?
The answer involves quantum mechanics, which is why I sidestepped the issue in my presentation. To keep the discussion simple, let’s just limit ourselves to up quarks and up anti-quarks and down quarks and down anti-quarks. Really we should at least include strange quarks too, but that will clutter the discussion without changing the conceptual point.
Our non-quantum mindset would tell us that if we were handed an electrically-neutral quark-antiquark pair, it would have to be either (a) an up quark u and an up anti-quark u or (b) a down quark d and a down antiquark d. But in our quantum mechanical world, it’s actually more complicated.
First — a little weird — in a quantum world I can have in my hand either uu or dd with certain probabilities, where the probabilities sum up to 100%. To be specific, I could be holding something that has 50% probability to be an up quark/anti-quark pair and 50% probability to be a down quark/anti-quark pair.
But I am afraid it gets much weirder. There are actually multiple ways to have this 50% probability for uu and 50% probability for dd.
- One of them can be written (u u + d d).
- Another one (the relevant one here) can be written (u u - d d).
These are not the same. And there is nothing you can do about the fact that the difference between them has no intuitive analogue. It is a property of quantum mechanics that these are two different ways to have 50% probability to have an up quark/anti-quark pair and 50% probability to have a down quark/anti-quark pair.
In a neutral pion, almost all of the quark/anti-quark pairs are in a configuration that is best described as (u u + d d). But crudely, there is one pair in the configuration (u u – d d). That is (partly) what makes this hadron a neutral pion.
A positively charged pion isn’t very different. There, almost all of the quark/anti-quark pairs are in a configuration that is best described as (u u + d d). But then there is one extra up quark and one extra down antiquark, in the configuration u d.
And a negatively charged pion has one quark/anti-quark pair in the configuration u d.
Now I’ve cheated you slightly, because some of the quark-antiquark pairs in the proton are strange quarks. If we include them, then roughly speaking the quark-antiquark pairs in the proton are typically of the form (u u + d d + s s). And what makes an eta meson is that one of its quark-antiquark pairs is instead roughly arranged as (- u u – d d + 2 s s). [I say “roughly” here because the numbers actually get modified slightly, as a result of the fact that the strange quark’s mass quite a bit larger than that of the up and down quarks. But that’s a detail.]
I’m still badly oversimplifying. A further problem with characterizing the issue in this way is that all up quarks are identical… so you can’t say which of the up quarks is in the special configuration. Accounting for this makes the conversation about the pion even more complicated. There’s an analogue here: in a Lithium atom, there are three electrons, two in the inner shell and one in the outer shell. But actually you can’t say, in quantum mechanics, which of the three electrons is which. For instance, there’s no way for you to grab the one in the outer shell, color it green, and check later whether it is still in the outer shell or whether it has changed places with one of the inner electrons. You can’t color it, or mark it in any way, to make it different from the other two. It’s as impossible as trying to say, when two waves on the ocean pass through and/or bounce off each other, which of the two waves is which.
Oh, and I’m afraid there are hadrons whose quark/anti-quark pairs are all arranged as (u u + d d). Such hadrons are all very unstable so you don’t hear much about them, but the lightest of them used to be called the σ, and is now usually called the f0. So clearly there’s something I’ve left out of the story.
Actually, there’s a lot that I’ve left out. But some of it is in the answer to the next question.
Are the quark/anti-quark pairs inside the proton a part of the proton or part of the vacuum of space, which also has quark/anti-quark pairs?
The answer is that the quark/anti-quark pairs that I referred to in my posts are part of the proton: crudely speaking, if I make a proton move, the quark/anti-quark pairs that are a part of the proton will move with it, while those that are part of the vacuum will not.
The main distinction between the types of quark/anti-quark pairs is, however, quantum mechanical. A quark/anti-quark pair that appears in the vacuum does not generate a strong gluon field, while those that are part of the proton typically do contribute to the strong gluon fields inside the proton. Why?
Well, not all quark/anti-quark pairs that you would naively think are the same actually are the same. The issue is similar to what came up in the answer to the previous question. There I pointed out that there are ways to arrange an up or down quark/anti-quark pair that a non-quantum thinker wouldn’t imagine were possible. It turns out there’s even if you just have an up quark and an up anti-quark, there are different arrangements possible. Most of these arrangements generate a strong gluon field (also called a “chromo-electric” field, in analogy to the electric [i.e. photon] field created by an electron.) But one of them — the arrangement you most often find in the vacuum — doesn’t.
It’s a little bit (but not precisely) analogous to why two electrons placed next to each other will generate an electric (i.e. photon) field that you can feel far away, but an electron and a positron placed very near each other don’t do that. This is because the electric fields from the electron and positron are equal and opposite, and mostly cancel far away, while those from the two electrons are almost identical and add together. It turns out it is possible to arrange a quark and an anti-quark so that their “chromo-electric” (i.e. gluon) fields either cancel or add together — a feature not possible for an electron/positron pair. The pairs in the proton mostly have fields that add; those in the vacuum have fields that cancel.
Another way to say this is that there is a sense in which most quark/anti-quark pairs in the proton are borderline-“virtual particles” (which aren’t really particles, but are more general disturbances in the quark fields) generated by gluons. (See Figure 5 of my virtual particle article, which shows the same thing for electron/positron pairs and photons.) I’ll say a bit more about this in the answer to the next question. Most of the quark-antiquark pairs in the vacuum are just spontaneous disturbances of the quark fields that happen on their own, and for such pairs their chromo-electric fields cancel.
Is there not perhaps some sense in which the proton should be thought of as three quarks, with all the gluons and quark-antiquark pairs being just an artifact, or an effect, of having accelerated the proton to high speed?
Well, although I have argued against this in my posts, and given you strong reasons, I should still tell you that actually there almost is such a sense, and this is part of why the issue of the proton’s structure has been debated for so long. I don’t think this is the right way to think about the problem, but I cannot promise you 100% that I’m right, and so, in fairness, I should present the dissenting minority view.
First you should read what I wrote about virtual particles here. (In particular, they’re not really particles at all.)
It is often useful in technical calculations to think of the quark/anti-quark pairs as virtual particles — which are not particles at all, but fluctuations in the quark fields — associated with gluons (analogous to fluctuations in the electron field associated with photons — see Figures 5 and 6 of this article), and then to think of the gluons as fluctuations in the gluon field created in the vicinity of quarks (the way electrons create disturbances in the photon [i.e., electromagnetic] field — see Figures 3 and 4 of this article.).
One might try to take this technical point to be a physical one, and suggest that all the quark/anti-quark pairs and the gluons arise as virtual particles associated to one of the three quarks intrinsic to the proton.
But as I’ve emphasized in earlier posts and answers to comments, it isn’t really meaningful to establish a clear difference between virtual particles (which aren’t particles) and real particles (which are nicely behaved ripples in a quantum field) when you’re trying to understand something as complicated as a proton’s interior.
In any case, it turns out that it is hard to get this line of thinking to work for all of the gluons, but you might get away with thinking about the quark/anti-quark pairs this way. I can’t tell you this is entirely excluded, because theorists cannot calculate the proton’s interior well enough to be sure such a picture is false. Nor is there any clarifying measurement you could make to check whether this picture made sense. So you should view this as an unsettled point, a caveat to the article I wrote giving you evidence that the proton’s interior is complicated.
However, even if the minority view turned out to be (at least in some sense) right, my main point for you still would stand: that you have to think about the gluons and quark/anti-quark pairs inside the proton — whatever their origin — in order to understand anything about Large Hadron Collider [LHC] physics. At the LHC (or even many earlier experiments) there’s no point in worrying about whether you can or can’t someday find some way of thinking about the proton as only three quarks. Any physics you do at the LHC will involve the gluons and the quark/anti-quark pairs in a big way; nothing of any interest arises merely from those three quarks of lore.
Could you perhaps explain the QCD vacuum?
No. Not now, not yet at least. It’s one of the most complicated things in particle physics.