6

The Bits Within the Its

Introduced in a theoretical improvisation and never observed in isolation, quarks at first seemed a convenient fiction. But when they showed up in ultrastroboscopic nanomicroscopic snapshots of protons, quarks became an inconvenient reality. Their strange behavior called basic principles of quantum mechanics and relativity into question. A new theory reinvented quarks as ideal objects of mathematical perfection. The equations of the new theory also demanded new particles, the color gluons. Within a few years, people were taking pictures of both quarks and gluons, at powerhouses of creative destruction built for the purpose.

 

 

THE TITLE OF THIS CHAPTER has two meanings. The first is simply that there are littler bits within what not so long ago were thought to be basic building blocks of ordinary matter, protons and neutrons. These littler bits are called quarks and gluons. Of course, knowing something’s name does not tell you what it is, as Shakespeare had Romeo explain:

What’s in a name? That which we call a rose
By any other name would smell as sweet.

Which brings us to the second, more profound meaning. If quarks and gluons were just another layer in a never-ending onion of complex structure within structure, their names would provide impressive-sounding buzzwords you could show off at a cocktail party, but they themselves would be of interest only to specialists. Quarks and gluons, are, however, not “just another layer.” When properly understood, they change our understanding of the nature of physical reality in a fundamental way. For quarks and gluons are bits in another and much deeper sense, the sense we use when we speak of bits of information. To an extent that is qualitatively new in science, they are embodied ideas.

For example, the equations that describe gluons were discovered before the gluons themselves. They belong to a class of equations invented by Chen Ning Yang and Robert Mills in 1954 as a natural mathematical generalization of Maxwell’s equations of electrodynamics. The Maxwell equations have long been renowned for their symmetry and power. Heinrich Hertz, the German physicist who proved experimentally the existence of the new electromagnetic waves Maxwell had predicted (what we now call radio waves), said of Maxwell’s equations:

One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.

The Yang-Mills equations are like Maxwell’s equations on steroids. They support many kinds of charges, instead of just the one kind (electric charge) that appears in Maxwell’s equations, and they support symmetry among those charges. The specific version that applies to the real-world gluons of the strong interaction, which uses three charges, was proposed by David Gross and me in 1973. The three kinds of charges that appear in the theory of the strong interaction are usually called color charges, or simply color, although of course they have nothing to do with color in the usual sense.

We’ll discuss the nuts and bolts of quarks and gluons much more below. The point I want to emphasize here, from the beginning, starting with the title, is that quarks and gluons, or more precisely their fields, are mathematically complete and perfect objects. You can describe their properties completely using concepts alone, without having to supply samples or make any measurements. And you can’t change those properties. You can’t fiddle with the equations without making them worse (indeed, inconsistent). Gluons are the objects that obey the equations of gluons. The its are the bits.

But enough of this all-too-free rhapsody! Pure mathematics is chockablock with beautiful ideas. The special music of physics lies in harmony between beautiful ideas and reality. It’s time to bring in some reality.

Quarks: Beta Release

By the early 1960s, experimenters had discovered dozens of hadrons, with different masses, lifetimes, and intrinsic rotation (spin). The orgy of discovery soon led to a hangover, as the mere accumulation of curious facts, absent any deeper meaning, became mind-numbing. In his 1955 Nobel Prize acceptance speech, Willis Lamb joked

When the Nobel Prizes were first awarded in 1901, physicists knew something of just two objects which are now called “elementary particles”: the electron and the proton. A deluge of other “elementary” particles appeared after 1930; neutron, neutrino, μ meson, π meson, heavier mesons, and various hyperons. I have heard it said that “the finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a $10,000 fine.”

In this situation, Murray Gell-Mann and George Zweig made a great advance in the theory of the strong interaction by proposing the quark model. They showed that patterns among the masses, lifetimes, and spins of hadrons click into place if you imagine that hadrons are assembled from a few more basic kinds of objects, which Gell-Mann named quarks. Dozens of hadrons could be understood, at least roughly, as different ways of putting together just three varieties, or flavors, of quarks: up u, down d, and strange s.⁶

How do you build dozens of hadrons from a few flavors of quarks? What are the simple rules behind the complicated patterns?

The original rules were improvised to fit the observations, and they’re a bit peculiar. They defined what is called the quark model. According to the quark model, there are just two basic body plans for hadrons. Mesons are constructed from a quark and an antiquark. Baryons are constructed from three quarks. (There are also antibaryons, constructed from three antiquarks.) Thus there are just a handful of possibilities for combining quarks and antiquarks of different flavor to make mesons: you can combine u with anti-d (ƌ), or d with s , and so forth. Similarly for baryons, there are only a few possible combinations.

According to the quark model, the great diversity of hadrons comes not so much from which pieces you put together as from how you assemble them. Specifically, a given set of quarks can be arranged in different spatial orbits, with their spins aligned in different ways, in roughly the same way that pairs or triples of stars can be bound together by gravity.

There’s a crucial difference between the submicroscopic “star systems” of quarks and their macroscopic brethren. Whereas macroscopic solar systems, governed by the laws of classical mechanics, can come in all sizes and shapes, the microscopic version cannot. For microscopic systems, which obey the laws of quantum mechanics, there are restrictions on the allowed orbits and spin alignments.⁷ We say that the system can be in different quantum states. Each allowed configuration of orbits and spins—each state—will have some definite total energy.

(Confession and preview: I’m being a little sloppy here, so as not to pile on too many complications at once. According to modern quantum mechanics, the correct way to describe the state of a particle is in terms of its wave function, which describes the probability of finding it at different places, rather than in terms of an orbit it follows. We’ll talk about this more in Chapter 9. The orbit picture is a relic of the so-called old quantum mechanics. It is easy to visualize, but it can’t be used for precision work.)

This setup for using quarks to understand hadrons runs strictly parallel to the way we use electrons to understand atoms. The electrons in an atom can have orbits of different shapes and can align their spins in different directions. Thus the atom can be in many different states, with different energies. The study of the possible states is a vast subject known as atomic spectroscopy. We use atomic spectroscopy to reveal what distant stars are made of, to design lasers, and for many other things. Because atomic spectroscopy is so relevant to the quark model, and is extremely important in itself, let’s take a moment to discuss it.

A hot gas, such as you find in a flame or a stellar atmosphere, contains atoms in different states. Even atoms with the same kind of nuclei and the same number of electrons can have their electrons in different orbits or with their spins aligned in different ways. These states have different energies. States of high energy can decay into states with lower energy, emitting light. Because energy is conserved overall, the energy of the emitted photon, betrayed by its color, encodes the difference in energy between the initial and final states. Every kind of atom emits light from a characteristic palette of colors. Hydrogen atoms emit one set of colors, helium atoms an entirely different set, and so forth. Physicists and chemists call that palette the spectrum of the atom. The spectrum of an atom functions as its signature and can be used to identify it. When you put light through a prism the different colors get separated, and the spectrum literally resembles a barcode.

It’s because the spectra we observe in starlight match the spectra we observe in terrestrial flames that we can be confident that distant stars are made of the same basic kind of material as we find on Earth. Also, because the light from distant stars may take billions of years to reach us, we can check whether the laws of physics that operate today are the same as those that operated long ago. So far, the evidence is that they are. (But there are good reasons to think that the very early universe, which we can’t see directly, at least in ordinary light, was governed by essentially different laws. We’ll discuss that later.)

Atomic spectra give us a lot of detailed guidance for contructing models of the internal structure of atoms. To be valid, a model must predict states whose energy differences match the pattern of colors that spectra reveal. Much of modern chemistry takes the form of a dialogue. Nature speaks in spectra; chemists reply in models.

With that background in mind, let’s return to the quark model of hadrons. The same ideas come into play, with one major refinement. In atoms, the difference in energy between any two states of the electrons is relatively small, so the effect of that energy difference on the overall mass of the atom is insignificant. A central idea of the quark model is that for quark “atoms” (that is, hadrons), the energy differences between different states are so large that they contribute to the mass in a big way. Turning it around, exploiting Einstein’s second law m = E/c², we can interpret hadrons with different masses as systems of quarks in different orbital patterns—different quantum states—that have different energies. In other words, we see atomic spectra, but we weigh hadron spectra. Thus what appeared to be unrelated particles now appear as merely different patterns of motion within a given “atom” of quarks. Using that idea, Gell-Mann and Zweig showed that one could interpret many different observed hadrons as different states of a few underlying quark “atoms.”

So far, so easy. Except for the refinement introduced by Einstein’s second law, the quark model of hadrons looks like a replay of chemistry. But the devil is in the details, and to see reality in the quark model, one had to turn a blind eye toward some truly fiendish deviltry.

The most wicked assumption is the one we already mentioned, that only meson (quark-antiquark) and baryon (three-quark) body plans are allowed. That assumption includes, in particular, the idea that quarks don’t exist as individual particles! For some reason, you had to suppose, the simplest body plan is impossible. Not just inefficient or unstable, but impossible. Nobody wanted to believe that, of course, so people worked hard to smash protons, trying to find particles they could identify as single quarks. They scrutinized the debris minutely. Nobel Prizes and everlasting glory surely would shower down like sweet rain upon the heads of the discoverers. But alas, that Holy Grail proved elusive. No particle that has the properties of a single quark has ever been observed. Eventually this failure to find individual quarks, like the failure of inventors to produce a perpetual motion machine, was elevated to a principle: the Principle of Confinement. But calling it a principle didn’t make it less crazy.

More deviltry came in when physicists tried to make fleshed-out models of the internal structure of mesons and baryons using quarks, to account for their masses in detail. In the most successful models, it appeared that when quarks (or antiquarks) are close together, they hardly notice one another. That feeble interaction between quarks was hard to reconcile with the finding that if you tried to isolate one quark—or two—you found you could not. If quarks don’t care about one another when they’re close, why do they object to being separated when they’re far away?

A fundamental force that grows with distance would be unprecedented. And it would pose an embarrassing question. If forces between quarks can grow with distance, why is astrology wrong? After all, the other planets contain lots of quarks. Maybe they could exert a big influence. . . . Well, maybe, but for centuries scientists and engineers have been very successful at predicting the results of delicate experiments and building bridges and designing microchips by ignoring any possible influence of distant objects. Astrology should be made of sterner stuff.

Because a good scientific theory has to explain why astrology is so lame, it had better not contain forces that grow with distance. The old saw “Absence makes the heart grow fonder” may or may not apply to romance, but it’s surely a bizarre way for particles to behave.

In software development, often a beta test version is supplied for use by brave early adopters. The beta test version works, more or less, but comes with no guarantees. There will be bugs and missing features. Even the parts that work won’t be smoothly polished.

The original quark model was a beta test physical theory. It used peculiar rules. It left basic questions, like why (or whether) quarks could ever be produced in isolation, unanswered. Worst of all, the quark model was vague. It did not come with precise equations for the forces between quarks. In that respect it resembled pre-Newtonian models of the solar system, or pre-Schrödinger (for experts: even pre-Bohr) models of atoms. Many physicists, including Gell-Mann himself, thought that quarks might turn out to be a useful fiction, like the epicycles of the old astronomy or the orbitals of old quantum theory. Quarks, it seemed, might turn out to be useful stopgaps in the mathematical description of nature, not to be taken too literally as elements of reality.

Quarks 1.0: Through an Ultrastroboscopic Nanomicroscope

The theoretical peculiarities of quarks ripened into juicy paradoxes in the early 1970s, when Jerome Friedman, Henry Kendall, Richard Taylor, and their collaborators at the Stanford Linear Accelerator (SLAC) studied protons in a new way.

Instead of bashing protons together and scrutinizing the debris, they photographed proton interiors. I don’t want to make that sound easy, because it isn’t. To look inside protons, you must use “light” of very short wavelength. Otherwise you’d be trying, in effect, to locate fish by looking for their effect on long ocean waves. The photons for this job are not particles of ordinary light. They lie beyond ultraviolet or even x-rays. A nanomicroscope fit for studying structures a billion times beyond the ken of ordinary optical microscopes requires extreme γ-rays.

Also, things move quickly inside protons, so to avoid blurring the picture we must have good time-resolution. Our photons, in other words, must also be extremely short-lived. We need flashes, or sparks, not long exposures. We’re talking about “flashes” that last 10^-24 second, or less. The photons we need are so short-lived that they themselves can’t be observed. That’s why they’re called virtual photons. An ultrastroboscope to look at features that last for a trillionth of a trillionth of the blink of an eye (actually, even less) requires extremely virtual photons. So the “picture” can’t be made using the transient “light” that provides the illumination! We have to be cleverer, and work indirectly.

At SLAC people actually shot electrons at protons, and observed electrons emerging after they collided. The emerging electrons have less energy and momentum than when they started. Because energy and momentum are conserved overall, what was lost by the electron had to be carried away by the virtual photon, and transmitted to the proton. This often causes the proton to break apart in complicated ways, as we’ve discussed. The stroke of genius—the new approach that won Friedman, Kendall, and Taylor their Nobel Prize—was to ignore all those complications and just keep track of the electron. In other words, we just go with the flow (of energy and momentum).

In this way, by accounting for the flow of energy and momentum, we can figure out what kind of virtual photon was involved, event by event, even though we don’t “see” that photon directly. The energy and momentum of the virtual photon are precisely the energy and momentum lost by the electron. By measuring the probability that different kinds of virtual photons, with different energies and momenta (corresponding to different lifetimes and wavelengths), “encountered something” and got absorbed, we can piece together a snapshot of the proton’s interior. The procedure is similar in spirit to the way we reconstruct a picture of a human body’s interior by measuring how x-rays get absorbed, although the details are considerably more complicated. Suffice it to say that some very fancy image processing is involved.

Now of course the interiors of protons don’t really look like anything you’ve ever seen, or could see. Our eyes were not designed (ahem, did not evolve) to resolve such small distances and times, so any visual representation of the ultrastrobonanomi-croworld must be a mixture of caricature, metaphor, and cheat. With that warning, please look now at the panels of Figure 6.1. We’ll be discussing various aspects of them further below.

In presenting these pictures, I’ve used a trick I owe to Richard Feynman. As we’ve noted, things move fast inside a proton. To slow things down, we imagine that the proton is moving past us at very nearly the speed of light. (In Chapter 9, we’ll discuss how protons look if we don’t use Feynman’s trick.) From the exterior, the proton then comes to look like a pancake, flattened in the direction of motion. This is the famous Fitzgerald-Lorentz contraction of special relativity. More important for our purposes is another famous relativistic effect, time dilation. Time dilation means that time appears to flow more slowly within a fast-moving object. Thus the stuff inside the protons appears nearly frozen in place. (It shares the overall motion of the proton as a whole, of course.) Fitzgerald-Lorentz contraction and time dilation have been explained in hundreds of popular books on relativity, so rather than belaboring them here, I’ll just use them.

It’s important to emphasize that quantum mechanics is absolutely essential for describing even the most elementary observations about proton interiors. In particular, the indeterminism for which quantum mechanics is famous, and which caused Einstein such anguish, hits you in the face. If you take several snapshots of a proton under strictly identical conditions, you see different results. Like it or not, the facts are straightforward and unavoidable. The best we can hope for is to predict the relative probabilities of the different results.

 

Figure 6.1 Pictures of the interior of a proton. a. A proton moving at nearly the speed of light appears flattened in the direction of motion, according to the theory of relativity. b. A good guess, before actual snapshots were available, for what the interior might look like. The reasoning behind this (wrong) guess is explained in the text. c-d. Two actual snapshots. Because quantum-mechanical uncertainty is a dominant effect in this domain, each snapshot looks different! Inside are quarks and gluons, also moving at nearly the speed of light. They share the total energy of the proton, and the sizes of the arrows indicate their relative shares. e-f. If you look with finer resolution, more details appear. For example, you may find that what appeared to be a quark resolves into a quark and a gluon, or that a gluon resolves into a quark and an antiquark.

This abundance of coexisting possibilities in the phenomena, and in the quantum theory that describes them, defies traditional logic. The success of quantum theory in describing reality transcends and in a sense unseats classical logic, which depends on one thing being “true,” and its contraries “false.” But this is a creative destruction that allows new imaginative constructions. For example, it enables us to reconcile two seemingly contradictory ideas about what protons are. On the one hand, the interior of a proton is a dynamic place, with things changing and moving around. On the other hand, all protons everywhere and everywhen behave in exactly the same way. (That is, each proton gives the same probabilities!) If a proton at one time is not the same as itself at a different time, how can all protons be identical??

Here’s how. Every individual possibility A for the proton’s interior evolves in time into a new and different possibility, say B. But meanwhile, some other possibility C evolves into A. So A is still there; the new copy replaces the old. And more generally, even though each individual possibility evolves, the complete distribution of possibilities remains the same. It is like a smoothly flowing river, which always looks the same even though every drop of it is in flux. Wade deeper into this river in Chapter 9.

Partons, Put-Ons, and Putdowns

The pictures taken by Friedman and company presented both a revelation and a puzzle. Within the pictures, you could discern some little entities, little sub-particles, inside protons. Feynman, who was responsible for a lot of the image processing, called these internal entities “partons” (for particles that are parts of protons).

That infuriated Murray Gell-Mann. As I learned firsthand, when I first met Gell-Mann. He asked me what I was working on. I made the mistake of saying, “I’m trying to improve the parton model.” I’ve heard that confession is good for the soul, so here I confess that it wasn’t entirely in innocence and ignorance that I mentioned partons. I was curious to see how Gell-Mann would react to his rival’s idiom. As Ishmael wrote of his first encounter with Captain Ahab, reality outran anticipation.

Gell-Mann gave me a quizzical look. “Partons?” Stage pause, facial expression of deep concentration. “Partons?? What are partons?” Then he paused again and looked very thoughtful, until suddenly his face brightened. “Oh, you must mean those put-ons that Dick Feynman talks about! The particles that don’t obey quantum field theory. There’s no such thing. They’re just quarks. You shouldn’t let Feynman pollute the language of science with his jokes.” Finally, with a quizzical expression, but a tone of authority: “Don’t you mean quarks?”

Some of the entities Friedman and company found really did appear to be quarks. They had both the funny fractional electric charges and the precise amount of spin that quarks were supposed to have. But protons also contain bits that don’t look like quarks. They were later interpreted as color gluons. So both Gell-Mann and Feynman had valid points: there are quarks inside, but also other things.

Too Simple

At my alma mater, the University of Chicago, they sell sweatshirts that read

 

That works in practice, but what about in theory?

 

Both Gell-Mann’s quarks and Feynman’s partons had the annoying feature that they worked well in practice but not in theory.

We’ve already discussed how the quark model helped to organize the hadron zoo, but only by using crazy rules. The parton model used different crazy rules, this time to interpret those pictures of the proton’s interior. The rules of the parton model are very simple: you’re supposed to assume, for purposes of calculation, that the bits inside the proton—quarks, partons, whatever you want to call them—have no internal structure and no interactions with each other. Of course they do interact; otherwise, protons would just fly apart. But the idea of the parton model is that you get a good approximate description of what happens in a very short time, over very short distances, by ignoring the interactions. And it is that short-time, short-distance behavior you access with the SLAC ultrascroboscopic nanomicroscope. So the parton model says you will get a clean view of the interior using that instrument—as in fact you do. And you should see more basic building blocks, if such there be—as in fact you do.

It all sounds very reasonable, almost intuitively obvious. Nothing much can happen in a very short time, in a very small volume. What’s crazy about that?

The trouble is that when you get down to really short distances and really short times, quantum mechanics comes into play. When you take quantum mechanics into account, the “reasonable, almost intuitively obvious” expectation that nothing much can happen in a short time in a small volume comes to seem very naïve.

One way to appreciate why, without going too deep into technicalities, is by considering Heisenberg’s uncertainty principles. According to the original uncertainty principle, to pin down a position accurately we must live with a large uncertainty in momentum. An addendum to Heisenberg’s original uncertainty principle is required by the theory of relativity, which relates space to time and momentum to energy. This additional principle says that to pin down a time accurately we must live with a large uncertainty in energy. Combining the two principles, we discover that to take high-resolution, short-time snapshots, we must let momentum and energy float.

Ironically, the central technique of the Friedman-Kendall-Taylor experiments, as we mentioned, was precisely to concentrate on measuring the energy and momentum. But there’s no contradiction. On the contrary, their technique is a wonderful example of Heisenberg’s uncertainty principle cleverly harnessed to give certainty. The point is that to get a sharply resolved space-time image you can—and must—combine results from many collisions with different amounts of energy and momentum going into the proton. Then, in effect, image processing runs the uncertainty principle backwards. You orchestrate a carefully designed sampling of results at different energies and momenta to extract accurate positions and times. (For experts: you do Fourier transforms.)

Because to get a sharp image you need to allow for a big spread in energy and momentum, you must in particular allow for the possibility of large values. With large values of energy and momentum you can access a lot of “stuff”—for instance, lots of particles and antiparticles. These virtual particles come to be and pass away very quickly, without going very far. Remember, we’ve only run into them in the process of making a short-time, high-resolution snapshot! We don’t see them, in any ordinary sense, unless we supply the energy and momentum needed to create them. And even then what we see is not the original, undisturbed virtual particles (the kind that appear and disappear spontaneously) but real particles we can use to recreate the original virtual particles by image processing.

Viruses can come to life only with the help of more complex organisms. Virtual particles are still more insubstantial, for they need external help to come into existence. Nevertheless, they appear in our quantum-mechanical equations, and according to those equations the virtual particles affect the behavior of the particles we see.

And so it seemed reasonable to expect that the virtual particles should have big effects when we’re dealing with particles that interact strongly, such as the things that make protons. Sophisticated quantum-mechanicians expected that the closer and faster you looked inside protons, the more virtual particles and complexities you’d see. And so the Friedman-Kendall-Taylor approach wasn’t considered very promising. The ultrastroboscopic nanomicroscopic snapshot would just be a blur.⁸

But it wasn’t a blur. It was those infuriating partons. A famous piece of wise advice from Einstein is to “Make everything as simple as possible, but not simpler.” Partons were too simple.

Asymptotic Freedom (Charge Without Charge)

Let’s imagine we’re virtual particles. We pop into existence and have to decide what to do in our all-too-brief lifetime. (That’s not so hard to imagine.) We sniff around. Suppose there’s a positively charged particle in the region. If we’re negatively charged, we find that particle attractive and try to snuggle up to it. If we’re positively charged, we find that other particle repulsive, or at least competitive and possibly intimidating, and we move away. (Neither is that.)

Individual virtual particles come and go, but together they make the entity we call empty space into a dynamic medium. Due to the behavior of virtual particles a (real) positive charge is partially screened. That is, the positive charge tends to be surrounded by a cloud of compensating negative charges that find it attractive. From far away we do not feel the full strength of the positive charge, because that strength is partially canceled by the negative cloud.⁹ Putting it another way, the effective charge grows as you get closer, and shrinks as you move farther away. For a picture of this situation, see Figure 6.2.

Figure 6.2 The screening of charge by virtual particles. The central world-line shows a positively charged real particle fixed in space—it traces out a vertical line as time advances. That real particle is surrounded by virtual particle-antiparticle pairs, which at random times pop up, briefly separate, and wink out. The positive charge of the real particle attracts the negatively charged member of each virtual pair and repels the positive member. Thus the real particle becomes surrounded, and its positivecharge is partially screened, by a negatively charged cloud of virtual particles. From far away we see a smaller effective charge, because the negative virtual cloud partially cancels the central positive charge.

 

Now this is just the opposite of the behavior we want from quarks in the quark model, or partons in the parton model. The quarks of the quark model are supposed to interact weakly when they’re close together. But if their effective charge is largest in their immediate vicinity, we’ll find just the opposite. They will interact most strongly when they’re close together, and more weakly when they are far apart and their charges are screened. The partons of the parton model are supposed to look like simple individual particles when you look closely. But if a thick cloud of virtual particles envelops each parton, we’ll see those clouds instead.

Clearly, we’d be much closer to describing quarks if we could arrange to get the opposite of screening—clouds that reinforce, rather than cancel, the central charge. With such antiscreening we could have forces that are feeble at short distances but grow powerful far away, thanks to the clouds. Electric charge is screened, not antiscreened, so we have to look elsewhere for a model. We’ll find it, of course; otherwise I wouldn’t be leading you down this garden path. Just so we can talk about it, let’s temporarily call the hypothetical thing that gets antiscreened “churge.” (What we’ll find is that a generalized kind of charge, color charge, behaves like churge.)

If virtual particle clouds antiscreen churge, then the power of the real, central churge increases as you go farther away. You can get strong forces at large distances from a small central churge, because its entourage of virtual particles builds up its influence. Thus if quarks have churge instead of (or in addition to) electric charge, you can have quarks that interact feebly when close together, as the quark model wants, but powerfully when far apart. You can even do this while avoiding astrology, as I’ll explain in a moment. And you can have partons that aren’t hidden in thick clouds, because their cloud-inducing power—their effective charge—wanes in their immediate proximity.

What about that unlimited growth of strength with distance, which threatened to bring back astrology? That growth is the result we get for an isolated churged particle. But the big cloud comes at a price. (You might say that expansive clouds are expensive.) It costs energy to create such a disturbance, and it would take an infinite amount of energy to keep it going out to infinite distances. Because the available energy is finite, Nature won’t let us create an isolated churged particle. On the other hand, we can get away with a system of churged particles whose churges cancel—for example, and most simply, a churged particle and its antiparticle. Virtual particles that are far from both the churge and its canceling antichurge will feel no net attraction, and therefore the clouds won’t keep building. All this begins to sound less like justifying astrology, and more like justifying the devilish rules of the quark model! We can both eliminate all the long-range influences and confine whole classes of particles with the same clever idea.

Antiscreening is a horrible word. The standard jargon in physics is asymptotic freedom, which may not be much better.¹⁰ The idea is that as the distance to a quark gets closer and closer to zero, the effective color charge deep inside its cloud approaches closser and closser to zero, but never quite gets there. Zero color charge means complete freedom—no influence exerted, and none felt. Such complete freedom is approached, as the mathematicians say, asymptotically.

Whatever you call it, asymptotic freedom is a promising idea for describing quarks and making partons respectable. We’d like to have a theory that includes asymptotic freedom and is also consistent with the basic principles of physics. But is there such a theory?

The rules of quantum mechanics and special relativity are so strict and powerful that it’s very hard to build theories that obey both. Those few that do are called relativistic quantum field theories. Because we know only a few basic ways to construct relativistic quantum field theories, it’s possible to explore all the possibilities, to see whether any of them leads to asymptotic freedom.

The necessary calculations are not easy to do, but not impossible either.¹¹ From this work emerged something that every scientist hopes for in a scientific investigation, but rarely finds: a clear, unique answer. Almost all relativistic quantum field theories screen. That intuitive, “reasonable” behavior is, indeed, almost inevitable. But not quite. There is a small class of asymptotically free (antiscreening) theories. They all feature, at their core, the generalized charges introduced by Yang and Mills. Within this small class of asymptotically free theories, there is exactly one that looks even remotely as if it might describe real-world quarks (and gluons). It’s the theory we call quantum chromodynamics, or QCD.

As I’ve already hinted, QCD is like the quantum version of electrodynamics—quantum electrodynamics, or QED—on steroids. It embodies an enormous amount of symmetry. To do QCD even rough justice, we need to lay some deep foundations using the concept of symmetry. Then we’ll build up our description of the theory using drawings and analogies.

The biggest challenge may be to imagine how all those abstractions and metaphors connect with anything real and concrete. To warm up our imaginations, let’s start by contemplating a photograph of things that don’t exist. Behold, in Color Plate 1, a quark, an antiquark, and a gluon.

Quarks and Gluons 2.0: Believing Is Seeing

Of course, a legitimate picture doesn’t emerge from the camera with labels “quark, antiquark, gluon” attached. It needs some interpretation.

First, let’s take stock of the objects in the picture using everyday language. The complicated-looking bits outline magnets and other components of the accelerator and detector. You can make out a narrow tube running through the middle. That’s the beam pipe, through which the electrons and positrons circulate. What’s in the picture is only a very small part, a few meters on a side, of the LEP machine, built inside a circular tunnel 27 kilometers in circumference. (By the way, the same tunnel houses the Large Hadron Collider (LHC), which uses protons instead of electrons and positrons, and which operates at higher energies. We’ll have much more to say about the LHC in later chapters.) Beams of electrons and positrons, circulating in opposite directions, were accelerated up to enormous energies, until their speed reached within a part in ten billion of the speed of light. The two beams crossed at a few points, where collisions occurred. Those special points were surrounded by big detectors, which could track sparks and capture heat from the particles that emerged from the collisions. The emerging explosion of lines you see are the tracks, and the dots on the outside represent the heat.

The next step is to translate our description of what we see from the language of surface appearance into the language of deep structure. This translation entails such a big conceptual step that you might say it involves a leap of faith.¹² Before taking the leap, let’s fortify our faith.

Father James Malley, S.J., taught me a most profound and valuable principle of scientific technique. (It has many other applications as well.) He claimed that he learned this principle at seminary, where it was taught as the Jesuit Credo. It states

 

It is more blessed to ask forgiveness than permission.

 

I’d been following this credo intuitively for years without realizing its ecclesiastical sanction. Now I use it more systematically, and with a clearer conscience.

In theoretical physics, there is a wonderful synergy between the Jesuit Credo and Einstein’s “make things simple, but not too simple.” Together, they tell us we should make the most optimistic assumptions we dare about how simple things are.¹³ If it turns out badly, we can always count on forgiveness and try again—without pausing for permission.

In that spirit, let’s make the simplest guess for how to account for what emerges from the collisions, starting from our ideas about the deep structure of the physical world. According to QED an electron and its antiparticle, a positron, can annihilate one another, producing a virtual photon. The virtual photon, in turn, can turn into a quark and an antiquark. So says QED. This core process is shown in Figure 6.3.

Figure 6.3 A space-time diagram of the core process, in which an electron and positron annihilate into a virtual photon, which then materializes as a quark-antiquarkpair.

 

At that point things get dicey because, as we’ve discussed, the quark (and antiquark) cannot exist in isolation. They must be confined inside hadrons. The process of acquiring virtual particle clouds and canceling color charges, which leads from quarks to hadrons, might be very complicated. These complications could make it difficult to identify signs of the original quark and antiquark, just as it would be very difficult, looking at the final mess, to figure out which rock started a rockslide. But let’s try to think it through, in the spirit of the Credo, hoping for the best.

The initial quark and antiquark that emerge from the collision have enormous energy and are moving in opposite directions.¹⁴ Now suppose that the process of acquiring clouds and canceling color charge is usually accomplished gently, by producing and rearranging color charges, without much disrupting the overall flow of energy and momentum. We call this kind of production of particles, without much change in the overall flow, “soft” radiation. Then we’d see two swarms of particles moving in opposite directions, each inheriting the total energy and momentum of the quark or antiquark that initiated it. And in fact that’s what we do see, most of the time. A typical picture is Color Plate 2.

Occasionally there is also “hard” radiation, which does affect the overall flow. The quark, or the antiquark, can radiate a gluon. Then we’ll see three jets instead of two. At LEP, this happens in about 10% of the collisions. In roughly 10% of 10% of the events (that is, in 1%) there will be four jets, and so on.

The theoretical interpretation of our photographs is sketched in Figure 6.4. With this interpretation, we can eat our quarks and have them too. Even though isolated quarks are never observed, we can see them through the flows they induce. In particular, we can check whether the probabilities for producing different numbers of jets, coming out at different angles and sharing the total energy in different ways, match the probabilities we calculate for quarks, antiquarks, and gluons doing these things in QCD. LEP produced hundreds of millions of collisions, so the comparison between theoretical predictions and experimental results can be done precisely and in great detail.

It works. And that’s why I can say with total confidence that the objects you’re seeing in Color Plate 1 are a quark, an antiquark, and a gluon. To see these particles, however, we’ve had to expand our notions of what it means to see something—and of what a particle is.

Let’s bring our appreciation of the quark/gluon photographs to a climax by connecting it to two big ideas: asymptotic freedom and quantum mechanics.

There’s a direct connection between quarks and gluons appearing as jets and asymptotic freedom. It’s easy to explain the connection using Fourier transforms, but unfortunately Fourier transforms themselves aren’t so easy to explain, so we won’t go there. Here’s a word explanation that is less precise but calls for more imagination (and less preparation):

Figure 6.4 a. How soft radiation makes hadron jets out of a quark and antiquark. b. How hard radiation of a gluon, followed by lots of soft radiation, makes three jets.

 

To explain why quarks and gluons appear (only) as jets, we have to explain why soft radiation is common but hard radiation is rare. The two central ideas of asymptotic freedom are: first, that the intrinsic color charge of the fundamental particle—whether quark, antiquark, or gluon—is small and not very powerful; second, that the cloud of virtual particles that surrounds the fundamental particle is thin nearby, but grows thicker far away. It’s the surrounding cloud that enhances the fundamental power of the particle. It’s the surrounding cloud, not the particle’s core charge, that makes the strong interaction strong.

Radiation occurs when a particle gets out of equilibrium with its cloud. Then rearrangements that restore the equilibrium in color fields cause radiation of gluons or quark-antiquark pairs, much as rearrangements in atmospheric electric fields cause lightning, or rearrangements in tectonic plates cause earthquakes and volcanos. How can a quark (or antiquark, or gluon) get out of equilibrium with its cloud? One way is if it suddenly pops out from a virtual photon, as happened in the experiments at LEP we’ve been discussing. To reach equilibrium, the newborn quark has to build up its cloud, starting from the center—where its small color charge initiates the process—and working its way out. The changes involved are small and graded, so they require only small flows of energy and momentum—that is, soft radiation. The other way a quark can get out of equilibrium with its cloud is if it’s jostled by quantum fluctuations of the gluon fields. If the jostling is violent, it can cause hard radiation. But because the quark’s intrinsic core color charge is small, the quark’s response to quantum fluctuations in the gluon fields tends to be limited, and thus hard radiation is rare. That’s why three jets are less likely than two.

The connection of our photographs to the profundities of quantum mechanics is even more direct, and needs no such elaborate explanation. It is simply that once more, we find that doing the same thing over and over again gives different results each time. We saw that before with the ultrastroboscopic nanomicroscope that takes pictures of protons; we’re seeing it now with the creative destruction machine that takes pictures of empty space. If the world behaved classically and predictably, the billion euros invested in LEP would have underwritten a very boring machine: every collision would just reproduce the result of the first one, and there’d be only one photograph to look at. Instead, our quantum-mechanical theories predict that many results can emerge from the same cause. And that is what we find. We can predict the relative probabilities of different results. Through many repetitions, we can check those predictions in detail. In that way, short-term unpredictability can be tamed. Short-term unpredictability is, in the end, perfectly compatible with long-term precision.