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The proton puzzlers

In scientists’ search for knowledge, tenacity can be as important as insight. A tale of research woe and triumph




• When Randolf Pohl scribbled “This is a horrible night” in his lab notebook at 5.44am on 4 July 2009, his nerves had been in shreds for hours. After 12 years of research, his entire scientific career hung in the balance. “I was doing research to save my life,” says Pohl in retrospect.

Pohl, now 47 and a professor of experimental nuclear physics at Mainz University, had planned things rather differently: he and an international team of 32 junior researchers and physics luminaries from France, Portugal, Taiwan, Switzerland and Germany wanted to measure the radius of a proton with unparalleled precision – an ambitious project that called for patience and meticulous care.

Protons – the building blocks, together with neutrons, of atomic nuclei – are already the most accurately measured particles in the physics universe. Even a high-order decimal-place improvement would call for big and expensive guns. Everyone involved knew this from the start.

They also knew that the experiment was a so-called “straightforward task”, the results of which keep the steady research cycle of physics moving along. Theoretical physicists use more accurate measurements of a proton radius to check and refine mathematical equations and assumptions about the interactions between particles of matter and light. Physicists such as Pohl then take these and find new experiments to test the expanded theory and optimise it further. “All in all, we were expecting at most five years to pass between the initial idea and publishing the results,” says Pohl. Projects that last several years are normal for scientists, especially in experimental physics.


Homing in on the radius of the proton: The physicist Randolf Pohl and his colleagues Marcel Willig and Jan Haack stare spellbound at their test apparatus in the laboratory at Mainz University – a diode laser for lithium spectroscopy

But 12 years without a measurement or relevant publications in journals threatened to plunge the physicist into insignificance. In the business of science, publications are the most important currency. “As a young scientist, having command of your field and showing yourself to be hard-working is not enough to attract attention,” says Aldo Antognini, who was involved in the project as a PhD student. “The measurements in the summer of 2009 were the last opportunity for Randolf and me to get anywhere in our field.”

Fortunately, says Antognini, who is now 42 and a research scientist at ETH Zurich and the Paul Scherrer Institute (PSI) in Villigen, Switzerland, they did not realise this while they were actually carrying out the experiment. “Otherwise we would have been even more nervous – and who knows what would have happened.”

Their ordeal began in 1997. Until then, physicists had estimated proton size using two different methods. The older involves firing electron beams at atomic nuclei. By observing how they are scattered, the size of the nuclei can be calculated. From the middle of the 1990s, that could also be achieved by, roughly speaking, using lasers to measure the energy levels of electrons orbiting the atomic nucleus.

The two methods give virtually identical results, within the margins of error. Averaging the two values led to the value that is today officially recognised as the radius of a proton: 0.877 femtometres – less than one quadrillionth of a metre, inconceivably small. At the time, the physicists Theodor Hänsch at the Max Planck Institute for Quantum Optics in Garching, Germany, and Franz Kottmann at the PSI proposed a new method of measuring the radius of a proton. Their version of the familiar laser spectroscopic method promised to improve the accuracy tenfold.

The scientists suggested tricking hydrogen into taking the electron’s exotic relative, the muon, into orbit instead of the electron itself. As muons are some 200 times heavier than electrons, their orbits are about 200 times closer to the proton. This in turn has a stronger effect on its energy levels. Measuring these with the help of a laser therefore promised to produce more accurate readings than achievable with electrons. Pohl, who was studying for his PhD at ETH Zurich at the time in a group headed by Kottmann, demonstrated that such a measurement ought to be possible. The young physicist had found his task.

By the spring of 1998, he and his colleagues on the newly assembled team had already booked time to conduct their experiment at the PSI. Here, midway between Zurich and Basel, near the German border, stands the world’s most powerful source of muon radiation, without which the experiment would not have been possible. While the heavy particles lead to greater precision, they are also extremely short-lived. Within just two millionths of a second, they decay back into electrons. So experiments using muons need to be carried out extremely quickly and the supply must be constantly replenished.

The scientists started developing the necessary technology, and in 2000 and 2001 they conducted some initial tests. In 2002, so they hoped, the experiment would get underway properly. “But then it took us months to get everything running properly,” says Pohl. They had to set up the equivalent of two double garages full of equipment and adjust countless magnets, lenses, apertures, mirrors and detectors. They had not yet developed a routine, so it took a long time. The time allotted to them by PSI for using the muon beam was running out. “In the end, we only managed to record five hours of data. We were devastated,” says Pohl.

However, Hänsch and Kottmann were thrilled that the measurement had worked at all. The following year, it was hoped, would see a breakthrough. But everything turned out differently again. That time, the equipment was ready to use on time and they were able to record data for three weeks under ideal conditions, but the signals they were looking for could not be found.

“I just couldn’t believe it,” says Pohl. He suspected that the software they were using to analyse the data was at fault and that the signals were hidden somewhere in the recording. Working like a man possessed, he spent months rewriting the program. A year later, he was finally convinced that the data did in fact contain no evidence of a successful measurement. He encouraged his team to refine the laser technology, thinking perhaps that was at fault.

When the group applied for experimental time at PSI for the third time in early 2005, the research facility voiced doubts about the chances of success. “The measurements had been carried out for several years. When nothing emerged in 2003 either, they suggested that we should give up the experiment,” says Hänsch. In the end, the group was helped by the fact that Hänsch, an expert in precision spectroscopy, received the Nobel prize that year. In the light of this triumph, the committee revised its opinion and approved a further round of measurements. It was to be the team’s very last chance.

A different large-scale project was given priority on the muon beam the following year, and because of this the grand finale was scheduled for the summer of 2007. However, the PSI now had problems producing muons. And the team was again struggling with the technology: Pohl and his colleagues had transported the laser components to Munich to tinker with, and taken too long about it, so the return journey by lorry to Switzerland ended up being “somewhat hectic”. The sensitive equipment was completely out of alignment. Again, it took them far too long to get the experiment up and running.

“This was annoying, of course, but as the main mistake had been made by the Swiss this time, our last attempt was postponed until 2009,” Pohl recalls. And this time, the preparations worked. “All the instruments were ready on cue, just like an orchestra,” says Antognini. The measurements were made, but despite the optimum conditions and an experimental technique that had been refined over the years, the anticipated signals failed to appear.


Shedding light on the world of tiny particles: a diode laser for lithium spectroscopy

Unexpected results

Early on 4 July, sleep was out of the question. Antognini and Pohl were in a fix. What should they do? Just before Pohl complained about the horrible night, they had come to a decision that flew in the face of what the team had agreed. They had assumed that the precise measurement would be slightly larger than the currently accepted value. But perhaps they were looking in the wrong direction: what if the proton was in fact smaller than quoted in the textbooks?

“In this predicament, we didn’t care how much trouble we would get into for going it alone. We had all but run out of time anyway,” says Pohl. They extended the scope of their search to a region that Antognini describes as “actually very, very unreasonable”. At 6.08am, Pohl wrote in his lab book: “We have it!” The detectors were recording the signal they had been hoping to see for the past 12 years, but in a place where no one expected it to be. The readings suggested that protons have a radius of just 0.842 femtometres – about 35 quintillionths of a metre (or 4%) smaller than the previously recognised value. In the world of high-precision physics, that is a lot.

“That really was a very good feeling,” says Pohl and grins. “But don’t ask me whether I would ever do something like that again.” The entries in the lab notebook suggest that the surprise gave the physicists a new lease of life. They kept on taking measurement after measurement, pasting graphs into the book and noting that the values were better when Bob Marley was playing in the background than when it was Abba. Two days later, Hänsch congratulated them by email. A printout was pasted into the lab notebook, along with the label of a bottle of Moët & Chandon champagne. At 5.45pm on 8 July 2009 they toasted each other; at 7.32pm the next measurement was recorded.

The physicists printed the news of their success on T-shirts and invited the head of the PSI to visit their lab. He extended their experimental slot by a few weeks. It was now a matter of substantiating their findings. A year later, Pohl and his colleagues published their results. At least they could rest assured that no other group could beat them to it after all their trials and tribulations: “No one is going to copy that experiment,” says Antognini. “Impossible.”

The proton radius puzzle, as the experts have called the phenomenon, has led to a wave of new projects on the topic in recent years. To this day, however, it remains unclear what is causing the discrepancy between Pohl’s measurements and the earlier values. “What would be really exciting is if we had in fact discovered a flaw in quantum electrodynamics,” says Hänsch. “In other words, if there were fundamentally new aspects that did not fit existing theory. But things like that only happen very, very rarely in science. The discrepancy is more likely to be caused by some error.”

“If the cause is an error,” says Pohl, “then it’s certainly very difficult to find.” At first, he was worried that one of the luminaries would find a simple mistake in his calculations. “Something embarrassing,” says the scientist. Today, nine years after the measurements, the results have ceased to be called into question. And even if a mistake did turn up – in the theory used to calculate the radius from the measured data, for example – that would not be such a problem: the patience and tenacity of everyone involved definitely paid off.

“Experiments like this, which test scientists to their very limits, unleash an incredible creativity,” says Antognini. “Some Nobel prizes have been awarded for developments that only arose as a means of solving a different problem.” Laser cooling, for example, in which atomic gases can be lowered to nearly absolute zero; or Hänsch’s laser frequency comb, an instrument capable of measuring the frequency of light to very high precision.

“Our project has more precise measuring techniques and improved laser components going for it, and not least an excellent level of scientific training,” says Antognini. “That really was a life-transforming challenge.” And who knows what other discoveries the proton puzzle will lead to? “Our national economy is largely based on past scientific discoveries, whereby unexpected discoveries have had the biggest effects,” says Hänsch. The 76-year-old concludes that: “If I set aside at least part of the research resources for fundamental research, which is conducted by people who are simply driven by curiosity, who simply want to understand nature, then that money will be well invested.”

Pohl agrees. At the moment, he is putting together a new team in Mainz, applying for grants and giving presentations of his findings. But he hopes that he will soon be able to spend more time in the laboratory again. “Two days a week would be nice,” he muses. Even nicer would be to secure a new measuring slot at the PSI. Pohl has plenty of ideas for experiments. “Nowadays, I have to consult my wife and my children, though,” says the scientist. “That is a point of honour to me, because without their patience I could never have seen it through to the end.”