Oh Asymptotic Freedom!

By Heidi Aspaturian

David Politzer, a member of the Caltech faculty since 1976, is a corecipient of the 2004 Nobel Prize in physics.

Asymptotic freedom is a term commonly associated with—well, not much of anything, really. This is a pity, because if the physicists are right, it is connected to just about everything. The odd language attests to an even odder fact about the edgy nature of reality.

Two of the oldest questions in science are, What is matter made of? What holds it together? About 40 years ago, physicists determined that protons and neutrons, those familiar denizens of the atomic nucleus, are not the fundamental building blocks of nature, but, along with their elementary particle cousins (collectively all called hadrons), are made up of subparticles called quarks. It turns out that quarks hold hadrons together via a force—or interaction, as the physicists are pleased to call it—that against all dictates of logic, actually increases with distance and diminishes with proximity. If one could step inside, say, a proton, and get up close and personal with any of its three quarks (a Fantastic Voyage for a new generation), one would discover that in the quark’s immediate vicinity, physical freedom (or whatever passes for it on a distance scale of something less than 10^-15 meters) is practically infinite. Head for the exits, however, and the quark’s pull increases until it too approaches infinity. This weird state is called asymptotic freedom. (An asymptote is a line that draws increasingly close to a curve but never quite meets it.)

Shorn of the physics equations, quark behavior inside hadrons (there are three quarks inside the heavier hadrons, including protons and neutrons; and a quark and antiquark pair inside the lighter ones) is said to resemble a rubber band’s. Just as the tension in a slack rubber band increases as the band is pulled harder, so do quarks resist separation the more strenuously they are forced apart—a Romeo and Juliet kind of thing, with mathematical instead of emotional baggage. In the subatomic realm of quantum mechanics, a Through the Looking Glass domain where particles act like waves, regularly annihilate their antiparticles, and are here, there, everywhere, and nowhere simultaneously, none of this seems particularly out of place. That this dynamic actually shapes the wider world is harder to fathom. But there it is.

Thirty-one years ago, three physicists fell far enough down the quantum rabbit hole to spot asymptotic freedom at work in the microworld, and by extension throughout nature. This was a striking development, so it seems a bit odd that the Nobel Foundation did not put a seal of approval on it a long time ago. Perhaps the judges too were caught up in the contrarian logic of it all—the more significant this work is, the longer we must wait to recognize it. But on October 5, 2004, they did: Caltech professor of theoretical physics David Politzer, Frank Wilczek of MIT, and David Gross of UC Santa Barbara were awarded the Nobel Prize in physics for “the key discovery that explained how quarks, the elementary constituents of the atomic nucleus, are bound together to form protons and neutrons.”

From that point, on the Caltech campus, events diverged from the usual “we have a laureate!” script. Politzer let it be known that he would not be making any public statements or giving interviews. At the Nobel press conference that Caltech held to explain the somewhat esoteric significance of the absentee laureate’s achievement, Politzer’s longtime colleague, Mark Wise (Caltech’s McCone Professor of High Energy Physics), gracefully translated the science. Wise did not even omit to mention that, just like always, the new Nobelist was a regular guy—“only a lot smarter than the rest of us.” He added that while the calculation Politzer had carried out was very difficult in its day, it was now routinely done by graduate students. Wise planned to assign it to several of his in the near future.

Politzer himself was a graduate student when he made his landmark discovery, and back in the day, or at least in the decade afterward, he talked to several journalists and historians of science about his role in the asymptotic freedom story. By his account, the Eureka moment was rather serendipitous—it certainly bears out Pasteur’s dictum that fortune favors the prepared mind. In 1973 Politzer was in his fourth year at Harvard and, having finished his coursework, was casting about for a thesis topic. One of the hottest areas in particle physics at the time was electroweak theory, which was an attempt to unify quantum electrodynamics (QED)—the quantum field theory of electromagnetism—with the weak force—which, roughly speaking, governs some forms of radioactive decay—into a framework that could be described by a single set of equations. According to Constructing Quarks, a sociological history of particle physics by Andrew Pickering (University of Chicago Press, 1984), Politzer thought he might uncover something new if he carried out a beta function calculation (more on this later) for an aspect of electroweak field theory. He asked his academic adviser, Sidney Coleman (Caltech PhD ’62), if he thought this was a good idea. Coleman told him to go ahead.

The excitement surrounding electroweak unification (which would ultimately unify a number of key players with Nobel Prizes) stemmed partly from the fact that the physics community saw it as a major step toward a goal championed by Albert Einstein: that of tying nature’s four forces—gravity, electromagnetism, the weak force, and the strong force—together into a single theoretical framework, whose laws held sway in the first moments of cosmic creation (the Big Bang and all that) and whose vestiges can still be detected in nature today. There still isn’t a verified quantum field theory for gravity, and at the time physicists didn’t have a satisfactory quantum theory for the strong force either. But they were certainly working on it.

The strong force got its name because physicists realized that it had to be stronger than electromagnetism (it’s about 100 times stronger at the scale of a proton) to weld protons, whose positive charges would otherwise repel each other, into a band of brothers inside the atomic nucelus. In 1948, Richard Feynman (shortly to move from Cornell to Caltech), Julian Schwinger of Harvard, and Sin-Itiro Tomonaga of Tokyo University had independently created the enormously successful quantum field theory for electromagnetism, QED. (The trio shared the Nobel Prize in physics in 1965.) Now theorists hoped to develop a similar model for the strong interaction.

The strong force did not yield its secrets easily, but by the early 1970s, the picture, greatly simplified, looked like this: Protons and neutrons and all the other hadrons—most of which hang around for the merest instant before they decay into still other hadrons— are all made out of fractionally charged particles called quarks. The concept of quarks originated in 1964 with Caltech’s Murray Gell-Mann (who named them after a nonsense word in Finnegans Wake) and, independently, George Zweig, then at the European Center for Nuclear Research, CERN.

Gell-Mann further proposed that quarks come in three different types or “flavors,” which he dubbed “up,” “down,” and “strange.” (Three more quarks would eventually join this roster—the existence of “charm,” “truth,” and “beauty” was experimentally confirmed in the ’70s and ’80s). Fractionally charged particles sounded looney, but in the right combinations they accounted for the overall makeup of every hadron. A proton, with +1 charge, is thus made up of 2 “up” quarks (each with an electric charge of +2/3) and one “down” quark (-1/3 charge); and the neutron, which has no charge, contains two “downs” and one “up.” “Strange” particles, which Gell-Mann had characterized in the 1950s, contain at least one strange quark. The entire taxonomy of hadrons, a classification system of remarkable explanatory and predictive power that Gell-Mann and, independently, Yuval Ne’eman had proposed in 1961, and that Gell-Mann of course had named—he called it the Eightfold Way—could be built out of these quarks. (Gell-Mann won the 1969 Nobel Prize in physics for “his contributions and discoveries concerning the classification of elementary particles and their interactions.”)

By analogy with QED, in which photons are the carriers of the electromagnetic field, particles called “gluons” carry the strong force, holding hadrons together as they shuttle from quark to quark. But quarks and gluons also possess a “color charge”—a quantum property that has nothing to do with Crayola products—and when quarks exchange gluons, they usually trade “color” (another Gell-Mann coinage) as well. This “color me beautiful” scheme stipulates color charges of blue, green, and red for quarks and gluons; and yellow, magenta, and cyan, respectively, for their antimatter counterparts.) All observable hadrons, starting with the protons and neutrons, are “colorless”—composed of quarks whose colors cancel one another out. Although theorists originally came up with it to avoid a problem of having two or more quarks occupying the same quantum state, the extremely powerful, short-range color charge would gradually emerge as the defining property of the strong interaction.

With its whimsical vocabulary and intimations of the ice-cream truck, construction paste, and primary colors, quark/gluon theory sounded pleasingly like an outtake from Sesame Street. However, the mathematics was fraught with complications, and the real-world implications anything but clear. If quarks existed, experimental physicists wanted to know, why hadn’t they surfaced with all the other rogue particles that had been pouring out of their cloud chambers and particle accelerators since the 1950s? What would a fractionally charged particle even look like, or, at least, how would it register its presence? Were quarks a concrete physical entity within protons and neutrons, or were they just an immensely useful mathematical device? At some point, Gell-Mann obtained a doctor’s note purporting to state that these “philosophical” disputations were bad for his health.

Then, in the late 1960s, investigators at the Stanford Linear Accelerator Center (SLAC) began to see empirical evidence that protons might indeed have an internal structure. Firing electrons into protons at speeds approaching those of light, the experimenters were startled to observe many more electrons than predicted rocketing out of the collisions as if they had struck something hard inside the protons. It was Feynman, passing through from Caltech (where he and Gell-Mann had offices on the same floor), who suggested that these results were consistent with the idea that at the high energies equivalent to very short distances, a proton acts like it is made up of freely moving, point-like subparticles. Feynman was not inclined to call these objects quarks—yet. Instead he called them partons—Gell-Mann in some annoyance referred to them as “Dick’s put-ons.” Whatever the nomenclature, Feynman’s insight posed a puzzle: if quarks were in some sense “real,” how could the strong force be powerful enough to confine them, yet weak enough to account for the SLAC experiments?

Forces of Nature. Between them, Caltech physicists Murray Gell-Mann (left) and Richard Feynman dominated the landscape of postwar theoretical physicis and laid much of the groundwork for the current work on unification.

Enter asymptotic freedom, which a handful of theorists had by then put forward as the solution to the quark confinement riddle. The speculation centered on the so-called beta function, which basically relates to a coupling constant, which basically refers to how strongly objects interact. An asymptotically free theory would have a negative coupling constant, that is to say, a negative beta function, and would explain why, at short distances and high energies (same thing in this context) quarks acted almost like liberated particles, while at greater distances (corresponding in this case to the diameter of the proton) and lower energies, they became strongly, indeed eternally attached. But no one, including the theory’s proponents, had offered a convincing formula for how a negative beta function might work, and most strong-force physicists dismissed the idea.

The scene now shifts to springtime at Harvard, where the curtain rises on David Politzer investigating the beta function as it applied to an aspect of electroweak theory. What happened next is described in The Second Creation, a lively account of the history of quantum physics (1986, Collier Books). “It comes out,” he told the book’s authors, Robert Crease and Charles Mann, “that it’s totally useless for the purpose that I had in mind.” Twenty-four hours had not passed, however, when it flashed across him that he had, in effect, been looking through the wrong end of the telescope. “Within the next sort of day it dawned on me” that his results were consistent with a negative beta function (that is to say, an asymptotically free model) for quarks.

Politzer got in touch with Coleman, who was spending the term at Prince- ton, and from here Constructing Quarks takes up the tale. “Hey, Sidney, this is stupendous!” exulted the student. Coleman wasn’t so sure. It seemed that Coleman’s Princeton colleague David Gross, and Gross’s graduate student Frank Wilczek had just wrapped up a calculation that reached precisely the opposite conclusion—the type of field theory Politzer was looking at could not be asymptotically free.

It was spring break, so Politzer went to Maine, taking his own voluminous calculation with him. On vacation, he reviewed his work. “I came back,” he told The Second Creation authors, “and said, ‘Sidney, I got the same numbers.’” The news did not exactly come as a shock to Coleman. In the interim, Wilczek and Gross had discovered a sign error in their math. Once they made good their mistake, their results and Politzer’s lined up. The twin solutions of different fathers were published back to back shortly afterward in the June 25, 1973, issue of Physical Review Letters. Politzer was 24. It was his first publication.

With asymptotic freedom established as key to quark confinement, the last major piece of the strong interaction puzzle fell into place. Physicists determined that the strong force that holds protons and neutrons together is in essence a subgenre of the more fundamental color force that binds quarks permanently into hadrons. Genies sealed in a quantum bottle, they conjure up the world.

Predictably, it was Gell-Mann who had the last word, or who at least took best advantage of the terrific naming opportunity that now presented itself. In homage to the color force at the heart of matter, he christened the strong-force model quantum chromodynamics, or QCD. Of course the name, quarklike, stuck.

As for the rest of us, what does it all mean? Well, as the Nobel Prize committee would comment: “Progress in particle physics or its relevance for our daily life can sometimes appear hard to grasp for anyone without a knowledge of physics. However, when analyzing an everyday phenomenon like a coin spinning on a table, its movements are in fact determined by the fundamental forces between the basic building blocks—protons, neutrons, electrons. In fact, about 80 percent of the coin’s weight is due to movements and processes in the interior of the protons and neutrons—the interaction between quarks.”

Convincing evidence that QCD is, so to speak, on the money, has been obtained during more than two decades’ worth of particle accelerator experiments. QCD and QED now constitute two of the three pillars of the Standard Model, which also describes the weak nuclear force and ultimately seeks to unite all three, along with a quantum treatment of gravity, into the unified framework originally envisioned by Einstein. (A unified quantum theory that encompasses gravity does now exist in the form of superstring theory, which posits that nature consists of ten dimensions instead of the usual four—the remaining six are folded up into a kind of space-time origami—and the fundamental building blocks of matter are not after all quarks, or at least not merely quarks, but tiny vibrating strings.) In the meantime, physicists are hoping to experimentally verify more aspects of the Standard Model when the next generation of particle accelerators comes on line later this decade.

During an interview some years back, David Politzer was asked for his thoughts on how closely QCD, the Standard Model, and some of the more exotic theories just then coming up over the horizon, physically approximate anything that goes on “out there”—how close they come to describing what is generally thought of as reality. The question itself was not easy to frame, and the response was an expressive shrug. There is a remark attributed to Politzer that has apparently floated for a while through cyberspace. “English,” it says, “is just what we use to fill in between the equations.”

Since this article was written, Politzer has posted his Nobel lecture, “The Dilemma of Attribution."

For more on Caltech’s latest laureate, go to “Our Man on the Manhattan Project.”