Everyday objects are made of atoms and every atom contains one or more protons. The simplest atom—hydrogen—consists of one proton and one electron. A proton can be modeled as a tiny ball with a constant radius. Using data from experiments with hydrogen, scientists have estimated the radius of the proton. Their current best estimate (the CODATA 2010 value) is 0.8775 femtometers, with an uncertainty of plus or minus 0.0051 femtometers. A femtometer (fm) is one quadrillionth of a meter.
Scientists wanted a smaller uncertainty than 0.0051, so Randolf Pohl and his colleagues did experiments with an exotic form of hydrogen called muonic hydrogen. It’s just like regular hydrogen, except the electron is replaced with a muon, a particle similar to an electron but with much greater mass. As expected, Pohl et al reduced the uncertainty down to 0.00067 fm and a later experiment reduced it even further. But there was a surprise—they got a much smaller value for the radius of the proton itself!
Here’s an analogy. Suppose you had a cheap measuring stick and you used it to measure the radius of a giant beach ball to be 1 meter, with an uncertainty of 0.1 meters. Then suppose you got some fancy giant calipers and you used them to get a measurement of 0.5 meters, with an uncertainty of 0.01 meters. What’s going on? The ball shouldn’t have a different radius depending on how you measure it! Yet that’s exactly what’s happening with the proton radius measurements.
Maybe the stated uncertainty in the CODATA 2010 value is too small? Maybe some other values used in the calculations are wrong? Or maybe some new physical phenomenon has been discovered? It’s a mystery.