# What's inside a proton?

What constitutes protons? When I see pictures, I can't understand. Protons are made of quarks, but some say that they are made of 99% empty space. Also, in this illustration from Wikipedia, what's between the quarks?

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I would presume that since 3 quarks make a proton, that the grey blob probably represents the proton size. Definitely not to scale though, given that we don't really know how big the quarks are (just a large range, from $10^{-35}$ m up to $10^{-15}$ m). – Kyle Kanos Oct 18 '13 at 14:13
We think that they might be point-like, but we're not really sure about that. – Kyle Kanos Oct 18 '13 at 14:30
Note that "empty space" is just a philosophical abstraction. Ultimately, space is the name we give to that handy utility which prevents everything from occupying the same spot. How much space is between two particles depends on how fat you consider them to be: where is the boundary between what is in the particle and what is outside. This is complicated by the boundary being fuzzy: just a sort of density function, which is not even time-invariant. – Kaz Oct 19 '13 at 0:39
@DavidZ Because due to surpassing some hotness threshold or whatever, it has appeared in the stackexchange-network-wide list of hot questions, which creates a positive feedback loop of upvoting. – Kaz Oct 19 '13 at 4:48
@DavidZ It has been linked from Hacker News. – Chris Taylor Oct 19 '13 at 10:17

The illustration doesn't show the underlined physical reality. A proton is made up of 3 quarks, namely $uud$, but it is also constituted, as jinawee pointed out, of virtual quarks and antiquarks who are constantly being created and annihilated via strong force which is mediated by gluons, described by Quantum Chromodynamics (QCD).

The grey sphere in Wikipedia's site, shows the region where quarks make the proton, in other terms, if the wave-function shows the probability of finding a particle in a region of space, then this sphere shows the probability where you can find the essential quarks making up a proton.

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Due to QED and QCD, protons can decay into positrons and pions too. What particles can change into is determined by their couplings to other fields. Though no one has ever observed proton decay so far. Probably because they are VERY stable. Stable bound states form due to resonance, which roughly it means there is a ridiculously high probability particles will collide to form a bound state and stay like that. – dj_mummy Oct 18 '13 at 16:12
This answer is vastly incomplete as it doesn't even mention gluons. – Wedge Oct 19 '13 at 9:08
@Wedge I mentioned the strong force, should I edit the post to incorporate 'gluons' to explain a bit more the strong force? – user29727 Oct 19 '13 at 9:11
@Adobe Since you included gluons, might as well include photons, W and Z bosons. They have a small contribution though, when compared to gluons. Quarks are unique since they interact via all 4 fundamental interactions. Note that if we include the existence of other elementary fermions in addition to quarks, we will also have virtual pair production of lighter fermions. – dj_mummy Oct 19 '13 at 20:38
@dj_mummy Thank you for your proposal. But I was more talking of a low energetic proton and I don't want to repeat or extend what David Z eloquently explained, only if you insist or if the OP finds it useful. – user29727 Oct 19 '13 at 20:44

Ah, I know this one!

# What's in a proton?

A proton is really made of quantum fields. Remember that. Any time you hear any other description of the composition of a proton, it's just some approximation of the behavior of quantum fields in terms of something people are likely to be more familiar with. We need to do this because quantum fields behave in very nonintuitive ways, so if you're not working with the full mathematical machinery of QCD (which is hard), you have to make some kind of simplified model to use as an analogy.

One of the more confusing things about quantum fields is that they react differently depending on how they are observed. The way we observe protons is by hitting them with other high-energy particles in a particle accelerator and seeing what comes out. In a slow collision, with very little energy involved, the proton acts like a single point particle. If we give the particles slightly more energy, the proton looks more like a blob with three points in it --- these are the three quarks of common knowledge. (Incidentally, the reason you see images like the one you found on Wikipedia is that for a long time, people were colliding protons at the intermediate energies where they appear to behave as a group of three quarks.) If we give the colliding particles even more and more energy, the proton will appear to be an ever-more-dense amalgamation of all sorts of particles: quarks, antiquarks, gluons, photons, electrons, and everything else. We call these particle partons (because they're part of the proton).

This diagram shows basically how a proton appears to different kinds of collisions. The vertical axis basically corresponds to collision energy, and the horizontal axis corresponds to the "resolving power" of the incident ("probe") particle. (Resolving power is basically transverse momentum, but I can't explain how that connection works without getting into more detail of quantum mechanics than I think is necessary.) The contents of each circle represents, roughly, a "snapshot" of how the proton behaves in a collision at the corresponding energy and resolving power.

So for example, if you hit a proton with a beam of high-energy probes that have weak resolving power, it behaves like a dense cluster of partons (quarks and gluons etc.), each of which is fairly large. That corresponds to the top left corner of the graph. Or if you hit the proton with a beam of low-energy probes with high resolving power, it behaves like a sparse cluster of partons, each of which is small. If you hit it with a beam of low-energy, low-resolving-power probes (but not too low), it behaves like a collection of three particles, as seen in the bottom left corner.

Physicists describe this apparently-changing composition using parton distribution functions, $f(x, Q^2)$, which under certain conditions can be interpreted as the probability density of the probe interacting with a particular type of parton with a particular amount of momentum. Basically, $f(x, Q^2)$ is related to the number of particles in the circle at the corresponding $(x,Q)$ point on the plot. For more information on parton distributions, I would refer you to this answer of mine and the resources named therein, as well as this one.

# What's the gray region?

In the preceding image, I displayed each snapshot of the proton as a set of partons (quarks and gluons etc.) uniformly distributed within a circle, as if the proton has a definite edge. But in reality, that's not the case; instead, the quantum fields that make up a proton gradually fade away to zero as you move further away from the center. It has a fuzzy edge. So a (somewhat) more accurate snapshot would look something like this:

Notice that there are more partons near the center of the proton, and progressively fewer as you move toward the edge. The ordinary parton distributions that I mentioned above, $f(x, Q^2)$, are part of a simplified model in which we ignore this fact and pretend that partons are distributed uniformly throughout space. But we can make a more complicated model that does take into account the fact that partons are clumped up toward the center of the proton. In such a model, instead of regular parton distributions, you get more complicated functions, called impact parameter-dependent parton distributions, and denoted $f(x, Q^2, b)$, where $b$ is the radial distance - the impact parameter.

There have been some theoretical studies showing that these impact parameter-dependent parton distributions trail off gradually as you go to large radii. For example, see figure 5 of this paper (arXiv) or figure 7 in this one (arXiv):

Here $N(y)$ is a quantity related to the parton distributions (specifically, it's the color dipole scattering amplitude), which kind of "condenses" the many different parton distributions into one quantity. (Huge oversimplification, but it's good enough for this.) You can then define the spatial extent of the proton as the region in which $N(y)$ is above, say, 5% of its maximum value. Or 10%. Or 50%. The exact number is somewhat arbitrary, but the point is, whatever number you pick, you'll wind up with a circle that encompasses the region in which the parton density is high, kind of like this:

This is roughly what the gray circle in the image from Wikipedia represents. It's a region with a size on the order of $1\text{ fm} \approx 5\text{ GeV}^{-1}$, where the chance of an incident particle (a probe) scattering off the proton is relatively significant. Equivalently, it's the region in which the parton distributions are large, and also the region in which the quantum fields that constitute the proton are much different from zero.

As you can guess, all this is pretty imprecise. You can make a more rigorous definition of the size of a proton by using the scattering cross section. You can also get a definition without using scattering, using the charge radius, which can be measured or calculated using various other methods. I won't go into those, as the details would be material for a whole separate question, but the results of all these methods come out to a radius a little less than $1\text{ fm}$.

Incidentally, this claim of a proton being 99% empty space is probably false using any reasonable definition. You might be thinking of atoms, where the volume in which the electron's quantum field has an appreciable value is much larger than the size of the electron itself, whatever it may be. People sometimes simplify that to say that the atom consists of a large fraction of empty space. But you can't really do the same with a proton, given the large number of particles in it and the strength of their interactions.

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This is a fairly complex answer and I wish the bit about partons were worded more clearly, but so far this is the only even remotely adequate answer to this question. – Wedge Oct 19 '13 at 9:36
you could maybe clarify how the x-Q graph's individual "images" are to be interpreted, and how that compares to the impact parameter discussion which only comes further down. as it looks now, I'd guess the "images" could be interpreted as random plots of the corresponding partition function value normalized by the spatial impact parameter curve to make good illustrations? but it's not apparent either way and the spatial dependence seems important to the original question. – BjornW Oct 19 '13 at 11:07
I believe it's worth adding the following precision: "it is at this point completely impossible to observe ANY particle without disrupting or destroying it, and because of that, the following post only contains the best explanation we have so far, which is thus very likely wrong.". You cannot prove that a proton is full or empty, you have no idea what a proton contains when it's not being collided, and you have no idea what a proton is. You do however have a good explanation for what you observe when you shoot it with a cannon, I'd like to see it presented that way. – Morg. Oct 19 '13 at 11:33
Probably a naive question, but how is 1/GeV a measure of distance? – RBarryYoung Oct 19 '13 at 20:48
@RBarryYoung in natural units where $\hbar$ and $c$ are left implicit, distance is measured in inverse energy. To recover a more familiar distance unit, multiply by $\hbar c = 0.197\text{ GeV fm}$. – David Z Oct 19 '13 at 21:13

You can't consider a proton just as three quarks (called valence quarks, because they determine the quantum numbers) because virtual quarks and antiquarks are constantly being created and anhilated via strong force. So a proton is more like a quark sea. In fact, this process gives most part of the proton's mass (the valence quarks are just the 2% of the mass).

It's something like this:

The lines that connect quarks are gluons (the force carrier particles of the strong interaction).

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If 3 quarks are confined to make a proton, then it is reasonable to think that these colored regions are (effectively) the proton size (and, again, without regard to scales). – Kyle Kanos Oct 18 '13 at 14:55
If you mean the circle of the background, it's nothing physical. Only what you would observe as the proton's approximate radius. – jinawee Oct 18 '13 at 14:59
@MyFavouritePhysicistIsNewtax In analogy with an hydrogen atom:how would you draw it? One proton and one electron or a sphere with a core? Both ways are correct. The interpretation of the last drawing should be like a long exposure photo, where the sphere is the zone where the electron can be. – cinico Oct 18 '13 at 15:09
And note that the proton's radius is about $10^{-15}$ m and the quark is smaller than $10^{-19}$ m (at least 10000 times smaller). – jinawee Oct 18 '13 at 15:15

The question you are asking has been answered in terms of popularized description.

The real physics picture is not simple and depends a lot on a number of experimental measurements by many experiments. If you look at figure 9.18 of the link you will see that the composition of the proton changes according to the momentum transfer from the probing particle.

Contrary to the statement that it is mainly empty space, it is not. Particles probing the proton do not sail through unscathed, they interact with the quarks and gluons that compose it and thus we get the parton functions in the figure. The reason it is not mostly empty is because Quantum Chromodynamics, contrary to the other forces does not diminish with distance, but increases, thus the constituents are tightly bound.

So the answer to "whats inside the proton" is "it depends on the way you look inside it". From outside, it has the quantum numbers assigned to it by the three valence quarks.

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The real problem here is that when things get really, really small, they don't behave like the world we see around us. That can make a lot of what goes on in that weird world quite hard to grasp.

The diagram is misleading. Protons aren't really round, grey blobs, and quarks aren't really little spheres that sit inside them. Down at the subatomic level, Quantum Mechanics rules.

One of the weird upshots of Quantum Mechanics is that really tiny things don't actually occupy a single space. Take a look at your hand. It's there, right? In one, single place. If you curl it into a fist, it takes up less space, and if you stretch it out, it takes up more. But it's always in one place.

Really tiny things don't work like this. Instead, they occupy many points in space at the same time. We usually draw diagrams where the actual positions of tiny things are represented like clouds: they're in lots of places, all at once.

Quarks are like this, too. They're held together by incredibly strong forces, but they're trying to get away from one another, too. Like when you're in a car with your parents on a long drive. What do I do on a long drive with my parents? I fidget. I couldn't tell you where I'll be - front seat, back seat - because I'm constantly moving around. But you know I'm somewhere inside the car, even if you can't tell me exactly where.

And so with quarks, with one twist: they really are in many different places at the same time. What we do know is that they're most likely stay within a boundary: in this case, the grey circle of the proton.

As for the 99% of empty space, the actual figure is much higher than that. Very little is actually 'made up' of matter (we usually call matter-like particles 'hadrons'). So why don't we fall through things all the time? Why doesn't my laptop slip through my desk, if it's mostly nothing? Well, because the forces between these tiny particles are tremendous, compared to their size (and, more importantly, compared to their mass). That allows them to stay a balanced distance from each other, and stops anything else from coming too close to them, or falling 'in between' the particles. When you catch a ball, the particles in your hand and the particles in the ball never even come close to 'touching', because the forces between particles are so strong. Instead, the ball is 'repulsed' from your hand. This repulsion balances against the ball's force due to gravity, so the ball stays where it is.

TL;DR: The diagram does the best it can at explaining how things work on the very very small-scale. Unfortunately, it's very misleading. The 'space between' particles is a) not really space, but 'point clouds' of possible particle positions (there's a mouthful), and b) it's forces between particles, rather than the particles themselves, that stop the 'empty space' in the proton from being something you could actually go through.

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+1, but just wanted to nitpick that, technically, your stretched-out hand and your curled-up hand take up the same amount of space and displace the same volume of air. :) – asteri Oct 18 '13 at 19:16
Actually, this is a very wrong and dangerous explanation. Every Physics theory is a failed attempt at explaining how the universe works. Every new theory is a better attempt, but it is critically important to remember that it is WRONG as long as it does not explain everything. It is instead VERY likely that quantum theory is only a statistical approximation of reality and that our understanding is strongly biased by our limited senses and sensors. – Morg. Oct 19 '13 at 11:25
Morg - no. This is not how Science works. What you are quoting is empirical realism, which was a very popular philosophical movement in the 30s but died out shortly after Karl Popper's introduction of falsification. The modern scientific method uses a Hypothetico-Deductive method: a hypothesis is deduced from existing research, asserted and tested. There is no 'right' or 'wrong' about it, merely self-consistent or inconsistent. Modern Science makes no claims about the nature of reality, rather offers an occasionally unusual, abstract or counterintuitive self-consistent theoretical model. – Sam James Oct 20 '13 at 12:10
Jeff - you're absolutely right, of course. I was using an analogy that would help differentiate between two concepts: extended spacial occupation (macroscopic, non-point objects) and distributed spacial occupation (quantum-mechanical objects). I hoped the question 'does a hand really take up more space when you stretch it out?' might have led to the question 'does a quantum-mechanical system really take up 'more space' when left to evolve unobserved?'. Of course, the answer comes down to a definition of 'space' and 'place', which both need to be treated differently at the quantum level. – Sam James Oct 20 '13 at 12:24

As some of the answers have pointed out, the "gray ball" shown in the picture is not really a physical entity in itself. It has to do more with the classical view that we have of subatomic particles as being a solid object, when in fact they are not. It's a representation of the average radius of the particle.

When you perform an experiment to detect the proton, you have a certain probability to find it inside the gray area, but also a small one of finding it outside. So a better way to show it would be to represent the ball with a lighter shade of gray as you are moving away from the centre of the particle. This would give a better notion of the fact that the particle is not a solid with defined edges. As you move away from the expected position (the centre of the gray zone), it is less and less probable to detect the proton.

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The point is, that is not a picture of a proton; it's a schematic representation. You can see it as a Euler diagram that says that in the proton you have 3 valence quarks and some gluons.

By the way the exact constituents of a proton is still an open question.

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As far as we know, nothing, i.e. "empty space" as you said.

An atom is also mostly constituted by empty space between the core and the electrons.

Illustrations may deceive you. You cannot see a proton as a static thing made of static building blocks called quarks. In a similar way, you cannot say that a atom has its core fixed in a certain position, and the electrons in a well defined orbit.

The distance in between, where there is nothing but vacuum, exists because is minimizes the energy of the system since there are different forces involved.

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Why I cannot see a proton as a static thing? I'm confused about your last statement. – MyFavouritePhysicistIsNewtax Oct 18 '13 at 14:29
Because it is always moving/vibrating – cinico Oct 18 '13 at 14:50
Elementary particles don't move and vibrating is a very unprecise and vague word. – MyFavouritePhysicistIsNewtax Oct 18 '13 at 14:51
Elementary particles do move. I mean "moving around a mean position" when I say "vibrating". – cinico Oct 18 '13 at 14:57
This is just plain wrong, the volume of a proton cannot reasonably be considered "empty space". – Wedge Oct 19 '13 at 9:23

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