[mattheww]

So there's no obvious practical application (right now).

Also, the proton is not 4% smaller. Protons are obviously whatever size they are.

The discrepancy comes from the fact there are two techniques to measure the proton size. Both experiments do their thing and then there's a way to interpret the results that would tell you the size of the proton (look up proton form factors).

However, when you do the interpretations, which depend on some theoretical calculations, you get different results. The general thinking around this result, because nobody has found any issue with the experimental results, is that there are some additional interactions that are stronger than expected that need to be accounted for (there are some unknown quantities that allow this).

One of the interactions would only affect the muonic hydrogen measurement - basically there are some different interactions between muons and protons than between electrons and protons because of the muon's mass and those might be different than originally thought.

The other is a type of interaction that could affect both normal and muonic hydrogen. This new measurement shows that the interactions that affect both has to play an important role in understanding this discrepancy. There are other measurements trying to measure this effect independently (not using hydrogen at all).