There is a new measurement of the size of the proton and it turns out that protons are smaller than we thought they were.
At some point in your education you probably got introduced to the Bohr model of the atom. The nucleus is made up of protons and neutrons, and electrons orbit around the nucleus. In the Bohr model, electrons orbit the nucleus in circular orbits like the Earth orbits the Sun, but these orbits are only allowed to have some radii (which correspond to an integer number of de Broglie wave lengths). Electrons can transition between these levels and when they do, they either absorb a photon (in the case of an electron being excited from, say, the ground state to an excited state) or emit a photon (in the case of an electron going from an excited state to a lower state.) This is shown below:
The Bohr model isn’t exactly right – but it’s close enough to get some feel for what’s going on. In a more precise quantum mechanical picture, the electron isn’t actually orbiting the nucleus – it’s smeared out in what we call a wave function. The square of the wave function tells us how likely we are to find the electron in a given place. The ground state orbital (the shape of the wave function of the electron in the atom) is spherical. The lowest excited state has four different possible orbitals, one spherical (S) and three which are shaped like a dumbbell (P), a sort of 3D figure-8.
What you probably learned in school was that these S and P orbitals have exactly the same energy – and they almost do. In a simple model, the nucleus is just a point particle – meaning it exists just at a single point, with no size in any dimension. But protons aren’t point particles – they’re just very small. In the S orbitals, the electron spends most of its time near the nucleus, but in the P orbitals, the electron spends less of its time near the nucleus. This difference in how much time the electron spends near the nucleus leads to a very small shift in the energy of the orbitals, called the Lamb shift. The Lamb shift is measured by measuring the photon emitted when an electron goes from the P to the S orbital in the second shell. It depends on the mass of the electron and the size of the proton. (Here’s the explanation of the Lamb shift on the experiment’s web site.)
In this new measurement, they looked at hydrogen with a muon (the heavier cousin of the electron) instead of an electron. Because the muon is about two hundred times heavier than the electron, it spends more time near the nucleus than the electron, meaning it’s more sensitive to the Lamb shift than the electron. Previously, the best measurement of the diameter of the proton was 0.877±0.007 femtometers (m) and this measurement measured it to be 0.8418±0.0007 fm. A femtometer is 10-15 meters. If you were a proton (you’re somewhere between 1-2m tall), this would mean traveling one millimeter would be like traveling from the Earth to the Sun (1011 m). This measurement would be like finding out that you’re 5’5″ instead of 5’8″ by looking at how long it takes for you to walk between Milwaukee, WI and Chicago, IL (150 km) and Milwaukee, WI and Madison, WI (141 km)*.
The fact that this measurement is so far off from our expectations indicates one of the following:
- The precise calculation we’re comparing to is flawed.The proton is actually a really complicated object – perhaps we forgot an important component.
- The measurement has some flaw we haven’t figured out yet. Maybe there was some systematic shift that wasn’t taken into account.
- Our theory is flawed. This could indicate some physics beyond the Standard Model – exactly what we’re looking for at the LHC.
We have to seriously consider the first two options, but the third would obviously be very exciting.
So why I am writing about this here? First, it illustrates that there are other ways of studying fundamental particle physics than by slamming things together. Second, it’s an interesting result that may hint at exciting new physics we’re hoping to see at the LHC. Third, it’s a great segue into my next post…
*Yes, this analogy breaks down at some point. Don’t take it too far.
Excellent explanation in elementary level! I hope you don’t mind me linking the post to my facebook page.
Demian
Hello Christine.
Are physicists sure that the proton is spherical? Isn’t it possible that it is a bit lumpy, because of its internal structure, and that both measurements are right? (In my very naive way, I could imagine the shape of the (P) wave functions of the electron/muon aligning somehow with the internal structure of the proton and hence giving different measures depending on the particular experiment being done and which (P) dominates.)
Demian – thanks! Glad you like it. And any publicity would be appreciated! You can also like the US LHC on Facebook and get updates on the LHC posted to your wall.
Jonathan – this is a really good question.
You’re right that in principle the proton is lumpy. We can study the proton’s structure using deep inelastic scattering, which means we hit the proton with a very high energy electron. By doing this we can see the lumps – which are actually quarks and gluons. But the quarks and gluons are “moving” very quickly. (Moving is in quotes because they actually have wave functions so this isn’t quite techinically correct, but it’s close. We’re really talking about the period of the time-dependent wave function.) The electron or muon “moves” much slower than the quarks and gluons so it can only see the average. This is analogous to taking pictures. If you take pictures at night you have to use a slow shutter speed so that the film is exposed to enough light – but if you take a picture of someone running using a slow shutter speed, all you’ll see is a blur because the shutter was open long enough for the person to move across the frame. So looking at the proton using electrons or muons in an atomic orbital is like taking a picture of the proton with a slow shutter speed.
There all sorts of fluctuations in a proton, but there’s no particular reason, for instance, for an up quark to be on the top rather than the bottom in this experiment. If we extend the picture analogy, our proton is like a bunch of kids (quarks and gluons) on a playground. If you look at any given point in time, each kid is on a particular piece of playground equipment. But if you took a picture of the playground where you exposed the film for, say, five minutes, each kid would show up as a blur in the photograph. The average distribution would be fairly smooth. So at any given point in time, the proton is lumpy – but we average over long times, so the proton looks smooth in this experiment.
But I can design an experiment where the average distribution of quarks and gluons isn’t uniform. Protons have a magnetic field (called spin) and electrons have a spin. If I put a hydrogen atom in a magnetic field, the proton’s spin will line up with the magnetic field and then I can see a difference in energy for electrons with their spin lined up with the proton spin and those with their spin in the opposite direction. This would be equivalent to going to the playground with a chocolate cake and passing out chocolate cake – the distribution of kids on the playground would no longer be uniform. This effect is called hyperfine splitting. Unfortunately, while we know that the different orientations of the proton’s spin correspond to different configurations of quarks and gluons in the proton, we don’t know what those configurations are. We know the proton has spin, but we haven’t figured out where it comes from. (This is another field of study in physics.)
So yes, protons are lumpy, but whether we see those lumps depends on how we look at them. This experiment is analogous to measuring how far away from the playground equipment the kids are on average. There are other ways to define the size of the proton and in what will likely be my next post I’ll talk about another way from ALICE data.
Hi,
I was wondering. You mention that the current best estimate for the diameter of a proton is 0.8418±0.0007 fm. That is about a 0.1% deviation. Can we expect atoms from one edge of the universe to match atoms plucked from the opposite reaches ? Is it possible that some atoms would be scaled up or down by multiple factors with respect to the lot we are familiar with ?
Thanks,
T.M.V.
tom – as far as we know, the laws of physics are the same everywhere in the observable Universe. Therefore we expect protons to be the same, identical, and indistinguishable, everywhere. There are symmetry arguments that corroborate this as well: https://secure.wikimedia.org/wikipedia/en/wiki/Noether%27s_theorem#Applications
How about protons being wavefunctions, too, whose location is somewhat uncertain? Or maybe the quarks in the protons are perturbed randomly by charged virtual particles from vacuum fluctuations. That might prevent a very precise estimate of proton diameter.
Hi Dave – so what you’re referring to is the Heisenberg Uncertainty Principle, which says (roughly) that the more precisely you know the momentum, the less precisely you know the position. However, if you know the wave function you know everything about the electron or muon. (Assuming you are not working at such a small scale that quantum mechanics is no longer sufficient to describe the data and you need to use quantum field theory… but this experiment is still at scale where quantum mechanics is sufficient.) You can get quarks (and anti-quarks and gluons) inside protons from vacuum fluctuations – but these are not the quarks we mean when we say that a proton is made up of three quarks. Vacuum fluctuations are already taken into account in what we call the Standard Model – so that’s not sufficient to explain why we measured the proton to be smaller than we expected.