Protons and Neutrons: The Massive Pandemonium in Matter

Matt Strassler [April 15, 2013]

At the center of every atom lies its nucleus, a tiny collection of particles called protons and neutrons. In this article we’ll explore the nature of those protons and neutrons, which are made from yet smaller particles, called quarks, gluons, and anti-quarks (the anti-particles of quarks.)  (Gluons, like photons, are their own anti-particles). Quarks and gluons, for all we know today, may be truly elementary (i.e. indivisible and not made from anything smaller).  But we’ll return to them later.

Strikingly, protons and neutrons have almost the same mass — to within a fraction of a percent:

  • 0.93827 GeV/c2 for a proton,
  • 0.93957 GeV/c2 for a neutron.

This is a clue to their nature: for they are, indeed, very similar. Yes, there’s one obvious difference between them — the proton has positive electric charge, while the neutron has no electric charge (i.e., is `neutral’, hence its name). Consequently the former is affected by electric forces while the latter is not. At first glance this difference seems like a very big deal! But it’s actually rather minor.  In all other ways, a proton and neutron are almost twins. Not only their masses but also their internal structures are almost identical.

Because they are so similar, and because they are the particles out of which nuclei are made, protons and neutrons are often collectively called “nucleons”.

Protons were identified and characterized around 1920 (though they were discovered earlier; the nucleus of a hydrogen atom is simply a single proton) and neutrons were discovered around 1933.  The fact that protons and neutrons are very similar was understood almost immediately.   But the fact that protons and neutrons have a measurable size, comparable in size to a nucleus (about 100,000 times smaller in radius than a typical atom), wasn’t learned til 1954.  That they are made from quarks, anti-quarks and gluons was gradually understood in a period lasting from the mid-1960s to the mid-1970s.  By the late 1970s and early 1980s, our understanding of protons and neutrons and what they are made of had largely stabilized, and has remained essentially unchanged since then.

It is much more difficult to describe nucleons than it is to describe atoms or nuclei. That’s not to say that atoms are altogether simple (you can read about my attempts here, which are made complicated by the subtleties of quantum mechanics) but at least one can say, without too much hesitation, that a helium atom is made from two electrons orbiting a tiny helium nucleus; and a helium nucleus is a relatively simple cluster of two neutrons and two protons. But a nucleon?  Here things are not so easy.  As I wrote elsewhere in my article “What’s a proton, anyway?” — useful reading for anyone who wants to understand the Large Hadron Collider [LHC] — an atom is like an elegant minuet, whereas a nucleon is like a wild dance party.

The complexity of the proton and of the neutron seems to be real, and not due to a lack of knowledge on the part of physicists. We have equations that we use for describing quarks, anti-quarks and gluons, and the strong nuclear forces that they exert on one another. [These equations are called ``QCD'', short for ``quantum chromodynamics''.] We can check the accuracy of those equations through many different measurements, including the rates for producing various types of particles at the LHC.  And when we put the QCD equations into a big computer, and make the computer calculate the properties of protons and neutrons, and other similar particles (collectively called “hadrons”), the computer’s predictions for the properties of these particles closely resemble what we see in the real world. So we do have good reason to believe that the QCD equations are right, and that our knowledge of the proton and neutron is based on the right equations. Yet having the right equations isn’t enough by itself, because

  • simple equations can have very complicated solutions, and
  • sometimes it is impossible to describe complicated solutions in a simple way.

As far as we can tell, that is the situation with nucleons: they are complicated solutions to the relatively simple equations of QCD, and there seems to be no way to describe them in a few words or pictures.

Because of the inherent complexity of nucleons, you, the reader, will have to make a choice at this point: how much of this complexity would you like to learn about? No matter how far you go, you will probably not be entirely satisfied; for although the answers to your questions may well become more enlightening as you learn more, the ultimate answer remains that the proton and neutron are complicated. So all I can offer you now is three layers of understanding, in increasing detail; you can choose to stop after any layer and move on to other subjects, or you can keep going to the last layer. Each layer begs questions that I can partially answer in the next layer, but the answers provided beg further questions. In the end — just as I do in professional conversations with my colleagues and advanced students — I can only appeal to data from real experiments, various powerful theoretical arguments, and the computer simulations I mentioned.

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.

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.

The First Layer of Understanding

What are protons and neutrons made of?

To try to make things easy, many books, articles and websites will tell you that protons are made from three quarks (two up quarks and a down quark) and draw a picture like the one shown in Figure 1. The neutron is the same, but with one up quark and two down quarks, as also shown in Figure 1. This simple picture represents what some (but not all) scientists first believed protons and neutrons were, mainly in the 1960s. But this view was soon realized to be a significant oversimplification… to the point that it really is not correct.

More sophisticated sources of information will tell you that protons are made from three quarks (two up quarks and a down quark) that are held together with gluons — and they might draw the picture something like that shown in Figure 2, with gluons drawn like springs or strings holding the quarks together. Neutrons are again the same but with one up quark and two down quarks.

Nucleons2

Fig. 2: This figure improves on Figure 1 by emphasizing the important role of the strong nuclear force in holding the quarks in the proton. Usually (and confusingly) the drawn springs are intended to schematically indicate that there are gluons in the proton.

This is not quite as bad a way to describe nucleons, because it emphasizes the important role of the strong nuclear force, whose associated particle is the gluon (in the same way that the particle associated with the electromagnetic force is the photon, the particle from which light is made.)  But it is also intrinsically confusing, partly because it doesn’t really reflect what gluons are or what they do.

So there are reasons to go further and describe things as I have elsewhere on this website: a proton is made from three quarks (two up quarks and a down quark), lots of gluons, and lots of quark-antiquark pairs (mostly up quarks and down quarks, but also even a few strange quarks); they are all flying around at very high speed (approaching or at the speed of light); and the whole collection is held together by the strong nuclear force. I’ve illustrated this with Figure 3. Again, neutrons are the same but with one up quark and two down quarks; the quark whose identity has been changed is marked with a violet arrow.

Not only are these quarks, anti-quarks and gluons whizzing around, but they are constantly colliding with each other and converting one to another, via processes such as particle-antiparticle annihilation (in which a quark plus an anti-quark of the same type converts to two gluons, or vice versa) and gluon absorption or emission (in which a quark and gluon may collide and a quark and two gluons may emerge, or vice versa).

Fig. 3

Fig. 3: A more realistic, though still imperfect, image of protons and neutrons as full of quarks, anti-quarks and gluons, moving around at high speed. More precisely, a proton consists of two up quarks and a down quark plus many gluons (g) plus many quark/anti-quark pairs (u, d, s stand for up, down and strange quarks; anti-quarks are marked with a bar.)  The edge of a proton or neutron is not sharp.  Ignore the color-coding for now; it will become clearer in future articles.

[If you don't trust my Figure 3, you may want to read this article, where I describe how processes at the LHC would be quite different if Figure 3 were wrong, and something like Figure 1 or Figure 2 were true instead.]

Let’s look at what all three descriptions have in common.

  • two up quarks and the down quark (plus other stuff) for the proton
  • one up quark and two down quarks (plus other stuff) for the neutron.
  • the “other stuff” in neutrons is essentially the same as the “other stuff” in protons; i.e., all nucleons have the same “other stuff”
  • the small difference in mass between the neutron and proton is due mainly to a difference between the down quark mass and the up quark mass

And because

  • up quarks have electric charge 2/3 e  (where “e” is the charge of the proton, -e the charge of the electron)
  • down quarks have charge -1/3 e ,
  • gluons have charge 0,
  • any quark and its corresponding anti-quark have total charge 0 (for instance, an anti-down quark has charge +1/3 e, so a down quark and a down anti-quark have charge -1/3 e +1/3 e = 0),

each of the figures attributes the proton’s electric charge to the charge of two up quarks and one down quark, with the “other stuff” contributing zero charge in total; similarly the neutron’s electric charge is due to that of one up quark and two down quarks:

  • the total electric charge of the proton is 2/3 e + 2/3 e – 1/3 e = e,
  • the total electric charge of the neutron is 2/3 e – 1/3 e – 1/3 e = zero.

Where the three descriptions differ is in

  • how much “other stuff” is inside a nucleon,
  • what that stuff is doing in there, and
  • where a nucleon’s mass, and its mass-energy (i.e. the E=mc2 energy that it has even when it is standing still), comes from. [Since the majority of the mass of an atom, and therefore of all ordinary matter, lies in the masses of protons and neutrons, this last point is rather important in understanding our own nature.]

Figure 1 would have you believe that quarks are basically one third of a nucleon, somewhat the way a proton or a neutron represents one quarter of a helium nucleus or one twelfth of a carbon nucleus. Were this picture right, the quarks in a nucleon would move around relatively slowly (at speeds much slower than the speed of light) with relatively weak forces between them (though with some kind of powerful force keeping them from escaping). The mass of an up quark, and that of a down quark, would be about 0.3 GeV/c2, about one third of the mass of a proton. But this simple picture, and the ideas that go with it, just isn’t correct.

Figure 3 (I’ll come back to Figure 2) gives an entirely different view of a proton, as a seething cauldron of particles rushing around at speeds approaching the speed of light. These particles are colliding with one another; in these collisions, some of those particles are annihilated, while others are created in their place. The gluons are massless particles, while up quarks have masses about 0.004 GeV/c2 and down quarks have masses about 0.008 GeV/c2 — hundreds of times smaller than the mass of the proton. Where the proton’s mass-energy comes from is complicated: some of it is from the mass-energy of the quarks and anti-quarks, some of it is from the motion-energy of the quarks, anti-quarks and gluons, and some of it (possibly positive, possibly negative) is from the energy stored in the strong nuclear forces that are needed to hold the quarks, anti-quarks and gluons together to form the proton.

In a sense, Figure 2 tries to split the difference between Figure 1 and Figure 3. It simplifies Figure 3 by removing the many quark-antiquark pairs, which one might argue are ephemeral, as they constantly appear and disappear, and are not essential. But it tends to give the impression that the gluons found in a nucleon are directly part of the strong nuclear force that holds the proton together. And it doesn’t really make very clear where the mass of the proton comes from.

Figure 1 has another flaw, when we look beyond the narrow confines of the proton and neutron. It is not so good for explaining some of the properties of other hadrons, like the pion and the rho meson. Figure 2 shares some of these problems.

These limitations of Figures 1 and 2 are the reason that I choose to convey, both to my students and here on this website, the image shown in Figure 3. But I must warn you already that there are many limitations to the picture, too, which I’ll get into in later layers.

Still, it is worth noting that the extreme internal complexity implied by Figure 3 is to be expected for an object held together with a force as strong as the strong nuclear force. If you want to know why, you can read on in the second layer of detail… after we discuss the mass of the proton and neutron.

One more comment: the three quarks (two ups and a down for a proton) that aren’t a part of a quark/anti-quark pair are often referred to as “valence quarks”, with the pairs of quarks and anti-quarks called “sea quarks”.  This language is technically very useful in many contexts.  But it gives the false impression that if you somehow could look inside a proton, and you looked at a particular quark, you could quickly identify whether it was a sea quark or a valence quark.  You can’t do that; there’s no way to tell.

The Mass of the Proton, and That of the Neutron

Since the proton and neutron masses are so similar, and since the proton and neutron differ only by the replacement of an up quark with a down quark, it seems likely that their masses arise in the same way, from the same source, with the difference in their masses due to a some minor difference between up quarks and down quarks. But the three figures above suggest three very different views of where the proton mass comes from.

Figure 1 would suggest that the up and down quarks are simply 1/3 of the mass of the proton and of the neutron: about 0.313 GeV/c2, or maybe a bit more or less due to the energy needed to hold the quarks together in the proton. And since the difference between the proton and neutron masses is just a fraction of a percent, the difference between the up and down quark mass should also be a fraction of a percent.

Figure 2 is a bit less clear. What fraction of the proton’s mass comes from the gluons? But certainly one would gather from the picture that much of the proton’s mass comes from the quarks’ masses, as in Figure 1.

But Figure 3 reflects the more subtle way in which the proton’s mass actually comes about (as we can check directly using computer calculations of the proton, and indirectly using other mathematical methods). It is very different from what is suggested in Figure 1 and 2, and not so simple.

To understand how this works, one should think first not in terms of the mass m of the proton but in terms of its mass-energy E = mc2, the energy associated to its mass. The right conceptual question to ask is not “where does the proton’s mass m come from”, after which you calculate its mass-energy E by multiplying m by c2, but rather the reverse: ask “where does the proton’s mass-energy E come from”, and then calculate the mass m by dividing E by c2.

It’s useful to classify the contributions to the proton’s mass-energy into three groupings

  • A) the mass-energy (or “rest-energy”) of the quarks and anti-quarks that it contains (the gluons, being massless particles, contribute nothing)
  • B) the motion-energy (or “kinetic energy”) of the quarks, anti-quarks and gluons as they move around
  • C) the interaction-energy (or “binding energy” or “potential energy”) stored in the strong nuclear forces (more precisely, in the “gluon fields”) that are holding the proton together

What Figure 3 suggests is that the particles inside the proton are rushing around at high speed, and there are many massless gluons in the proton, so contribution (B) is bigger than contribution (A). Typically, in most physical systems, (B) and (C) turn out to be of comparable size, though often (C) is actually negative! So the proton mass-energy (and similarly the neutron mass-energy) is mostly coming from a combination of (B) and (C), with (A) a small contributor. And therefore this is also true of the proton and neutron mass; they are arising not so much from the masses of the particles they contain but from the motion-energies of the particles they contain and from interaction-energy, associated with the gluon fields that exert the forces holding the proton together.  (The balance of energies is very different in most other systems we’re familiar.  For instance, in atoms and in the solar system, (A) dominates, with (B) and (C) much smaller and comparable to each other.)

To summarize all this, consider that

  1. Figure 1 suggests that contribution (A) is where the proton’s mass-energy comes from
  2. Figure 2 suggests that contributions (A) and (C) are both important, with some impact from (B)
  3. Figure 3 suggests that (B) and (C) are important, with limited impact from (A).

And we know that Figure 3 is essentially right. That’s because we can do computer simulations to check it, and because (most importantly!) we know, from various powerful arguments that theorists have developed, that if the up and down quark masses were zero (and everything else was left unchanged), the proton mass would barely change from what we observe it to be. So it would appear that the masses of the quarks can’t be important contributors to the mass of the proton.

If Figure 3 is right, the quark and anti-quark masses are rather small.  How small are they really? The up quark mass (same as the mass of the anti-quark) is at most 0.005 GeV/c2, far, far smaller than the 0.313 GeV/c2 suggested by Figure 1. (The up quark mass is hard to measure and its apparent value is shifted by subtle effects, so in fact it might be much smaller than 0.005 GeV/c2.) And the down quark mass is about 0.004 GeV/c2 larger than the up quark mass.  That means the mass of any quark or antiquark is less than a percent of the proton’s mass.

Notice also that (in contrast to what Figure 1 would imply) this means that the ratio of the down quark mass to the up quark mass is not close to one! In fact the down quark mass is roughly double the mass of the up quark, or more. The reason that the neutron and proton masses are so similar is not that the up and down quark masses are similar, but that the up and down quark masses are both very small — the difference between them is small relative to the proton and neutron masses.  And remember that to turn a proton into a neutron you merely have to replace one of its up quarks by a down quark (Figure 3); that replacement is enough to make the neutron slightly heavier than a proton, and shift its electric charge from +e to zero.

By the way, the fact that the various particles inside the proton are colliding with each other, appearing and disappearing in the process, doesn’t affect this discussion — because in every such collision, energy is conserved (i.e. the amount of it is unchanged).  The mass-energy and motion-energy of the quarks and gluons may change, and their overall interaction-energy may change, but the total energy of the proton doesn’t change, even though the stuff inside is continually rearranged.  So the proton’s mass is constant, despite the maelstrom within.

Ok.  It’s important to take a moment to drink this all in.  How remarkable is this!  Almost all mass found in the ordinary matter around us is that of the nucleons within atoms.  And most of that mass comes from the chaos intrinsic to a proton or neutron — from the motion-energy of a nucleon’s quarks, gluons and anti-quarks, and from the interaction-energy of the strong nuclear forces that hold a nucleon intact.  Yes: our planet, our bodies and our breath are what they are as a result of a silent, and until recently unimaginable, internal pandemonium.

But… But…

Some of you may be satisfied with these explanations. For those who have further questions, please be patient! A second and third layer of discussion, perhaps answering some of your questions, will be coming soon.

105 responses to “Protons and Neutrons: The Massive Pandemonium in Matter

  1. Pingback: The Bedlam Within Protons and Neutrons | Of Particular Significance

  2. Prof. Strassler,

    Great layer of info on the structure of nucleons!.

    It is my understanding that you may discuss later how the value of the spin for the proton and the neutron is formed. Being both fermions, it makes some sense that how the spin comes out of the details of the picture might be of some importance to the comprehension of the proton and the neutron.

    Now we know that the most of the mass of both the neutron and the proton come from the kinetic energy of all the particles bumping into each other in the first place, from the interaction energy (binding enery) due to the strong nuclear force (this energy, being the result of a potential that binds the particles confined within closed quarters is negative energy, so it discounts some of the positive energy coming out of the other two sources), and third, with a lower contribution, from the “rest mass” of the three quarks.

    It seems to make some sense that some of the properties of the proton and the neutron could be explained by these relative contibutions:

    is that correct?

    if this is correct, what properties could be explained by this contributions?

    Kind regards, Gastón E. Nusimovich

  3. Jyri Tynkkynen

    Oh Lord, please give me patience to wait for the 2nd and 3rd part… RIGHT NOW!!! ;)

  4. So in the end all the mass of cosmic matter is due to ….
    Moving of something…
    Holding of that thing…..
    Really amazing !!!!!
    But the Higgs field does not interact with moving or holding , so where are we ??

    • There are other ways to have energy: not just by moving and holding, but also by simply changing with time, or changing across space. You may want to look again at http://profmattstrassler.com/articles-and-posts/the-higgs-particle/how-the-higgs-field-works/

      • Yes Professor, rupture in spacetime metric due to the change in Conctancy of the heavens. Part of the proton mass comes from rupture in spacetime metric(3D)- exposing dark matter(positive pressure) – thus increase the negative pressure or dark energy(at a point or mass). So change in constancy of the heavens means, slight change in proton mass – thus change in electron mass(the ratio of the electron mass to the proton mass is sensitive to several important quantities in nature).
        But the overall impact is neutralized by “conservation of energy)?
        In context with Higgs like field, electron mass is simple. But in context with the definition of “mass” itself make the Higgs like field complicated?
        My intution says, “mass” means protrude of dark matter. Higgs field’s disturbance of simple harmonic motion(mass) also create this protrude?

        /But Figure 3 reflects the more subtle way in which the proton’s mass actually comes about (as we can check directly using computer calculations of the proton, and indirectly using other mathematical methods). It is very different from what is suggested in Figure 1 and 2, and not so simple./

      • Before the change in Conctancy of the heavens, Higgs particles had spin “0″ – behaved within 3D spacetime metric. Now it is spin “2″ – appear and disappear like neutrino ?
        The behaviour is like graviton? It does not escape 3D spacetime metric like photons because of its relation with mass of matter and its relation with Goldstone bosons ?

      • There is mistakes due to my rush. Rupture in spacetime metric means, concentration of high energy- like it was in bigbang- converted linear momentum into angular momentum. Change in constancy of the heavens in quantum level means, change in “R”(the proton mass is proportional to 1/R).
        My assumption is, positive pressure(protrude of dark matter or mass) and negative pressure are proportional. But the protrude(mass) create curvature in spacetime metric, inversely proportional to negative pressure(dark energy) ?

        Higgs field’s disturbance of simple harmonic motion also create this protrude(mass)?

      • How did the Universe come by its angular momentum?
        It seems the universe is full of angular momentum. … Yet the origin of the universe was the big bang where everything exploded outward from a point source. … was formed there was no or very little gravitational effect to force matter to … little or nothing to stop what must have been a fairly linear expansion…..

        http://www.thenakedscientists.com/HTML/questions/question/3392/

      • If dark matter accounts for most of the mass of the universe, how it could encompass the visible parts our 3D galaxy ? – It is counterintuitive and collapsing my brain.
        Professor, please explain how a 3D spacetime metric(Lorentzian manifold, Einstein’s field equation) could sustain dark matter undetected, while 3D spacetime(mathematical structure of a manifold) bounded by photons ?

        We observe the behaviour of matter, and infer the existence of space-time structure, but cannot actually observe it. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst, it is in conflict with observations in quantum theory.

        The logical error lies in thinking that if we have a set of actual observations, B, and a theory, A with A => B, then A must be true. In fact, there may be some other theory, C, which we may not know about, which also has C => B, and such that C contradicts A. Modern physicists usually avoid the issue by denying that it is possible to describe nature ?

        • If you are asking why we cannot ‘see’ dark matter, it is because it is not black or ‘dark’ as such, but does not react with light at all. It is invisible, transparent. There is certainly precedent for this, solar neutrinos bathe our planet, but are almost impossible to detect.

          As for theories, you will find far more than dark matter out there, though it is certainly the current favorite. MOND was a hot one a few years ago for example. While some physicists claim we may never understand the universe (And there is no good reason why we should after all.) I like to think the community as a whole is quite open minded.

          • Thank you Mr Kudzu, some relief in my brain. I thought, there may be difference between “does not react with light at all” and “light cannot enter at all” !

            Wraped extra dimension ?: Apart from evoking the science-fiction fantasy of parallel universes,
            the new view of space offers possible solutions to several cosmic problems.
            In a flurry of recent research papers, physicists have explored the hidden
            dimensions for clues about the nature of gravity, the origin of the universe,
            and the identity of the elusive “dark matter” thought to lurk throughout the cosmos.
            http://www.physics.ucdavis.edu/~kaloper/siegfr.txt

          • Astronomers have argued that such matter cannot be seen
            merely because it is not bright like stars; dozens of
            suspects have been proposed to account for this “dark”
            matter. But it’s possible, says Dr. Lykken, that dark matter
            is actually “transparent” matter, residing in nearby braneworlds
            and therefore invisible.

            “This would be a new kind of dark matter,” he said.
            “We could never see it or ever feel it by anything other
            than its gravitational pull.”

  5. In addition , till now fields are mere math./mind construct not solid aspect of reality , so it all dissolves into mere motion and restriction ……..OF WHAT ? …… IN WHAT??
    I like that very much , this is the way it should be.

  6. [Sorry, first posted as a reply to the blog post instead of the article.]

    Thank you very much for your post, Professor Strassler!

    There are a few points I’d like to understand better; maybe you can clarify them in subsequent posts:

    1) You mention that the classical “quark composition” is significant and there is a significant distinction between valence quarks and sea quarks. My naive understanding is that the “valence quarks” are those quarks which, if hypothetically free and then combined (say, 2 up + 1 down), would produce the baryon of that “quark composition”, uud in this case = a proton. In other words, that while a proton and a neutron may have innumerable quarks, anti-quarks, and gluons, it is the “quark composition” that makes a proton a proton and a neutron a neutron.

    Is this correct?

    2) I understand that there are other “ingredients” that differentiate baryons from each other – a delta-+, for example, has the same quark composition as a proton, but, if I recall correctly, all its quarks have the same spin, unlike the proton. If no individual quark can be distinguished as a “valence quark”, how are the delta-+ and the proton distinguished?

    3) What meaning do “quarkonium” quark compositions have, if there is no excess of quarks of any flavor – how is a neutral pion distinguished from an eta, J/psi or upsilon? (For that matter, how is a spin-zero quarkonium meson distinguishable from a vacuum or a photon [here my ignorance shows, I guess...])

  7. kashyap vasavada

    Nice article.I should wait for the second and third layers.But let me ask questions anyway. Are number of parameters in these calculations fewer than number of predicted values? Also do they explain magnetic moments also? What about other baryons? Thanks.
    kashyap vasavada

  8. Allow me to repeat a previous un-answered question :
    If the third peak of the CMB-PS is not a proof of DM , then it could be explained by other proposals that does not include DM…..i mean it only cosistent with DM proposal not required by it.
    Am i correct ?

  9. That last paragraph is amazing.

    Almost as amazing as that I understood this article pretty well. Well done!

  10. As I understand, in a molecule, atoms share valence electrons, to the extent that asking “In a carbon monoxide molecule, does that electron belong to the C or the O” isn’t a good question.

    Is there something similar about quarks of adjacent nucleons? That is, in a deuteron, do the proton’s quarks and gluons stay in the proton, with virtual gluons embodying the residual strong force holding the proton and neutron together? Or do the two nucleons swap quarks around too?

    • Isn’t the interchange of pions between protons and neutrons the same, effectively, as “swapping of quarks”?

    • Yes, and then again, no. To answer the core of your question, gluons do not mediate the nuclear force, quark containing particles do. But the answer is more complicated.

      In a CO molecule some electrons are ‘shared’; there are orbitals that cover both atoms, making assigning them to one or the other meaningless. On the other hand those in lower orbits are bound to one atom and need serious energy to jump from one atom to another.

      Nucleons are reasonably distinct in a nucleus, but they exchange ‘virtual pions’; (Nominally an quark-antiquark pair, but, like protons, being full of other ‘stuff.) to experience the strong force allowing a neutron and proton for example to ‘swap’ becoming a proton and neutron. This could be considered ‘quark swapping’

      However electrons are stable; though you cannot ‘pin them down’ you can be quite sure they’re not going anywhere. Nucleons however do not have such permanent constituents, the particles of which they are made are not quite ‘real’; they don’t stay around for any appreciable length of time before interacting and being changed or annihilated. Due to this it is not entirely accurate to call this swapping of quarks either in the same way we cannot consider three quarks to be the ‘special real’ quarks in a nucleon.

  11. I hope that you cover in future articles what the actual shape of the Proton is. We always see it depicted as a sphere but I suspect the reality is more complex than that. I am also curious about the shape when a proton and a neutron bond in a nucleus of say Deuterium or Helium. Is it shaped like what we see in text books with a white ball and a red ball glued together or is it more a giant amorphous blob where it where you can’t even tell the proton from the neutron?

    • This too is an interesting subject. One of the problems is what we mean by ‘shape’; protons have a surface in the same way atoms do; there is not a solid boundary, but a gradual change. (Though in the case of protons that change is relatively sharp.) Protons are also not static, they deform and of course emit\receive particles (‘virtual’ pions.) In this case, as with atoms, a sphere is a basic approximation.

      In nuclei however we’re on firmer ground. Textbooks show the nucleus without order, just a blob of particles stuck together, all touching. In reality nuclei have ‘shells’, like electron shells, one set for protons, another for neutrons. They have much in common with electrons in this situation, being comparatively far apart (And in so called ‘halo nuclei’ certain nucleons can spend appreciable time at distances many times that of the ‘core’s’ radius. http://en.wikipedia.org/wiki/Halo_nucleus )

      When you combine these two considerations questions arise, such as whether the nucleus is a series of ‘fuzzy shells’ of particles, at which point you need a more knowledgeable explainer than me.

  12. Very interesting.

    I also have one question: why is the case of the mass of an atom so much different from the case of the nucleon? I mean some of the heavier atoms have plenty of electrons and those on the inner shells move close to the speed of light (or so I’ve read) there should also be countless associated virtual photons and electron-positron pairs present. So why isn’t a big chunk of their mass coming from the chaotic motion of those electrons, photons and pairs? Why is such contribution negligible in this case?

    For example the mass of the lead atom is 207,2 u (values from wikipedia) which is pretty much the number of nucleons (averaged over isotopic abundances it’s 207.24) times the atomic unit of mass (which is based on C12) – so the kinetic and interaction energy of all those extra 76 electrons and associated virtual photons and electron-positron pairs seems to be below 0.1%. When compared to hydrogen instead of carbon the lead actually has a mass deficit over the numbers of nucleons times the mass of the hydrogen atom since it would amount to 208.9u.

    • One problem with taking the mass of an atom as that of all its constituent particles summed is that nuclei have a high ‘binding energy’; that is to say, due to complex interaction phenomena a nucleon in helium is lower energy than one in hydrogen, and on in lead is lower energy still. (With iron 56 nucleons being the lowest energy of all.) If this were not so then nuclei would fall apart. This energy is VERY significant; carbon-12′s proton is designated the standard mass unit, a proton in hydrogen-1 is 1.007276 of these, while one in lead 204 is 0.9998678 of these (203.9730436 / 204 nucleons.) As such your math is off at the start, even two hundred electrons’ rest mass is barely a tenth of an AMU, buried under the loss of mass due to binding energy.

      But what about all the electromagnetic interactions? Surely as you ask, there should be e-p pairs, virtual photons and suchlike? Well… no. The electromagnetic force is much much weaker than the strong force, and an atom is much, much much bigger than a nucleon. As such while electrons are indeed disturbing the electron and photon fields in ways that have significant effects in chemistry (Such as the shielding of valence electrons.) these effects are remarkably weak compared to strong interactions; in the same way that a nuclear bomb is more powerful than the same mass of even the best chemical explosive.

      And of course electrons in an atom are lower energy than free electrons, there are all sorts of effects there. An electron orbiting a proton has less mass than a free electron at rest and this is the case for ALL bound electrons, even those moving very fast in a heavy atom. (Otherwise it would just escape.) If you do a back of the envelope calculation (not as easy as it sounds.) you’ll find that adding an electron results in an atom getting a little less than an electron’s worth of mass. (‘Electrons’ make up more of a heavy atom’s mass than a light atom’s as a percentage, but they can never appreciably contribute.)

      • You are right about my rough calculation being off because of binding energy and about electron mass being not significant but that doesn’t answer my question. Quark mass is also insignificant yet their interaction and kinetic energies are crucial.
        You say there are no virtual photons in the atom, that is certainly wrong, all EM interactions between protons and electrons and electrons themselves are mediated by virtual photons. As for the e-p pairs they are also surely there, vacuum polarization is a well established fact. Maybe they are not as numerous as quark-antiquark pairs in the nucleon, but they have to be there.
        Also while strong force is indeed stronger, it’s only about 100 times stronger then EM so it’s not such a vast difference, (Also chemical reactions are as weak as they are because only the outermost electrons partake in them, not because EM forces in an atom are that weak in general. Transformations involving inner electrons are much more energetic they just don’t lead to any practical chemistry, but for example xray sources take advantage of them)

        • Ah, my reply contains an error. You are correct, atoms DO contain virtual photons at least. I should have worded that better. What I wrote came off as a complete dismissal, when what I should have said was they were not very significant. But why, as you ask?

          Now, we can get an intuitive (but wrong) idea of the contribution of the electromagnetic force by considering its strength (100 times less than the strong) and the distance over which it is acting. (More than 1’000 times greater.) However, given your apparent level of knowledge you can dismiss this argument, it is much too basic.

          A more fundamental issue is the issue of containment; quarks and gluons interact such that there can never be free particles of either; if photons had electric charge then it would be quite likely that electromagnetic interactions would be much more ‘messy’. As it stands most EM interactions are mediated by photons which do not, in themselves, create more particles. An electron in a hydrogen atom disturbs the photon field a given amount and that is the end of it. Two quarks in proximity to each other create a bridge of gluons that themselves create more gluons, that can create further quarks… this leads rapidly to a massive increase in the number of particles and thus the amount of ‘extra stuff’ involved. Possibly the Professor can explain it more succinctly.

          Also, while chemical interactions are indeed rather weak compared to the energies involved in core electrons, these too pale next to nuclear energies. Even in the heaviest atoms a single gamma ray photon can knock out 1s electrons at an energy scale below that needed to make even electron-positron pairs.

  13. Hi Matt,

    As you’ve explained elsewhere, all these particles inside the nucleon are ripples in their corresponding fields. What generates and maintains this “storm”?

    • This is an interesting subject. Briefly, the ‘storm’ maintains itself. Something can only dissipate if energy leaks from it, a regular storm’s energy dissipates as head for example. But something that is already in a very low energy state (compared to any other possible states.) cannot do that. Ordinary air contains a storm of rapidly moving atoms, yet any given patch has nowhere to expel the energy it contains. Hadrons are similar, the immense amount of energy they contain is in the most stable configuration, just because it is so chaotic does not mean it can dissipate, the laws of physics forbid it.

      Aside from that, what ‘generates’ this storm initially is related to the fact that you cannot simply create a single quark by itself, all the processes that do require the creation of an entire hadron. So hadrons can only be created in very high energy situations.

      • Matt, I know you’ll explain this later but I’ll ask anyway; for quarks/anti-quarks collisions there has to be space for them to move, yet that space, which is a field of ZPE is a field that when excited produces pairs of virtual particles. So every time the field gets excited by a collision, a new particles are born and added to nucleons, so the overall mass remains constant. I’m probably missing a detail of what you already explained to us. The collision increases level of energy due to velocity/ kinetic energy, which gets re-absorbed by the field and the status-qua is maintained indefinitely. A bit like water boiling in a pressure-cooker. Am I right in concluding that there is a field of ZPE in there?

  14. If the gluon is massless, like the photon, why does it have speedwithin a hadron that is variable , rather that only c?

  15. thetasteofscience

    Hi Matt,

    You wrote “How remarkable is this!” Indeed! Indeed!
    This is just great for me! When I was in graduate school for a short time in the early 60s, the professors didn’t discuss their research with lowly first year grad students. When I free-lanced in Physics in the early 80s, I discussed my research with my colleagues, which wasn’t in particle Physics. So FINALLY, I get to know what’s going on.
    After that many years, I guess i have enough patience to wait for parts 2 and 3. Thank you so much for your lucid descriptions!

  16. I’m afraid that what figure 3 will suggest to many people is that nucleons are so massive relative to quarks because the former contain so many of the latter! Just as a Uranium nucleus is so massive because it contains a lot of nucleons. I think you need to say something about this…..

    • But in a sense they DO contain many quarks, they’re not filled with empty space or some fuzzy ‘energy’ a simple diagram that accurately communicated the true structure is hard to envision. If the ‘other’ quarks were made different, light colored say, to show they were ‘virtual’ then it would send the message that the ‘core three’ quarks were somehow special and distinct, which they aren’t. If we dispensed with quarks entirely and tried to show the interior as a fuzzy mash of fields (or a plum pudding model) it would ignore the fact that there are semi- discrete particles in hadrons that have very definite effects, viz deep elastic scatter. I think the current diagram, though not perfect, is a good compromise.

  17. Hi Professor Strassler,

    I understand from this and other writings of yours that in a proton-proton collision to produce a Higgs, one of the most common channels is the collision of two gluons. If so, I have a bit of a tangle in my head. Please point out my error:

    1) gluons are massless
    2) therefore gluons always travel at the speed of light
    3) therefore, what difference does it make how fast the LHC accelerates protons if the collision is between massless, light speed gluons?

    Clearly I’ve made a mistake here somewhere. Or at least one.

    • One error is in thinking that because mass-less particles always have the same velocity, they always have the same energy.

      • Does that mean that gluons within an accelerated proton have in some sense a higher vibrational frequency than gluons in a stationary proton?

        • Yes, when viewed in the reference fame where the proton is moving towards you. This would be a ‘blueshift’ of gluons similar to that which occurs with light. (Though you may be more familiar with the redshift instead.)

          • stephenwhitt

            OK, this makes sense to me now. Increasing the speed of protons at the LHC causes a blueshift of gluons and through E=hf the energy of those gluons increases. Thanks!

  18. Do you have an article describing the cycle that the collisions inside the nucleons go through? I understand that the energy is conserved but am not seeing how the continual collisions does not eventually lead to a soup of the lowest energy particles.

    • The important thing to remember is that they already ARE a soup of the lowest energy particles, or at least there is nothing lower energy to which they could decay. You can excite a proton or neutron, in which case it will emit particles and return to its ground state.

      This is a bit counter-intuitive, since it seems like a nucleon is so full of energy it ‘must’ have to decay into something less energetic, but we see many examples of this (albeit less extreme) in everyday life. The air we breathe contains a massive amount of energy in rapidly moving particles, yet these cannot vent their energy anywhere (or at least not much of it.) The case of nucleons is similar.

  19. A substantial mystery is how a dimensionless coupling constant (alpha_s) gives rise to an energy with dimensions (Lambda_QCD). Dimensional transmutation, I guess, itself a fascinating topic.

    Seems to me that Rabi (with others, and maybe in conjunction with other work throughout the world) found proton and neutron substructure through measurements of the anomalous magnetic moments in the 1930′s. Nuclear size was deduced earlier, in the 1920′s, via the Cavendish’ groups observations of deviations from Rutherford scattering at large momentum transfer. Maybe that came as early as the ejection of protons from nuclei, which I thought Rutherford saw in the midst of WW1 when most of his students and lab staff were off fighting (some prisoners in German POW camps). Well, except for Moseley, who died at Gallipoli.

    Not clear who specifically measured nucleon (as opposed to nuclear) sizes, although I think the A^(1/3) scaling of nuclear size was deduced quite early. Hard to see how nucleons radii would differ from that… But in general, in that era, the experimental picture was far better developed than the theoretical.

  20. Hi Matt

    I found this article fascinating and very clear. I am not an expert in this area, but I was wondering if perhaps one might argue that for low energy reactions (e.g. beta decay) it is the valence quarks that are the main players. While at high energies one gets much more participation from the sea quarks and gluons. Perhaps, one could argue that there is some merit to the simple three quark picture at low energies, at least when thinking about how the proton or neutron interact or decay?

  21. kashyap vasavada

    I have a similar question as the one above. If sea quarks are as much or more important than valence quarks ,how can one calculate anything like weak decays, strong cross sections etc? I remember a recent Nobel prize was given for CKM matrix for quark mixing. If the sea quarks continually exchange with the valence quarks of the right kind then perhaps it would not make any difference. Is this correct? We know you are going to address these questions in the forthcoming articles but we keep on bombarding you with questions anyway!!! I hope you excuse us. Thanks.
    kashyap vasavada

    • I do not think he is saying that ‘valence quarks’ are less important than ‘sea quarks’, but that there is no difference; it is impossible to pick three quarks and say ‘they are special’

      This does in fact have very important ramifications for things like beta decay since in the more complex model not every quark can change flavor while in the simply model 2/3 can. The physics is too complex for me but it seems to hold up.

  22. Matt, great article.
    My questions:
    1) If the motions and interactions inside the protons and neutrons determine its mass – how come that any two protons (or neutrons) have exactly the same energy (or mass)? Naively, one might expect that the chaos inside the protons and neutrons may have different states, in the sense of different energy levels – but this seems not to be the case.
    2) Further, if we had some probing device (“microscope”) that could look “inside” the proton and reveal some of its details – could we distinguish one proton from another by seeing that one chaos is different from another one? In case we cannot meaningfully distinguish two protons by their internal state – wouldn´t that mean that “effectively” the chaos in any proton (or neutron) is the same (and always remains the same), regardless of all the many different interactions?
    Looking forward to your next articles!
    Markus

    • These are two very interesting questions.

      In the first case, what we must keep in mind is that while there are many states a proton may be in, many arrangements of its constituents, they are all equal, there is no barrier between one state and another. This has several odd consequences, but classically you can think of the proton as a deck of cards. There are many, many ways to order a deck of cards, but it is still a deck of cards and there is very little difference energy-wise between the orderings.

      However protons and neutrons DO have excited states which they can be converted into by giving them a great deal of energy. These are known as Delta baryons (Specifically Δ+ and Δ0) and they rapidly decay back to a proton or neutron (and a pion.)

      Your second question raises its own, broader question, ‘What is “identical”?’ We can say two glasses of water are identical, but look close enough and one is likely to have more or less water, scratches and marks, not to mention a totally different arrangement of molecules at any one time. We only say protons are identical when we ignore their specific internal structure at any time. (Ignoring the quantum effects and the nature of ‘virtual particles.’) If you look at the proton ‘from the outside’ it appears to be a spherical object of certain radius and positive charge.

      But we have in fact created situations where we view the proton ‘from the inside’; notably in the LHC where the constituent particles of protons collide. Here each collision is different, quark-quark differs from quark-gluon and so on. This is in fact one of the best lines of evidence for protons having the structure outlined here.

  23. Thanks for a great article.
    Can you explain how a particle as apparently stable as proton can arise from the maelstrom of particles of which it is comprised? Is it that the strong nuclear force plays an analogous role to the force of gravity when it draws stars from the interstellar gas? Is it reasonable to imagine a similar process acting in the early universe on the chaos of fundamental particles to form the order of things like protons?

    • What we must keep in mind is that as chaotic the proton is, there is nothing for that chaos to do; protons are the lowest energy state for that maelstrom to be in. Other hadrons, indeed ALL other hadrons rapidly and violently decay in factions of a millisecond. It’s like the chaos in a glass of water, with all its molecules moving at hundreds of meters a second, yet so calm externally.

      • So is the strong nuclear force that is playing the role of the glass in your water analogy?

        • Not really,t he strong force is an attraction, like gravity or surface tension. But it doesn’t guarantee stability, Gravity causes landslides for example. What matters is there is no way for a system to get *more* chaotic, a boulder sitting on the ground is fine, one at the very top of a slope isn’t. A glass of water on earth is stable, one in the vacuum of space will explode into vapor. A proton is stable not because something powerful holds it together but because it is not allowed to do anything else. The chaos within it is ‘stuck’, forbidden to escape by its very situation.

          • What is that situation “angular momentum”? The “spacetime metric” or local or geometrical symmetry is our limit of science and start of new physics ?
            We can identify a particle only with the help of “photons” or in the case of neutrino with Cherenkov effect. Albert Einstein’s relativity was not his own, but, become prominent after its connection with speed of light. It is geometrical and local symmetry. If Einstein’s postulates does’t work with dark matter means, the man made “spacetime metric” (mathematical) bound to photons of 3D spacetime metric ?
            At the start of new physics c^2 become 0^2 ?

  24. Tienzen (Jeh-Tween) Gong

    Your bedlam model (with sea quarks) is, of course, not wrong, as being supported by enough gadget data. Yet, I must disagree with you as it is a very bad idea because that there is a much better idea available. I, of course, will not use another particle theory for this argument at a place like here, but it will be fair by just using an analogy.

    The key points of your bedlam model (B-model) are the sources of the proton’s mass and the gadget data showing the existence of the sea quarks. Yet, these two points can be fully accounted by a kaleidoscope model (K-model) which is composed of three parts.
    a. Some color beads — the valence quarks.
    b. A container (the envelope) — the gluons.
    c. A set of mirrors + void space (zillions of beautiful patterns) — the sea quarks.

    First, the color beads account about 5% of the mass of the kaleidoscope. Then, there are indeed zillions of patterns which can be videotaped as gadget data, but we all know that those patterns are optical illusions although they follow the physics laws exactly. Thus, the two models are identical for equations, that is, the differences between the two are transparent to the equations describing them. Yet, conceptually, their differences are very, very huge.

    For the K-model, there are three spacetime sheets.
    i. The envelope — the spacetime sheet separates its internal from the spacetime sheet of the universe.
    ii. The internal spacetime sheet (the set of mirrors and void space) — giving rise to the sea quarks.

    Then, the valence quarks are the protrusions from the internal spacetime sheet. Thus, the proton is composed of three parts.
    1. An envelope — viewed as gluons in the B-model.
    2. The internal spacetime sheet (different from the two other spacetime sheets) — viewed as sea quarks in the B-model.
    3. The protrusions — the valence quarks.

    This K-model is conceptually different from the B-model while their differences are transparent to the equations.
    A. The valence quarks (or leptons) are conceptually different from all force carriers which are not truly “particles” but are envelopes (a special kind of spacetime sheet), except for the weak force which is the envelope cracker. By excluding the force carriers as the matter particle, the exact number of the “elementary matter particle” should be “derived”, Neff = 3.

    B. The K-model is an iceberg-like model which is the model thus far consisting with the Planck data. That is, the K-model is not only good for accounting for the proton’s mass but is good for the dark matter + dark energy situation.

    You said, “Quarks and gluons, for all we know today, may be truly elementary (i.e. indivisible and not made from anything smaller).” In this, your understanding of “indivisible” is not adequate. The three parts of this K-model (or iceberg) are not divisible in terms of defining a “proton”, while they are indeed three completely different parts. That is, something which is indivisible does not connote as not having parts. Furthermore, for the iceberg model, the parts need not to be smaller than their composed entity (the visible part of the iceberg).

  25. Re; “One more comment: the three quarks (two ups and a down for a proton) that aren’t a part of a quark/anti-quark pair are often referred to as “valence quarks”, with the pairs of quarks and anti-quarks called “sea quarks”. This language is technically very useful in many contexts.
    But it gives the false impression that if you somehow could look inside a proton, and you looked at a particular quark, you could quickly identify whether it was a sea quark or a valence quark. You can’t do that; there’s no way to tell.”

    The important thing seems to be the imbalance of quarks and ant-quarks. Protons and neutrons are characterized by having three more quarks than anti-quarks, in the correct combination of up and down.
    To use your dance analogy, we have a big dance party with 2 groups (ups and downs), each members of each group may only dance with a member of the opposite sex of its own group (particle or anti-particle), and we have three wallflowers – 2 ups and a down, or two downs and up, and they are all of the same gender (i.e. particles rather than anti –particles).

    It begs the question, what is so special about this combination of wallflowers at the dance.
    Why three? Why not three up or three down? Why no antiparticles?

    • All particles composed of quarks must be color neutral, in the same way all atoms must be electrically neutral, but much, MUCH more so. There are infinite ways to do this that can be split into two groups. The first is composed of one quark and one antiquark that are each an opposite color (Blue and antiblue say or green and antigreen) which are called mesons. They are their own antiparticles and don’t last long.

      The second way is one quark of each color, red, green and blue. These are baryons, and the lightest one of these, the proton, is stable. Antiparticles exist for each baryon, like the antiproton made of three antiquarks.

      In both these cases adding a quark anti-quark pair to the mix doesn’t affect color which is what all the ‘other stuff’ (In a slightly more complicated manner) is.

      There ARE other mesons and baryons out there of any quark combination you can imagine, three downs, two stranges and a top… they’re all massively unstable and quickly decay however, like most particles. See http://en.wikipedia.org/wiki/List_of_baryons

      • (One small quibble: “any quark combination you can imagine, three downs, two stranges and a top” – top quarks can’t hadronize, I think.)

        • The problem with the top quark is that it is the heaviest and least stable of the quarks. It is so unstable that it does not have time (On average at least) It is rather like trying to study the chemistry of exceedingly radioactive elements. So you are right, the top quark is an exception in that the chance of hadron containing one forming are astronomically small.

  26. /Figure 3 suggests that (B) and (C) are important, with limited impact from (A).
    And remember that to turn a proton into a neutron you merely have to replace one of its up quarks by a down quark (Figure 3); that replacement is enough to make the neutron slightly heavier than a proton, and shift its electric charge from +e to zero.
    our planet, our bodies and our breath are what they are as a result of a silent, and until recently unimaginable, internal pandemonium./

    If massless photons create gravitational field, why not massless gluons in the proton create gravitational field ?

    Gravity is not about mass, it is about energy – momentum more generally. Particles doesn’t have any mass. Newton connected mass with gravity. Even there is no gravity in the world, particles get their mass.
    MASS DISTORT SPACETIME.
    Dark matter accounts for most of the mass of the universe. The potential energy of an harmonic oscillator is mass.

    Like in pendulum’s potential energy is spent by gravity, the motion-energy of proton have decay?. But Amplitude carries the physical effect, the amplitude retain strength even in lowest energy level (even in zero E/c^2 = 0) – the mass remain intact at 0^2 – means, if the realm of photons is stopped, creation of proton mass is not distorted ?

  27. The gluon assocated with the electromagnetic interaction is the photon, colored gluons provide the quark binding force. In hydrogen atom, two quanta — the electron and proton — are exchanging a third quanta — the photon. From this point of view there are not particles and fields; there are only quanta.

    At what point the quanta of a gluon become “particle” (ripple of a field or stuff) like photon ?

    • Your statement is not entirely accurate, a ‘qunata’ is the smallest possible amount of something. A photon is a quanta of light, if you make a light dimmer and dimmer eventually you reach a point where only one photon is being produced. You cannot dim that any more, it’s either 1 photon or none. In a similar manner a single atom is a quantum of an element, you either have the atom or not, you cannot have half the atom and have it be the same kind of atom.

      In a hydrogen atom two quanta (a quanta of proton and a quanta of electron) do not exchange other quanta, they exchange ‘virtual particles’; these are far more messy than photons which have a definite energy and frequency. They are more like unstable spasms in the photon field. Only in specific situations can an electron in an atom emit actual, real, visible photons that then usually leave the atom and get to your eyes. (Think of a candle flame or a street light.)

      In a quark there are ‘virtual gluons’ too as was as ‘real’ ones, but because everything is so much more messy in a proton is can be very hard to tell the difference between the two. (To be considered ‘real’ a particle usually has to exist for a ‘long’ time and most of the particles in a proton don’t get to last that long at all.)

  28. Quantum chromodynamics (QCD) is a relativistic quantum field theory that gave a mathematical description of these strong gluons just as the quantum electrodynamics, QED, gave a description of the photon as the gluon of electromagnetic fields.
    Where was a satisfactory renormalizable theory that could explain the force that held these quarks together – Yang-Mills QCD ?
    In high school physics, we learned that force fields, like gravity and the electric field, obeyed something called the “inverse square law”. The mass of the proton is set by a curious and crucial feature of the strong nuclear force. However, the strong nuclear force is different. If you take a quark and an antiquark that are extremely microscopically close together, the strong nuclear force between them will first become weaker, but then, at about a distance of a tenth of a millionth of a millionth of a centimeter (a centimeter is a bit more than 1/3 of an inch), the force will stop decreasing. Well, that special distance is called the “confinement scale” (let’s call it “R”), and at larger distances the “confinement force” holds the quark and antiquark together in a constant and firm grip from which they cannot (directly) escape. How strong is the strong nuclear force at a distance scale where quantum gravity is important — the sort of question that theoretical physicists might ask when trying to make a complete theory of the world — the answer is that R depends exponentially on the answer! Just a 1% change in the strength of the strong nuclear force at very short distance can lead to a 10% change in R!

    For example, the further one travels from the the sun, the weaker its gravitational pull will be. This means that as one approaches the particle that is the source of field, the force increases dramatically. In fact, the force field of a point particle at the surface of the particle must be the inverse of “ZERO SQUARED”, which is 1/0. Mathematical expressions like 1/0 are infinities and not defined. The result of introducing point particles into our theory of fields is that all our calculations of physical quantities, such as energy, are riddle with 1/0s. This is enough to make the theory useless.

    But gluons of strong interaction are not point particles like photons ?

  29. At the “confinement scale” (let’s call it “R”), the force will stop decreasing – the force field of a point particle at the surface of the particle must be the inverse of “zero squared”, which is 1/0. The mass of the proton is set by a curious and crucial feature of the strong nuclear force. Gravity is not about mass, it is about energy – momentum more generally. Point particles also doesn’t have any mass. Even there is no gravity in the world, particles get their mass.
    MASS DISTORT SPACETIME.

    Now how do we figure out the proton mass from this? Roughly speaking, trapping quarks and antiquarks and gluons in a little sphere with radius about equal to the confinement scale assures, by the uncertainty principle of Heisenberg, that the amount of energy in that little box will be related to Planck’s constant h divided by R and by the speed of light c. You see, Heisenberg tells us that you can’t know the position and the momentum of a particle at the same time; so if you squeeze down the position of a particle into a sphere of radius R , the particle will, on average, be speeding around with a momentum proportional to 1/R. So if the proton were to become smaller, its mass would increase. the proton mass is proportional to 1/R; roughly it equals h/(2πcR). what determines R?

    Just a 1% change in the strength of the strong nuclear force at very short distance can lead to a 10% change in R!
    So the the energy – momentum of massless gluons (quantum gravity) determines R? – which is out of 3D spacetime and realm of photons ?

    But the confinement scale R is affected somewhat by the masses of the top quark, bottom quark and charm quark is not significant because of their overall contribution to proton mass ?

    • Sir, you make a fundamental error in your first paragraph. When the force goes from increasing to decreasing there is a point where the amount it *changes* is 0, like a ball tossed in the air stopping at the top of its jump. This does NOT make the field itself there 0.

  30. Kudzu, you are correct for Newton’s inverse-square law. But the confinement scale(R) here is very tiny even at quantum level. In context with strong force(between quarks), the stickiness of gluons decreases as R increases- but why stop decreasing at distance R? – there is enough escape velocity.
    /The inverse-square law generally applies when some force, energy, or other conserved quantity is radiated outward radially in three-dimensional space from a point source. Since the surface area of a sphere (which is 4πr2 ) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source./

    I mean the “confinement force” is created by gluon gravity (quantum gravity) ?

    If you squeeze down the position of a particle into a sphere of radius R, the particle will, on average, be speeding around with a momentum proportional to 1/R (angular momentum) ? – this energy – momentum came from gluon gravity – this gravity arouse because the force field of gluon point particle at the surface of the particle is the inverse of “zero squared”, which is 1/0. But where its mass came from to DISTORT SPACETIME ? -may be dark matter ?

    • I see.. If I understand you correctly there are few things I would take issue with.

      Firstly confinement is a separate issue from the strong force. Inasmuch as it has been explained to me it arises from the fact that gluons themselves feel the strong force and the fact that the strong force is strong enough that production of gluons is energetically favored.

      When two quarks of dissimilar color are pulled apart their energy increases. At a certain distance they can lower their energy by making a pair of gluons of opposite colors to themselves, lowering the ‘color charge seperation’ between them. This process continues, forming expanding ‘tubes’ of gluons between the quarks which eventually ‘snap’ by rearranging into more quarks. THIS causes quarks to be confined. If gluons had no color charge then their production would not lower the color charge separation, meaning it would not be energetically favorable to produce them and quarks could be freed from hadrons.

      The fact that nucleons have the sizes they do is due to a complex interaction between basic quantum laws like the uncertainty principle and the strength of the strong force between particles. (Which is constant.) The apparent variability of the strong force with increasing R is because that is not due to the force between two particles, but between many particles. (This is similar to how the force of gravity increases as you get closer to the earth, but then decreases as you go underground, being zero in the center of the earth.)

      Because of this particles in a nucleon are not forced to ‘orbit’ anything or occupy the the surface of an imaginary sphere. During their brief lifetimes they move in straight lines for the most part. (A proton radiates ‘virtual particles’ in all directions. Thankfully, they’re ‘virtual’.) This means their energies and momenta do not depend on R.

      As for point particles, this question bothered me also in regards to the electron. But it turns out that as you decrease the size of an object to 0 various interactions arise that stop energies or field strengths heading towards infinity (1/0 in your parlance.)

  31. Mr. Kudzu, first I thank you and Professor Strassler for considering and answering me.

    It is all again my 7th standard question “turning around” – may be the “angular momentum”. “c” is the linear momentum and c^2 is angular momentum. Particles contain momentum and energy, where did the mass came from? – “angular(quantum gravity)” momentum ?
    Feynman diagram and Higgs like particle made solutions ?

    (.) Does the strong force have enough energy to create this angular momentum ?
    (.) Production of gluons is energetically favored means, the stickiness of gluons confined by strong force by creating new quarks- the escape velocity is lowered by “color charge” confinement force – But how ?
    (.) At the time of production of more quarks by color charge, it needs extra energy. Does the energy conservation is compatible with this?
    (.) In uncertanity principle, we can measure momentum or position, or cannot measure both is pertaining to 3D spacetime ?
    (.) The “constant” strength of the strong forces between particles doesn’t create mass ?

    The non zero Higgs like field is reacting with massless other field, create “Higgs particle(mass of known particles)” is only a patchwork – because of “angular momentum” which creates Higgs particle h’s “mass” itself ?

    Colored gluons provide the quark binding force – From this point of view there are not particles and fields; there are only quanta.
    /Confinement is a separate issue from the strong force – gluons themselves feel the strong force and the fact that the strong force is strong enough that production of gluons is energetically favored.
    Strong force is an attraction, like gravity or surface tension – but for stability, at lowest energy level in nucleus?
    Hadrons can only be created in very high energy situations. Two quarks in proximity to each other create a bridge of gluons that themselves create more gluons, that can create further quarks… this leads rapidly to a massive increase in the number of particles and thus the amount of ‘extra stuff’ involved. Possibly the Professor can explain it more succinctly.
    The apparent variability of the strong force with increasing R is because that is not due to the force between two particles, but between many particles(like gravity)/

    • I cannot comment on your question about c and C^2. However,

      * No force ‘has enough energy’ to create something, it depends on the situation. For the strong force to give energy to something you will need TWO particles of different color to be pulled apart some distance and kept there. And if particles are produced they must be in particle antiparticle pairs and the lowest energy ones will be produced first and in greatest number. This immediately limits what any force can do. (The Higgs mechanism works by mixing various particles, a different mechanism entirely.)

      * ‘Escape velocity’ is a deceptive term; instead a better idea would be that of ‘escape energy’; escape velocity is a measure of how fast something must be going to have enough energy to leave a gravitational system if nothing else gives it energy after it is launched.

      To see why confinement occurs, let’s look at 3 systems, a proton in a hydrogen atom, you on earth and a quark-antiquark pair in a proton. Both are bound by a force (electromagnetic, gravitational, strong.) and we’ll pull them apart and see what happens.

      For the proton-electron system, as we pull them apart both gain energy because of how the electromagnetic force works. They would like to become lower energy any way they can. The only way they can do this, if we don’t let them fly together, is to create electrically charged particles. The lightest pair (and thus easiest to make) is the electron-positron pair. Two ‘virtual particles’ will borrow energy from the proton and electron to become real. When they do so the positron could pair with the electron and the new electron with the proton, releasing energy because the charge separation will have decreased. (If you ask WHY like charges attract and are lower energy, that’s a deep question.)

      But the maximum energy a proton and electron can get when moved apart from hydrogen is about 10eV, not even a fraction of a percent of what is needed to make an electron positron pair. This could still work, if the energy release were great enough, but it isn’t (It would be less than the input energy, a few eV or so.) So an electron-positron pair can’t be created, you’d need energy from nowhere. Another thing the electron-proton system could do is make photons; because they are massless they can have any energy. But if a photon pair was created. of any energy, no matter how low, energy… they don’t lower the energy of the system in any way because they’re not electrically charged. Which means again some energy is needed that is not ‘paid back’ and so photons can’t be created. This means the electron proton system is forbidden from creating any particles as it is separated and charged particles are not confined.

      Next the earth-you system. As we move you away from the earth you and the earth gain gravitational energy. Again the system would like to move to a lower energy by creating particles. In this case any particles will do, all particles are ‘gravitationally charged’ so to speak. But the easiest would be a pair of gravitons. (Massless.) Now in this case the creation of gravitons DOES reduce the energy of the system, but because the force of gravity is so weak, it does not reduce the energy ENOUGH to pay back the energy needed to make them. (This is the same for any particle pair in nearly all situations, the gravitational energy released by the energy they contain is less than the energy they contain.) So the earth-you system cannot make any particles and you are not confined. (Nor are any particles with energy, black holes are a different kind of confinement.)

      Finally consider the two quarks. As we pull them apart their energy increases and they want to make particles to lower their energy. The easiest to make are gluon pairs. In this case the gluons, being color charged lower the energy of the system, but importantly they lower it by more than the energy ‘borrowed’ to make them. (They, being massless can be made with the smallest energy you want, but any gluon pair lowers the energy by the same amount.) This means the quark-antiquark pair CAN make gluons, (as long as the gluons’ energy is not too high!) and in fact can make multiple pairs. In turn the gluons can create (lower energy) gluon pairs of their own. Even if this were all there was, color charged particles would be confined, always tied together by gluons.

      That is the root of confinement, a massless ‘force charged’ particle and a force strong enough to make that particle ‘worth’ producing.

      * Now we can see that gluon production doesn’t ‘lower escape velocity’; and it doesn’t violate conservation of energy. WE are GIVING the system energy when we pull it apart, when we smash particles together at the LHC for example. Only when the system HAS energy can it try and do something with that energy. And in the case of color charged particles creating more particles ‘works’

      * We know what ’causes’ the uncertainty principle, it is the basic nature of all fields. ‘Particles’ don’t exist, everything is a wave of some sort. An electron isn’t an infinitely tiny point, but a wave in the electron field. And the basic nature of waves states that the only way you can squash a wave up tiny in space is by making its momentum uncertain, and the only way to can make the momentum certain is by letting the wave ‘spread out’ into a larger volume of space. It is like a see-saw; there is no ‘deep’ reason why one person is up when the other is down and vice versa, that is just a basic fact about how see-saws work, what they ARE. If the universe WERE made of tiny solid particles there would be no uncertainty principle.

      We can in fact make waves in water that obey the uncertainty principle or on flat surfaces or in 1-D strings (Like guitar strings) So it is not a property of 3D space. For example, imagine I want to make a note on a guitar, a note that I know the frequency and amplitude of (and thus momentum) exactly. To do that I need to make sure that there’s no ‘edge stuff’; messy bits near the ends of the wave. To do THAT I need to make the whole guitar string vibrate, the wave must take up ALL the space, be located EVERYWHERE on it. Exact momentum = inexact location.

      Now say I want to make a wave on the string that is only in one tiny place on the string, an exact location. But you can’t do that with one finger, one wave of known momentum, it’s impossible. Instead I need to ‘add’ more waves in of different frequencies, amplitudes and thus momenta. They will interfere and almost cancel out except for one place. The more I want to ‘squash’ the wave I make, the more waves I need when building it. The more waves I need, the more different momenta are used. Exact location = inexact momentum.

      * Finally, ANY force between particles creates mass IF you look at the whole system and not the parts. Usually this is ‘negative mass’ because the force is attractive. A proton and electron by themselves are heavier than a hydrogen atom. When the two meet the electromagnetic force decreases their energy and they emit photons. This means that the strong force, which is also (when you add it up) attractive in nucleons actually lowers its mass a bit. (BUT, if it didn’t exist or was repulsive nucleons wouldn’t form!)

      But the existence of the gluon, a color charged massless particle is what allows nucleons to form, what results in them having all that mass compared to naked quarks. If everything else was the same, but gluons were color neutral, we’d live in a universe very much different.

      I hope this long ramble answers a few questions.

  32. Curious George

    Is it still true that we can’t directly observe any particles with a fractional electrical charge? Do you believe that an electron is intrinsically simpler than a proton?

  33. Kudzu sir, great explanation, I have learned a lot.
    In micro level like “R”(color gluon, quarks), things seems behave different than in proton-electron and in me-earth cases.

    /Quantum realm is a term of art in physics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−7 metres) or less or at very low temperature. More precisely, it is where the action or angular momentum is quantized.
    While originating on the nanometer scale, such effects can operate on a macro level generating some paradoxes like in the Schrödinger’s cat thought experiment./

  34. Great introduction into QCD. Can’t wait for part II and part III. This is my favorite subject, by far. Gluons are very similar to photons in that they are a) mass-less therefore able to zoom at ‘c’ and, b) also bosons, force carriers. So the natural question is why is nuclear force stronger then EM force? Any volunteers?

    • That is a very good question indeed. A more oft-asked one is ‘Why is gravity so much weaker than the other three forces’ (And it is incredibly weaker, amazingly so.) The differing strengths of the elctromagnetic and weak forces is well understood, they can be modeled as a single electroweak force whose symmetry is broken by the Higgs mechanism: http://en.wikipedia.org/wiki/Electroweak_interaction

      I am not actually sure if this has been answered in any meaningful way, in regards to the strong force however, certainly when I was in physics it was a great unanswered question.

  35. Thanks, your input is much appreciated.

  36. Thank you very much for this article – it is very clear and helpful.

    Two questions came to my mind:

    (1) What stops two nucleons (say a proton and neutron) from merging into a single quark-gluon pool when they are close (say in a deuterium nucleus)?

    (2) Why and how does the total energy of the pair reduce when a proton and neutron cling together to form a deuterium nucleus? (I understand that a gamma will be emitted, but why and how does the gamma form and why are the proton and neutron stable at one total energy when they are separated and stable with a different and lower total energy once they are adjacent?)

    • Two nucleons cannot merge into one because that is the way the binding forces inside them work out. In essence quarks and gluons like to form ‘small’ balls of a certain size this is similar to why only certain atomic nuclei are stable (And why a smallish one, Iron-56 is the most stable of all.)

      You can think of this very roughly as similar to trying to make a bigger raindrop in a cloud. For a while smaller raindrops will fuse to make larger ones, but larger drops are harder to hold together. Eventually the drop becomes so unstable that it breaks up if you try and add more mass. This is because the strong surface tension force holding the drop together increases with the square of the drop’s radius, while the (maximum) turbulent shattering force increases with the cube of it.

      The difference with nucleons is that a hadron of six quarks cannot even be transiently formed, any close approach of two nucleons results in an ever increasing repulsive force and increase in energy.

      At a distance however nucleons of any type feel an attractive force. When a proton and neutron approach one another this attractive force lowers their energy and they emit photons in the same way an electron does when binding to an atom. The two nucleons will spiral in towards each other until they reach the most stable configuration. Their binding energy is negative.

      This is not always the case of course, two protons cannot do this, their positive charges overwhelm their attraction. (They are also the same particle, which means the exclusion principle is at play and thus two neutrons do not form a stable nucleus either.) This is the entire basis of radioactivity among other things. An excellent article on this site on binding energy here: http://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/the-energy-that-holds-things-together/

      • Thank you for your reply, and the link to Matt Strassler’s page “the energy that holds things together”.
        But neither that page, nor your reply, give me the understanding I hoped for.
        They both say and . You also say (in different words) that when they move closer due to an attraction, they lose energy and emit a gamma.
        But that was my understanding already.
        What I was hoping for is some insight into why and how a sea of quark-gluons would behave this way.
        Let me ask my questions a different way:
        What needs to be added to Matt’s Figure-3 to illustrate the essential mechanism within the quark-gluon dance that results in (1) the short-range repulsion, and (2) an approach from longer range converting dance energy into a photon?

      • Horrid comment system with lack of preview….
        Here is a revised version without disallowed characters (I hope):

        Thank you for your reply, and the link to Matt Strassler’s page “the energy that holds things together”.
        But neither that page, nor your reply, give me the understanding I hoped for.
        They both say (in essence) “it’s complicated” and “the result of all the complication is that nucleons attract each other at nuclear distances and repel each other if they get too close”. You also say (in different words) that when they move closer due to an attraction, they lose energy and emit a gamma.
        But that was my understanding already.
        What I was hoping for is some insight into why and how a sea of quark-gluons would behave this way.
        Let me ask my questions a different way:
        What needs to be added to Matt’s Figure-3 to illustrate the essential mechanism within the quark-gluon dance that results in (1) the short-range repulsion, and (2) an approach from longer range converting dance energy into a photon?

        • Your second question is the easiest to answer. In this case we add a maelstrom of photons to the nucleon as well. As you are probably aware any moving charged particle can emit photons if it is not in its ground state. However a nucleon (if stable) is in its ground state, all the photons in the nucleon are ‘virtual’, they have a significant impact on the energy and the structure of the nucleon, but less so than the gluons and quarks. They are very much less ‘real’, crazy irregular ripples in the electromagnetic field.

          When two nucleons approach and bind however they are no longer in their ground state, there is energy to spare. In this case any of the moving quarks can produce a real photon which, because it is not bound, will quickly exit the nucleon that produced it, lowering its energy. This can happen several times and in several ways but the basic approach is simple enough.

          The first question is more complex since it asks for more precise details of a ‘just so’ description. The basic answer is ‘that’s how the equations work out.’ and indeed you can work them out and see this, but it’s hardly a satisfying explanation. We do better to consider these points:

          * Quarks, gluons and nucleons are waves and
          * Obey the exclusion principle and
          * Obey the uncertainty principle meaning,
          * Nuclei have shells like atoms but most importantly,
          * Gluon creation shields two colored particles from each other

          So firstly, when you take two differently colored particles and pull them apart they of course create gluons (and maybe quarks.) however doing this ‘shields’ the two particles from each other, they don’t feel the color force between the two of them, it is ‘jumbled up’ by all the gluons and quarks created. Pulled far enough apart they become individual nucleons and don’t feel each other at all. (Or nearly so.)

          What this means is that if you have too many quarks and gluons they begin to ‘block each other out’, adding more means that the average particle will feel *less* color force and thus be higher energy. This is what stops nucleons having an infinite number of gluons in them and basically sets the size of a nucleon. (The specific size depending on the particles involved, the strength of the color force and how effective shielding is.)

          Now a lone nucleon is not quite in the lowest energy state it can possibly be, or rather there are environments that it would prefer to be in instead of being alone. Particles at its surface are less shielded than those within and so their attractive force ‘leaks out’ of the nucleon. Thus at ‘large’ distances all nucleons attract.

          But as they approach each other they begin to exchange virtual particles made up of quarks and gluons. The constant exchange makes the environment at the nucleon’s surface more and more like that inside it; shielded. As the distance decreases the shielding effect grows faster than the attractive effect, making the sum of the forces less and less attractive and eventually repulsive.. *This* is what stops two nucleons from merging when close.

          A more minor consideration is that like an electron around an atom proton’s and neutron’s velocities become less and less well defined as they are confined in a nucleus, the Uncertainty principle. They also obey the Pauli Exclusion principle meaning that as you try and force them together they refuse to occupy the same space by moving faster and becoming higher energy.

          This means nuclei have shells like atoms, the first proton shell can hold two protons, the first neutron shell two neutrons and so on. These effects are more subtle in ordinary matter and control a lot of radioactivity, but in, say, neutron stars the degeneracy pressure is the only thing stopping utter collapse.

          I hope this is a better explanation.

          • Thank you for taking the trouble to make a second reply, but it does raise several additional questions.

            Adding virtual photons into the maelstrom does help to answer the basic question of how quarks can emit real photons, but how would the virtual photons assemble themselves into a _single_ real photon? As I understand it, nuclear reactions (such as radioactive decay) typically emit a single gamma, and this is how experiments determine exactly what nuclear reaction has taken place. You say “This [quark emitting a gamma] can happen several times”. So is it the case that if an isolated neutron and isolated proton encounter each other and form a deuterium nucleus, there will be multiple gammas of various energies, and no characteristic energy that allows observers to deduce that a proton+neutron has just formed a deuterium nucleus?

            Another question: you say “when you take two differently colored particles and pull them apart … far enough … they become individual nucleons “. Do you mean nucleons? Or mesons in this case?

            Regarding my question of why nucleons feel a short-range repulsion, you say “As the distance decreases the shielding effect grows faster than the attractive effect, making the sum of the forces less and less attractive and eventually repulsive”. I don’t understand how shielding of an attraction force can ever reverse the attraction into a repulsion. Can you explain how this can occur?

            You also mention the Pauli exclusion principle as a reason for nucleons repelling each other at close range. Is the Pauli exclusion principle for nucleons, an axiom of nuclear theory (like the very existence of quantum fields), or a consequence of the shielding mechanism?

            You say “This means nuclei have shells like atoms, the first proton shell can hold two protons, the first neutron shell two neutrons and so on”. How are the two types of shell (proton shell, and neutron shell) arranged? Do they alternate?

  37. Very clear! (I’m worried it will get less clear as I go on to part 2 and 3.) I had been trying to understand beta+ and beta- decay: how can both processes occur when both emit equally massive particles (positron or electron plus massless neutrinos) yet leave behind lesser or more massive particles? (Proton to neutron vs. neutron to proton.) I suspect an answer to this may be somewhere in the comments or elsewhere on your blog, so I’ll look around.

    • It has to do with binding energy, An individual proton is less massive than a neutron so it cannot decay into one via B+ decay. However in a nucleus the binding energy means that the whole nucleus has LES mass than the individual free particles would. This is why fusion releases energy and why nuclei don’t just fall apart.

      A naive but intuitive view of B+ decay would be to think of a proton ‘borrowing’ some energy to become a neutron and a positron. The new neutron is bound more strongly than it was a s a proton which releases energy that then ‘pays back’ the borrowed energy, with some left over. The sum of the process releases energy.

      • Thank you, this helps. Could I ask you, then, to explain for me B- decay? The two types of decay look to be just about mirror images of one another, but for the annoyingly small mass difference between proton and neutron. Everything looks so symmetrical between the two, but there must be some additional asymmetry to balance the scales. (Be advised: I’m using “symmetry” like a lay person; I gather this term has some specialized meanings in physics, but I’m barely acquainted with that meaning.)

        In B+ decay, a positron and a neutrino are liberated from the nucleus. In B- decay, an electron and an anti-neutrino are liberated from the nucleus. My understanding is that the mass of what is liberated in each case is identical. However, the man of what remains in the nucleus is not identical (a mass gain in the case of B+ decay, where a proton becomes a neutron and a mass loss in the case of B- decay, where a neutron becomes a proton).

        If I understand you, in B+ decay, that mass gain is borrowed from the binding energy of the nucleus. You then say that “the new neutron is bound more strongly… the process releases energy.” I think this must be because the nucleus is more stable with a neutron than a proton in that particular case, which prompted the decay in the first place.

        So, what then for B- decay? Is there, in this case, no need to “borrow binding energy” since the proton is lass massive than the neutron, or is it the case that less is borrowed? Or is less energy released at the end of the event?

        And, when you speak of energy release, is this in the form of the speed of the ejected electron/positron?

        • If we consider B- decay in the same way we considered B+ decay AND we want to be more symmetric we can say the neutron also borrows energy to create a positron and neutrino BUT the energy it pays with is not just binding energy but its mass change as well. Or we could simply say it doesn’t bowwow any energy as you say.

          The problem with our model is that it splits up energy and mass when in fact they’re the same thing. Because of the incredible binding energy; every proton and neutron in a nucleus *weighs less than it does when free*. In fact all neutrons in all the nuclei you are likely to meet weigh less than a free proton! This is what keeps matter stable. If an average neutron in a nucleus wanted to B- decay it would GAIN mass not loose it.

          So in radioactive decay of any kind the big concern is not the mass of the individual particles involved, rather it is the energy\mass of the *entire nucleus*. Taking that viewpoint there is no problem with protons and neutrons, the only question is whether the daughter nucleus (and radiation) weighs less than the parent.

          And yes, the ‘left over’ energy from a radioactive decay will show up as the combined motion energy of the neutrino AND electron\positron. (Something that confused early investigators was the fact that in B-\B+ decay the ejected particle had different amounts of energy. Something else was taking some of it. This resulted in the prediction of the neutrino long before its observation.)

  38. Professor, I was wandering what you think of the Pilot-Wave theory, and why is it so unpopular with majority of physicists when it’s been experimentally proven?

    • Pilot-wave theory and its more modern version the Bohm interpretation has not been *proven* experimentally in that we do not have an experiment that can differentiate between that interpretation and various others. It thus remains only one of several possible interpretations of which only one or even none may be correct.

      Its unpopularity seems chiefly to stem from its non-locality; that is it is unlike the laws of physics with which most physicists are comfortable. Any object obeying the pilot-wave interpretation is affected by the whole universe at once which is not a concept physicists are fond of.

  39. Thanks Kudzu, but (sorry to put but into it) didn’t physicist Aephraim Steinberg of the University of Toronto in Canada and his colleagues shown that it is possible to precisely measure photons’ position and obtain approximate information about their momentum, in an approach known as ‘weak measurement’?

    • The area of ‘weak measurements’ is somewhat overstated and hyped. Like the gravity radio many people are saying that it shows things that have not been proven or verified.

      Weak measurement itself lies within the bounds of the uncertainty principle. It is not a way of ‘getting around’ QM but rather an ingenious way to circumvent some traditional problems. When considering this area it is important to remember two things.

      Firstly no measurement is *ever* exact. Te word ‘precisely’ should always be understood to mean ‘accurately but not exactly’ Secondly it IS possible to know both momentum and position to within certain, quite accurate limits.

      Weak measurements are an interesting area of research but they have yet to challenge conventional thinking. You will know if they do. (Mostly because there will be a big row and it will start appearing in science articles i mainstream newspapers.)

      • Thanks, Kudzu, its just that I find some comfort with this research because if the veil of uncertainty principle is lifted off from physics, many more mysteries might be resolved such as gravity, dark matter and dark energy. The notion is; if you can measure both momentum and locality, you can discard with some theories which are fogging up our understanding of natural world, such as ie., parallel universes, multiverse, alternate realities, and also space-time, big bang, and finally, singularity. Check out this link, please if you will, its only a short mention of it, still interesting…http://www.scientificamerican.com/article.cfm?id=new-double-slit-experiment-skirts-uncertainty-principle

        • Krystal – you should learn more about the Bell inequality. There are some veils that will not be so easily lifted… experiment has spoken, and whatever happens to the uncertainty principle in future, the resulting picture of reality will not be so simple as you are hoping.

          But the resulting picture may in fact be much deeper and more exciting than what you are hoping.

          Or perhaps the veil is intrinsic to nature and cannot be lifted.

  40. Thanks for the tip, Matt. I shell certainly do that.

  41. Thanks, Professor Strassler, for writing such awesomely detailed yet accessible articles! I’m waiting in suspense for Layer 2.
    And thanks Kudzu for all of your explanations here!
    I have two lingering questions that might be very basic:
    1 – What keeps a proton or neutron from radiating away its internal energy?
    2 – I learned in physics for premeds that mass and energy could be “interconverted,” which made me think that “mass” and “energy” were two discreet things, and I thought for some reason that only the thing called “mass” had inertia. I did not realize until now that there isn’t a true dichotomy. This article made it clear that most of the mass of atoms (and therefore the inertia of everyday objects) is due to various forms of non-rest-mass energy in the nucleons. Since I had erroneously thought that these “pure” forms of “energy,” such as kinetic energy, had no inertia of their own, my mind has just been completely blown. Good work, sir! Now that you’ve shattered my paradigm and cleared up this foggy misconception I had, I’m curious if there is an answer to this question: how does energy resist acceleration?

    • 1.) In order to radiate energy, to ‘decay’ an object must be able to transform into a lower energy state. The proton does not decay for the same reason a rock on the ground doesn’t fall or ash doesn’t burn; it is the lowest energy possible already. There simply is no mechanism available. The proton is utterly unique; it is the ONLY ‘quarky’ particle that is stable. The bottom of the heap as it were. In fact if protons were unstable it would require some major rewrites to physics: http://en.wikipedia.org/wiki/Proton_decay

      2.) The short answer to this question is ‘Because energy is equivalent to mass’

      This question is hard to answer in part because we don’t know how how ‘mass’ resists acceleration. It is something very fundamental. If I can turn the question around, ‘how does mass resist acceleration?’ There’s no simple, obvious answer to this. In the end it helps to realize that our intuitive ideas of mas as ‘solid, hard, heavy stuff’ and energy as ‘light, invisible, ghostly stuff’ are just convenient generalizations we humans have made from everyday experience. Massive neutrinos pass through us like mist while the gamma ray energy from a pulsar at close range would burn the earth away like a cosmic blowtorch.

      • Thanks!
        For 1 – It looks like I had another misconception that when a particle and antiparticle collide, they always radiate their energy as photons (pop culture science writing has clearly led to a tremendous amount of misunderstanding for me). I looked back at the article and found this link, which cleared that up: http://profmattstrassler.com/articles-and-posts/particle-physics-basics/particleanti-particle-annihilation/ . So if the sea quarks and antiquarks are only able to turn into other particle/antiparticle pairs that are still bound by the strong force, and vice versa, then I see why the whole thing would be very stable.
        For 2 – Why go back to this idea of “mass” and drag in our preconceptions from experience, especially when it seems here that energy is the more general concept? I wonder, if you take for granted the phenomenon of time dilation in the vicinity of mass or energy, then isn’t “resistance” to acceleration the natural way for an object to react? I’m thinking about the way a force is transmitted to an ordinary object: You push on it, the electrons in your atoms transmit a repulsive force to the electrons in the object’s atoms, which in turn exert a force on the atomic nuclei to move them. If this force is being transmitted by photons, and time is “slower” near the nucleus, then won’t those photons be delayed a little bit? And if, from your perspective, it takes more time to get the object moving at a certain speed with a given amount of applied force, then (thinking of that Physics 1 equation, impulse = force * time) I would think that this explains why you end up transferring more momentum, which is what we intuitively associate with mass. I imagine that this is how relativity is explained to physics students who have moved beyond the ol’ “rubber sheet” model.

        • I am glad my answers help.

          1.) It’s not strictly true however that quarks can only decay to other particles bound by the strong force. The key instead is always energy, the fact that particles are waves in fields and the fact that all fields are ‘connected’.

          Any particle, in fact any disturbance at all, in a field will randomly ‘wiggle’ (or put energy into) all other fields it can. So a quark ‘wiggles’ the strong field, but also the electromagnetic, gravitational and weak fields. When two (electromagnetically same) charged quarks bounce off each other we can think of one quark wiggling the electromagnetic field then that wiggle affecting the other quark. Pop physics would say that they have exchanged a virtual photon. No particles were actually exchanged however because the wiggle was to messy, too low energy to be a nice, organized particle. It dissolves and its energy returns to ‘real’ particles.

          Now consider a free neutron, this decays with a half-life of about 10 minutes to a proton, electron and antineutrino. To do this one of the quarks wiggles the weak field. This wiggle again is not a proper particle, it doesn’t have enough energy and soon vanishes, returning its energy to the quark that made it. However sometimes before it goes it then wiggles the neutrino and electron fields hard enough to make actual particles. These particles then move away and the quark, which has lost energy, has changed type. The neutron has decayed.

          A free proton can try and do the same thing, its quarks too are always wiggling the weak field which wiggles the electron (positron) and neutrino fields. There is one difference however, there is not enough energy in the weak wiggle to make real particles. As such all the wiggles collapse and vanish whenever they are produced, the quarks keep their energy and stay as they are and the proton does not decay.

          2.) Your proposition is ingenious and a nifty piece of thinking. Unfortunately there are several problems that arise.

          Firstly there’s black holes. At the event horizon of a black hole time should stop, meaning any signal sent to it would never reach it and it would have infinite inertia.

          This arises neatly from the math of the effect. Time dilation depends on the gravitational field around an object. If we imagine an object of mass x then pushing it will have my signal delayed by some amount, x’ If I now split the object into two connected masses of .5x, each has a gravitational field that is 1/4 as strong as x’s was at any distance r. Thus pushing this connected system would slow my signal by 2* .25 or half as much as when I pushed x. Objects would get more inertia as they became denser, until at the density of a black hole their inertia would go to infinity.

          Secondly there’s the problem of the ‘abruptness’ of your model. In your model there is no smooth acceleration; objects simply start moving at a speed after a delay. So if I had a very heavy object I could ‘kick’ that object with an abrupt signal (say a single particle), stand back and watch it sitting still as the signal slowly reached it then see it suddenly move away at speed. We can’t rescue the theory by saying that the smooth acceleration we see on human scales is the result of many small ‘stepped’ accelerations since the math breaks down when we reach very small scales for complex reasons.

          • Good points. If I understand your “abruptness” argument, if it was really just about delay, the transfer of a given amount of kinetic energy might cause objects of different mass to end up moving at the same speed in the end, and the only difference would be the length of the delay before each mass moved, which definitely doesn’t fit reality.

            I think I’m at the limit of my physics education, at least what I can communicate more-or-less coherently about, but this is really interesting to me. I think I’ll look into taking another physics class if my work schedule opens up in the fall. Right now I’m teaching basic gen chem labs for premed students, and I’m starting to feel like one of my own students with these questions! Someone asked me today why a proton doesn’t weigh exactly 1 amu, and it felt like some kind of weird nested deja-vu.

  42. Good points. If I understand your “abruptness” argument, if it was really just about delay, the transfer of a given amount of kinetic energy might cause objects of different mass to end up moving at the same speed in the end, and the only difference would be the length of the delay before each mass moved, which definitely doesn’t fit reality.

    I think I’m at the limit of my physics education, at least what I can communicate more-or-less coherently about, but this is really interesting to me. I think I’ll look into taking another physics class if my work schedule opens up in the fall. Right now I’m teaching basic gen chem labs for premed students, and I’m starting to feel like one of my own students with these questions! Someone asked me today why a proton doesn’t weigh exactly 1 amu, and it felt like some kind of weird nested deja-vu.

    • You never leave that feeling behind. Cherish it because it makes you a great teacher, especially when someone asks a ‘dumb’ question. Frankly if you learn enough physics to confront questions like the origin of inertia on your own terms you will have exceeded me. You certainly have the right mind for it.

  43. i just want to ask u professor that how excess neutrons can cause unstability of nuclie? means to say that why it will convert to a proton rather if it can remain in neutron form only? why plzz explain

  44. Pingback: Massa van de lichtste quarks nog nauwkeuriger bepaald | Astroblogs

  45. Pingback: A 100 TeV Proton-Proton Collider? | Of Particular Significance

  46. PLEASE – I’m desperate to read about the next 2 layers. I really hope you haven’t just abandoned this article unfinished.

    • Hi Prof. Strassler,

      It’s been more than one year since this article was published. Please do not leave us orphaned, the text above is the most enlightening piece of info on the topic that I’ve ever read. Completing it with the 2nd and 3rd layers would constitute a great contribution to our society, we are in much need of this kind of works.

      Thanks in any case for your dedication.

  47. Pingback: ¿Qué son los protones? | E7radio noticias, de Venezuela y el mundo

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s