Can someone who is more well-studied in physics tell me: what are the implications of this? Is it a curiosity, but of no practical matter? Or is it "Oh my god, a 4% smaller proton could mean cold fusion and jetpacks"?
For me, it's mainly interesting because two different fields of physics meet, nuclear physics (electron scattering) experiments, and atomic physics (spectroscopy).
Otherwise, it's the same as with all basic science. We don't know what it is "good for" until somebody figures out how to cure cancer with it.
The paper this article refers to is in particular interesting, because it finds a value not in agreement with earlier measurements of the /same/ type. The indicated 3.3 sigma shift in the Rydberg constant, one of the most exact measured quantities in existence, is a little bit worrying, but such shifts happen more often than they should.
Since you asserted an answer to the question before I managed to ask, I'm happy to subordinate my question. But I will also suggest your specific answer, cure cancer, won't work. I need to kill cells, which requires a cascade of large molecules interacting at energies on the order of a fraction of an eV, or massive amounts of high energy radiation.
I can kill cells directly with high energy radiation, however, the energies for this investigation, the hydrogen 2s-4p transition, (1,2) are trivial (486 nm is visible light). Also, radiotherapy isn't really good at interrogating cell type, the current standard for new cancer therapies (immunotherapy).
(1) http://science.sciencemag.org/content/358/6359/79
(2) https://indico.mitp.uni-mainz.de/event/14/contribution/11/ma...
Sometimes we don't know what new knowledge will enable us to do until the PhDs, engineers, and technicians get their hands on it.
People care because it's jarring that something so 'known' and basic might be different.
And yeah the cancer part was more a 'holy grail' thing. replace it with 'cures poverty' and his point still stands
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).
It does raise curious questions, namely what is it that we missed that lead us to believe the previous results. If the proton is indeed so much smaller, what is it that was skewing the results of the previous experiments? Perhaps this signals new physics and strange new effects.
And that may eventually lead to cold fusion and jetpacs :)
If the proton and muon sizes were different, then a bunch of physicists would be chomping away at being able to replace the Standard Model and get the Nobel Prize.
As it stands, it looks like there's a question of why the old measurements were off, and that's about it.
They are different, in fact the muon is believed to be a point particle and not to have any internal structure like, for example, the proton. Nonetheless one can assign a non-zero radius to the muon in specific contexts due to its interaction with the vacuum.
Thank you for your correction.