Thinking about basic physics calculation

Q&A with physicist David Politzer about solving the mystery of the strong force more than 50 years ago

When David Politzer, the Richard Chace Tolman Professor of Theoretical Physics at Caltech, was a fourth-year graduate student at Harvard in 1973, he made a stunning discovery that forever reshaped the field of particle physics. He pondered a physics problem and decided to do a long, painstaking calculation to better understand it. When he finished, he realized that the formula he had derived had profound implications for another puzzling question: How strong is the force that binds the nuclei of atoms together?

Politzer’s calculations revealed that the strong force—one of the four fundamental forces of nature besides gravity, the weak force, and electromagnetism—acts differently than the others. The strong force is what holds the smallest known bits of matter, quarks, together inside the nuclei of atoms. But rather than weakening as quarks move further apart, as with other forces, the strong force remains very strong.

This phenomenon can be likened to pulling a string that has “quantum mechanical and relativistic mojo,” as Politzer puts it. Inside atoms, these quantum chains bind quarks together. Any attempt to pull the string between the quarks just creates another string. If one pulls hard enough, the string snaps and turns into more quarks. “But the strings are very pliable when the quarks are close together,” says Politzer. This floppiness means that quarks behave like free when they are very close together. Technically, this phenomenon is called asymptotic freedom.

For the discovery of asymptotic freedom, Politzer won the Nobel Prize in Physics in 2004 together with David Gross and Frank Wilczek, who made the same discovery independently. This breakthrough had major implications for quantum chromodynamics (QCD), a theory proposed by the late Caltech professor Murray Gell-Mann in 1972 to describe the strong force. Politzer’s discovery essentially provided QCD with working equations that could be used to calculate the interaction of particles. Gell-Mann, who famously coined the term “quarks” after a line from a James Joyce novel Finnegans Wakewon the 1969 Nobel Prize in Physics for proposing that quarks are the basic building blocks of matter.

“Politzer’s work has changed particle physics more than any other work in the last 50 years,” says Mark Wise, the John A. McCone Professor of High Energy Physics at Caltech and a colleague of Politzer’s. “It has allowed physicists to quantitatively understand many processes that were incomprehensible before 1973. This includes processes that relate to physical problems beyond the strong interaction itself, such as the discovery of the Higgs boson at the Large Hadron Collider.”

We sat down with Politzer to learn more about the roots of his far-reaching discovery.

Were you interested in physics when you were young?

My older brother, six years older, went to Bronx Science, a magnet high school in New York, and then MIT. He did real physics and good experiments. He made it clear that the cool guys do physics, and I caught the bug from him. I also went to Bronx Science, took the subway from Manhattan with friends one hour each way. One summer, towards the end of high school, I wanted to learn to be a banjo maker. I just built a banjo. So I wrote to a banjo maker in Colorado, but he thought the folk thing was over, sold his business, and never wrote back. I ended up going to college instead at the University of Michigan and I loved it. I got as many B’s as A’s in physics and math. But I loved working in the research labs.

What was known about the strong force and quarks when you were in graduate school?

In the mid-1960s, Murray Gell-Mann invented the “eightfold way”, where three kinds of quarks combine in different ways to form strongly interacting particles known as hadrons. [which include protons and neutrons]. Some days he thought quarks were just mathematical fictions that let you see patterns, and other days he thought they were a physical reality. That was the theoretical side of things. There were also experiments that did not correspond to the theories. One of the most famous experiments took place at SLAC [a federally funded particle accelerator operated by Stanford University] in 1968 and produced confusing results that became known as the Gee Whiz plot because whenever anyone saw the plot, all they could say was “Gee Whiz.”

In this experiment, electrons were accelerated to a high speed and bounced off some fixed target. The electrons came back as if they hit something very hard and with a lot of inertia inside the protons. Of course, we now know that electrons collided with quarks and the process generated new particles. Richard Feynman [who, before Politzer, was the Richard Chace Tolman Professor of Theoretical Physics at Caltech] he had his own theory about what was going on and didn’t believe Gell-Mann quarks had anything to do with it. The two of them would make fun of it.

Did you do any research on quarks at this time?

Earlier, as a freshman, I worked with an experiment known as oyster vaporization. That is absolutely true. We knew it must be hard to get a quark out of the nucleus by itself because we’ve never seen it and we still haven’t seen it. High-energy cosmic rays come from the sky and hit the ocean. What happens when they release quarks from atoms? We looked for evidence of the fractional charges of quarks. The idea was that wherever the quark ended up, it would have a net charge. So maybe it’s in the seawater, maybe it’s in the salt, maybe it’s in the algae. Things get concentrated biologically. There was a barrel of oysters and we steamed them too. We passed the steam between the charged plates, trying to concentrate the fractional charge. Well, we’ve never seen a quark. But there was a reason we ate a lot of oysters.

How did you get into the strong force problem?

I haven’t started working on the problem. In graduate school at Harvard, my friend and I traveled to New York by car to go to a conference. We talked about physics the whole way. I had a question related to his project with our professor Sidney Coleman [PhD ’62]. I asked Coleman about it later and he said, “That’s really interesting. We never got very far, but I learned a lot. One calculation I tried in this project didn’t help, but it turned out to be amazing for the strong force question.

Around this time there was something called the Weinberg–Salam model that described the weak force and how it was intertwined with electromagnetism. We call this model the non-Abelian calibration theory. It’s a lot like electromagnetism, except it has several different kinds of charge instead of one electric charge, and they add up in a funny way. Physicists wanted to use the same kind of theory for the strong force, but weren’t sure how to put it into the equations. Meanwhile, in 1971, a Dutch graduate student named Gerard ‘t Hooft [formerly the Sherman Fairchild Distinguished Scholar at Caltech in 1981] he did the calculations and made them work. At first, no one paid much attention to it. Another of my professors at Harvard, Shelly Glashow, gave me a copy of the paper and said, “This guy is either a genius or crazy.” Gerard ‘t Hooft’s solution was very eccentric and virtually impossible to follow, but his mathematics solved the problems with infinities in the Weinberg-Salam model. He made the equations kosher.

Anyway, this mathematical framework is what I turned to at some point in my own research for a non-strong force problem. The first thing I did was a straightforward but lengthy calculation related to non-Abelian gauge theories. Today the calculation is homework for physics students, but back then it took a few days by hand on paper. I soon realized that the results represent something called a beta function because the strong force has a minus sign. This basically means that the effects of the strong force, unlike the other forces, diminish as the quarks get closer. This is asymptotic freedom. I realized that this would make the Gee Whiz plot work. I did the calculations over and over and still got the same answer.

Did people immediately believe your result?

I sent a draft of the document to my advisor, Sidney Coleman, and he didn’t believe it. By the way, I nominated Sidney for the Caltech Distinguished Alumni Award because he was a great teacher with an impact on the particle physics community, and he won. Anyway, because of him, the title of the paper “Reliable perturbative results for strong interactions?” it has a question mark which I now regret years later because I knew the calculation was correct.

Murray Gell-Mann immediately knew what the calculation meant—that his QCD theory was not hypothetical. This meant that the possibility of performing exact calculations within this theory immediately opened up. Feynman was skeptical and it took him several years to realize that some of the experiments he thought contradicted QCD actually agreed. He needed to wait for the lessons learned from higher energy collisions. Everything connects in higher energies.

What were the broader implications of your calculation?

When I entered graduate school, particle physics was a mess. There was a lot of experimental and theoretical stuff in the field that was interesting, provocative, exciting, contradicting each other. By the time I finished graduate school, there was a standard model that worked, accurate predictions that could be made, and experiments that you could do. As my colleague Mark Wise said, the state of particle physics changed completely after the mystery of the strong force was finally solved.

What is your favorite part of research, both in basic physics and in your more recent studies of stringed instruments?

For me, I love figuring out how something works. That’s great. Whether other people know it doesn’t change how it feels to figure it out for yourself. Maybe they tell you and you don’t understand them, and that happened to me. But it’s fun to figure it out on your own.

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