In April of 2021, a group of my colleagues made
an ultra-precise measurement of the magnetic properties of an ephemeral particle called a
muon. This long-awaited announcement could well be crucial evidence that our understanding of
the subatomic world is incomplete. Let’s take a deep dive into what we know and what we don’t
about this very exciting scientific measurement. So, what was the measurement? Scientists used a
fifty-foot diameter ring of very uniform magnets to measure the magnetic properties of the
muon, which is a heavy cousin of the electron. Basically, they were trying to measure
how strong a magnet the muon is. I’m going to just sketch out how the
measurement worked. That’s because Fermilab has made a series of videos
that describe this all in detail. If you want to know how it was done, I put
a bunch of links in the video description. The key measurement is a factor called
g, short for gyromagnetic ratio, which, if you ignore a few constants,
is basically the ratio of the magnetic strength of a muon
compared to how much it’s spinning. Using a version of state of the art 1930s
quantum mechanics, g should equal exactly two. Now in 1948, scientists announced a super
precise measurement of g for electrons and found that it wasn’t exactly two. Instead, g
was equal to 2.00238 or 0.1 percent higher. Shortly after the measurement was reported, physicists devised a more complete
theory of quantum mechanics that agreed with this measurement. This theory
is called quantum electrodynamics, or QED, and I’ve made videos about that theory as
well. Again, the links are in the description. The tiny extra bit of magnetic strength comes from
an amazing source. It turns out that the strength of the electric field close to an electron
is so strong and it contains enough energy, that the energy converts into pairs
of matter and antimatter particles. Those pairs then convert back
into energy very quickly. And more than one pair appears at a time. At
a subatomic level, space near a particle like an electron or a muon looks like a swarm of
fireflies, blinking into and out of existence. This cloud is important, because the interactions
between the electron and the cloud slightly enhance the magnetic properties of the electron.
What scientists actually measure is a combination of the electron and the cloud. And the cloud
is the source of that extra tenth of a percent. In the late 1950s, researchers announced
the first measurement of g for muons and it wasn’t 2 either. It was bigger.
And the reason is the same. Since Fermilab recent announcement was for the g
factor for muons, let’s focus on just them. Over the last five decades or
so, scientists have measured g for muons with increasing precision. By 2006,
researchers at Brookhaven National Laboratory had measured the muon’s g to be this number
you see here, with a tiny, tiny uncertainty. Meanwhile, theorists were calculating the same
quantity and they achieved a similar number with a similar level of precision. Their
result back in 2006 is the number here. So…the first thing you’ll notice is that both the
measurement and the theory have lots of digits and very small uncertainties, meaning that they're
very precise. In addition, the measurement and the theory agree with each other, digit for digit
for eight digits and disagree only in the ninth. For two things to agree disagree in the ninth
digit means that they agree to a couple parts per billion. That’s like someone predicting the
circumference of the Earth with a precision of ten or thirty centimeters or so – call it
slightly under a foot for Americans. This level of agreement is pretty impressive,
but all those digits can be distracting when we’re trying to understand the recent
Fermilab measurement. So, let’s change how I’m presenting them to make them easier
to understand. We just want to concentrate on what fraction of the muon's g comes from that
cloud of particles surrounding it. That means we need to get rid of the part from ordinary
quantum mechanics and we also need to divide our multi-digit numbers by the old-school
quantum number, which I remind you is two. You can see how that works here. We take
the measured g and subtract off the 1930s quantum prediction. Then we divide the
whole thing by the quantum prediction, what’s left is the fraction caused by the quantum
effects of the cloud surrounding the muon. That’s a lot of words, so I can say it a bunch
easier if we remember that the gyromagnetic ratio is written as g and the old-school
prediction is just 2. When you do that, you get that the fraction of the gyromagnetic
ratio caused by precisely known modern physics is simply just g minus 2, all divided by 2. For no
good reason, scientists call that quantity alpha. If we do all of that, we can rewrite our
measurement and prediction for the part of the muon’s gyromagnetic ratio caused by
modern physics for both the experiment and the prediction and, in the year 2006, the
numbers you see here were state of the art. We’re getting somewhere, but to
understand the scientific situation, we need to focus on where the two disagree. So, the easiest way to do that is to simply
mentally erase the number that are the same in experiment and theory – after all, there is no
controversy there – and just keep the ones where they disagree. If we do that, we’re left with the
way more manageable set of numbers we see here. Now we’re in business. We’ve shown
that data and theory are basically in excellent agreement and we can now explore
any residual differences. And these residual differences are important. Let’s swap to a
visual way to represent the two sets of data. Here I show the prediction and measurement as
dots, with lines representing their uncertainties. The first thing we notice is that the two
dots are far apart, and the uncertainties are small compared to how far apart they
are. Basically, the lines don’t overlap. This sort of situation can
mean a couple of things. First, the measurement or prediction can
simply be wrong. That happens all too often, even when researchers try to make sure
that they get the numbers correctly. The second and more interesting, explanation
is that there is some physical phenomena that the prediction just doesn’t include. If that’s
true, then the discrepancy means a discovery and that we need to come up with an
improved theory. That’s really exciting. What I’ve talked about so far
is the situation back in 2006. What's happened since then? Well, theoretical
physicists have revisited the prediction and found that it’s basically sound. They made
some tiny changes, but nothing of substance. So, eyes turned to the measurement. Could have
the researchers at Brookhaven Lab made a mistake? Well, in 2021, researchers at
Fermilab repeated the measurement. I don’t want to get into all of the fascinating
details because, like I said, there have been lots of amazing videos made that already
have discussed them. I put links in the description if you’re interested. What I want
to do is focus entirely on the bottom line. So, what’s the answer? It turns out that the
Brookhaven scientists did a good job. The Fermilab and Brookhaven measurement agreed pretty well. And
now we’re in an exciting place. If the theoretical calculation is sound and the measurement is
accurate, we could be looking at a discovery. Now, what do we do? Well – we can combine the
Fermilab and Brookhaven measurements into a single experimental result. That should get both
a more accurate and precise measurement. Okay - now we’ve come to the place where
we can start discussing the bottom line. What does it all mean? Well, first
- let’s be honest, we don’t know. Nobody has a definitive answer. All we know are
the possibilities. There are two big classes, one exciting and one humbling.
Let’s start with the humbling one. On the same day that Fermilab scientists announced
their amazing measurement, a paper was published in the prestigious journal Nature. It made a
different prediction for the gyromagnetic ratio of the muon. Let’s take a step back and consider
how the prediction is done. Let’s briefly return to the full theoretical number for the muon’s
gyromagnetic ratio and sort of unpack it. Basically, it’s a series of numbers that get
smaller and smaller as you go to the right. The first 2 is handled by
old-time quantum mechanics. The zeros mean that nothing is contributed
by effects that are 10% or 1% of what 1930s quantum predictions cover. The second 2
says that a 0.1% size effect matters and the first 3 says there is a contribution
from a 0.01% effect, and so it goes. When one considers what contributes to
the correction to the gyromagnetic ratio due to the cloud of particles surrounding the
muon, it’s easy to calculate bigger effects, like photons and electrons and antimatter
electrons. These are the things that cause that tenth of a percent addition. But smaller
effects include the case when the muon’s electric field creates a photon that then makes a quark and
antimatter quark. It’s a very small contribution to the gyromagnetic ratio, and furthermore,
it’s also hard to calculate precisely. That’s because quarks interact with quarks,
and the whole thing is pretty messy. In the traditional calculation, physicists estimate
the result using other measurements from other experiments. The resulting prediction gives a
discrepancy between measurements and predictions. However, the new paper published in
Nature takes a different approach. Rather than estimate the effect to the
muon’s magnetic moment from quarks, these researchers try to calculate it by
a brute force method called lattice QCD. Basically, they set up a three dimensional
grid and use supercomputers to calculate how the equations governing the strong force
predict how all of these grid points interact. It takes a lot of computer power, but the approach
has had some success in other areas of physics. The lattice QCD calculation doesn’t agree
with the earlier theory calculations. In fact, it agrees better with the experimental measurement
recently released by Fermilab scientists. So that could be a big letdown. Maybe there
never was a tension between data and prediction. Maybe the early prediction was just
wrong. But it’s too soon to conclude that. For instance, the uncertainty quoted
by the lattice QCD researchers originates from how certain they
are of their methodology. In short, they’re not entirely certain that they’ve
approached the problem completely correctly. Now this doesn’t mean that they made a mistake.
After all, they are excellent scientists. But it shows you how hard it is to do calculations
involving quarks. The bottom line is we need to be careful about drawing conclusions. Luckily,
by my count, there are about six equally talented groups of theorists and computer professionals
in the world who can also try to reproduce the lattice QCD calculation. It will probably take
a year for them to announce their results. So, putting aside the lattice QCD calculation for
a moment, and assuming that the new measurement and the old way of predicting the muon’s
gyromagnetic ratio are correct, what could explain that? Well, that’s where things can be
exciting. It means that new physics is required. What might that new physics be? Unfortunately,
the data can’t answer that. It could be that there are low mass particles that
interact very rarely with muons. Or it could be that there are high mass particles
that interact more frequently with muons. Such a range of possible behaviors is a bit
frustrating, but it’s similar to being in the situation where somebody made a
measurement of an object’s density, but people want to know how big it is and what its
mass is. Density is just mass divided by volume, so any specific density could be a low mass object
with a small size, or a high mass object with a big size. A density measurement alone won’t
tell you either the size or the mass. But it would tell you that a huge mass and a small size
is forbidden by the data. So, you know something. Similarly, if the prediction and measurement
of the muon’s gyromagnetic ratio continue to disagree, it doesn’t give us an exact prediction
of what the new possible physics will be. So, where do we stand? Well, we stand where
scientists often stand – where we know a lot, but not enough, and we have more and more
questions. If the discrepancy persists, we know that there is some sort of new physics and we
have some information about what is possible. On the other hand, if the new theoretical prediction
from lattice QCD is validated, it may be that what we’ve found is that existing theory does a
good job predicting this property of the muon. Now you might be asking
when we’ll know the answer, and for that you’re going to just have to wait. The experimenters at Fermilab will be recording
something like 16 times more data than they’ve reported so far. So, the measurement will improve,
and we’ll learn more in a year or two. And getting other groups to reproduce the lattice QCD
calculations will take a similar amount of time. And that means we just have to
wait to see what the future brings. But there is no question that there is
enormous interest in what the Fermilab Muon g-2 experiment will tell us about the laws
of nature. It’s incredibly, incredibly, exciting. Okay – so this video covered a lot of
fantastic ground and was kind of a deep dive into how frontier science is done. If you
enjoyed learning about this amazing effort, please like and subscribe to the
channel and share on social media. If you do, that means more people will learn
about this riveting bit of physics drama. And who wouldn’t like that? After all,
as we all know, physics is everything.
