What’s the size a proton? It may sound like a fairly straightforward question, but it has proven to have the potential to destroy much of modern physics. This is because different methods of measuring the charge radius of the proton are produced. results disagree– and not just a little. Responses were spaced four standard deviations apart. But now a new and improved measure brings them much closer together, but not enough for us to consider the problem solved.
There are several ways to measure the charge radius of a proton. The first is to bounce other charged particles off the proton and deduce its size by measuring the deviations. Another is to examine how the charge of the proton influences the behavior of an electron orbiting a hydrogen atom, which consists of a single proton and a single electron. The difference in energy between the different orbitals is the product of the proton’s charge radius. And, if an electron goes from one orbital to another, it will emit (or absorb) a photon with an energy that matches that difference. Measure the photon and you can go back to the energy difference, and therefore the proton’s charge radius.
(The actual wavelength depends on both the charge radius and a physical constant, so you need to measure the wavelengths of two transitions to get values for the charge radius and the physical constant. for the purposes of this article, we’ll just focus on one measurement.)
A loose fit between these two methods once seemed to leave physics in good shape. But then the physicists did something funny: they replaced the electron with its heavier and somewhat unstable equivalent, the muon. According to what we understand from physics, the muon should behave like the electron except for the difference in mass. So if you can measure the muon orbiting a proton in the brief flash of time before it decays, you should be able to produce the same value for the proton’s charge radius.
Of course he produces a different value. And the difference was big enough that a simple experimental error probably didn’t explain it.
If the measurements were really different, it would indicate a serious flaw in our understanding of physics. If the muon and the electron do not behave equally, then quantum chromodynamics, a major theory of physics, is somehow irreparably broken. And having a broken theory is something that makes physicists very excited.
The new work is largely an improved version of past experiences in that it measures a specific orbital transition in standard hydrogen composed of an electron and a proton. First, the hydrogen itself was brought to a very low temperature by passing it through an extremely cold metal nozzle on its way to the vacuum vessel where the measurements were taken. This limits the impact of thermal noise on the measurements.
The second improvement is that the researchers worked in the ultraviolet part of the spectrum, where shorter wavelengths helped improve accuracy. They measured the wavelength of photons emitted by hydrogen atoms using what is called a frequency comb, which produces photons at a series of evenly spaced wavelengths that act much like marks on a ruler. All of this made it possible to measure the orbital transition with an accuracy 20 times more precise than the team’s previous effort.
The result the researchers get is at odds with previous measurements of normal (but not more recent) hydrogen. And it’s much, much closer to measurements made using muons orbiting protons. So from a quantum mechanical precision standpoint, that’s good news.
But that’s not good news, as both results are still outside of each other’s error bars. Part of the problem is that the added mass of the muon makes the error bars on these experiments extremely small. This makes it very difficult to keep the results obtained with a normal electron consistent with the muon results without completely overlapping them. The authors acknowledge that the difference is likely to be simply errors that were not taken into account, citing the prospect of “systematic effects in one (or both) of these measures”. These effects could broaden the uncertainty enough to allow overlap.