# Proton Collisions Vs. Quark/Gluon/Antiquark Mini-Collisions

Matt Strassler [February 13, 2012]

Protons, which are the particles smashed together at the Large Hadron Collider [LHC] during most of the year, are made from many quarks, gluons and antiquarks. The proton-proton collisions take place at a definite energy: 7 TeV = 7000 GeV per collision in 2011, 8 TeV = 8000 GeV  in 2012. But what particle physicists are mainly interested in — what can really create new physical phenomena for us to observe — are the collisions of a quark in one proton with an antiquark in the other proton, or the collision of two gluons, etc. These “mini-collisions” carry only a fraction — typically a very small fraction — of the total proton-proton collision energy. How large a fraction can they carry? and what are the motivations for increasing the LHC energy from 7 TeV per collision to 8 TeV?

The answer is given by the figure below. This is a plot showing the number of collisions detected in the ATLAS detector, using its  data through early summer 2011, that involve the scattering of a quark, antiquark or gluon off another quark, antiquark or gluon. Such mini-collisions most often produce two jets (sprays of hadrons which are the manifestation of high-energy quarks, gluons or antiquarks that have been knocked out of their parent protons) and these are observed in ATLAS. (The CMS detector experimenters have made a similar plot, using the collisions that occurred inside CMS.)  The jets’ energies and directions are measured, and from that information it is determined how much energy the original mini-collision must have had in order to produce them. The plot shown is essentially the number of mini-collisions of this type as a function of the energy of the mini-collision.  The vertical axis is logarithmic; each long tickmark is another factor of 10 higher (and 10n indicates a 1 with n zeroes after it; 105 = 100000.)  For instance, the number of mini-collisions observed that had energy between about 1550 and 1650 GeV was about 103 = 1000 (indicated by the blue lines.)  [Note that the plot starts only at an energy of 750 GeV and goes up from there, but the number of mini-collisions keeps rising as you study lower energy jets, all the way down to where the jets are too wimpy to measure.]

Fig. 1: The number of collisions (notice the vertical axis is logarithmic, increasing by 10 with each large notch) in which quarks/gluons/antiquarks scatter off each other, as a function of the energy (here called "Reconstructed m_jj") of the scattering, within proton-proton collisions at 7000 GeV = 7 TeV. Data points (from the ATLAS experiment) are in black, a fit to the curve is in red. Green and blue lines (added by me) indicate the number of events at 1400 and 1600 GeV, energies which are in a 7 to 8 ratio; what 7 TeV collisions can do at 1400, 8 TeV collisions can (roughly) do at 1600. Notice the horizontal bins are not all the same size, and also that the energy range only extends down to 750 GeV; if it went down to zero the curve would continue to rise rapidly. The total number of proton-proton collisions during this data period was nearly 100,000,000,000,000.

Keep in mind that the total number of 7 TeV = 7000 GeV proton-proton collisions that took place in ATLAS while they were accumulating the data for the plot above was about 100,000,000,000,000.  [The total 2011 data set was 5 times larger, but the corresponding plot won’t appear for a few months.]  Of all these collisions, just two had mini-collisions that passed above 3500 GeV — half the collision energy of the protons.  In principle the energy of the mini-collisions can go up all the way to 7000 GeV, but the probability goes down and down, and it is so rare to get a 6000 GeV mini-collision that chances are we wouldn’t get one even with 100 times this much data.

Now — what are the advantages of going up from 7 TeV per collision, in 2010-2011 LHC running, to 8 TeV in 2012?  The obvious point is that whatever you could do at a given energy E, you can now hope to do it at 8/7 E ~ 1.14 E.  So if before you could hope, with this much data, to see signs of a certain type of hypothetical particle with mass as large as 1000 GeV/c2, now you can hope to reach 1100 GeV/c2 or more with the same amount of data.  So the “reach” of the machine goes up — you can look for particles of slightly higher mass.  And if the total amount of 2012 data turns out to be three times as large as was collected in 2011, then you get more collisions at each energy, and so you might be able to see signs of that hypothetical particle up to a mass of, say, 1200 GeV/c2.

But that’s not all.  Look at the green and blue lines on Figure 1; they are there to guide your eye in seeing what is happening at around 1400 and 1600 GeV, two energies which are in a 7 to 8 ratio.  What this tells you is that at a fixed 7 TeV proton-proton collision energy, the number of quark-quark or quark-gluon or etc. mini-collisions is more than twice as large at 1400 GeV as at 1600.  But when the machine goes up in energy by 8/7, what used to be true of 1400 will now be true of 1600.  In other words, if you are interested in mini-collisions of a fixed energy, the number of them will go up — by a lot more than the 14% increase in the proton-proton collision energy!!  And that means that for any given process with a preferred energy, such as the production of lightweight Higgs particles, which involves energies around 100-200  GeV, you get more bang for your buck.  Going from 7 to 8 TeV means that now, for the same number of proton-proton collisions, you produce more Higgs particles.  The increase for Higgs particle production (if the Higgs mass is at 125 GeV) will be a factor of about 1.5.  For top quarks, and for certain other types of hypothetical particles, the increase is slightly larger.

And that means that although the plan is to increase the total number of collisions in 2012 to be 3 times as many as in 2011, the total number of Higgs particles produced will go up by more than 4 times, just because of increasing the energy.

Fig. 2: If protons really looked something like this, the data shown in Figure 1 would look completely different.

By the way, in case you weren’t really sure about it, Figure 1 gives you a strong indication that protons are not simply made from two up quarks and a down quark, as shown in so many misleading figures, such as Figure 2, taken from Wikipedia.  If they were, you’d expect quarks to carry about a third of the protons’ energy, and most collisions to carry about a third of the proton-proton collisions’ energy: about 2300 GeV.  But you notice that nothing special happens to the curve around 2300 GeV.  There are far more collisions below 2300 GeV than above, and the lower you go, the more collisions you find.  This is because there are huge numbers of gluons and of quarks and antiquarks inside the proton, each carrying a small fraction of the protons’ energies, but so numerous that they are involved in the vast majority of mini-collisions.  That basic feature of the proton is somewhat more accurately illustrated in Figure 3, though the number of low-energy gluons and quark-antiquark pairs is far, far larger than shown in the picture.

Fig. 3: A somewhat more accurate picture of a proton, filled with gluons (g) and quarks (u,d,s for up, down and strange) and antiquarks (same letters but with an overline bar.) These particles are whizzing around at speeds that are a significant fraction of the speed of light. The number of gluons and quark-antiquark pairs is enormously understated, for reasons of clarity. (If you look carefully, you'll see there are two more up quarks than up antiquarks, and one more down quark than down antiquark; that EXCESS of two up quarks and one down quark is what leads to the shorthand: "a proton is made from two up quarks and one down quark.")

One thing Figure 1 doesn’t show is what fraction of the mini-collisions at a given energy are due to quark-quark collisions, quark-gluon collisions, gluon-gluon collisions, quark-antiquark collisions, etc. In fact you can’t tell this from the LHC experiments directly, because jets from quarks, antiquarks and gluons look pretty much the same. How we know these fractions is a complicated story involving many different past experiments and some theory that combines them together. These tell us that the highest energy mini-collisions are mostly quark-quark and quark-gluon. The lower energy mini-collisions are mostly gluon-gluon (which works well for the search for the Higgs particle, since this is the dominant means of producing it.) Quark-antiquark collisions are relatively rare, but very important for certain physical processes.

### 49 responses to “Proton Collisions Vs. Quark/Gluon/Antiquark Mini-Collisions”

1. Harry Bostock

I was very surprised to hear that the proton has so many quarks and anti quarks in it. But if that is the case why doesn’t a proton have the mass and charge of all these particles?

• Right. Great question.

First, the charges do add up. An up quark has a charge of 2/3 of the proton’s charge, but an up anti-quark has a charge of -2/3; so every quark-antiquark pair of the same “flavor” [up, down, or strange] has net charge of zero. The gluons also have charge zero. So the total charge of the proton is given by looking at the excess quarks, of which there are two up quarks and one down quark, with a charge of 2/3 + 2/3 + (-1/3) = 1 .

Second, the mass is much more complicated. There are many things to keep track of, and in the end the answer isn’t going to be entirely satisfactory, because the calculation is extremely complex and hard to turn into words.

a) Gluons are massless.

b) Quarks are a lot lighter than a lot of older books say they are. This is because the original quark model from the 1960s wasn’t correct, and was revised in the 1970s amid considerable public confusion, and even confusion among some professionals. You will sometimes read that the masses of the up and down quarks are a third of the proton mass, but this is an archaic notion [for experts, see Dashen, Jenkins and Manohar 1994 for its final demise.] The masses of up and down quarks are in fact less than 1/100 the mass of the proton. So naively that would seem to make it easier to stuff more of them in there than you might otherwise think.

c) But even this last part doesn’t matter much, because as you know, E = m c-squared for a particle that isn’t moving relative to you. What the mass of the proton reflects is not the MASS of everything inside of it but the ENERGY of everything inside of it, not all of which is mass-energy. And energy is sufficiently complicated that I haven’t even figured out how to write a good article about it yet… what I’m about to tell you is both extremely important and very obscure.

The energies of the particles inside the proton are given by their mass-energies (m c-squared for each one of them) plus their motion energies (which are always positive, and quite large, because the quarks and gluons are running around at high speed) plus [and this is the confusing part] the energy of the forces that hold them together inside the proton, which are mainly negative. [The energy that holds the earth around the sun — called gravitational potential energy — is negative; that’s why you would have to add positive energy to the earth’s motion to allow it to escape from the sun.]

So only by tallying up all of these energies — some of which are negative — would you get the total energy, and thus the mass, of the proton. There is no simple formula for this; the only way we can calculate the proton’s mass is using very big computers (which I intend to write about in the next few days, for other reasons, so stay tuned.) But the computers do give answers that agree with the picture I have shown you. So do many past experiments. And LHC data would be completely different if the picture were wrong.

2. This post is the biggest shock for me since I first learnt that protons were not fundamental particles (I can’t remember when that as it was so long ago). I had to check it wasn’t April 1st as I am still somewhat in denial about there being more than 3 quarks in a proton. You are often talking about virtual particles in Feynman diagrams but I take it all these little quarks are not so virtual?

• Well — now it gets complicated. Inside a proton the quarks and gluons have very high velocities, are constantly interacting with each other, colliding, disappearing, appearing, bouncing off the proton’s edges, etc. So it becomes difficult to give meaning to your question as to whether they are real or virtual. A real particle is the quantum mechanical version of a wave that is nicely behaved, travels smoothly for long distances with a well-defined frequency, etc. You can make sense of such a wave on the surface of a calm pond. But the proton is not like a calm pond; it is more like a stormy sea, and it gets hard to say what is a nice well-behaved wave and what is a more general disturbance. [At some point analogies and pictures fail, which is why to calculate the properties of a proton we use big computers, or we use a combination of experiments and some theoretical background.] It is best to say that the distinction between real and virtual particles breaks down in sufficiently complex and messy situations, and the interior of a proton is one of them. This is one reason why no attempt is made to actually count the number of quarks or antiquarks inside the proton (it wouldn’t mean anything since it is constantly changing, and it wouldn’t be entirely clear what is real and what is virtual anyway.)

Yes, the strong nuclear force produces some very complicated physical phenomena. It took decades to figure this stuff out. But we clearly got it right; so many successful predictions at the LHC (and its predecessors, including the Tevatron) depend upon it.

By the way, the reason we were able to get it right is that despite this complexity the strong nuclear force actually becomes simpler for phenomena at distances much smaller than a proton. The buzz-words that go with this are “asymptotic freedom” — suggested in experiments in the very late 60s (Nobel Prize 1990), and shown in 1973 to be the case in the modern theory of the strong nuclear force (Nobel Prize 2004).

• Brian

“bouncing off the proton’s edges”

I’m fairly sure that’s a shorthand way of expressing something. If you tell me that a proton is like a pingpong ball with a bunch of grains of sand bouncing around inside I shall be quite irate.

Do you mean that there is a boundary (presumably somewhat fuzzy) established by the interactions of all the particles that comprise a proton?

• Brian — you are absolutely right in your final sentence: there is a boundary, somewhat fuzzy, established by the interactions of all those particles that comprise a proton with each other.

The location of this rough boundary is determined by some features of the strong nuclear force. Roughly, if a quark tries to escape from a proton, the force that it feels from the other particles inside the proton becomes so strong that the quark is slowed down and pulled back inside, almost as though it had bounced off a wall. So indeed I was not very precise when I said “bouncing off the edge”; what actually happens is that as a quark or gluon or antiquark approaches the boundary it is prevented from escaping by the strong nuclear force.

This effect is often called “confinement” of quarks (and gluons and antiquarks) but there is a subtlety with this term. Some of these issues and subtleties are addressed in my article on jets (the sprays of hadrons that are the manifestation of a high-energy quark or gluon or antiquark at the Large Hadron Collider and its predecessors.)

• jimvj

1. Does this confined sea of quarks & gluons have (quantized?) vibrational modes?
2. In a nucleus, do quarks/gluons tunnel back & forth between neighboring protons/neutrons?

• 1. Yes — we call these excited states of the proton, including the Delta and the nucleon* and many others.

2. Yes, occasionally — meaning not nearly as often as quarks bounce off the edges of their parent proton — and this is part of what generates the force that holds the nucleus together.

3. This is a most shocking article in decades, what is going on matt. ? now we must wonder , what is the explanation for many theories having correct predictions of observation matching results while they are far away from reality per se?
What do you mean by ( the edge of the proton ?

• Well, it may be shocking to you, but it is common knowledge in particle physics; I was taught this over 20 years ago and have been teaching it for many years. The people who figured this stuff out are no longer young.

Now when you say, “what is the explanation for many theories having correct predictions of observation matching results while they are far away from reality per se?”, I assume you mean that there are so many discussions of the original (1960’s era) quark theory predicting the masses of hadrons [particles made from quarks, gluons and antiquarks] successfully, even though the theory wasn’t really right about the properties of quarks as we understand them today.

A substantial answer to this question, for the proton, neutron and their cousins, was provided by the work of Dashen, Jenkins and Manohar in 1994 (though it had been hinted at before.) It turns out to be a consequence of symmetries — long story, but in short, the original 1960’s era quarks were a sort of mathematical artifact that matched on rather well in some ways to what the 1970’s understood quarks to be, but are not correct in their details.

1960s quarks and 1970s quarks are similar but crucially different. 1970s quarks — very lightweight, much less in mass than the proton [to be precise: the up and down quarks are very light, while the others are heavier] — are the ones you have to work with if you want to understand modern experiments. 1960s quarks — much heavier, a third the mass of the proton — are mainly good for explaining why the masses of many of the hadrons come out the way they do. But they would do a terrible job on the high energy collisions that take place at the LHC.

In other words, 1960’s quarks and 1970’s quarks are related but different models of nature. For many years they both had their regimes of validity; it wasn’t obvious that you didn’t need them both, somehow. Even when I was a graduate student this was discussed occasionally. But in the 1990s, through the development of more powerful computers and new theoretical insights, it became crystal clear that 1970’s quarks could explain most things that the 1960’s quarks explained, while the reverse was not true. So the 1970’s quark model, with much wider validity, has won the day.

1960’s quarks remain useful, though… you can use them to get quick estimates of hadron masses without having to run huge computer programs that you would need with 1970’s quarks. You just need to understand where they can and can’t be used.

The history of science is full of partial answers to questions that have to be revised over time, or struggles between conflicting versions of a theoretical idea. 1960’s quarks were a great idea that led to great progress, but it took a while to figure out what they were, and weren’t. It is 1970’s quarks — the ones that are very light [specifically, the up and down quarks are light], and interact with gluons through the equations known as Quantum Chromodynamics — that go into the Standard Model of particle physics. And there are an enormous number of them (along with antiquarks and gluons) in the proton.

The Dashen et al. paper is very technical (and very clever); experts only, I am afraid: http://arxiv.org/abs/hep-ph/9310379

4. My mind is reeling, wait a minute , what about the neutron decay where ONE quark is transformed into another?
I still need your opinion of how can we explain the success of ontologically wrong theory to match observation or solve problems——look at supersymmetry for example.where there are no sparticles?
Do not blame me , most non-expert references proclaim the 3Q-3G proton.
I WOULD LOSE VERY MUCH IF I DID NOT DISCOVER YOUR SITE, YOU ARE TRUE ,HONEST ,SINCERE SCIENTIST.
Previously i lost confidence in evolutionary science as it is fact-free-fantasy but now thanks to you i realized the true meaning of being a scientist.

• Neutron decay: no problem.

Notation: Let’s call an up quark u, a down quark d, a gluon g, an up antiquark u*, and a down antiquark u*

Naive version of neutron decay is

u d d [neutron]
–>
u u d [proton]
via
d –> u + antineutrino + electron

Modern version of neutron decay is

u d d g g g g g g g g g g u u* u u* u u* d d* d d* d d* d d*… [neutron]
–>
u u d g g g g g g g g g g u u* u u* u u* d d* d d* d d* d d*… [proton]
via
d –> u + antineutrino + electron

As for “wrong” theories giving correct answers; it happens all the time, throughout the history of science. What does it mean to be “wrong”? Scientists often prefer the word “incomplete” for theories that give correct answers (to some level of precision) for a large class of questions but don’t work elsewhere. Newton’s laws of motion are incomplete — they work beautifully in some arenas, but there are others where you have to appeal to Einstein’s equations or Dirac’s equations or Maxwell’s equations to go beyond them.

The equations we have now in particle physics work beautifully too, within the arenas where we have tested them. But there is no way to know if they are ontologically correct. Someday they may prove incomplete, and we will move beyond them as we moved beyond Newton’s equations.

“i lost confidence in evolutionary science as it is fact-free-fantasy”.

Well, never mind the fact that it is the science with the largest number of distinguished observations and the most precise testing (due to the combinatorial nature of phylogenies, see for example TalkOrigins on this) then. Do proceed with fantasy “biology”, if you don’t care for the fantastic nature.

5. physicsphile

Matt,

I also find this pretty shocking which I guess reveals my ignorance of particle physics. It would be great if someone could fix the wikipedia site about this, not to mention probably several thousand other sites and books which give the impression that a proton is made up of uud.

• Well — that’s part of why I have this site… to help address these little mostly-harmless lies that are often told to the public. Obviously particle physics cannot be explained in every detail to a non-expert. But the little lies scientists tell, to try to keep things simple, often instead generate great confusion. (It’s similar with “virtual particles”, which, as I’ve emphasized, aren’t particles at all, and don’t, for instance, have a definite mass the way particles do.) How in the world can physicists expect the public to understand anything at the LHC — where Higgs particles are created most often in gluon-gluon collisions, and where it is difficult to discover new particles whose mass-energy is even 1/6th of the total collision energy — if we insist on telling the public that a proton is made up of three and only three quarks? Such a story just makes no sense… and so people naturally get very confused.

6. So, Matt, would you please do all of us starry-eyed, amateur particle physics afficionados a big favor, and boldly update Wikki for us??! ??! (hint: that’s kinda like UUD, ha,ha!)

7. Then can i affirm that in principle physics can never calculate the ribosome for example as a super-complex assembly of interacting quantum fields ?
What is the directing causal effect that on the macro level the proton is such well behaved , stable and permanent entity ? why during such enormous stormy situation the thing just does not blow-up? this needs explanation beyond the mere equations, even here we have a deeper question ; why that stormy sea surface with such enormous turbulence adhere to the equations which does not have causal power to implement its “directions” on that turbulence ?
Physics is one of the most exciting fields of science as thru it we are dealing face to face with ontology either our vision of it or our rational faculty as applied to it …… human mind is the most superior miracle of existence.

8. Some more clarification please ;
1-Can a quark inside the proton change to another type ? if so are not this is a kind of decay thru weak force ?
2- Are there any rate control in that vast turbulent stormy sea ?
3- You say ( negative energy ) , but energy is always positive causal action , its sign is a math. convention , am i right
4- Does the proton has a kind of edge ? some kind of force boundary? you said that quarks are bouncing at that edge , what is that mean physically ?

9. Paul

One thing I always wonder about when I read about proton structure is how do we know that low energy protons aren’t made of just those 3 valence quarks?

Isn’t it possible that the number of extra quark-anitquark pairs inside the proton is directly related to it’s kinetic energy? Maybe all those extra pairs we observe were actually created by LHC accelerating magnets?

I am imagining something roughly analogous to how Hawking radiation is popularly explained – a particle-antiparticle pair created at the event horizon cannot recombine and instead one flies off and the other falls into BH. In the case of LHC certain quark-antiquark pairs coming into existence inside the accelerated proton could become perturbed by the combination of gluon fields and accelerating fields to such an extent that they cannot immediately recombine and instead become bound as part of the proton. Is such possibility ruled out for some reason?

• The answer to your question — how we know that there aren’t just three valence quarks and nothing else — comes from several places. First, deep inelastic scattering [slamming electrons into protons and seeing how the electrons scatter off them] even at rather low energy shows signs that the gluons carry much of the proton’s energy; there is no sign that as you reduce the electron beam’s energy and study lower energy collisions that you see the gluons’ contribution to the proton approaching zero. Second, there’s no theoretical reason to expect the proton to be simple; it has a much stronger force holding it together than does hydrogen, one that gives the particles inside it velocities comparable to the speed of light [unlike hydrogen] and allows various relativistic effects, such as gluon production and quark-antiquark pair production, to occur easily. Third, the success of the 1960s view of the proton as a non-relativistic system of three quarks, and indeed of all baryons as systems of three quarks, was explained as a consequence of subtle symmetries that were not obvious for decades — this is the work of Dashen, Jenkins and Manohar that I mentioned — which undercuts the argument that the success of that model reflects anything about the true internal dynamics of the proton. And finally, numerical simulations of the proton do not, as far as I know, support a simple view of the proton.

In the end, the only definitive answer must come from detailed numerical simulations of the proton. We just don’t have the technical ability to calculate the details of the proton in any other way.

10. Paul

OK, thanks for reply. I would really love to learn more about it but unfortunately the paper you mention is way too technical for me.

• Yes, I am afraid that the Dashen, Jenkins and Manohar paper seems very difficult to translate into lay-terms. It is a very clever paper, by very clever people, one that isn’t even so trivial for experts to understand. [And that is presumably why it took people 20 years, from the point when all the conceptual and technical ingredients were available, to put all the ingredients together in the right way.] Maybe someday I’ll understand that paper so well that I’ll see how to translate it into simpler terms … but this appears very challenging.

11. In your response to aa.sh about neutron decay, you show 10 gluons after the quarks without dance partners. Was that simply for purposes of illustration, or is 10 what modern theory holds to be true? If it is theoretically accurate, could you recommend a textbook or paper or something explaining the number? I’d appreciate it. Thanks.

12. zbynek

maybe an observable up is actually a conglomerate of many antiups and one more up
maybe a down is a conglomerate of antiups, one more up, positrons and one more electron
maybe a strange is a conglomerate of antiups, one more up, many more positrons and many more + 1 electron
maybe a charm is a conglomerate of may more antiups, many more + 1ups, many more positrons and many more electrons
maybe a bottom is a conglomerate of thousands of antiups, thousands and one up, thousands of positrons and thousands and one electrons
??

• Can’t answer this properly today, but no, we know a great deal about these particles, and your suggestion would be inconsistent with lots and lots and lots of data.

13. zbynek

I assume that the same scheme would also not apply to the lepton generations then

14. Eyal Cohen

I keep wondering about 2 things:
1. Was the range of very low energies tested for those mini collisions? I mean, those countless quarks and gluons exposed by the LHC could be the result of high energy interaction between fast coliding protons. It might be that very low energy protons are made of three quarks after all.
2. How does it work with gravity? When I’m weighting a “classical”object and computing its mass, it is roughly the sum of the masses of all its nucleons. But these nucleons are made of quarks of a much smaller mass, and the rest is energy. How, when going up in the scale of size, the quarks kinetic energy turnes into a weightable mass?

• 1. Your question is a good one, and the answer is subtle and not satisfactorily clear-cut. Efforts to study this question always have come to the conclusion that there must, at least, be gluons in addition to quarks, and moreover the three quarks that would make up a proton (if that were indeed a viable picture) would have properties quite different (in particular, much heavier) than the quarks that we talk about in the mini-collision picture. But it is also tricky to say exactly what you mean when you get down to lower and lower energies, because the forces at work become stronger and stronger and more and more difficult to compute. I did have a few words to say about this in a follow-up article. https://profmattstrassler.com/2012/02/29/following-up-on-the-protons-structure/

But even if this were true, this picture of a proton as three quarks would be completely useless at the Large Hadron Collider, where most mini-collisions involve gluons and at lower energies antiquarks are as common as quarks. So at best, one has to adopt a very different intuition for how protons behave from what a three-quark picture would suggest. And since the three-quark picture for protons at rest cannot be substantiated experimentally — whereas the gluon and quark and antiquark distributions for high-energy protons can in fact be substantiated experimentally — I would rather discuss the second picture, which I know is true, and not fight too hard for the first picture.

2. This isn’t an issue of gravity at all; it is an issue of mass. [Gravity pulls on mass, yes, but you can talk about mass just as Newton did, as inertia — a measure of the difficulty of accelerating something when you push on it.]

The mass of an object at rest is the sum of all of its energy, divided by the speed of light squared. That is one of the most important consequences of Einstein’s special (i.e. before including gravity) relativity. For a complicated composite object like the proton, whose constituent quarks and gluons and antiquarks are moving at near-relativistic speeds, its mass is nowhere near the sum of the masses of its constituents, but an extremely complicated sum over mass-energy (i.e E = mc^2 energy), motion energy (i.e. “kinetic” energy), and various forms of energy due to the relationships between the quarks and gluons and antiquarks (i.e. “potential” energy). There’s no simple formula for this sum — in fact we can only do this calculation using very large computers and very long calculations.

Once the proton and neutron’s masses are established from this calculation, there’s no real problem to go up in scale; the kinetic energy and potential energy among the protons and neutrons in a nucleus are relatively small, so the mass of the nucleus is almost given by the sum of the masses of the protons and neutrons that make it up; the kinetic and potential energy between electrons and an atomic nucleus is smaller still, so the mass of an atom is very accurately given by the sum of the masses of its constituents; the kinetic and potential energies between atoms within molecules are smaller, so again the masses basically add; and so on. So in the whole structure of matter, there is only one (known) complicated calculation, where masses of constituents do not approximately add to make the mass of the larger object, and that is the calculation of the mass of the proton (and its cousin the neutron, which involves virtually the same calculation.)

15. Eyal Cohen

Thanks for the prompt and informative response. And yes, you have answered my questions in a broader sense.
1. “I would rather discuss the second picture, which I know is true, and not fight too hard for the first picture”. I realy appreciate this comment, but I feel this second picture does not give an answer to the more interesting question question: “what is a proton made of?” Rather, it tells me what happens when you smash protons moving close to the speed of light at each other. Assuming the sparse structure of protons and the known nature of the vacum in interactions of such energy I would suspect that not all light quarks and gluons were present in the protons prior to the collision.
2. I think it has a lot to do with gravity, and my question inquires whether we have an (yet another) unsolved issue of the so called correspondence principle.

• 1. Ok — you’ve pushed hard enough that I have to take a step back.

One of the things that you learn as a quantum physicist is that the question “what is something made of” is ambiguous, because you really can only ask the question “what does something appear to be made of when I do THIS or THAT to it” or “what does something contain from THIS or THAT perspective?” That’s what we are running into here. There’s no way around this.

So your suspicion isn’t wrong, but neither is it right. It is really more that it is naive. To say “this particle was in the proton before the collision” and “this particle was not in the proton before the collision” cannot be done; different observers will even disagree about it. There are ambiguities here that are a matter of perspective. [A hint of why this is difficult; on sufficiently short time scales you cannot determine whether you are dealing with a real particle (a nicely-behaved ripple in a quantum field) or a “virtual particle” (which is not a particle at all, but just a more generalized disturbance in a quantum field).]

What I’ve done in this article is introduce what I believe is pedagogically the least confusing way to understand Large Hadron Collider physics. To do this correctly really requires understanding relativity and quantum field theory in detail. I may be able to find some ways to illustrate the ambiguities at some point. But this is reaching the edge of what I can explain without equations…

As an example of how bad it can get in quantum field theory: You can even have situations where from one point of view an object is a fundamental particle, whereas from another point of view it is like a proton, made from other fundamental particles. This is a feature that quantum field theorists like me were studying very actively in the last two decades, though the original examples of this phenomenon date back many decades.

So that may help to explain to you why I’m being a little circumspect. There is a Pandora’s box here — one which I will try to explain someday on this website, but I do not have the structures in place to do that yet.

2) No, this is a big error. You really do not want to confuse gravitational effects from things that have nothing to do with gravity. Even if gravity were turned off altogether, the mass of the proton would be exactly the same. The same is true of the mass of your body. Far out in the middle of intergalactic space, as far from every galaxy you can think of, the mass of your body would be determined entirely by the forces inside the proton. And those forces are strong nuclear forces — 100,000,000,000,000,000,000,000,000,000,000 times stronger than any gravitational effects among the particles inside the proton.

16. Eyal Cohen

Thanks for taking a step back. Now I see that we have similar views about the subject. In fact, I am going to give a popular science lecture titled “What we are (not) made of”, and being away from physics for a long time it was important to me to clarify these matters.

• I am still unclear what your precise background is, but if it is sufficiently technical I would recommend you glance at the work of theorists Dashen, Jenkins and Manohar from around 1994. They explained why the three-quark non-relativistic model of baryons works so well for the baryon mass spectrum (and also why the very different “skyrmion model” also works.) It turns out there is a hidden symmetry of QCD, not visible in the original equations, which is exact only when the number of colors is infinite, and this symmetry controls the spectrum (and a few other things.) In other words, the three-quark model works not because it correctly describes what’s going on inside the proton, but because it is a good way to keep track of the symmetry structure that was sitting there all along, unrecognized. Skyrmions, with a completely different description of what the proton is, also keep track of the symmetry structure, and therefore give almost the same results.

17. Eyal Cohen

I will go over it. Thanks.
I studied physics during the 80’s at the Haifa Technion. My MSc thesis was on quantum clocks and gravity wave detectors, but I haven’t done any serious physics after that.

18. David Thurgood

We are advised that electron-positron collisions will result in complete annihilation of the two particles. Is this also true of quark-antiquark collisions? Perhaps this question only has meaning if there are “free” quarks. I raise the question because of the idea, if I understand it correctly, that there is a frenzy of quarks inside a proton, rather like a soup that is boiling with great vigour. So, what prevents collisions and mutual annihilation? I posit that there is more likely an ordered internal structure, possibly somewhat like a smaller version of an atom, with an orbital nature. If so, this would contribute to the stable and predictable nature of these particles. Will we ever be able to confirm this speculation? If we break open a nut with a large hammer (aka LHC!), we will indeed find that it had a kernel, but never the form as it is now just a paste! I cannot begin to imagine a delicate way of peeking inside a proton. Your comments will be appreciated.

19. Bill Hoffman

how does one understand that protons (and neutrons) exist as the only baryons encountered under usual conditions (Actually, I guess stellar interiors, neutron stars and black hole horizons may be statistically more ‘usual’ than my lab, but I haven’t first hand knowledge of them). That is, I assume there is something in the equations of QCD that predicts ‘proton’ and ‘neutron’ as an overwhelmingly statistically favored ground state of particles that feel the color force. I am rather familiar (I’m a physical chemist/neuroscientist) with garden variety quantum mechanics (e.g., I understand and could reproduce the solution to the time independent Schroedinger equation for the hydrogen atom [given a bit of time and paper]) and it’s mathematical formalism. But the solution to that problem is based on the idea that one has a proton and an electron with known properties (albeit somewhat simplified) and some mathematical rules for calculating what happens when they interact.

Your description of proton structure is clearly not something that can be approached by writing down an equation that describes the interactions among a fixed number of particles. Is it correct to think that ‘proton’ is a favored solution to a more complex (and relativistic?) eigenvalue problem? I realize this is way technical for your aim on this forum, but when I read accurate descriptions of particle physics such as those on this blog, I get a terrible ‘tip of the brain’ feeling, where it seems that with just a bit more math (and way more time than I have), I could get more insight.

Feel free to simply refer me to a book or article.

• The number of baryons (and mesons) produced in the lab is very large, actually. But they are all extremely unstable, except for the proton and neutron, so under usual conditions they’re gone within a tiny fraction of a second. It’s not that protons and neutrons are statistically favored but that they are the “last ones standing.”

Actually stars and supernovas aren’t hot enough to make the other baryons; the most likely place for you to find them are in the collisions of cosmic rays (themselves mostly protons and heavier nuclei) with atoms at the top of the atmosphere… however, again, very very few of these exotic particles make it to the earth’s surface.

You’re right describing these other baryons and mesons requires the solution to a complex, relativistic eigenvalue problem that can only be solved with very large computers. The codeword is “Lattice QCD”.

20. Bobby

Wow. Just found this page, and really wish I’d found it much sooner [how do I subscribe to your articles?].

Mind blown. Interest in going back to school to get a Physics Phd rekindled!

Question (assuming you are still answering questions on this old a topic), more of a presumption:

Based on what you say above, I now believe that every proton is essentially unique, not the lego-blocks I’ve always thought they were. If bits are continually coming into and departing the “proton edge” radius, tunneling to other protons, etc., then, at any given moment each one is uniquely different. I suppose they all average out, and individuals average out over time, but they’re not legos any longer.

Wow. Thank you.

• You’d think so! but no! This is where quantum mechanics comes in and surprises you.

All protons are indistinguishable. If they weren’t, nuclear physics would be completely different from what we observe.

You could already worry about this question in, say, a helium atom. After all, there are two electrons orbiting the nucleus — how can every helium atom have its two electrons doing exactly the same thing, so that all helium atoms are identical?

The answer is subtle. The state of a system does not specify precisely what the electrons are doing at any given time; it only specifies a few things, and that’s enough to make the helium identical. In a similar way, the proton is very complex, but all protons are in exactly the same state, which does not tell you precisely what the quarks and antiquarks and gluons are doing at any given time.

If that’s confusing — that’s quantum mechanics. There’s no completely satisfying intuitive picture; even experts rely on math to get the full story right.

21. Not necessarily confusing, just not the answer I expected.

So, although there are random arrivals and departures constantly, they are sufficiently uniform acorss the population of protons that there is no effective difference? [this is why I need to go back to school – I want to understand, not just repeat]

To my discrete-leaning CompSci background, “indistinguishable” is not the same as “identical”; so I think that may satisfy my “they are different” statement while I can still accept the “incapable of being differentiated” as the operating fact — there is no practical way to assert any difference, although we know that the exact same arrivals/departures cannot happen simultaneously in all protons. To use your helium example, we know that the electrons are not always at the same place and speed, but that difference is not meaningful to the nature of helium, and could be considered a mathematical transform of rotation, position, time. etc. … maybe? 🙂

In any case, I must educate myself, and I sincerely thank you for the approachability of your articles!

Hi!Only a few days back I became aware of your excellent blog. I am a retired physics prof. here.Can you give me a reference which calculates with what energy quarks or gluons collide for a given cm energy of the two protons. I suspect it is quite involved and depends in which direction they are moving at the instance of collision and for each event one has to reconstruct.Thanks. From now on I will read your blog carefully!

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24. Krystal

OK, all this make a great sense to me, but I need to know what particles are created in gluon – antigluon collisions, and quark – anti quark collisions. Help!

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