Of Particular Significance

Celebrating the Standard Model: The Twins We’re Made Of

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 05/29/2024

At the core of every atom lies its nucleus, where protons and neutrons are found. As their names suggest, these two subatomic particles are profoundly different.

  • Protons carry positive electric charge, and can attract negatively-charged electrons, making atoms possible.
  • Neutrons have no electric charge and are thus electrically neutral, hence their name; they have no impact on the electrons in atoms.

The distinctions extend to their magnetic effects. Both protons and neutrons have a “magnetic moment,” meaning that in a magnetic field, they will point like compasses. But neutrons point in the opposite direction from protons, and less agressively.

Nevertheless, the proton and neutron have almost identical masses, differing by less than two tenths of a percent! If we ignored their electric and magnetic effects, they’d almost be twins. Why are they so different in some ways and so similar in others? What does it reflect about nature?

(in units of GeV/c2)
electric charge
(in units of e)
magnetic moment
(in units of e ℏ / 2 mp)
Table 1: The masses (specifically the intrinsic, speed-independent “rest masses”) of the proton and neutron are almost identical, but their electric charge (in units of e) and magnetic responses (in units of e ℏ / 2 mp, where mp is the proton’s mass) are quite different.

To resolve this puzzle required three stages of enlightenment…

Step 1: The Nuclear Force is Strong in These Ones

Atomic nuclei were a puzzle for several decades. The proton was discovered, and identified as the nucleus of hydrogen, before 1920. But other nuclei had larger electric charge and mass; for instance, the helium nucleus has double the charge and about four times the mass of a proton. Only in 1932 was the neutron discovered, after which point it soon became clear that nuclei are made of protons and neutrons combined together. Physicists then realized that to prevent the protons’ mutual electric repulsion from blowing a nucleus apart, there must exist an additional attractive force between the protons and neutrons, now known to be an effect of the “strong nuclear force”, that pulls harder and holds the nucleus together.

Almost immediately following the discovery of the neutron, and noting its similar mass to that of the proton, Heisenberg proposed that perhaps they were the same particle in two different manifestations, despite their different electric charges. Soon it was learned that small atomic nuclei that differ only in the replacing of one proton with one neutron often have remarkably similar masses. For example,

nucleusMagnesium 27Aluminum 27Silicon 27
# protons121314
# neutrons151413
mass (in GeV/c^2)25.135725.133125.1380

Thus, not only are protons and neutrons in isolation almost interchangable (excepting electromagnetism), they remain so when bound together by the strong nuclear force. This is a clue that the strong nuclear force treats them identically, or nearly so. Meanwhile, although their different electromagnetic properties seem of great importance to us at first, they are actually little more than a shiny but irrelevant detail, akin to two different paint colors on cars of exactly the same make.

It turns out the proton and neutron are not quite the same object. But their similarities can still be attributed to similarities in their contents.

Step 2: Bags of Three

Based on the properties of many other particles discovered in the 1940s and 1950s, both Murray Gell-Mann and George Zweig (see also work by A. Petermann) proposed an idea that I’ll refer to as “kuarqs”, in which

  • the proton involves two up kuarqs and one down kuarq;
  • the neutron involves two down kuarqs and one up kuarq;
  • the reason that the proton and neutron are twins is that the up kuarq and down kuarq are twins, differing only in their electric and magnetic effects.

You should note, in addition to my odd spelling, that I did not say “the proton is made of two up kuarqs and one down kuarq”. That’s for a very good reason.

Some physicists, including Zweig, considered that these kuarqs might truly be particles inside a proton. In this view, much as a helium nucleus is a bag made of two protons and two neutrons, each carrying about a quarter of the nucleus’s mass, a proton would be a bag made of three kuarqs, each kuarq carrying a third of the proton’s mass. The neutron would be the same except with one up kuarq replaced with one down kuarq.

Fig. 1: An oversimplified vision of protons as made from two up quarks and a down quark, and neutrons as made from two down quarks and an up quark --- and nothing else.
A naive picture: protons and neutrons made from three kuarqs each.

These physicists were able to make quite a lot of successful predictions using this viewpoint, in which:

quantityup kuarqdown kuarq
(in units of GeV/c2)
0.30 – 0.330.30 – 0.33
electric charge
(in units of e)
2/3– 1/3
magnetic moment
(in units of e ℏ / 2 mkuarq)
1.9– 0.9
Table 3: The simplistic picture of protons and neutrons made from three kuarqs requires they have the above properties; specifically, their masses are roughly 1/3 that of a proton or neutron.

But Gell-Mann (and to some extent Zweig also) emphasized that it would be a mistake to literally view the proton as a simple bag of three objects. The strong nuclear force is too strong for this; such a simplistic view would make the picture inconsistent. Most importantly, other types of related particles, especially pions, would be impossible to explain in a simple way using this method; so how could one expect protons and neutrons to be so simple?

Gell-Mann therefore argued that his kuarqs were mainly a mathematical trick, an organizing device, and were unlikely to actually exist as actual particles. Even if they did exist, he reasoned, they should have very large masses, with the proton mass reduced by the strong nuclear force (due to binding energy, which makes an atom’s mass slightly less than the combined mass of its electrons, protons and neutrons, and similarly reduces the mass of a nucleus below that of its protons and neutrons.)

Step 3: Bags of Plenty

The full story only began to become clear ten years later, in the early 1970s. It turned out that Gell-Mann was right: his kuarqs do not exist. And yet they reflect something that does: a subset of the elementary particles that we call “quarks”.

There are indeed up and down quarks, just as there are up and down kuarqs. But in contrast to kuarqs,

  • quarks are real particles, not mere mathematical tools;
  • the up and down quarks are not twins;
  • protons and neutrons are not made from three quarks.
quantityup quarkdown quark
(in units of GeV/c2)
electric charge
(in units of e)
2/3– 1/3
magnetic moment
(in units of e ℏ / 2 mquark)
Table 4: The elementary up and down quarks. Their masses cannot be precisely determined, but are small and quite different. Their electric charges are the same as for the kuarqs. The magnetic properties of individual quarks are both simple — that of elementary particles — and complex — thanks to the strong nuclear force — but they are certainly very different from those of the kuarqs, thanks to their small masses.

As you see, quarks are very different from kuarqs; their masses are very small compared to a proton’s mass, and the down quark mass is more than double that of the up quark. (Actually it took several decades for the table shown above to stabilize, because quarks are never seen individually and their masses must be inferred indirectly.)

The picture of a proton and neutron is then also very different. Instead of imagining three kuarqs moving slowly around a proton, one finds large numbers of fast-moving particles inside. The proton and neutron have almost identical interiors; they contain essentially the same combinations of quarks, anti-quarks and gluons. Their only difference is that a single up quark of the former is exchanged for a single down quark in the latter. More about this viewpoint is explained here or, more carefully, in my book chapter 6.3.

Fig. 3
A more realistic, though still quite imperfect, snapshot of a proton and neutron: full of quarks (u,d,s), anti-quarks (with an overbar) and gluons (g), moving around at high speed. Just a single quark distinguishes a proton from a neutron (note the arrow.)

What this means is that the proton and neutron are twins not because the up and down quarks are twins, but rather in spite of the fact that the up and down quarks are not twins. If we convert a proton to a neutron by trading an up quark for a down quark, the neutron’s mass remains the same as the proton’s because the difference between the up and down quark masses is much smaller than that of the proton’s mass, and is thus almost irrelevant.

Essentially, the strong nuclear force brings about the proton and neutron as bags of many fast-moving particles. So strong is that force that any differences in the quarks’ electric effects, magnetic effects, and even their masses are minor details, all of which combine together to explain the very small difference between the proton and neutron masses, as well as their electric and magnetic differences.

With protons and neutrons so complicated, you might well wonder why all protons are the same, all neutrons are the same, and why protons and neutrons are so similar inside. Some discussion of this quantum-physics effect is given in my book’s final chapters.

Kuarqs and Quarks

When quarks of very low mass were discovered in experiments and confirmed in theory, Gell-Mann was quick to insist that he’d known his kuarqs were real particles all along. Clearly this is revisionist history,. Not to take much away from the great man, who deserved his Nobel prize, but he was right the first time. His kuarqs were mathematical objects, and the reason that his kuarq approach (and that of Zweig) worked so well for protons, neutrons and other similar particles is indeed due to the existence of somewhat obscure mathematical symmetries, as pointed out in a wonderful 1994 paper of Dashen, Jenkins and Manohar. This paper does not settle all the issues (specifically it does not address pions and other “mesons”), but it does help make clear the senses in which kuarqs differ from quarks. It also explains why models of protons and neutrons that have no kuarqs in them at all (cf. the “Skyrme model”) can make just as good predictions as those that do, as long as they contain the same obscure mathematical symmetries. Kuarqs, in short, are useful but not necessary concepts.

This is in contrast to quarks, which are elementary particles appearing directly and explicitly in the equations of the Standard Model of particle physics. There are six types, only three of which are reflected in Gell-Mann and Zweig’s kuarqs. They are fundamental ingredients to modern computer simulations that can directly compute the difference between the proton and neutron masses. We can’t do particle physics without them.

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23 Responses

  1. Naively, one would think that the whole atomic nucleus should be one big bag of quarks and gluons, rather than separate bags ( the protons and neutrons ).

    1. Right: this isn’t obvious. Which of these possibilities wins depends on which configuration minimizes the energy, and one could imagine that this might not be true in all similar universes, even though it is true in ours. That is, a universe with a different combination of low-mass quarks, with different masses, might exhibit the other behavior.

  2. What are the main physical reasons behind three kuarqs making up a proton, could be interpreted from the results of the MIT/SLAC scattering experiments of electrons off protons?

    As a lay reader, I agree 100% with you that it’s confusing to present the three kuarq model nowadays; especially since it was quickly replaced within a decade. I suppose popular publishers have books to sell and the kuarq model was, and still is, good enough for the vaguely interested public.

    1. Sorry, I’m not sure I can interpret your original question — it’s not a complete sentence — but I’ll try.

      The MIT/SLAC experiments, scattering electrons off of protons, showed that there are low-mass electrically charged particles inside of protons. They had nothing directly to say about there being three more quarks than anti-quarks in a proton. Certain interpretations of the experiments assumed that there were three more quarks than anti-quarks, and that two had charge 2/3 and one had charge -1/3. But the experiments did not directly show this. Quark charges were resolved another way: see https://profmattstrassler.com/2022/08/25/celebrating-the-standard-model-the-electric-charges-of-quarks/ and https://profmattstrassler.com/2022/08/26/celebrating-the-standard-model-checking-the-electric-charges-of-quarks/

      As for kuarqs — the MIT/SLAC experiments showed that the naive view of the kuarq model was simply wrong.

      The reason the kuarq model works, as I mentioned, is explained by a subtle mathematical symmetry that was only discovered in 1994 by Dashen, Jenkins and Manohar.

      1. Thanks Matt, I’ll be studying carefully those links for a few days. For interested readers I’ve also come across this:

        The Discovery of the Point-Like Structure of Matter, Professor R.E. Taylor
        Stanford Linear Accelerator Center, https://www.slac.stanford.edu/pubs/slacpubs/8500/slac-pub-8640.pdf

        A fascinating account of just how hectic theoretical physics becomes in a short space of time when new experimental data comes in. I know that Murray Gell-Mann, from various accounts, had a very snobbish, dismissive view towards the talents of the experimentalists that make experiments like these possible. Apparently, Leon Max Lederman was a ‘plumber’.

        1. I was a Stanford/SLAC graduate student when Dick Taylor won the Nobel prize in 1990. There was a celebration in which everyone spoke about how important he was in the experiment. Notably, no one mentioned how nice he was, and everyone somehow mentioned how loud he was. Great scientist, anyway. Everyone was sad that BJ Bjorken didn’t win also, though; the limit of 3 per year was the problem.

          Stanford won a lot of Nobels in those days…Mel Schwartz in 88, and then (after I left in 93) Martin Perl, Doug Osheroff, Steve Chu, Bob Laughlin, 95-98, one per year. It was kind of wild to see all these people I knew get awarded.

          Gell-Mann wasn’t just dismissive of experimenters. Theorists too. He had a photographic memory and was too erudite for his own good. I once had an after-dinner drink with him and two other scientists, I think maybe Pierre Ramond and Jeremy Bernstein. Each of us carried on an in-depth conversation with Gell-Mann about our respective avocations; for instance, I think one of my colleagues collected encyclopedias. Most people would be asking questions out of curiosity, hoping to learn something new and engage personally. But Gell-Mann was just showing us how much he knew already about each of our hobbies.

          I’m told that if one of the physicists at the table had been female, Gell-Mann would have taken on a different personality — suddenly quite charming.

          Anyway, a great scientist.

          1. Your story about Gell-Mann reminds me of one I heard from an Indian friend. When Murray Gell-Mann visited their institute in India, they took him on a wildlife tour, and played a prank on him. One of the scientists was skilled at making bird noises, and went out and hid in the woods and made ridiculous fake bird noises. Gell-Mann then eruditely “identified” the birds from the noises, to the merriment of the others.

          2. Web of Stories has a very interesting interview with Murray Gell-Mann giving his opinion on various scientists; including Schwinger and Feynman, which isn’t entirely positive:

            Lots of interesting physics is discussed and in particular for me: 20/200 Murray Gell-Mann – Parity conservation: an inviolable principle?

            The physicist Herman Feshbach is named in the episode as giving a homework problem: to prove, by reflection of coordinates, that parity was conserved.

            Murray: “I spent the weekend on the problem and no matter how I twisted it, I could not prove from mathematics alone that parity was conserved. So I sent in a note saying: ‘I don’t believe parity conservation can be proved by reflection of coordinates… it’s a matter of how the Hamiltonian behaves under reflection of coordinates; and that’s a matter of the laws of physics’. So I was not one of those people who thought that parity had to be conserved.”

            I wonder if it was part of the homework to realize that a physics model was needed, or if Herman didn’t realize this when he gave the problem?

            This is especially relevant to me after our discussion under your article on C,P,T where you corrected me on some confusion I had on parity having an ‘arrow’ analogous to an arrow of time under your article:

      2. Murray has this to say about the experiment in episode 130 of the interview linked below; Murray Gell-Mann – Bjorken’s idea (130/200):

        “In the long term, what they had accomplished was to confirm the kuarq hypothesis. What I tell audiences in popular talks is that, what they did essentially is take an electron micrograph of the proton, and find that it was made of *three*, nearly punctiformed objects, with the properties of kuarks. Bjorken’s idea helped them accomplish this interpretation. But it was somewhat unclear theoretically, why one should be able to abstract the result that wasn’t even true in the model field theory we were throwing away, but was only true in the limit of very weak coupling.”

        From your reply, it looks to me that Murray didn’t correctly interpret the results of the experiment!

        1. Hmm — possibly. But I doubt that he misinterpreted anything; he was far too smart for that. It seems to me that this ends mid-thought. He’s right that between 1969 and 1973 it was “somewhat unclear theoretically” why Bjorken’s method should work, and this only changed with the discovery of asymptotic freedom — the relative weakening of the strong nuclear force at short distances — in 1973.

          On the other hand, his statement that they had “confirmed the kuarq hypothesis” is clearly revisionist history; no, there aren’t three punctiformed objects in a proton, and no, what they found was not what his hypothesis was. It confirmed Feynman’s parton hypothesis, where the proton is full of many “parts”; Gell-Mann states very clearly in his early papers that he means something else. But who can blame him for trying to claim that he’d known it all along? He certainly discovered the flavor symmetries which govern the hadron spectrum… And it is true that a proton has three more quarks than anti-quarks, which means that Gell-Mann’s ideas captured something of importance, even if it was far from the full story.

          Anyway, Feynman and Bjorken deserve more credit and Gell-Mann a little less, but they were all brilliant physicists who had a major role to play. I’m only sorry Bjorken isn’t better known.

  3. How many quarks a proton and a neutron can ne contain. Their spin motion is due to quarks? confused about that’s kindly explain me

    1. The number is always changing; two gluons inside the proton can collide and be converted to a quark-antiquark pair, and vice versa. Only the fact that there are two more up quarks than up anti-quarks, and one more down quark than down anti-quarks, never changes. [[More precisely, in a quantum sense, the number of quarks in a proton is not defined.]]

      Quarks’ and anti-quarks’ spin contributes to the proton’s spin, but so does the spin of gluons, and on top of that, so does their angular motion inside the proton. A simple understanding of how the proton’s spin arises has not been achieved, to my knowledge; it’s complicated.

  4. Words such as ‘same’ and ‘identical’ have always been troublesome to me, in the way or ‘quark’. One may ask ‘Why are all protons the same?’ without examining exactly what ‘same’ means. A glass of water in front of me is ‘the same’ from second to second, yet practically none of its molecules are in the same place as before and a constant stream of them evaporates away. A surprising number of questions vanish when you look more carefully at what exactly you’re asking.

    1. Same in this case means literally identical — that no experiment, no matter how cleverly designed, can tell the difference between the state 1, with proton A at position x and proton B at position y, and state 2, with proton A at position y and proton B at position x. Your existence depends on this literal identity, because without it the Pauli exclusion principle would be logically inconsistent and your nuclei would collapse.

  5. Dr.Stassler:
    The neutron is neutral, overall. So I’m guessing at “long ranges” it does not interact in any way with the electron. However, if I was to fire an electron into a neutron, can’t the electron interact with the internal “components” of the neutron, which do have electrical charge?

    1. Yes, it can and does. People have been studying this since the 1970s.

      More specifically (since we don’t have pure neutron targets) we scatter electrons off of deuterons (nuclei of deuterium consisting of one proton and one neutron) and compare the results with scattering electrons off of protons, inferring the difference as due to the electrons scattering off the neutrons. Here’s a paper about this from 1973, the first few paragraphs are readable without technical knowledge: https://academic.oup.com/ptp/article/49/2/699/1858433

  6. QM says all is made of waves! Waves of what? So, why stick with the particle concepts? The truth is that the standard model is a blind mathematical construct. Like a cheat sheet it gives the right answer without any reference to what makes up the universe, i.e., it has no metaphysical basis. On the other hand, a wave can part into four types of quadrants, all different and exchangeable given a specific sequence within a continuous wave combination. Once you know the stuff of the wave, all necessities draw the rest clearly. Celebrate nothing yet!

  7. With regard to the use (and mis-use) of language, I suggest the reading of S.I. Hayakawa’s “Language in Thought and Action” [Harcourt Brace 1939] which makes similar points about how the construct of words and phrases influence not only actual outcomes, but public attitudes about science.

  8. I have always been puzzled by the term (force) as in Strong or Weak nuclear. Beyond the scope of repulsion and attraction, keeping an equilibrium, still confirms in my mind an external force exerting on the internal force which I call ‘God’, to keep things stable except where man reorganizes for the sake of research and study, which includes destruction and or balance

    1. Well, the word “Force” in English means many things, and poetically we can connect the many meanings in many ways. Physicists are also casual in their speech about “force”, especially when talking to non-scientists, and that was true in this post.

      But when it’s time to make a prediction about how nature will behave, then physicists don their helmets and start working precisely, using not language but math and/or clear experimental prescriptions.

      As a theorist, what I usually mean by “strong nuclear force” is this: somewhere in my calculation I will have to account for the interaction of the gluon field (and typically gluons, ripples in the gluon field) with other fields. I mean no more and no less.

      Experimentally, what is usually meant is that somewhere in the physical process being studied, some kind of interaction among “hadrons” (the class of particles that includes protons, neutrons, pions, and many others) will play a major role.

      These types of interactions, which we view as involving the gluons inside of hadrons, are central in holding the nucleus together, where indeed they are not so different from a Newtonian “force.” But they do many other things too. Calling all of those things the “strong nuclear force” is indeed abuse of language; physicists speaking more precisely will say “the strong nuclear interaction.” The change of name from “force” to “interaction” might not so immediately evoke the divine, but one should recognize that what has been named is just as it was before. It is a rose by any other name…

      1. “strong nuclear force” is this: somewhere in my calculation I will have to account for the interaction of the gluon field (and typically gluons, ripples in the gluon field) with other fields.”

        So, a “force” is the interactions of ripples (resonances in the fields) in different fields (mediums of similar characteristics).

        Also, electrical and magnetic fields are also mediums with a difference based on the electromagnetic waves, they are polarized at 90 degreses.

        Also, the protons and neutrons and electrons in the atom, there are differences but also similarites, possess, charge, spin, mass, and magnetic moments.

        If one is to compose a unified theory, I would start form the two fundamental principles, conservation of energy and momentum. Then I would seek an explanation how all the quantum characterisitcs relate to these two principles and search for common denomenators. For example, the differemce between the proton and neutron is because of asymmetry in the angular momentums (which causes entropy, not the other way around) and the electron was created to balance the asymmetry.

        Further, I would search how to derive but electric and magnetic fields wrt to momentum vectors. The masses and velocities would be derived from the conservation of energy.

        Maybe the universe is not as random, maybe (ex: GR) there is order at the smallest scale, maybe even below Planck’s scale, that connects every field and ripple to just energy and momentum?


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