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Odd Ruler. To infer the proton's radius, physicists measured the energies of the 2S (left) and 2P orbitals in hydrogen atoms in which they replaced the electron with a particle called a muon.

Wolfgang Christian/Davidson College;

The Incredible Shrinking Proton?

Perhaps the recession is to blame. The most precise measurement ever made of the proton's radius shows that the subatomic particle is 4% smaller than previously thought. That's a big puzzle for physicists, because the theory used to deduce the size—quantum electrodynamics (QED)—is the most precise one in physics and has proved accurate to a few hundred millionths of a percent in certain circumstances.

"The most elegant solution would be that there's a miscalculation in there somewhere, but the theorists tell us everything is fine," says Randolf Pohl, an experimenter at the Max Planck Institute of Quantum Optics in Garching, Germany, and the first author on the study. But some theorists say that the problem may not be that the proton is smaller than had been thought, but that they do not really understand what's going on inside it.

Rather than measuring the radius of a proton directly, the international team of 32 physicists inferred it more accurately by measuring energy levels in an odd type of hydrogen. An ordinary hydrogen atom consists of a wispy electron bound to a beefy proton. The electron can occupy various cloudlike quantum states called orbitals, which give the probability of finding it at any particular place. Each orbital has a precise energy, and at first blush some orbitals should have exactly the same energy.

But in 1947, American physicists Willis Lamb and Robert Retherford discovered that two such "degenerate" orbitals actually had very slightly different energies. The difference, called the "Lamb shift," comes about because of quantum fluctuations in the electromagnetic field that binds the electron to the proton, as famed theorist Hans Bethe soon explained. Bethe's calculation was a key first step toward a fully quantum mechanical theory of the electromagnetic field, QED, still the most accurate and precise theory physicists have ever developed.

Pohl and colleagues have spent 10 years trying to test the limits of that accuracy in a new way. Using a particle accelerator at the Paul Scherrer Institute in Villigen, Switzerland, they generated hydrogen atoms in which they replaced the electron with a muon, a particle 207 times as massive that lasts for only 2 microseconds before decaying. They used a high-precision laser system to measure Lamb shift in the "muonic hydrogen" atoms.

Because the muon is so massive, it hovers closer to the proton than an electron does and probes different manifestations of the quantum fluctuations. Whereas the fluctuations kick the electron around and effectively smear it into a diffuse cloud of charge, the fluctuations in muonic hydrogen tend to polarize the empty space in the atom and create an even bigger Lamb shift.

When Pohl and colleagues measured the Lamb shift in muonic hydrogen, however, the result was even larger than expected from data from ordinary hydrogen combined with QED calculations, they report in tomorrow's issue of Nature. The size of the shift depends on the radius of the proton, and the team extracts a value of 0.84184 millionths of a nanometer—4% smaller than the previous estimate based on studies of ordinary hydrogen.

So is QED faulty? Not likely, says Rudolf Faustov, a theorist at the Russian Academy of Sciences in Moscow. He notes that the proton is actually a roiling mass of particles called quarks and gluons, all held together by the so-called strong force. That inner complexity, Faustov says, makes it difficult for physicists to handle precisely the electromagnetic force between the proton and muon in their calculations. "It's not quite clear how to separate these interactions," he says. In particular, he says, physicists may have to reconsider how the muon affects the proton.

The result may even point to new physics, says Krzysztof Pachucki, a theorist at the University of Warsaw. Thanks to quantum fluctuations, the proton is chock full of quark-antiquark pairs flitting into and out of existence. If the proton also contained lots of electron-positron pairs, they would increase the polarization of space with the muonic atom and resolve the discrepancy in the Lamb shift with no need to revise the textbook value of the proton's radius, Pachucki says. "That would be the first thing I would check."