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.