asymptoticfreedom:fromparadoxto paradigm · 2005-06-06 · asymptoticfreedom:fromparadoxto paradigm...

Asymptotic freedom: From paradox to paradigmFrank Wilczek*

A Pair of Paradoxes

In theoretical physics, paradoxes aregood. That’s paradoxical, since aparadox appears to be a contradic-tion, and contradictions imply seri-

ous error. But Nature cannot realizecontradictions. When our physical theo-ries lead to paradox we must find a wayout. Paradoxes focus our attention, andwe think harder.

When David Gross and I began thework that led to this Nobel Prize (1–3)†

in 1972, we were driven by paradoxes.In resolving the paradoxes, we were ledto discover a new dynamical principle,asymptotic freedom. This principle, inturn, has led to an expanded conceptionof fundamental particles, a new under-standing of how matter gets its mass, anew and much clearer picture of theearly universe, and new ideas about theunity of Nature’s forces. Today I’d liketo share with you the story of theseideas.

Paradox 1: Quarks Are Born Free, but Every-where They Are in Chains. The first para-dox was phenomenological.

Near the beginning of the 20th cen-tury, after pioneering experiments byRutherford, Geiger, and Marsden, phys-icists discovered that most of the massand all of the positive charge inside anatom is concentrated in a tiny centralnucleus. In 1932, Chadwick discoveredneutrons, which together with protonscould be considered as the ingredientsout of which atomic nuclei could beconstructed. But the known forces, grav-ity and electromagnetism, were insuffi-cient to bind protons and neutronstightly together into objects as small asthe observed nuclei. Physicists were con-fronted with a new force, the most pow-erful in Nature. Understanding this newforce became a major challenge in fun-damental physics.

For many years, physicists gathereddata to address that challenge, basicallyby bashing protons and neutrons to-gether and studying what came out. Theresults that emerged from these studies,however, were complicated and hard tointerpret.

What you would expect, if the parti-cles were really fundamental (indestruc-tible), would be the same particles youstarted with, coming out with just theirtrajectories changed.

Instead, the outcome of the collisionswas often many particles. The final statemight contain several copies of the orig-inals, or different particles altogether. A

plethora of new particles was discoveredin this way. Although these particles,generically called hadrons, are unstable,they otherwise behave in ways thatbroadly resemble the way protons andneutrons behave. So the character of thesubject changed. It was no longer natu-ral to think of it as simply as the studyof a new force that binds protons andneutrons into atomic nuclei. Rather, anew world of phenomena had come intoview. This world contained many unex-pected new particles that could trans-form into one another in a bewilderingvariety of ways. Reflecting this changein perspective, there was a change interminology. Instead of the nuclearforce, physicists came to speak of thestrong interaction.

In the early 1960s, Murray Gell-Mannand George Zweig made a great ad-vance in the theory of the strong inter-action by proposing the concept ofquarks. If you imagined that hadronswere not fundamental particles, butrather that they were assembled from afew more basic types, the quarks, pat-terns clicked into place. The dozens ofobserved hadrons could be understood,at least roughly, as different ways ofputting together just three kinds (‘‘f la-vors’’) of quarks. You can have a givenset of quarks in different spatial orbits,or with their spins aligned in differentways. The energy of the configurationwill depend on these things, and sothere will be a number of states withdifferent energies, giving rise to particleswith different masses, according to m �E�c2. It is analogous to the way we un-derstand the spectrum of excited statesof an atom, as arising from differentorbits and spin alignments of electrons.(For electrons in atoms, the interactionenergies are relatively small, however,and the effect of these energies on theoverall mass of the atoms is insignifi-cant.) The rules for using quarks to modelreality seemed quite weird, however.

Quarks were supposed to hardly noticeone another when they were close to-gether, but if you tried to isolate one, youfound that you could not. People lookedvery hard for individual quarks, but with-out success. Only bound states of a quarkand an antiquark—mesons—or boundstates of three quarks—baryons—areobserved. This experimental regularitywas elevated into The Principle of Con-finement. But giving it a dignified namedidn’t make it less weird.

There were other peculiar thingsabout quarks. They were supposed to

have electric charges whose magnitudesare fractions (2�3 or 1�3) of what ap-pears to be the basic unit, namely themagnitude of charge carried by an elec-tron or proton. All other observed electriccharges are known, with great accuracy,to be whole-number multiples of thisunit. Also, identical quarks did not ap-pear to obey the normal rules of quan-tum statistics. These rules would requirethat, as spin 1�2 particles, quarks shouldbe fermions, with antisymmetric wavefunctions. The pattern of observed bary-ons cannot be understood using anti-symmetric wave functions; it requiressymmetric wave functions.

The atmosphere of weirdness and pe-culiarity surrounding quarks thickenedinto paradox when J. Friedman, H. Ken-dall, R. Taylor, and their collaboratorsat the Stanford Linear Accelerator(SLAC) used energetic photons to pokeinto the inside of protons (J. Friedman,H. Kendall, and R. Taylor received theNobel Prize for this work in 1990). Theydiscovered that there are indeed entitiesthat look like quarks inside protons.Surprisingly, though, they found thatwhen quarks are hit hard they seem tomove (more accurately, to transport en-ergy and momentum) as if they werefree particles. Before the experiment,most physicists had expected that what-ever caused the strong interaction ofquarks would also cause quarks to radi-ate energy abundantly, and thus rapidlyto dissipate their motion, when they gotviolently accelerated.

At a certain level of sophistication,this association of radiation with forcesappears inevitable, and profound. In-deed, the connection between forcesand radiation is associated with someof the most glorious episodes in the his-tory of physics. In 1864, Maxwell pre-

*E-mail: [email protected].

Adapted from Les Prix Nobel, 2004. © 2004 by the NobelFoundation

Editor’s Note: This article is a version of Frank Wilczek’sNobel Lecture, ‘‘Asymptotic Freedom: From Paradox to Par-adigm.’’ The 2004 Nobel Prize in Physics was awarded to Drs.Wilczek, H. David Politzer, and David J. Gross for theirdiscovery of asymptotic freedom in the theory of the stronginteraction. The Nobel Foundation graciously has grantedus permission to reprint this article. The Nobel Lecturesprovide examples of successful approaches to major scien-tific problems. However, in recent years, these lectures haverarely been read, perhaps because of the difficulty in ob-taining the collections. By reprinting this lecture, we hopeto broaden their exposure.

†In view of the nature and scope of this write-up, its foot-noting will be light. Our major original papers (1–3) arecarefully referenced.

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dicted the existence of electromagneticradiation—including, but not limited to,ordinary light—as a consequence of hisconsistent and comprehensive formula-tion of electric and magnetic forces.Maxwell’s new radiation was subse-quently generated and detected byHertz, in 1883 (and over the 20th cen-tury its development has revolutionizedthe way we manipulate matter and com-municate with one another). Much later,in 1935, Yukawa predicted the existenceof pions based on his analysis of nuclearforces, and they were subsequently dis-covered in the late 1940s; the existencesof many other hadrons were predictedsuccessfully by using a generalizationthese ideas. (For experts: I have in mindthe many resonances that were first seenin partial wave analyses, and then laterin production.) More recently, the exis-tence of W and Z bosons, and of colorgluons, and their properties, was in-ferred before their experimental discov-ery. Those discoveries were, in 1972,still ahead of us, but they serve to con-firm, retroactively, that our concernswere worthy ones. Powerful interactionsought to be associated with powerfulradiation. When the most powerful in-teraction in nature, the strong interac-tion, did not obey this rule, it posed asharp paradox.

Paradox 2: Special Relativity and QuantumMechanics both Work. The second para-dox is more conceptual. Quantum me-chanics and special relativity are twogreat theories of 20th-century physics.Both are very successful. But these twotheories are based on entirely differentideas, which are not easy to reconcile.In particular, special relativity putsspace and time on the same footing, butquantum mechanics treats them verydifferently. This leads to a creative ten-sion, whose resolution has led to threeprevious Nobel Prizes (and ours isanother).

The first of these prizes went toP. A. M. Dirac in 1933. Imagine a parti-cle moving on average at very nearly thespeed of light, but with an uncertaintyin position, as required by quantum the-ory. Evidently, there will be some prob-ability for observing this particle tomove a little faster than average, andtherefore faster than light, which specialrelativity won’t permit. The only knownway to resolve this tension involves in-troducing the idea of antiparticles. Veryroughly speaking, the required uncer-tainty in position is accommodated byallowing for the possibility that the actof measurement can involve the creationof several particles, each indistinguish-able from the original, with differentpositions. To maintain the balance of

conserved quantum numbers, the extraparticles must be accompanied by anequal number of antiparticles. (Diracwas led to predict the existence ofantiparticles through a sequence of inge-nious interpretations and reinterpreta-tions of the elegant relativistic waveequation he invented, rather than byheuristic reasoning of the sort I’ve pre-sented. The inevitability and generalityof his conclusions, and their direct rela-tionship to basic principles of quantummechanics and special relativity, areonly clear in retrospect.)

The second and third of these prizeswere to R. Feynman, J. Schwinger, andS.-I. Tomonaga (in 1965) and to G. ’tHooft and M. Veltman (in 1999), respec-tively. The main problem that all theseauthors, in one way or another, addressedis the problem of UV divergences.

When special relativity is taken intoaccount, quantum theory must allow forfluctuations in energy over brief inter-vals of time. This is a generalization ofthe complementarity between momen-tum and position that is fundamental forordinary, nonrelativistic quantum me-chanics. Loosely speaking, energy canbe borrowed to make evanescent virtualparticles, including particle–antiparticlepairs. Each pair passes away soon afterit comes into being, but new pairs areconstantly boiling up, to establish anequilibrium distribution. In this way, thewave function of (superficially) emptyspace becomes densely populated withvirtual particles, and empty space comesto behave as a dynamical medium.

The virtual particles with very highenergy create special problems. If youcalculate how much the properties ofreal particles and their interactions arechanged by their interaction with virtualparticles, you tend to get divergent an-swers, due to the contributions fromvirtual particles of very high energy.

This problem is a direct descendant ofthe problem that triggered the introduc-tion of quantum theory in the firstplace, i.e., the ‘‘UV catastrophe’’ ofblack body radiation theory, addressedby Planck. There the problem was thathigh-energy modes of the electromag-netic field are predicted, classically, tooccur as thermal fluctuations, to suchan extent that equilibrium at any finitetemperature requires that there is aninfinite amount of energy in thesemodes. The difficulty came from thepossibility of small-amplitude fluctua-tions with rapid variations in space andtime. The element of discreteness intro-duced by quantum theory eliminates thepossibility of very small-amplitude fluc-tuations, because it imposes a lowerbound on their size. The (relatively)large-amplitude fluctuations that remain

are predicted to occur very rarely inthermal equilibrium, and cause no prob-lem. But quantum fluctuations are muchmore efficient than are thermal fluctua-tions at exciting the high-energy modes,in the form of virtual particles, and sothose modes come back to haunt us. Forexample, they give a divergent contribu-tion to the energy of empty space, theso-called zero-point energy.

Renormalization theory was devel-oped to deal with this sort of difficulty.The central observation that is exploitedin renormalization theory is that, al-though interactions with high-energyvirtual particles appear to produce di-vergent corrections, they do so in a verystructured way. That is, the same correc-tions appear over and over again in thecalculations of many different physicalprocesses. For example, in quantumelectrodynamics (QED), exactly two in-dependent divergent expressions appear,one of which occurs when we calculatethe correction to the mass of the elec-tron, the other of which occurs when wecalculate the correction to its charge. Tomake the calculation mathematicallywell defined, we must artificially excludethe highest energy modes, or dampentheir interactions, a procedure calledapplying a cutoff, or regularization. Inthe end we want to remove the cutoff,but at intermediate stages we need toleave it in, so as to have well defined(finite) mathematical expressions. If weare willing to take the mass and chargeof the electron from experiment, we canidentify the formal expressions for thesequantities, including the potentially di-vergent corrections, with their measuredvalues. Having made this identification,we can remove the cutoff. We therebyobtain well defined answers, in terms ofthe measured mass and charge, for ev-erything else of interest in QED.

Feynman, Schwinger, and Tomonogadeveloped the technique for writingdown the corrections due to interactionswith any finite number of virtual parti-cles in QED, and showed that renormal-ization theory worked in the simplestcases. (I’m being a little sloppy in myterminology; instead of saying the num-ber of virtual particles, it would be moreproper to speak of the number of inter-nal loops in a Feynman graph.) Free-man Dyson supplied a general proof.This was intricate work that requirednew mathematical techniques. ’t Hooftand Veltman showed that renormaliza-tion theory applied to a much widerclass of theories, including the sort ofspontaneously broken gauge theoriesthat had been used by Glashow, Salam,and Weinberg to construct the (now)standard model of electroweak interac-

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tions. Again, this was intricate andhighly innovative work.

This brilliant work, however, still didnot eliminate all of the difficulties. Avery profound problem was identified byLandau (4). Landau argued that virtualparticles would tend to accumulatearound a real particle as long as therewas any uncancelled influence. This iscalled screening. The only way for thisscreening process to terminate is for thesource plus its cloud of virtual particlesto cease to be of interest to additionalvirtual particles. But then, in the end,no uncancelled influence would re-main—and no interaction! Thus, all ofthe brilliant work in QED and moregeneral field theories represented, ac-cording to Landau, no more than a tem-porary fix. You could get finite resultsfor the effect of any particular numberof virtual particles, but when you triedto sum the whole thing up, to allow forthe possibility of an arbitrary number ofvirtual particles, you would get non-sense—either infinite answers, or nointeraction at all.

Landau and his school backed up thisintuition with calculations in manydifferent quantum field theories. Theyshowed, in all of the cases they calcu-lated, that screening in fact occurred,and that it doomed any straightforwardattempt to perform a complete, consis-tent calculation by adding up the contri-butions of more and more virtualparticles. We can sweep this problemunder the rug in QED or in electroweaktheory, because the answers includingonly a small finite number of virtualparticles provide an excellent fit to ex-periment, and we make a virtue of ne-cessity by stopping there. But for thestrong interaction, that pragmatic ap-proach seemed highly questionable, be-cause there is no reason to expect thatlots of virtual particles won’t come intoplay, when they interact strongly.

Landau thought that he had destroyedquantum field theory as a way of recon-ciling quantum mechanics and specialrelativity. Something would have to give.Either quantum mechanics or specialrelativity might ultimately fail, or elseessentially new methods would have tobe invented, beyond quantum field the-ory, to reconcile them. Landau was notdispleased with this conclusion, becausein practice quantum field theory had notbeen very helpful in understanding thestrong interaction, even though a lot ofeffort had been put into it. But neitherhe, nor anyone else, proposed a usefulalternative.

So we had the paradox, that combin-ing quantum mechanics and specialrelativity seemed to lead inevitably toquantum field theory; but quantum field

theory, despite substantial pragmaticsuccess, self-destructed logically due tocatastrophic screening.

Paradox Lost: Antiscreening, orAsymptotic FreedomThese paradoxes were resolved by ourdiscovery of asymptotic freedom. Wefound that some very special quantumfield theories actually have antiscreen-ing. We called this property asymptoticfreedom, for reasons that will soon beclear. Before describing the specifics ofthe theories, I’d like to indicate in arough, general way how the phenome-non of antiscreening allows us to resolveour paradoxes.

Antiscreening turns Landau’s problemon its head. In the case of screening, asource of influence—let us call itcharge, understanding that it can repre-sent something quite different fromelectric charge—induces a cancelingcloud of virtual particles. From a largecharge, at the center, you get a smallobservable influence far away. Anti-screening, or asymptotic freedom, im-plies instead that a charge of intrinsicallysmall magnitude catalyzes a cloud ofvirtual particles that enhances its power.I like to think of it as a thundercloudthat grows thicker and thicker as youmove away from the source.

Since the virtual particles themselvescarry charge, this growth is a self-reinforcing, runaway process. The situa-tion appears to be out of control. Inparticular, energy is required to build upthe thundercloud, and the required en-ergy threatens to diverge to infinity. Ifthat is the case, then the source couldnever be produced in the first place.We’ve discovered a way to avoid Landau’sdisease—by banishing the patients!

At this point our first paradox, theconfinement of quarks, makes a virtueof theoretical necessity. For it suggeststhat there are in fact sources—specifi-cally, quarks—that cannot exist on theirown. Nevertheless, Nature teaches us,these confined particles can play a roleas building blocks. If we have, nearby toa source particle, its antiparticle (forexample, quark and antiquark), then thecatastrophic growth of the antiscreeningthundercloud is no longer inevitable.For where they overlap, the cloud of thesource can be canceled by the anticloudof the antisource. Quarks and anti-quarks, bound together, can be accom-modated with finite energy, althougheither in isolation would cause an infi-nite disturbance.

Because it was closely tied to detailed,quantitative experiments, the sharpestproblem we needed to address was theparadoxical failure of quarks to radiatewhen Friedman, Kendall, and Taylor

subjected them to violent acceleration.This too can be understood from thephysics of antiscreening. According toantiscreening, the color charge of aquark, viewed up close, is small. Itbuilds up its power to drive the stronginteraction by accumulating a growingcloud at larger distances. Since thepower of its intrinsic color charge issmall, the quark is actually only looselyattached to its cloud. We can jerk itaway from its cloud, and it will—for ashort while—behave almost as if it hadno color charge, and no strong interac-tion. As the virtual particles in spacerespond to the altered situation, theyrebuild a new cloud, moving along withthe quark, but this process does not in-volve significant radiation of energy andmomentum. That, according to us, waswhy you could analyze the most salientaspects of the SLAC experiments—theinclusive cross sections, which only keeptrack of overall energy-momentumflow—as if the quarks were free parti-cles, although in fact they are stronglyinteracting and ultimately confined.

Thus, both of our paradoxes, nicelydovetailed, get resolved togetherthrough antiscreening.

The theories that we found to displayasymptotic freedom are called non-Abelian gauge theories, or Yang–Millstheories (5). They form a vast generali-zation of electrodynamics. They postu-late the existence of several differentkinds of charge, with complete symme-try among them. So instead of one en-tity, ‘‘charge,’’ we have several ‘‘colors.’’Also, instead of one photon, we have afamily of color gluons.

The color gluons themselves carrycolor charges. In this respect thenon-Abelian theories differ fromelectrodynamics, where the photon iselectrically neutral. Thus gluons innon-Abelian theories play a much moreactive role in the dynamics of these the-ories than do photons in electrodynam-ics. Indeed, it is the effect of virtualgluons that is responsible for antiscreen-ing, which does not occur in QED.

It became evident to us very early onthat one particular asymptotically freetheory was uniquely suited as a candi-date to provide the theory of the stronginteraction. On phenomenologicalgrounds, we wanted to have the possibil-ity to accommodate baryons, based onthree quarks, as well as mesons, basedon quark and antiquark. In light of thepreceding discussion, this requires thatthe color charges of three differentquarks can cancel, when you add themup. This can occur if the three colorsexhaust all possibilities; so we arrived atthe gauge group SU(3), with three col-ors and eight gluons. To be fair, several

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physicists had, with various motivations,suggested the existence of a three-valuedinternal color label for quarks years be-fore.‡ It did not require a great leap ofimagination to see how we could adaptthose ideas to our tight requirements.

By using elaborate technical machin-ery of quantum field theory (includingthe renormalization group, operatorproduct expansions, and appropriatedispersion relations), we were able to bemuch more specific and quantitativeabout the implications our theory thanmy loose pictorial language suggests. Inparticular, the strong interaction doesnot simply turn off abruptly, and thereis a nonzero probability that quarks willradiate when poked. It is only asymptot-ically, as energies involved go to infinity,that the probability for radiation van-ishes. We could calculate in great detailthe observable effects of the radiation atfinite energy, and make experimentalpredictions based on these calculations.At the time, and for several years later,the data were not accurate enough totest these particular predictions, but bythe end of the 1970s they began to lookgood, and by now they’re beautiful.

Our discovery of asymptotic freedom,and its essentially unique realization inquantum field theory, led us to a newattitude toward the problem of thestrong interaction. In place of the broadresearch programs and fragmentary in-sights that had characterized earlierwork, we now had a single, specific can-didate theory—a theory that could betested, and perhaps falsified, but couldnot be fudged. Even now, when I rereadour declaration (2)

‘‘Finally let us recall that the pro-posed theories appear to be uniquelysingled out by nature, if one takesboth the SLAC results and the renor-malization-group approach to quan-tum field theory at face value.’’

I relive the mixture of exhilaration andanxiety that I felt at the time.

A Foursome of ParadigmsOur resolution of the paradoxes thatdrove us had ramifications in unantici-pated directions, and extending far be-yond their initial scope.

Paradigm 1: The Hard Reality of Quarks andGluons. Because, to fit the facts, you hadto ascribe several bizarre properties toquarks—paradoxical dynamics, peculiarcharge, and anomalous statistics—their‘‘reality’’ was, in 1972, still very much inquestion. This despite the fact that they

were helpful in organizing the hadrons,and even though Friedman, Kendall,and Taylor had ‘‘observed’’ them! Theexperimental facts wouldn’t go away, ofcourse, but their ultimate significanceremained doubtful. Were quarks basicparticles, with simple properties thatcould be used to in formulating a pro-found theory—or just a curious inter-mediate device that would need to bereplaced by deeper conceptions?

Now we know how the story playedout, and it requires an act of imagina-tion to conceive how it might have beendifferent. But Nature is imaginative, andso are theoretical physicists, and so it’snot impossible to fantasize alternativehistories. For example, the quasiparticlesof the fractional quantum Hall effect,which are not basic but rather emerge ascollective excitations involving ordinaryelectrons, also cannot exist in isolation,and they have fractional charge andanomalous statistics! Related thingshappen in the Skyrme model, where nu-cleons emerge as collective excitationsof pions. One might have fantasized thatquarks would follow a similar script,emerging somehow as collective excita-tions of hadrons, or of more fundamen-tal preons, or of strings.

Together with the new attitude to-ward the strong interaction problem,that I just mentioned, came a new atti-tude toward quarks and gluons. Thesewords were no longer just names at-tached to empirical patterns, or to no-tional building blocks within roughphenomenological models. Quarks and(especially) gluons had become ideally

simple entities, whose properties arefully defined by mathematically precisealgorithms.

You can even see them! Here’s a pic-ture, which I’ll now explain.

Asymptotic freedom is a great boonfor experimental physics, because itleads to the beautiful phenomenon ofjets. As I remarked before, an importantpart of the atmosphere of mystery sur-rounding quarks arose from the fact thatthey could not be isolated. But if wechange our focus, to follow flows of en-ergy and momentum rather than indi-vidual hadrons, then quarks and gluonscome into view, as I’ll now explain.

There is a contrast between two dif-ferent kinds of radiation, which expressesthe essence of asymptotic freedom. Hardradiation, capable of significantly redi-recting the flow of energy and momen-tum, is rare. But soft radiation, whichproduces additional particles moving inthe same direction without deflectingthe overall f low, is common. Indeed,soft radiation is associated with thebuild-up of the clouds I discussed be-fore, as it occurs in time. Let’s considerwhat it means for experiments, say to beconcrete the sort of experiment done atthe Large Electron Positron collider(LEP) at CERN during the 1990s, andcontemplated for the International Lin-ear Collider (ILC) in the future. Atthese facilities, one studies what emergesfrom the annihilation of electrons andpositrons that collide at high energies.By well understood processes that be-long to QED or electroweak theory, theannihilation proceeds through a virtual

‡An especially clear and insightful early paper, in which adynamical role for color was proposed, is Y. Nambu (6).

Fig. 1. A photograph from the L3 collaboration, showing three jets emerging from electron–positronannihilation at high energy. These jets are the materialization of a quark, antiquark, and gluon.(Reprinted with permission of the L3 Collaboration.)


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photon or Z boson into a quark and anantiquark. Conservation and energy andmomentum dictate that the quark andantiquark will be moving at high speedin opposite directions. If there is nohard radiation, then the effect of softradiation will be to convert the quarkinto a spray of hadrons moving in acommon direction: a jet. Similarly, theantiquark becomes a jet moving in theopposite direction. The observed resultis then a 2-jet event. Occasionally(�10% of the time, at LEP) there willbe hard radiation, with the quark (orantiquark) emitting a gluon in a signifi-cantly new direction. From that point onthe same logic applies, and we have athree-jet event, like the one shown inFig. 1. The theory of the underlyingspace-time process is depicted in Fig. 2.And �1% of the time, four jets will oc-cur, and so forth. The relative probabil-ity of different numbers of jets, how itvaries with the overall energy, the rela-tive frequency of different angles atwhich the jets emerge and the total en-ergy in each—all these detailed aspectsof the ‘‘antenna pattern’’ can be pre-dicted quantitatively. These predictionsreflect the basic couplings amongquarks and gluons, which define QCD,quite directly.

The predictions agree well with verycomprehensive experimental measure-ments. So we can conclude with confi-dence that QCD is right, and that whatyou are seeing, in Fig. 1, is a quark, anantiquark, and a gluon—although, sincethe predictions are statistical, we can’tsay for sure which is which!

By exploiting the idea that hard radia-tion processes, reflecting fundamentalquark and gluon interactions, controlthe overall f low of energy and momen-tum in high-energy processes, one cananalyze and predict the behavior of

many different kinds of experiments. Inmost of these applications, including theoriginal one to deep inelastic scattering,the analysis necessary to separate outhard and soft radiation is much moreinvolved and harder to visualize than inthe case of electron-positron annihila-tion. A lot of ingenuity has gone, andcontinues to go, into this subject, knownas perturbative QCD. The results havebeen quite successful and gratifying. Fig.3 shows one aspect of the success. Manydifferent kinds of experiments, per-formed at many different energies, havebeen successfully described by QCDpredictions, each in terms of the onerelevant parameter of the theory, theoverall coupling strength. Not only must

each experiment, which may involvehundreds of independent measurements,be fit consistently, but one can thencheck whether the values of the cou-pling change with the energy scale inthe way we predicted. As you can see, itdoes. A remarkable tribute to the suc-cess of the theory, which I’ve beenamused to watch evolve, is that a lot ofthe same activity that used to be calledtesting QCD is now called calculatingbackgrounds.

As a result of all this success, a newparadigm has emerged for the operationalmeaning of the concept of a fundamentalparticle. Physicists designing and interpret-ing high-energy experiments now routinelydescribe their results in terms of produc-ing and detecting quarks and gluons: whatthey mean, of course, is the correspondingjets.

Paradigm 2: Mass Comes from Energy. Myfriend and mentor Sam Treiman liked torelate his experience of how, duringWorld War II, the U.S. Army respondedto the challenge of training a large num-ber of radio engineers starting with verydifferent levels of preparation, rangingdown to near zero. They designed acrash course for it, which Sam took. Inthe training manual, the first chapterwas devoted to Ohm’s three laws. Ohm’sfirst law is V � IR. Ohm’s second law isI � V�R. I’ll leave it to you to recon-struct Ohm’s third law.

Similarly, as a companion to Ein-stein’s famous equation E � mc2, wehave his second law, m � E�c2. Here, of

Fig. 3. Many quite different experiments, performed at different energies, have been successfullyanalyzed by using QCD. Each fits a large quantity of data to a single parameter, the strong coupling �s. Bycomparing the values they report, we obtain direct confirmation that the coupling evolves as predicted.(Figure courtesy S. Bethke, ref. 8.)

Fig. 2. These Feynman graphs are schematic representations of the fundamental processes in electron–positron annihilation, as they take place in space and time. They show the origin of two-jet and three-jetevents.


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course, E denotes the energy of a bodyat rest, and m its mass.

All this isn’t quite as silly as it mayseem, because different forms of thesame equation can suggest very differentthings. The usual way of writing theequation, E � mc2, suggests the possibil-ity of obtaining large amounts of energyby converting small amounts of mass. Itbrings to mind the possibilities of nu-clear reactors, or bombs. Stated as m �E�c2, Einstein’s law suggests the possi-bility of explaining mass in terms of en-ergy. That is a good thing to do, be-cause in modern physics energy is amore basic concept than mass. Actually,Einstein’s original paper does not con-tain the equation E � mc2, but ratherm � E�c2. In fact, the title is a question:‘‘Does the Inertia of a Body DependUpon its Energy Content?’’ From thebeginning, Einstein was thinking aboutthe origin of mass, not about makingbombs.

Modern QCD answers Einstein’squestion with a resounding ‘‘Yes!’’ In-deed, the mass of ordinary matter de-rives almost entirely from energy—theenergy of massless gluons and nearlymassless quarks, which are the ingredi-ents from which protons, neutrons, andatomic nuclei are made.

The runaway build-up of antiscreen-ing clouds, which I described before,cannot continue indefinitely. The result-ing color fields would carry infinite en-ergy, which is not available. The colorcharge that threatens to induce this run-away must be cancelled. The colorcharge of a quark can be cancelled ei-ther with an antiquark of the oppositecolor (making a meson), or with twoquarks of the complementary colors(making a baryon). In either case, per-fect cancellation would occur only if theparticles doing the canceling were lo-cated right on top of the originalquark—then there would be no uncan-celled source of color charge anywherein space, and hence no color field.Quantum mechanics does not permitthis perfect cancellation, however. Thequarks and antiquarks are described bywave functions, and spatial gradients inthese wave function cost energy, and sothere is a high price to pay for localizingthe wave function within a small regionof space. Thus, in seeking to minimizethe energy, there are two conflictingconsiderations: to minimize the fieldenergy, you want to cancel the sourcesaccurately; but to minimize the wave-function localization energy, you want tokeep the sources fuzzy. The stable con-figurations will be based on differentways of compromising between thesetwo considerations. In each such config-uration, there will be both field energy

and localization energy. This gives riseto mass, according to m � E�c2, even ifthe gluons and quarks started out with-out any nonzero mass of their own. Sothe different stable compromises will beassociated with particles that we canobserve, with different masses; andmetastable compromises will be associ-ated with observable particles that havefinite lifetimes.

To determine the stable compromisesconcretely, and so to predict the massesof mesons and baryons, is hard work. Itrequires difficult calculations that con-tinue to push the frontiers of massivelyparallel processing. I find it quite ironicthat, if we want to compute the mass ofa proton, we need to deploy somethinglike 1030 protons and neutrons, doingtrillions of multiplications per second,working for months, to do what oneproton does in 10�24 seconds, namelyfigure out its mass. Maybe it qualifies asa paradox. At the least, it suggests thatthere may be much more efficient waysto calculate than the ones we’re using.

In any case, the results that emergefrom these calculations are very gratifying.They are displayed in Fig. 4. The ob-served masses of prominent mesons andbaryons are reproduced quite well, statingfrom an extremely tight and rigid theory.Now is the time to notice also that one ofthe data points in Fig. 3, the one labeled‘‘Lattice,’’ is of a quite different characterfrom the others. It is based not on theperturbative physics of hard radiation, butrather on the comparison of a direct inte-gration of the full equations of QCD withexperiment, using the techniques of latticegauge theory.

The success of these calculations rep-resents the ultimate triumph over ourtwo paradoxes:

Y The calculated spectrum does notcontain anything with the charges orother quantum numbers of quarks;nor of course does it contain masslessgluons. The observed particles do notmap in a straightforward way to theprimary fields from which they ulti-mately arise.

Y Lattice discretization of the quantumfield theory provides a cutoff proce-dure that is independent of any ex-pansion in the number of virtualparticle loops. The renormalizationprocedure must be, and is, carried outwithout reference to perturbation the-ory, as one takes the lattice spacing tozero. Asymptotic freedom is crucialfor this, as I discussed—it saves usfrom Landau’s catastrophe.

By fitting some fine details of the pat-tern of masses, one can get an estimateof what the quark masses are and howmuch their masses are contributing tothe mass of the proton and neutron. Itturns out that what I call QCD Lite—the version in which you put the u and dquark masses to zero, and ignore theother quarks entirely—provides a re-markably good approximation to reality.Since QCD Lite is a theory whose basicbuilding blocks have zero mass, this re-sult quantifies and makes precise theidea that most of the mass of ordinarymatter—90% or more—arises from pureenergy, via m � E�c2.

The calculations make beautiful im-ages, if we work to put them in eye-friendly form. Derek Leinweber hasdone made some striking animations ofQCD fields as they fluctuate in emptyspace. Fig. 5 is a snapshot from one ofhis animations. Fig. 6 from Greg Kilcup,displays the (average) color fields, over

Fig. 4. Comparison of observed hadron masses to the energy spectrum predicted by QCD, upon directnumerical integration of the equations, exploiting immense computer power. The small remainingdiscrepancies are consistent with what is expected given the approximations that were necessary to makethe calculation practical. (Figure reprinted with permission from the Center for Computational Physics,University of Tsukuba, Tsukuba, Japan.)


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and above the fluctuations, that are as-sociated with a very simple hadron, thepion, moving through space–time. Inser-tion of a quark–antiquark pair, which wesubsequently remove, produces this dis-turbance in the fields.

These pictures make it clear and tan-gible that the quantum vacuum is a dy-namic medium, whose properties andresponses largely determine the behav-ior of matter. In quantum mechanics,energies are associated with frequencies,according to the Planck relation E � h�.The masses of hadrons, then, areuniquely associated to tones emitted bythe dynamic medium of space when itdisturbed in various ways, according to

� � mc2�h. [1]

We thereby discover, in the reality ofmasses, an algorithmic, precise Music ofthe Void. It is a modern embodimentof the ancients’ elusive, mystical ‘‘Musicof the Spheres.’’

Paradigm 3: The Early Universe Was Simple.In 1972, the early universe seemed hope-lessly opaque. In conditions of ultra-hightemperatures, as occurred close to the BigBang singularity, one would have lots ofhadrons and antihadrons, each one anextended entity that interacts stronglyand in complicated ways with its neigh-bors. They’d start to overlap with oneanother, and thereby produce a theoreti-cally intractable mess.

But asymptotic freedom renders ultra-high temperatures friendly to theorists.It says that if we switch from a descrip-

tion based on hadrons to a descriptionbased on quark and gluon variables, andfocus on quantities that, like total en-ergy, are not sensitive to soft radiation,then the treatment of the strong interac-tion, which was the great difficulty, be-comes simple. We can calculate to afirst approximate by pretending that thequarks, antiquarks and gluons behave asfree particles, then add in the effects ofrare hard interactions. This makes itquite practical to formulate a precise

description of the properties of ultra-high temperature matter that are rele-vant to cosmology. We can even, overan extremely limited volume of spaceand time, reproduce Big Bang condi-tions in terrestrial laboratories. Whenheavy ions are caused to collide at highenergy, they produce a fireball thatbriefly attains temperatures as high as200 MeV. ‘‘Simple’’ may not be theword that occurs to you in describingthe explosive outcome of this event, asdisplayed in Fig. 7, but in fact, detailedstudy does permit us to reconstruct as-pects of the initial fireball, and to checkthat it was a plasma of quarks andgluons.

Paradigm 4: Symmetry Rules. Over thecourse of the 20th century, symmetryhas been immensely fruitful as a sourceof insight into Nature’s basic operatingprinciples. QCD, in particular, is con-structed as the unique embodiment of ahuge symmetry group, local SU(3) colorgauge symmetry (working together withspecial relativity, in the context of quan-tum field theory). As we try to discovernew laws, that improve on what weknow, it seems good strategy to con-tinue to use symmetry as our guide.This strategy has led physicists to sev-eral compelling suggestions, which I’msure you’ll be hearing more about infuture years! QCD plays an importantrole in all of them—either directly, astheir inspiration, or as an essential toolin devising strategies for experimentalexploration.

I will discuss one of these suggestions

Fig. 6. The calculated net distribution of field energy caused by injecting and removing a quark–antiquark pair. By calculating the energy in these fields and the energy in analogous fields produced byother disturbances, we predict the masses of hadrons. In a profound sense, these fields are the hadrons.(Figure courtesy of G. Kilcup.)

Fig. 5. A snapshot of spontaneous quantum fluctuations in the gluon fields. For experts: what is shownis the topological charge density in a typical contribution to the functional integral, with high-frequencymodes filtered out. (Image courtesy of Derek B. Leinweber, CSSM, University of Adelaide, Adelaide,Australia; www.physics.adelaide.edu.au�theory�staff�leinweber�VisualQCD�Nobel.)


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schematically, and mention three otherstelegraphically.Unified field theories. Both QCD and thestandard electroweak standard modelare founded on gauge symmetries. Thiscombination of theories gives a wonder-fully economical and powerful accountof an astonishing range of phenomena.Just because it is so concrete and sosuccessful, this rendering of Nature canand should be closely scrutinized for itsaesthetic f laws and possibilities. Indeed,the structure of the gauge system givespowerful suggestions for its furtherfruitful development. Its product struc-ture SU(3) � SU(2) � U(1), the reduc-ibility of the fermion representation(that is, the fact that the symmetry doesnot make connections linking all of thefermions), and the peculiar values of thequantum number hypercharge assignedto the known particles all suggest thedesirability of a larger symmetry.

The devil is in the details, and it isnot at all automatic that the superfi-cially complex and messy observed pat-tern of matter will fit neatly into a sim-ple mathematical structure. But, to aremarkable extent, it does.

Most of what we know about thestrong, electromagnetic, and weak interac-tions is summarized (rather schemati-cally!) in Fig. 8. QCD connects particleshorizontally in groups of three [SU(3)],the weak interaction connects particlesvertically in groups of two [SU(2)], in thehorizontal direction and hypercharge[U(1)] senses the little subscript numbers.Neither the different interactions nor thedifferent particles are unified. There are

three different interaction symmetries,and five disconnected sets of particles(actually 15 sets, taking into account thethreefold repetition of families).

We can do much better by havingmore symmetry, implemented by addi-tional gluons that also change stronginto weak colors. Then everything clicksinto place quite beautifully, as displayedin Fig. 9.

There seems to be a problem, how-ever. The different interactions, as ob-served, do not have the same overallstrength, as would be required by the

extended symmetry. Fortunately, asymp-totic freedom informs us that the ob-served interaction strengths at a largedistance can be different from the basicstrengths of the seed couplings viewedat short distance. To see whether thebasic theory might have the full symme-try, we have to look inside the clouds ofvirtual particles, and to track the evolu-tion of the couplings. We can do this byusing the same sort of calculations thatunderlie Fig. 3, extended to include theelectroweak interactions, and extrapo-lated to much shorter distances (orequivalently, larger energy scales). It isconvenient to display inverse couplingsand work on a logarthmic scale, for thenthe evolution is (approximately) linear.When we do the calculation using onlythe virtual particles for which we haveconvincing evidence, we find that thecouplings do approach each other in apromising way, although ultimately theydon’t quite meet. This is shown in Fig.10 Upper.

Interpreting things optimistically, wemight surmise from this near-successthat the general idea of unification is onthe right track, as is our continued reli-ance on quantum field theory to calcu-late the evolution of couplings. After all,it is hardly shocking that extrapolationof the equations for evolution of thecouplings beyond their observationalfoundation by many orders of magni-tude is missing some quantitatively sig-nificant ingredient. In a moment I’llmention an attractive hypothesis forwhat’s missing.

A very general consequence of thisline of thought is that an enormouslylarge energy scale, of order 1015 GeV ormore, emerges naturally as the scale ofunification. This is a profound and wel-come result. It is profound, because thelarge energy scale—which is far beyondany energy we can access directly—emerges from careful consideration ofexperimental realities at energies morethan 10 orders of magnitude smaller!The underlying logic that gives us thisleverage is a synergy of unification andasymptotic freedom, as follows. If evolu-tion of couplings is to be responsible fortheir observed gross inequality then,since this evolution is only logarithmicin energy, it must act over a very widerange.

The emergence of a large mass scalefor unification is welcome, first, becausemany effects we might expect to be as-sociated with unification are observed tobe highly suppressed. Symmetries thatunify SU(3) � SU(2) � U(1) will almostinevitably involve wide possibilities fortransformation among quarks, leptons,and their antiparticles. These extendedpossibilities of transformation, mediated

Fig. 7. A picture of particle tracks emerging from the collision of two gold ions at high energy. The resultingfireball and its subsequent expansion recreate, on a small scale and briefly, physical conditions that lastoccurred during the Big Bang. (Figure courtesy of Brookhaven National Laboratory–Star Collaboration.)

Fig. 8. A schematic representation of the symme-try structure of the standard model. There arethree independent symmetry transformations, un-der which the known fermions fall into five inde-pendent units (or fifteen, after threefold familyrepetition). The color gauge group SU(3) of QCDacts horizontally, the weak interaction gaugegroup SU(2) acts vertically, and the hyperchargeU(1) acts with the relative strengths indicated bythe subscripts. Right-handed neutrinos do not par-ticipate in any of these symmetries.


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by the corresponding gauge bosons, un-dermine conservation laws includinglepton and baryon number conservation.Violation of lepton number is closelyassociated with neutrino oscillations.Violation of baryon number is closelyassociated with proton instability. Inrecent years, neutrino oscillations havebeen observed; they correspond to mi-niscule neutrino masses, indicating avery feeble violation of lepton number.Proton instability has not yet been ob-served, despite heroic efforts to do so.To keep these processes sufficientlysmall, so as to be consistent with obser-vation, a high scale for unification,which suppresses the occurrence of thetransformative gauge bosons as virtualparticles, is most welcome. In fact, theunification scale we infer from the evo-lution of couplings is broadly consistentwith the observed value of neutrinomasses and encourages further vigorouspursuit of the quest to observe proton

decay. The emergence of a large massscale for unification is welcome, sec-ondly, because it opens up possibilitiesfor making quantitative connections tothe remaining fundamental interactionin Nature: gravity. It is notorious thatgravity is absurdly feebler than the otherinteractions, when they are comparedacting between fundamental particles ataccessible energies. The gravitationalforce between proton and electron, atany macroscopic distance, is aboutGmemp�e2 � 10�40 of the electric force.On the face of it, this fact poses a se-vere challenge to the idea that theseforces are different manifestations of acommon source—and an even more se-vere challenge to the idea that gravity,because of its deep connection tospace–time dynamics, is the primaryforce.

By extending our consideration of theevolution of couplings to include gravity,we can begin to meet these challenges.

Y Whereas the evolution of gauge the-ory couplings with energy is a subtlequantum-mechanical effect, the gravi-tational coupling evolves even classi-cally, and much more rapidly. Forgravity responds directly to energymomentum, and so it appears stron-

ger when viewed with high-energyprobes. In moving from the small en-ergies where we ordinarily measure tounification energy scales, the ratioGE2�� ascends to values that are nolonger absurdly small.

Y If gravity is the primary force, andspecial relativity and quantum me-chanics frame the discussion, thenPlanck’s system of physical units,based on Newton’s constant G, thespeed of light c, and Planck’s quan-tum of action h, is privileged. Dimen-sional analysis then suggests that thevalue of naturally defined quantities,measured in these units, should be oforder unity. But when we measure theproton mass in Planck units, we dis-cover mp � 10�18�hc�G. On this hy-pothesis, it makes no sense to ask‘‘Why is gravity so feeble?’’ Gravity,as the primary force, just is what it is.The right question is the one we con-front here: ‘‘Why is the proton solight?’’ Given our new, profound un-derstanding of the origin of the pro-ton’s mass, which I’ve sketched foryou today, we can formulate a tenta-tive answer. The proton’s mass is setby the scale at which the strong cou-pling, evolved down from its primaryvalue at the Planck energy, comes to

Fig. 9. The hypothetical enlarged symmetrySO(10) [unification based on SO(10) symmetry wasfirst outlined in ref. 7] accommodates all of thesymmetries of the standard model, and more, intoa unified mathematical structure. The fermions,including a right-handed neutrino that plays animportant role in understanding observed neu-trino phenomena, now form an irreducible unit(neglecting family repetition). The allowed colorcharges, both strong and weak, form a perfectmatch to what is observed. The phenomenologi-cally required hypercharges, which appear so pe-culiar in the standard model, are now theoreticallydetermined by the color and weak charges, accord-ing to the formula displayed.

Fig. 10. We can test the hypothesis that the disparate coupling strengths of the different gaugeinteractions derive a common value at short distances by doing calculations to take into account the effectof virtual particle clouds (9). These are the same sort of calculations that go into Fig. 3, but extrapolatedto much higher energies, or equivalently shorter distances. (Upper) Extrapolated by using known virtualparticles. (Lower) Including also the virtual particles required by low-energy supersymmetry (10).


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be of order unity. It is then that itbecomes worthwhile to cancel off thegrowing color fields of quarks, ab-sorbing the cost of quantum localiza-tion energy. In this way, we find,quantitatively, that the tiny value ofthe proton mass in Planck units arisesfrom the fact that the basic unit ofcolor coupling strength, g2, is of order1�2 at the Planck scale! Thus, dimen-sional reasoning is no longer mocked.The apparent feebleness of gravityresults from our partiality toward theperspective supplied by matter madefrom protons and neutrons.

Supersymmetry. As I mentioned a momentago, the approach of couplings to a uni-fied value is suggested, but not accuratelyrealized, if we infer their evolution by in-cluding the effect of known virtual parti-cles. There is one particular proposal toexpand the world of virtual particles,which is well motivated on several inde-pendent grounds. It is known as low-energy supersymmetry.§ As the namesuggests, supersymmetry involves expand-ing the symmetry of the basic equations ofphysics. This proposed expansion of sym-metry goes in a different direction fromthe enlargement of gauge symmetry. Su-persymmetry makes transformations be-tween particles having the same colorcharges and different spins, whereas ex-panded gauge symmetry changes the colorcharges while leaving spin untouched. Su-persymmetry expands the space–timesymmetry of special relativity.

To implement low-energy supersym-metry, we must postulate the existenceof a whole new world of heavy particles,none of which has yet been observeddirectly. There is, however, a most in-triguing indirect hint that this idea maybe on the right track: If we include theparticles needed for low-energy super-symmetry, in their virtual form, in thecalculation of how couplings evolve withenergy, then accurate unification isachieved! This is shown in Fig. 10Lower.

By ascending a tower of speculation,involving now both extended gauge sym-metry and extended space-time symmetry,we seem to break although the clouds,into clarity and breathtaking vision. Is itan illusion, or reality? This question cre-ates a most exciting situation for theLarge Hadron Collider (LHC), due tobegin operating at CERN in 2007, for thisgreat accelerator will achieve the energiesnecessary to access the new world ofheavy particles, if it exists. How the storywill play out, only time will tell. But inany case, I think it is fair to say that the

pursuit of unified field theories, which inpast (and many present) incarnations hasbeen vague and not fruitful of testableconsequences, has in the circle of ideasI’ve been describing here attained entirelynew levels of concreteness and fecundity.Axions.¶ As I have emphasized repeat-edly, QCD is in a profound and literalsense constructed as the embodiment ofsymmetry. There is an almost perfectmatch between the observed propertiesof quarks and gluons and the most gen-eral properties allowed by color gaugesymmetry, in the framework of specialrelativity and quantum mechanics. Theexception is that the established symme-tries of QCD fail to forbid one sort ofbehavior that is not observed to occur.The established symmetries permit asort of interaction among gluons—theso-called � term—that violates the in-variance of the equations of QCD undera change in the direction of time. Ex-periments provide extremely severe lim-its on the strength of this interaction,much more severe than might be ex-pected to arise accidentally.

By postulating a new symmetry, wecan explain the absence of the undesiredinteraction. The required symmetry iscalled Peccei–Quinn symmetry after thephysicists who first proposed it. If it ispresent, this symmetry has remarkableconsequences. It leads us to predict theexistence of new very light, very weaklyinteracting particles, axions. (I namedthem after a laundry detergent, sincethey clean up a problem with an axialcurrent.) In principle, axions might beobserved in a variety of ways, althoughnone is easy. They have interesting im-plications for cosmology, and they are aleading candidate to provide cosmologi-cal dark matter.In search of symmetry lost.� It has been al-most four decades since our current,wonderfully successful theory of theelectroweak interaction was formulated.Central to that theory is the concept ofspontaneously broken gauge symmetry.According to this concept, the funda-mental equations of physics have moresymmetry than the actual physical worlddoes. Although its specific use in elec-troweak theory involves exotic hypothet-ical substances and some sophisticatedmathematics, the underlying theme ofbroken symmetry is quite old. It goesback at least to the dawn of modernphysics, when Newton postulated thatthe basic laws of mechanics exhibit fullsymmetry in three dimensions of spacedespite the fact that everyday experi-

ence clearly distinguishes ‘‘up anddown’’ from ‘‘sideways’’ directions in ourlocal environment. Newton, of course,traced this asymmetry to the influenceof Earth’s gravity. In the framework ofelectroweak theory, modern physicistssimilarly postulate that the physicalworld is described by a solution whereinall space, throughout the currently ob-served Universe, is permeated by one ormore (quantum) fields that spoil the fullsymmetry of the primary equations.

Fortunately, this hypothesis, whichmight at first hearing sound quite ex-travagant, has testable implications. Thesymmetry-breaking fields, when suitablyexcited, must bring forth characteristicparticles: their quanta. Using the mosteconomical implementation of the re-quired symmetry breaking, one predictsthe existence of a remarkable new parti-cle, the so-called Higgs particle. Moreambitious speculations suggest that thereshould be not just a single Higgs parti-cle, but rather a complex of related par-ticles. Low-energy supersymmetry, forexample, requires at least five Higgsparticles.

Elucidation of the Higgs complex willbe another major task for the LHC. Inplanning this endeavor, QCD and as-ymptotic freedom play a vital supportingrole. The strong interaction will be re-sponsible for most of what occurs in col-lisions at the LHC. To discern the neweffects, which will be manifest only in asmall proportion of the events, we mustunderstand the dominant backgroundsvery well. Also, the production and de-cay of the Higgs particles themselvesusually involves quarks and gluons. Toanticipate their signatures, and eventu-ally to interpret the observations, wemust use our understanding of how pro-tons—the projectiles at LHC—are as-sembled from quarks and gluons, andhow quarks and gluons show themselvesas jets.

The Greatest LessonEvidently asymptotic freedom, besidesresolving the paradoxes that originallyconcerned us, provides a conceptual foun-dation for several major insights into Na-ture’s fundamental workings, and a versa-tile instrument for further investigation.

The greatest lesson, however, is amoral and philosophical one. It is trulyawesome to discover, by example, thatwe humans can come to comprehendNature’s deepest principles, even whenthey are hidden in remote and alienrealms. Our minds were not created forthis task, nor were appropriate toolsready at hand. Understanding wasachieved through a vast internationaleffort involving thousands of peopleworking hard for decades, competing in§A standard review is H. P. Nilles (11).

¶A standard review is J. Kim (12). I also recommend F.Wilczek (13).

�I treat this topic more amply in ref. 14.


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the small but cooperating in the large,abiding by rules of openness and hon-esty. Using these methods—which donot come to us effortlessly, but requirenurture and vigilance—we can accom-plish wonders.

Thanks. Before concluding I’d like to distrib-ute thanks.

First, I’d like to thank my parents, whocared for my human needs and encouragedmy curiosity from the beginning. They werechildren of immigrants from Poland and It-aly, and grew up in difficult circumstancesduring the Great Depression, but managed toemerge as generous souls with an inspiringadmiration for science and learning. I’d liketo thank the people of New York, for sup-porting a public school system that served meextremely well. I also got a superb under-graduate education at the University of Chi-cago. In this connection, I’d especially like tomention the inspiring influence of PeterFreund, whose tremendous enthusiasm andclarity in teaching a course on group theoryin physics was a major influence in nudgingme from pure mathematics toward physics.

Next I’d like to thank the people aroundPrinceton who contributed in crucial ways tothe circumstances that made my developmentand major work in the 1970s possible. On thepersonal side, this includes especially my wifeBetsy Devine. I don’t think it’s any coinci-dence that the beginning of my scientificmaturity, and a special surge of energy, hap-pened at the same time as I was falling in

love with her. Also Robert Shrock and BillCaswell, my fellow graduate students, fromwhom I learned a lot, and who made our ex-tremely intense lifestyle seem natural andeven fun. On the scientific side, I must ofcourse thank David Gross above all. Heswept me up in his drive to know and to cal-culate, and through both his generous guid-ance and his personal example started andinspired my whole career in physics. The en-vironment for theoretical physics in Princetonin the 1970s was superb. There was an atmo-sphere of passion for understanding, intellec-tual toughness, and inner confidence whosecreation was a great achievement. MurphGoldberger, Sam Treiman, and Curt Callanespecially deserve enormous credit for this.Also Sidney Coleman, who was visitingPrinceton at the time, was very actively inter-ested in our work. Such interest from a physi-cist I regarded as uniquely brilliant wasinspiring in itself; Sidney also asked manychallenging specific questions that helped uscome to grips with our results as they devel-oped. Ken Wilson had visited and lectured alittle earlier, and his renormalization groupideas were reverberating in our heads.

Fundamental understanding of the stronginteraction was the outcome of decades ofresearch involving thousands of talented peo-ple. I’d like to thank my fellow physicistsmore generally. My theoretical efforts havebeen inspired by, and of course informed by,the ingenious persistence of my experimentalcolleagues. Thanks, and congratulations, toall. Beyond that generic thanks I’d like tomention specifically a trio of physicists whose

work was particularly important in leadingto ours, and who have not (yet?) received aNobel Prize for it. These are YoichiroNambu, Stephen Adler, and James Bjorken.Those heroes advanced the cause of trying tounderstand hadronic physics by taking theconcepts of quantum field theory seriously,and embodying them in specific mechanisticmodels, when doing so was difficult and un-fashionable. I’d like to thank Murray Gell-Mann and Gerard ’t Hooft for not quiteinventing everything, and so leaving us some-thing to do. And finally I’d like to thankMother Nature for her extraordinarily goodtaste, which gave us such a beautiful andpowerful theory to discover.

This work is supported in part by fundsprovided by the U.S. Department of Energyunder cooperative research agreement DE-FC02-94ER40818.

A Note to Historians. I have not, here, givenan extensive account of my personal experi-ences in discovery. In general, I don’t believethat such accounts, composed well after thefact, are reliable as history. I urge historiansof science instead to focus on the contempo-rary documents, and especially the originalpapers, which by definition accurately reflectthe understanding that the authors had at thetime, as they could best articulate it. Fromthis literature, it is I think not difficult toidentify where the watershed changes in atti-tude I mentioned earlier occurred, and wherethe outstanding paradoxes of strong interac-tion physics and quantum field theory wereresolved into modern paradigms for our un-derstanding of Nature.

1. Gross, D. & Wilczek, F. (1973) Phys. Rev. Lett. 30,1343–1346.

2. Gross, D. & Wilczek, F. (1973) Phys. Rev. D 8,3633–3652.

3. Gross, D. & Wilczek, F. (1974) Phys. Rev. D 9,980–993.

4. Landau, L. (1955) in Niels Bohr and the Develop-ment of Physics, ed. Pauli, W. (McGraw-Hill, NewYork), pp. 52–69.

5. Yang, C.-N. & Mills, R. (1954) Phys. Rev. 96,191–195.

6. Nambu, Y. (1966) in Preludes in Theoretical Phys-ics, eds. De-Shalit, A., Feshbach, H. & van Hove,L. (North-Holland, Amsterdam), pp. 133–142.

7. Georgi, H. (1975) in Particles and Fields 1974, ed.Carlson, C. (AIP, New York), pp. 575–582.

8. Bethke, S. (2000) J. Phys. G 26, R27; hep-ex�0004021.

9. Georgi, H., Quinn, H. R. & Weinberg, S. (1974)Phys. Rev. Lett. 33, 451–454.

10. Dimopoulos, S., Raby, S. & Wilczek, F. (1981)Phys. Rev. D 24, 1681–1683.

11. Nilles, H. P. (1984) Phys. Rep. 110, 1–162.12. Kim, J. (1987) Phys. Rep. 150, 1–177.13. Wilczek, F. (2004) http:��arxiv.org�abs�hep-ph�

0408167.14. Wilczek, F. (2005) Nature 433, 239–247.


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asymptoticfreedom:fromparadoxto paradigm · 2005-06-06 · asymptoticfreedom:fromparadoxto paradigm...

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