Of Particular Significance

Following Up on the Proton’s Structure

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 02/29/2012

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.

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48 Responses

  1. wonderfully written Mr Strassler, someone should offer you a TV documentary fascinating insight, i am gripped by your comments.

  2. Another brilliant piece.

    I am curious though, what stops quarks and antiquarks colliding and producing photons? There’s always enough energy for that to happen. I’m guessing it’s because the proton is the lowest energy assembly of the particles involved so that anything producing non-strong force feeling particles would require energy and thus be impossible, but I’m not sure that’s right.

    1. Virtual photons are rare, but they are in there. But for one of those photons to be real and escape the proton, there would have to a way for the proton to emit a photon without violating energy and momentum conservation… and that’s not possible. The process proton –> proton + photon violates energy momentum conservation no matter how you try to distribute energy and momentum among the particles. Meanwhile, te decay proton –> photon + something-else is disallowed too, because, by the various conservation laws (energy, momentum, electric charge, and “quark” [i.e. “baryon”] number (the last of which may be approximate but violated only by an extremely tiny amount), there is no allowed “something-else”.

  3. If the number of quarks, gluons, anti-quarks etc. are incalculable how do you arrive at the number of extra particles in neutrons and protons I.e. 2 up and 1 down?

    Thank you for a great blog and information.

    1. Because the ‘other’ particles all cancel out. you can think of it as adding three spoonfuls of sugar to a cup of water. I may not know how much water is there, I can add more water, or let some evaporate, but I am SURE of the three spoonfuls of sugar being in there somewhere.

      The three ‘extra’ quarks are what determines many of the proton’s properties, such as its electric charge. (Just as the spoonfuls of sugar would determine how sweet the water tasted.)

      We can’t pin them down or separate them, but we know they must be ‘in there somewhere.’

      1. Thanks for the response and sorry to have come back late.

        Although I very much appreciate your answer I also see some probems with it. First, if the rest of the fundamental particles cancel each other out then they can’t be there at all, right? Or if you mean to imply how electrons and protons cancel each other out in neutral atoms but isotopes can be distingushed we are still left with an uncertainty as per my question. So how do we know there are 3 quarks in excess?

        Second, adding water to 3 teaspoonful of sugar analogy is problematic because both of thse quantities are measureable, controllerable and definite, whereas the gluons and quarks are something we’re trying to measure.

        1. Some good questions.

          Just because several things cancel out on average, does not mean they are not there; if my feet are in an oven and my head in a freezer, it is not the same as being at room temperature. This is called ‘dynamic equilibrium’ and the world is made of it. A cup of water does not appear to do anything; it just sits there. Yet all of its molecules are in constant motion, a dust grain in water jerks about wildly as it is hit on all sides. The same is true of the proton, the ‘other’ particles would all cancel out… if they were all in the same place. But they’re not, they’re all over the place within the proton. On average they wouldn’t exist, but they never manage to average out, indeed they cannot ever average out.

          We know there are 3 quarks in excess because while in the proton things don’t average out, far from it they do. Think of your computer screen. it is made up of three colors of pixels that combine together to make whatever colors you see. Imagine watching a movie on it. Up close all you would see is a sea of pixels, red blue green, you could try counting them to see what color they’d make, but they’d be changing so fast you’d have no hope. But zoom out now to the scale of the screen and you can clearly see the average color. You can take a patch of screen and knowing that it is yellow state with confidence that there is an excess of red and green pixels. Indeed a single measurement of the average color will tell you exactly what proportions the three colors are in.

          A proton is the same, seeing it from afar we see the average, even though that average is just due to how we’re looking at it.

          I hope this helps answer your question.

  4. I worded my question badly; the question should have be worded this way: ” . . . then what force is it that holds all the positive charges of the protons together to form, along with neutrons, the nucleus itself?

    I hope I’m being clear.

    BTW: let me join the list of appreciative readers. You have a kind of a “nuts-and-bolts” approach that somehow still manages to achieve significant (we all know you’re keeping it rather simple) depth. So, thanks. I’m learning a lot; and, quite easily.

  5. If the strong force is mediated by gluons, and consists of quark-anti-quark pairs, that are themselves located within protons and neutrons, then what force is it that holds all the positive charges of the protons together? Is this a residue of the motion of the protons and neutrons within the nucleus, along with the residual effects of all the gluon-gluon, quark-anti-quark interactions taking place within these hadrons?

    1. The strong nuclear force is mediated by the gluon field, yes.

      Gluons are not quark-antiquark pairs, no.

      The strong nuclear forces mediated by the gluon field pull on all of the quarks, antiquarks and gluons inside the proton. (Yes, gluon fields pull on gluons, just as gravitational fields pull on gravitons.) These effects are so strong that they hold the quarks and antiquarks of the proton together, even though the total electric charge of the proton is positive. The electric repulsion of the total positive charge of the proton is far too small to overcome the attractive pull of the strong interaction, so the proton remains intact.

      The proton is intact even outside of an atomic nucleus, so no, what you ask about has nothing to do with the motion of objects inside of a nucleus.

  6. I have read elsewhere that in a helium nucleus, as long as they have different spins, all four nucleons can inhabit the same space. Is this true? Can these four groups of zillions of quarks and gluons each occupy the same space without interfering with each other?

    1. Not really. First, occupying the same state is not the same as occupying the same space; a state is a spread-out thing in quantum mechanics. For instance, the two electrons in helium are also in the same state (except for their spin), but that is a big spherical blob and the electrons are rarely near each other. Furthermore, the two electrons repel each other because they have the same electric charge, so the statement that they occupy exactly the same state is an approximation. The same is true for the four nucleons; the statement that they are all in exactly the same state is an approximation; what one of them is doing is in fact affected by what the other three are doing, and no, they probably don’t occupy the same space very often.

      In Bose-Einstein condensates you can have many atoms in essentially the same state, to a very good approximation. Lasers also have photons all in the same state. But these are very different physical system from helium.

  7. Excellent blog — I am enjoying it very much. Did you mean to type “proton” in the paragraph that starts with “Now I’ve cheated you slightly…”? The quark content you give there is that of an eta’.

    1. No, I had it right. You’ve got to pay very close attention to follow these details.

      The “quark content” of a proton is uud, but I’ve just explained to you that the physical content of a proton is not uud. Most (by number) of what is in a proton is gluons and quark-antiquark pairs.

      Similarly, the physical content of an eta’ is (like an eta or a neutral pion) huge and equal numbers of quarks and antiquarks, but not all in exactly the same arrangement. So the fact that its “quark content” looks similar to a single quark-antiquark pair is irrelevant; that’s not actually what it’s made from.

      Even more important, the eta’ does not emit strong nuclear forces; but as I explained, most of the quark-antiquark pairs inside hadrons do. So the resemblance is skin deep.

      You might ask what makes the eta’ different from the vacuum. And the answer is: parity. If you don’t know what parity is, let’s put that off for a while. The point is that there are far more things going on inside these complex objects than can be understood from their “quark content”.

    2. Now its getting very exciting , but a huge point remain; there must be some kind of control/supervisor/ director to keep the number of protons ALWAYS constant , otherwise if the process proton-neutron-proton……etc is not tightly controlled then we can face a change in the number of protons then all chemistry collapses…….how the number of protons is kept constant in that stormy ocean??

      1. The same rules that prevent certain particles (such as the proton itself) from decaying prevent any change in the number of protons. See http://profmattstrassler.com/articles-and-posts/particle-physics-basics/most-particles-decay-yet-some-dont/

        Also note that the nucleus is not nearly so stormy as the interior of the proton itself; while quark-antiquark pairs are constantly appearing and disappearing inside the proton, proton-antiproton pairs do not appear and disappear within the nucleus.

        1. In reality then there is a rule that ” commands ” : whenever a P/N exchange identity then another N/P MUST exchange identity in the same time so that the number of protons never change…..
          Well , please elaborate upon the mechanism by which this rule is dictated and implemented , or is it a rule to be taken without explanation same as why the world is quntized ?
          I apologize for being persistent in asking but it is your fault as you are so wonderful a teacher that i claim i knew from your dialog much more than many many books on the atomic world.
          THANKS MATT.

  8. IF space is digital/quantized then looking inside the proton we must find a rule similar to the electron jump rule from energy shell level to another , but in the proton the inside jungle would follow the quantized space-time lattice, then ALL what we say now about happenings inside the proton would be a very rough approximation of the unimaginable , even radiating gravity waves in this scale would be a big factor…..what i aim at is broadening the scope of our vision so that even all the wonder-full things you said about the secret life of the proton is diminishing compared to reality, i believe that for us reality is an unreachable mirage so subtle , so wonderful , so strange that our full-power imagination stands still in utter awe.
    This is NOT philosophy , this is the greatness of true science when it becomes the greatest stimulating agent to the human mind.

    1. Let me write it down in another way. If we stress the particle-side of the question when we study the quantum realm, then we forget that this realm has got another side. In order not to get lost in the zoo of particles would be convenient to remind that together with particles there are waves, forces and fields of energy and matter. I´m not interested in focusing the issue in “ultra small particles” neither in some ontological perspective. I have no idea if the universe is digitalized, I´m really fascinated for the thread of arguments that lead to some of us to show another perspective to understand the FTL neutrinos.

      1. TO MATT.: What is the difference between what you said happening inside a nucleus as : proton + neutron ~~ neutron+proton where a proton is “transformed” to a neutron by exchanging quarks , and the concept of decay which is also a kind of transformation.
        is this a silly question? maybe

        1. Let’s see… there are two issues here.

          Any process can occur in reverse order. So in a decay A –> B + C, the process B + C –> A is possible too. What’s the difference?

          1) For A –> B + C, you only need to have A sitting there on the table. It will decay spontaneously, without your help.

          2) For the decay to be possible A must be heavier than B and C put together. But energy is conserved, so what happens in this process is

          mass-energy of A –> mass-energy of B + motion-energy of B + mass-energy of C + motion-energy of C.

          What about B + C –> A ?

          1) In order for this to happen, you need to bring a B close to a C. That will not necessarily happen unless you make it happen.

          2) It isn’t enough to put B and C next to each other, since if they don’t have any motion energy, the sum of their mass-energies is less than the mass-energy of A, so B + C –> A is impossible. The only way that B + C –> A can occur is if B or C has considerable motion-energy. That’s something that you (or high temperatures or a rare accident) will have to arrange.

          So A –> B + C can occur anywhere and anytime, but B + C –> A can only occur when a B finds a C and one or the other has enough energy to make B + C –> A energetically possible.

          Now, what about processes like A + B –> C + D ? Well, again they can go either way; C + D –> A + B is also possible. In both cases something has to arrange for the process to be possible by bringing A and B together, or C and D together. And you have to keep track of the energies; one of the processes may occur easily, and the other less easily, because one requires no motion-energy while the other does require it. An example would be electron + positron –> photon + photon; an electron and positron will spontaneously turn into two photons if you bring them too close, but to make an electron and positron from two photons requires the photons have lots of energy.

          Finally: A + B –> B + A. Since the initial and final state are the same, this is just a rearrangement of the chairs, so it can occur both directions with equal rates and probabilities. You certainly don’t need any extra energy. The only thing you need to do is bring A and B together. Well, the forces that hold a nucleus together bring protons and neutrons near each other, and once that happens, they can be rearranged continually within the nucleus.

          Another technical point: the process proton + neutron –> neutron + proton involves the strong nuclear force and happens very fast, while the process neutron –> proton + electron + neutrino involves the weak nuclear force and happens very, very slowly.

  9. TO MATT.: If quantum gravity ever discovered as an ontological fact –not scientific psuedo-fact– do you think that we may need to revise our understanding of the world of the ultra-small ? do you think that then you may tell another story of the secret life of the proton?
    I ask this since good science starts with ultra- wondering as you know.
    You did not tell us why the proton is not ONLY 3q+3g??where is the presumed okam,s razor??which i take as mere just-so fancy.

    1. I can´t understand the concept of “ultra small” related to this issue. After Faraday and Maxwell we no longer face ultra small particles but fields of matter and energy that extend unlimited across the micro and macro universe. We are here writing down our opinions in this blog not because we are “ontological” determined to do it, the point is that we are here because there is a probability between millions of them. So, I think what you call ontological barely has something to do with the issue we are dealing.

      1. I am talking about quantum gravity scale –plank,s??–not particles JEP missed my point which is IF SPACE-TIME IS QUANTIZED / DIGITAL then every elementary particle including quarks inside the proton are ” directed” by the lattice / nodes /?? of the digital space-time then every description as per now will change , so i am wondering , is the story presented by matt. will change ? how much? ,AS all physics will change.
        I recommend reading ( scientific american ) article of 2/2012 “” is space digital?

    2. See the answer above to the questioner who asked about gravity in the proton. The proton is unimaginably insensitive to gravity and any details of space-time. So the answer is: in principle yes, but in practice no — there will be no need to revise the story of the proton. Our discovery of how the interior of the proton works in the 1970s and 1980s did not force us to tell a new story about how the earth rotates on its axis, or even how cells work in your body, because the earth and even cells are too big to care about the precise structure of the proton. And a proton is too big to care (directly) about any possible improvements in our understanding of space, time and gravity. That said, there still could be important indirect effects (just as understanding nuclei better allows us to understand that radioactivity is an important aspect of keeping the earth warm, maintaining volcanic activity and seismic activity.)

  10. This is an astonishingly careful and lucid explanation of the way the enigmatic mathematics of QCD works — and without using a single equation!
    Stephen Hawking says in the introduction to his first book for a general audience that he was told by his editor he would lose half his readers for each equation he included, so he decided to settle for a single one (E = mc^2) and take the hit. You have surpassed that high mark with this series and I applaud you for it, Dr. S.

  11. Please forgive the silly layman metaphysics: “how much does a the sound of a piano weigh?” This question doesn’t make sense because the sound particle has no rest mass. 🙂 If you find yourself in a frame of reference in which the sound particle is stationary (and so you’re travelling at exactly speed of sound c ), the sound particle has no energy, it doesn’t “ring” any more. One can argue it doesn’t exist any more. 🙂

    1. Well, the reason the sound of a piano doesn’t weigh anything is that the sound of a piano involves many sound particles (“phonons”) and you’d have to tell me how loud was the sound you played before I could try to answer the question. In other words, the question as stated is ill-posed. Many questions that you can ask about quantum systems (such as “at what radius is the electron in a hydrogen atom located?”) are ill-posed. There may be variants that make sense, but they always involve additional information that you, as questioner, must provide.

  12. Got to ask a question. I don’t doubt for a second that this little dance goes on between the proton and neutron, exchanging particles, but considering the huge difference in decay rates in their unbounded states, what mediates this exchange between these very different creatures? Is it simple proximity or must we consider the proton and neutron in a nucleus almost as a single particle, kind of like a married couple joined at the hip, I think? I can understand the neutron giving up a particle, but the proton that seemingly lives nearly forever, well the timing must be exquisite otherwise none of us would be here.

    1. I think the difference between the free proton and free neutron lifetimes is mainly because the proton is lighter. The neutron has enough mass to make a proton, an electron, and an anti-electron neutrino. But the proton, which is slightly lighter, doesn’t have the energy to make a neutron + other stuff. But that’s a *free* proton; in the nucleus, there’s plenty of stuff for it to borrow energy from.

    2. No, there’s no exquisite timing involved. It’s actually very simple. First read this article:


      All particles decay unless something prevents it. A neutron (outside a nucleus) can decay via the weak nuclear force to a proton, an electron and a neutrino because the sum of the masses of the decay products is less than the mass of the neutron. The reverse is not true, so the proton cannot decay in a similar fashion.

      For the proton (outside a nucleus) to decay at all requires some other process that does not involve the weak nuclear force, but instead involves some new and much much weaker force. Whether such processes even exist is not established experimentally.

      What is a little less simple is to understand why a neutron inside a nucleus may not decay at all. That has to do with keeping track of mass and energy carefully. An article on that issue is on the agenda.

  13. I have been able to understand your presentation.

    Where is the dividing line between theory/models and observation?

    Since the value of the speed of light in vacuum is exactly 299,792,458 m/s, then it would be impossible to see what is happening at smaller time intervals of 1/299 792 458 of a second.

    1. No, that’s not true. That would only be true if it were impossible to see something smaller than a meter. But your hand is smaller than that.

      In fact, since it is possible to effectively “see” (not with our eyes, but with our scientific instruments) distances as small as about 1/1,000,000,000,000,000,000 meters, we can already study times as short as about 1/300,000,000,000,000,000,000,000,000 seconds. Such times are studied regularly at the Large Hadron Collider. The lifetime of the top quark, for instance, is about 1000 times longer than this.

  14. Dear Matt. : allow me a simple– maybe complicated — question : Is the mentioned reality of the proton a logical necessity ? a quantum necessity ? an ontological necessity ? i mean could it be possible in principle for the proton to=3quarks+gluons ONLY ? or its reality as you described is dictated by a some kind of necessity ? if yes ,what IS IT ? if no then why it is so complicated ? or we just can never know …..even IF we got some T.O.E.

    1. Sorry for replaying the question, but I think you have to ask Nature whether the reality of the proton is a necessity. Physicists did not invent the proton structure, they only describe the structure invented by Nature.

      Other possible answer is that the proton structure is logical consequence of SO(3) symmetry of strong force, but again you have to ask Nature why strong force has SO(3) symmetry.

    2. Well, we’ll see what Matt says, but I think it must be required by quantum field theory, and in particular quantum chromodynamics (the theory that describes quarks interacting by exchanging gluons). There’s a certain probability for a quark to emit a gluon (the diagram for this looks like quark comes in, gluon and quark come out) and so, similarly there is a certain probability for a gluon to turn into a quark-antiquark pair (the diagram for this is kind of the same thing turned around, so now it’s gluon comes in, quark and antiquark go out). So the production of quark-antiquark pairs is the flip side of the force that’s binding the quarks together — a “quantum necessity”, as you put it.

      The thing is, all that stuff I just said would be true with an electron and a proton interacting by exchanging a photon, in other words, in a hydrogen atom. There’s a certain probability for a photon to turn into an electron-positron pair (the positron being an antielectron). But if I’ve understood Matt’s explanation on this point, the difference is that the probability of that happening is less, because the coupling from electrons to photons is weaker than the coupling from quarks to gluons, and moreover there isn’t enough energy available in the hydrogen atom to make new particles (which doesn’t stop you from making “virtual particles”, but it further reduces the probability). So only a very small fraction of the hydrogen atom’s energy is in virtual electron-positron pairs, whereas a significant fraction of the protons energy is in quark-antiquark pairs. Because of this, a proton electron pair is a good approximation for what a hydrogen atom really is, but a trio of quarks is a much poorer approximation of what a proton really is.

    3. As in a previous answer to one of your questions: the properties of the proton are due to the specifics of the quantum fields with which we live: the gluon fields and the up quark and down quark fields, and the Higgs field, which determines the masses of the up and down quarks. As I said before, we have no idea why the world is made from fields, or what explains why nature has the specific types of fields that we find, or why they interact with the strength that they do. But once you tell me what those fields are, I can tell you (with considerable effort) whether there is something like a proton. So the question of necessity has to go back to the fields and their interactions with each other; the proton is just an epiphenomenon.

  15. Thanks for the answer. That makes a lot of sense.

    Besides gluons, there have to be photons inside a proton too (since the quarks all have charges). There should be gravitons too (or whatever propagates gravity), since they have mass and thus exert gravitational fields. That’s 3 of the 4 forces. What about the weak force? W particles are too massive to be in protons, but what about disturbances in their W-field (as per your previous article)? Neutrons decay via weak force, so something inside of them must have the ability to disturb the W-field (right?)? Can particles inside of protons do it too?

    1. The number of photons inside the proton is very small, and the number of gravitons zero. Why?

      Because the electromagnetic forces inside the proton are much, much weaker than the strong nuclear forces inside the proton (at least 100 times weaker, though in many senses weaker even than that.) The weak nuclear forces inside the proton are about 10,000 times weaker than the strong nuclear forces. And the gravitational forces are about 100,000,000,000,000,000,000,000,000,000,000 weaker than the strong nuclear interactions. That’s why the number of photons is almost negligible, the number of (virtual) W and Z particles can be ignored for all practical purposes, and worrying about gravity is like wondering whether the location of a drop of water might affect the motion of the earth.

  16. Your lay readers might be interested to know that explaining (to a mathematician’s satisfaction) just a part of the QCD vacuum (only gluons and nothing else) is sufficient to win a million dollar math prize.

  17. Wow, thank you. You have a really good writing style – If you have not already written a book please do.

    Your recent articles on protons inspired me to do my A level coursework on this subject and your articles have proved most useful. This is my thank you note 🙂 Please keep up the good work.

  18. Are quark and anti-quark in the pairs really each other’s antiparticles? If so why don’t they annihilate? If not, why can’t true antiparticles meet inside a proton and annihilate? Is this because they are in some sense virtual?

    1. They are constantly banging into each other, annihilating, and reappearing. (For instance when two gluons run into each other, they can turn into a quark and anti-quark pair.)

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