What Goes Around Is Really Round: "Improved measurement of the shape of the electron"

The big physics story of the week is undoubtedly the new limit on the electric dipole moment (EDM) of the electron from Ed Hinds's group at Imperial College in the UK. As this is something I wrote a long article on for Physics World, I'm pretty psyched to see this getting lots of media attention, and not just from physics outlets.

My extremely hectic end-of-term schedule and general laziness almost make me want to just point to my earlier article and have done with it. But really, it's a big story, and one I've been following for a while, so how can I pass up the chance for a ResearchBlogging post on this?

OK, you said this is about a dipole moment, but the headlines all talk about measuring the shape of an electron. What do these have to do with one another? A "dipole moment" is just a bit of mathematical apparatus used to describe a non-spherical distribution of charge. It turns out to be mathematically convenient to talk about "polar moments" of various fields in electricity and magnetism. The simplest sort of field is a "monopole," made by a point charge, which pushes other like charges directly outward from itself. Slightly more complicated than that is a "dipole" pattern, which is like what you get when you sprinkle iron filings over a magnet-- the field pushes out at one end, and pulls in at the other, and has some sideways component in between. You can make an electric dipole by putting a negative point charge close to but not exactly on top of a positive point charge.

So, an electron is made up of a little positive thing stuck to a bigger negative thing? There doesn't need to be actual positive charge present-- you can just take some of the negative charge from one pole of a spherical ball of charge and move it to the other pole. That creates a little bit of a dipole moment, too, without needing any of the opposite charge.

OK, so an electron is supposed to be like a ball of charge with a bump on one side and a divot on the other? Well, it could effectively look like that, but this measurement shows that it doesn't. Which in some ways isn't surprising, because it shouldn't be anything but round, according to the simplest models of physics.

Wait, what? These guys set out to measure something that shouldn't exist, and they're getting in all the papers for not finding it? Isn't that kind of a racket? Yes and no. The simplest models of physics tell us that the electron shouldn't have an EDM, because it would violate time-reversal symmetry.

What does making an electron lumpy have to do with time? The thing is, the electron isn't just a point charge. It also has a magnetic dipole moment, which is associated with a property called "spin," because it looks like what you would get if the electron were a spinning ball of charge (it's not literally a spinning ball, but it behaves as if it were). The magnetic dipole moment points along the axis of the spin, and the electric dipole moment, if it exists, must also point along the spin axis, in either the same direction or exactly the opposite direction.

Now, the laws of physics should be symmetric in time-- that is, if you made a movie of a simple particle's behavior, and ran it backwards, there shouldn't be any way to tell which direction the video was playing. An electron EDM violates this, though, as seen in this picture lifted from my Physics World article:

In the figure, the blue arrow represents the direction of the spin of the electron, the purplish ball of charge. If you take a little bit of charge from one pole and move it to the other, as in the second figure, you create an EDM, shown by the red arrow in the middle figure, which points in the same direction as the spin.

When you reverse the flow of time, though, as shown in the picture on the right, the blue spin arrow reverses its direction, because the electron is now "spinning" the other direction. The EDM, however, stays where it is, because reversing the spin direction doesn't affect the position of the extra lump of charge. So, the electron with time going forward has both arrows in the same direction, while with time going backwards, they point in opposite directions. This violates time-reversal symmetry.

So the electron shouldn't have an EDM, and these guys were wasting their time looking for it. Why is this news? The thing is, we know that there should be some processes in the universe that violate time-reversal symmetry. If time-reversal symmetry were never violated, then another symmetry of the universe, "CP" symmetry would never be violated, either. But if CP-symmetry wasn't violated, the Big Bang would've created equal amounts of matter and antimatter, which would've annihiliated leaving nothing but photons. Since nearly everything we see in the visible universe is matter, not antimatter, we know there must be CP-violation, which means there must also be T-violation. Thus, it should be possible for an electron to have an EDM.

So, wait, if there are time-reversal symmetry violations, does that explain the arrow of time? Do I look like Sean Carroll? Go ask him.

OK, OK, don't get touchy. So, now you're telling me that this EDM thing ought to exist, even though it shouldn't, and that's why it's big news that they didn't find it? Well, it can exist. The problem is, the Standard Model of particle physics predicts an absurdly tiny EDM, so small you could never hope to measure it.

We know that the Standard Model can't be the complete story, though, and most theories of particle physics that go beyond the Standard Model predict the existence of exotic particles that would allow a bigger electron EDM. The predictions of those models are much larger, in a range that a really clever experiment can hope to detect.

So, this experiment is looking for an EDM that would only exist if some exotic theory of physics was true? Right. The basic situation is summed up in this plot, again lifted from the Physics World article, which I got from Dave DeMille at Yale before that:

The horizontal axis here represents the size of the EDM predicted by various theories, with smaller EDM's to the right, and each line representing an order of magnitude decrease in size (it's like an astronomy plot, basically-- backwards and logarithmic). The red blob in the upper right is the Standard Model prediction, while the other colored blobs represent the possible ranges of EDM's predicted by a host of more exotic theories. The solid line represents the best experimental limit on the electron EDM, which you can see is already cutting into the theoretical predictions.

And this new paper shifts that line to the right? Exactly. It moves the experimental limit most of the way to the next tick mark.

And they did this by, what, grabbing a bunch of electrons and sticking them in an electric field? Not exactly. If you just stuck a bunch of electrons in an electric field, you would just make a particle accelerator-- they'd go whoosing off toward the positive side of your field, and not stick around to be measured.

To do this sort of measurement, you need electrons that will stick around for a while, but that experience a big electric field at the same time. The way to do that is with polar molecules.

Polar molecules? Molecules from Antarctica? No, molecules that are positive on one end, and negative on the other (very roughly speaking). If you take a really heavy atom (ytterbium, in this case), and bind it into a molecule with a really light atom (fluorine, in this case), you get a situation where the electrons inside the YbF molecule see a really big electric field. And if you apply a moderately large electric field to a sample of these molecules, you can line them all up in a way that produces a measurable shift in the energy levels of those electrons. You can measure that shift using clever techniques from atomic spectroscopy, which are explained in more detail in that Physics World article.

You're really high on that, aren't you? It's some of my best work. Anyway, the point is, you can measure exceedingly tiny shifts in the energy levels of these molecules. And the direction of the shift should depend on the direction of the electric field that you apply to the molecules. For one field direction, they shift up, while for the opposite direction of the field, they shift down.

So, you take a bunch of them, put an electric field on and measure the energy levels, then reverse the field and see what happens? In broad outline, yes. Of course, it's much more complicated than that, because there are all sorts of systematic effects that might make it look like the shift changed due to the changing field, when really it didn't. The bulk of the work for this paper, like any precision measurement paper, was in tracking down and ruling out as many of these systematic errors as possible.

Such as? They looked at things like a possible slight offset in the field, which would prevent them making a complete reversal. And a possible leakage current from the high-voltage electric fields plates slowly discharging through the rest of their vacuum system. And a possible stray magnetic field cause by induced polarization of their magnetic shields due to the transient current when they switched the electric field direction. And lots of other things.

That sounds... Kind of maddening, really. It does take a certain personality type to succeed in that business.

And after all that, they measured nothing? Yes. They measured nothing better than anybody has ever measured nothing before. Their data look deceptively simple:

Those eight points represent a total of 25 million individual measurements of the edm shift, not counting a bunch of additional checks on systematic errors. The error bars are due to the uncertainties in the individual measurements, while the solid line represents the average of all eight. The dashed lines give the uncertainty in the average, which you can see is more than big enough to include zero. Thus, the end result of all the work is that they have not detected any EDM distinguishable from zero.

That's... not as dramatic as it might be. Which is probably a big reason why they phrase the report in terms of an absurdly precise measurement of the "roundness" of the electron charge distribution. They're accentuating the positive.

So, does this answer any outstanding questions in particle physics? Not yet, no. It does make life even tougher for some moderately popular theories, though. It takes another small bite out of that theory graph up above.

But is that it? I mean, they've done their best measurement, so is it hopeless from here? Hardly. They've done a really spectacular job with this measurement, but there are some clear steps forward to the next round. They know what they need to do to reduce some of their biggest sources of systematic uncertainty, and push the limit down even farther.

There are also lots of other groups at work in this area, trying to find an electron EDM in other types of molecules-- thorium monoxide is a fun new contender-- and other systems as well. DAMOP has a whole session on precision measurements coming up in a couple of weeks, with about half of the talks having to do with EDM searches, and there are probably a slew of posters on the subject as well. It's a hot field right now.

Thanks, that was very helpful. Would you like to close this with a cheap shot at particle physicists? Not a real cheap shot, no, but I do think it's worth pointing out that these experiments explore some of the same areas of fundamental physics that you get in experiments at the LHC, with a budget 3-4 orders of magnitude smaller than the cost of the LHC. These are incredibly impressive examples of the art of experimental physics, and all these experiments fit into ordinary-size labs in physics departments all over the world.

I think these are amazing experiments that don't get enough publicity most of the time, so it's good to see them finally getting some press. And I think it would be absolutely awesome if one of the many EDM search experiments managed to scoop the LHC by either ruling out all the popular variants of supersymmetry by pushing the EDM limit down below the range they can predict, or turned up the first positive proof of some beyond-the-Standard-Model theory by finding a non-zero EDM. But then, I'm biased, because this stuff originates in my little corner of physics...

(In addition to the oft-mentioned Physics World article, there's a good ResearchBlogging write-up of this over at A Quantum of Knowledge, which I discovered when I went to ResearchBlogging to get the citation code below.)

Hudson, J., Kara, D., Smallman, I., Sauer, B., Tarbutt, M., & Hinds, E. (2011). Improved measurement of the shape of the electron Nature, 473 (7348), 493-496 DOI: 10.1038/nature10104