PERSPECTIVE Asymptotic freedom: From paradox to paradigm Frank Wilczek* A Pair of Paradoxes plethora of new particles was discovered have electric charges whose magnitudes n theoretical physics, paradoxes are in this way. Although these particles, are fractions (2͞3or1͞3) of what ap- good. That’s paradoxical, since a generically called hadrons, are unstable, pears to be the basic unit, namely the paradox appears to be a contradic- they otherwise behave in ways that magnitude of charge carried by an elec- tion, and contradictions imply seri- broadly resemble the way protons and tron or proton. All other observed electric Ious error. But Nature cannot realize neutrons behave. So the character of the charges are known, with great accuracy, contradictions. When our physical theo- subject changed. It was no longer natu- to be whole-number multiples of this ries lead to paradox we must find a way ral to think of it as simply as the study unit. Also, identical quarks did not ap- out. Paradoxes focus our attention, and of a new force that binds protons and pear to obey the normal rules of quan- we think harder. neutrons into atomic nuclei. Rather, a tum statistics. These rules would require When David Gross and I began the new world of phenomena had come into that, as spin 1͞2 particles, quarks should work that led to this Nobel Prize (1–3)† view. This world contained many unex- be fermions, with antisymmetric wave in 1972, we were driven by paradoxes. pected new particles that could trans- functions. The pattern of observed bary- In resolving the paradoxes, we were led form into one another in a bewildering ons cannot be understood using anti- to discover a new dynamical principle, variety of ways. Reflecting this change symmetric wave functions; it requires asymptotic freedom. This principle, in in perspective, there was a change in symmetric wave functions. turn, has led to an expanded conception terminology. Instead of the nuclear The atmosphere of weirdness and pe- of fundamental particles, a new under- force, physicists came to speak of the culiarity surrounding quarks thickened standing of how matter gets its mass, a strong interaction. into paradox when J. Friedman, H. Ken- new and much clearer picture of the In the early 1960s, Murray Gell-Mann dall, R. Taylor, and their collaborators early universe, and new ideas about the and George Zweig made a great ad- at the Stanford Linear Accelerator unity of Nature’s forces. Today I’d like vance in the theory of the strong inter- (SLAC) used energetic photons to poke to share with you the story of these action by proposing the concept of into the inside of protons (J. Friedman, ideas. quarks. If you imagined that hadrons H. Kendall, and R. Taylor received the were not fundamental particles, but Nobel Prize for this work in 1990). They Paradox 1: Quarks Are Born Free, but Every- rather that they were assembled from a discovered that there are indeed entities where They Are in Chains. The first para- few more basic types, the quarks, pat- that look like quarks inside protons. dox was phenomenological. terns clicked into place. The dozens of Surprisingly, though, they found that Near the beginning of the 20th cen- observed hadrons could be understood, when quarks are hit hard they seem to tury, after pioneering experiments by at least roughly, as different ways of move (more accurately, to transport en- Rutherford, Geiger, and Marsden, phys- putting together just three kinds (‘‘fla- ergy and momentum) as if they were icists discovered that most of the mass vors’’) of quarks. You can have a given free particles. Before the experiment, and all of the positive charge inside an set of quarks in different spatial orbits, most physicists had expected that what- atom is concentrated in a tiny central or with their spins aligned in different ever caused the strong interaction of nucleus. In 1932, Chadwick discovered ways. The energy of the configuration quarks would also cause quarks to radi- neutrons, which together with protons will depend on these things, and so could be considered as the ingredients there will be a number of states with ate energy abundantly, and thus rapidly out of which atomic nuclei could be different energies, giving rise to particles to dissipate their motion, when they got constructed. But the known forces, grav- with different masses, according to m ϭ violently accelerated. ity and electromagnetism, were insuffi- E͞c2. It is analogous to the way we un- At a certain level of sophistication, cient to bind protons and neutrons derstand the spectrum of excited states this association of radiation with forces tightly together into objects as small as of an atom, as arising from different appears inevitable, and profound. In- the observed nuclei. Physicists were con- orbits and spin alignments of electrons. deed, the connection between forces fronted with a new force, the most pow- (For electrons in atoms, the interaction and radiation is associated with some erful in Nature. Understanding this new energies are relatively small, however, of the most glorious episodes in the his- force became a major challenge in fun- and the effect of these energies on the tory of physics. In 1864, Maxwell pre- damental physics. overall mass of the atoms is insignifi- For many years, physicists gathered cant.) The rules for using quarks to model data to address that challenge, basically reality seemed quite weird, however. *E-mail: [email protected]. by bashing protons and neutrons to- Quarks were supposed to hardly notice Adapted from Les Prix Nobel, 2004. © 2004 by the Nobel Foundation gether and studying what came out. The one another when they were close to- Editor’s Note: This article is a version of Frank Wilczek’s results that emerged from these studies, gether, but if you tried to isolate one, you Nobel Lecture, ‘‘Asymptotic Freedom: From Paradox to Par- however, were complicated and hard to found that you could not. People looked adigm.’’ The 2004 Nobel Prize in Physics was awarded to Drs. interpret. very hard for individual quarks, but with- Wilczek, H. David Politzer, and David J. Gross for their What you would expect, if the parti- out success. Only bound states of a quark discovery of asymptotic freedom in the theory of the strong interaction. The Nobel Foundation graciously has granted cles were really fundamental (indestruc- and an antiquark—mesons—or bound us permission to reprint this article. The Nobel Lectures tible), would be the same particles you states of three quarks—baryons—are provide examples of successful approaches to major scien- started with, coming out with just their observed. This experimental regularity tific problems. However, in recent years, these lectures have trajectories changed. was elevated into The Principle of Con- rarely been read, perhaps because of the difficulty in ob- taining the collections. By reprinting this lecture, we hope Instead, the outcome of the collisions finement. But giving it a dignified name to broaden their exposure. was often many particles. The final state didn’t make it less weird. †In view of the nature and scope of this write-up, its foot- might contain several copies of the orig- There were other peculiar things noting will be light. Our major original papers (1–3) are inals, or different particles altogether. A about quarks. They were supposed to carefully referenced. www.pnas.org͞cgi͞doi͞10.1073͞pnas.0501642102 PNAS ͉ June 14, 2005 ͉ vol. 102 ͉ no. 24 ͉ 8403–8413 Downloaded by guest on September 23, 2021 dicted the existence of electromagnetic conserved quantum numbers, the extra are predicted to occur very rarely in radiation—including, but not limited to, particles must be accompanied by an thermal equilibrium, and cause no prob- ordinary light—as a consequence of his equal number of antiparticles. (Dirac lem. But quantum fluctuations are much consistent and comprehensive formula- was led to predict the existence of more efficient than are thermal fluctua- tion of electric and magnetic forces. antiparticles through a sequence of inge- tions at exciting the high-energy modes, Maxwell’s new radiation was subse- nious interpretations and reinterpreta- in the form of virtual particles, and so quently generated and detected by tions of the elegant relativistic wave those modes come back to haunt us. For Hertz, in 1883 (and over the 20th cen- equation he invented, rather than by example, they give a divergent contribu- tury its development has revolutionized heuristic reasoning of the sort I’ve pre- tion to the energy of empty space, the the way we manipulate matter and com- sented. The inevitability and generality so-called zero-point energy. municate with one another). Much later, of his conclusions, and their direct rela- Renormalization theory was devel- in 1935, Yukawa predicted the existence tionship to basic principles of quantum oped to deal with this sort of difficulty. of pions based on his analysis of nuclear mechanics and special relativity, are The central observation that is exploited forces, and they were subsequently dis- only clear in retrospect.) in renormalization theory is that, al- covered in the late 1940s; the existences The second and third of these prizes though interactions with high-energy of many other hadrons were predicted were to R. Feynman, J. Schwinger, and virtual particles appear to produce di- successfully by using a generalization S.-I. Tomonaga (in 1965) and to G. ’t vergent corrections, they do so in a very these ideas. (For experts: I have in mind Hooft and M. Veltman (in 1999), respec- structured way. That is, the same correc- the many resonances that were first seen tively. The main problem that all these tions appear over and over again in the in partial wave analyses, and then later authors, in one way or another, addressed calculations of many different physical in production.) More recently, the exis- is the problem of UV divergences.