The big physics story at the moment is probably the new measurement of the size of the proton, which is reported in this Nature paper (which does not seem to be on the arxiv, alas). This is kind of a hybrid of nuclear and atomic physics, as it’s a spectroscopic measurement of a quasi-atom involving an exotic particle produced in an accelerator. In a technical sense, it’s a really impressive piece of work, and as a bonus, the result is surprising.
This is worth a little explanation, in the usual Q&A format.
So, what did they do to measure the size of a proton? Can you get rulers that small? They use a particle accelerator to create atoms of “muonic hydrogen,” which are just like hydrogen atoms, but with the electron replaced by a muon, an exotic particle that’s just like an electron but about 200 times heavier. Once the atoms were created, they used lasers to measure the “Lamb shift,” which is the very small energy difference between two levels in hydrogen.
How does that tell you anything about the proton? Aren’t the energy levels related to the orbit of the electron? The Lamb shift is an extremely important phenomenon in the history of quantum physics, because the simplest version of quantum theory predicts that these two levels, the 2S and 2P states, ought to have exactly the same energy. The fact that they don’t, as discovered by Lamb and Retherford in 1947, was the first clear indication of a need to move beyond the simplest version of quantum theory, and led to the development of Quantum Electro-Dynamics (QED).
The size of the Lamb shift depends on a bunch of factors, but in normal hydrogen is mostly due to modifications of the electron-proton interaction by “virtual particles” in QED. There’s a small contribution due to the size of the proton, though, and that contribution gets a lot bigger when you replace the electron with a muon.
How does the size of the proton matter? Isn’t it, like, 10,000 times smaller than the electron orbit? The proton is, indeed, really tiny, but its size is not zero. And that makes a difference when you look at how these two states behave.
The two states separated by the Lamb shift are states of different angular momentum– the 2S state has zero angular momentum, while the 2P state has one unit of angular momentum. This leads to a significant difference in the wavefunctions of the two states, with the 2S state spending much more time close to the proton than the 2P state does.
Angular momentum? I thought that was just about gyroscopes and ice skaters? What’s it got to do with atoms? In classical physics, the angular momentum of a moving object depends on two things: how fast it’s moving, and how far it is away from the central point. Two objects moving at the same speed can have very different angular momenta, if one is orbiting close in to a central point while the other is much farther out. The object that is farther away has more angular momentum.
The states of electrons in atoms are not really like planetary orbits, but much of the physics carries over in a conceptual way. The 2S state has zero angular momentum, while the 2P state has one unit of angular momentum, and that means that the 2P state is, on average, farther away from the center of the atom than the 2S state (the two states have the same “speed” because they’re both 2 states). In fact, if you look at the probability of finding the electron exactly at the center of the atom, where the proton is, the probability is zero for the 2P state, but non-zero for the 2S state.
When you take the finite size of the proton into account, that means that an electron in the 2S state will spend more of its time close enough to the proton to see that it’s not a point, but a small sphere of charge (more or less). That changes the interaction energy between the electron and the proton, which in turn changes the total energy of the state. This leads to a shift of the 2S energy compared to the 2P energy, and contributes to the Lamb shift.
So, the Lamb shift is due to the finite size of the proton? I said it contributes to the shift. It’s actually a really tiny contribution in hydrogen– the vast majority of the shift measured by Lamb and Retherford, and in numerous experiments since, is due to other effects. The proton size is part of the shift, though, and is actually one of the main sources of uncertainty in current theoretical calculations of the Lamb shift in hydrogen.
Why is it so small? Becuase, as you noted earlier, the proton is around 10-15 meters across, while the electron orbits are around 10-10 meters across. The region where the proton size matters for the interaction is so small that it’s almost negligible. It’s only because modern spectroscopic methods are so utterly amazing that you can see any contribution to the shift at all.
So this is where the muons come in? Right. A muon is roughly 200 times the mass of an electron, which means its orbit is roughly 200 times smaller than that of an electron. Which leads to a corresponding increase in the size of the proton size contribution. When you replace the electron with a muon, and measure the energy splitting between the 2S and 2P states of this muonic hydrogen, the Lamb shift analogue has a much larger contribution from the proton size. If you know the rest of the effects (and we understand QED pretty well), then you can work out the size of the proton by measuring the size of the shift.
How do they measure the size of the shift? They use laser spectroscopy, and take advantage of the fact that the energy shift is also vastly larger than the Lamb shift in ordinary hydrogen (again, because of the larger mass and smaller orbit). The Lamb shift corresponds to an frequency in the microwave range of the spectrum, but the Lamb shift in muonic hydrogen is in the far infrared range, at around 6 microns. That’s an inconvenient wavelength, but one that can be generated with pulsed lasers.
So, they just shine the alser in, and see if it gets absorbed? Actually, they shine the infrared laser in, and look for x-rays coming out. The way it works is that a small fraction of the muonic hydrogen they produce ends up in the 2S state. That state has a ridiculously long lifetime– limited mostly by the fact that the muons only last two microseconds before they decay– so once they’re in that state, they stick around. A short time after the atoms are created, they blast in a pulse of laser light with its frequency tuned close to the frequency corresponding to the splitting between the 2S and 2P states. The 2P state has a very short lifetime, so any atoms that get excited by the laser will decay very quickly, and emit an x-ray in the process (because the energy difference between the ground state and the 2P state is enormous, thanks to the heavy muon).
When the laser is tuned to exactly the right frequency, they see lots of x-rays from decaying atoms. When it’s a little bit off, the number of x-rays drops off dramatically. Then they just need to measure the laser frequency, and they get the Lamb shift directly. And with a bit of math, they can convert that to a measurement of the proton size.
And this is a good measurement? It’s a phenomenally good measurement. The uncertainty they report in the size is just 0.00067 femto-meters, compared to 0.0069 femto-meters for the best previous measurement. That’s a full order of magnitude better, which is an impressive jump for something this tricky.
What’s the catch? The catch is that their result doesn’t agree with the previous value. The best previous measurement gives the size as 0.8768 fm, while this measurement gives 0.84184 fm. Even taking the uncertainties into account, these do not agree with each other. The difference is about five times the uncertainty, which just shouldn’t happen.
So, protons are way smaller than we thought? Yes and no. This measurement suggests that the size is smaller than that measured in previous experiments, but the difference isn’t all that big in absolute terms. And it’s possible that there’s some effect they haven’t accounted for properly in making this measurement.
What sort of effect? Well, if they knew that, they would’ve accounted for it. There’s a fearsome amount of theory going into the conversion from Lamb shift to proton size, so it’s possible that something there is a little bit off. It’s also possible that there’s something wrong experimentally– this is the first time anybody has ever done laser spectroscopy of muonic hydrogen, so they might’ve overlooked something.
Or it could be completely new physics.
What’s your guess as to the reason? I’m inclined to think it’s in the theory somewhere, but that’s mostly because I’m an experimentalist by inclination and training. There’s an awful lot of theoretical stuff going into the conversion, and it wouldn’t surprise me if six months from now, somebody discovers a small tweak that brings this measurement into line with the others, or brings the other ones in line with this measurement. It’s a whopping huge error as such things go– 64 times the uncertainty they think is associated with the theory– but I wouldn’t be too surprised if that turns out to be unduly optimistic. They mention some other determination that gives results more in line with their result, which may point to something.
The experiment that they’re doing here is really pretty clean, and there aren’t too many factors that need to be accounted for. They seem to have most of those under control, at least from the uncertainty estimates they give for the obvious possible experimental shifts.
“New physics” is obviously the most exciting possibility, here, but it would be really surprising. The physics going into this is really just QED, which is one of the best-tested theories in the history of science. It would be really surprising if QED turned out to be that far wrong, though I’m sure the hep-th arxiv will see a flood of papers proposing one scheme or another for coming up with this kind of result (a new kind of dark-matter particle that couples only to muons, not electrons, or some such).
Whatever it is, it’ll be interesting to see how this plays out.
Pohl, R., Antognini, A., Nez, F., Amaro, F., Biraben, F., Cardoso, J., Covita, D., Dax, A., Dhawan, S., Fernandes, L., Giesen, A., Graf, T., HÃ¤nsch, T., Indelicato, P., Julien, L., Kao, C., Knowles, P., Le Bigot, E., Liu, Y., Lopes, J., Ludhova, L., Monteiro, C., Mulhauser, F., Nebel, T., Rabinowitz, P., dos Santos, J., Schaller, L., Schuhmann, K., Schwob, C., Taqqu, D., Veloso, J., & Kottmann, F. (2010). The size of the proton Nature, 466 (7303), 213-216 DOI: 10.1038/nature09250