Size of a proton? Really small

But physicists can't agree on one number

There are three possibilities: Either physicists have made a mistake in their calculations, protons are playing a terrible practical joke on physicists, or — a really long shot — the quantum theory describing charged particles is wrong.

This month scientists in Germany reported measuring the size of the proton by scattering electrons off it, an experiment they’ve done before. But the diameter they found is decidedly different from other recent measurements using energy shifts in hydrogen, they report in the Dec. 10 Physical Review Letters.

Measuring a consistent size for the proton was supposed to be yet another check on the theory that marries the quantum world with electromagnetic fields, called quantum electrodynamics or QED. Some physicists were hoping that revisiting the electron-scattering experiment would move the proton’s size closer to the value found in July, when physicists in Switzerland made the surprising announcement that by their experimental yardstick, the proton was 4 percent smaller than previously thought.

But now, that discrepancy stands even firmer.

“In a way, it’s reinforced the problem rather than solved it,” says Jeff Flowers, a physicist at the National Physical Laboratory in Middlesex, England.

The A1 Collaboration in Germany used a standard method of measuring the size of protons, the positively charged particles that nestle in the nuclei of atoms. Using the MAMI particle accelerator in Mainz, Germany, the team fired electrons at a stationary target of protons and measured the angle at which the electrons scattered. Using QED theory, the team worked backwards to measure a proton diameter in agreement with the currently accepted value, 0.88 femtometers.

In July, scientists at the Paul Scherrer Institute in Switzerland got a smaller figure by using a different method. The team also relied on the theory of QED, which explains the energy levels that electrons can occupy in hydrogen. In particular, the theory predicts a tiny difference called the Lamb shift between two energy levels. Researchers measured the Lamb shift in a hydrogen atom where the electron was replaced by a muon. Because the muon is more massive than the electron, it orbits closer to the proton, so the Lamb shift is exaggerated and easier to measure. They measured the proton to be about 0.84 femtometers. It was the most precise measurement so far — and too far below the accepted value to be the result of random error.

“A huge disagreement requires some explanation,” says Flowers.

Because QED’s predictions have been confirmed for more than 60 years, it’s unlikely this disagreement will overturn the theory, says Flowers. Instead, physicists will hunt for errors in the complicated calculations.

“There’s a small chance it’s really the theory itself that’s wrong,” says Flowers.

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