Precision is something that is valued in experimental science.
And while there are many precise measurements that have been made over the years, there
is one that is truly impressive. And that is the measurement of how strong of a magnet
an electron is. The technical term for that, by the way, is the magnetic moment of the
electron.
Now, that might sound like an esoteric topic and I suppose it is if you were the kind of
person who lacks curiosity and refinement.
But YOU are watching a physics video, which means that you’re my kind of people. So
I’m going to tell you about a really cool and extremely precise measurement that is
not only instrumental in proving the theory of quantum electrodynamics, but is also at
the forefront of modern research.
I made a video on the theory of QED which you can watch if you’re interested in that
sort of thing. But in this video, I want to concentrate more on the experimental side.
While there’s a lot wrong about this mental image, you can picture the electron as a tiny,
spinning, ball of electric charge. And if you spin a charge, you make a magnet. Plain
and simple.
Now there are a number of ways you can measure how strong a magnet is, but the easiest way
is to put the magnet in an external magnetic field. Just like a spinning top will precess
because of gravity, a magnet will precess around the bigger magnetic field.
By watching the precession, we can determine precisely the magnetic moment of the electron,
so, that’s the basic idea.
The electron has a particular electric charge and a particular spin- which happens to be
a half- and using straightforward traditional electromagnetic theory, you can calculate
how strong a magnet it should be.
There are many ways you could write the numerical value for this quantity, depending on the
units you pick. So what we do is pick the most convenient set of units possible and
in those units, the predicted magnetic moment is just the number one or unity.
This just makes life easier, but if you want to see the number in, say, metric units, you
can google the term Bohr magneton.
But I’m just going to use the convenient units in which an electron with a spin of
one half is predicted to have a magnetic moment of precisely one.
In science, prediction isn’t good enough. So in 1947, an American physicist with the
unlikely name of Polykarp Kusch measured the magnetic moment of the electron and got a
number that was 1.00119.
So the measured number was very close to 1, but different. And his measurement was precise
enough that he knew that this wasn’t measurement error.
So this was cool and it was a big deal at the time. It proved the simplest theory wasn’t
quite right. The tiny shift, which was just shy of 0.12%, was real- and to explain it,
physicists needed the theory of quantum electrodynamics or QED.
1947 was about seventy years ago and we’ve improved our experimental and calculational
techniques. That means that these days we can test the theory of QED to incredible precision.
The current measured value for the magnetic moment of the electron is 1.001159652181,
while the predicted value is 1.001159652182. You can see that the prediction and measurement
agree exactly, digit-for-digit, for 12 places. Where they start to disagree it’s due to
known uncertainties in both the prediction and the measurement. In fact, within uncertainties,
the two numbers agree.
To give you a sense of scale, that’s like predicting and measuring the diameter of the
Earth with an accuracy of a fifth the diameter of a human hair. This is crazy accurate.
Any time you can get that kind of agreement between a measurement and a prediction means
that you’re doing something right. And from this exercise, physicists have concluded that
the theory of QED is an accurate description of the laws of the universe.
There are plenty of other examples where the calculations and measurements of QED agree,
but this is the most precise. If you’re looking for another example that is less numeric
and more mind blowing, QED also predicts that empty space isn’t empty at all, but rather
a constantly writhing, bubbling, place; with matter and antimatter particles constantly
appearing and disappearing. You can take a look at my video on quantum foam if that interests
you.
Despite QED’s incredible success, there is a research effort in which this topic possibly
points to undiscovered physics.
When scientists turn the precision of QED to investigating the properties of the muon,
which is kind of like the electron’s heavier cousin, there are tantalizing hints of new
physics.
When physicists study the magnetic moment of the muon, there is a discrepancy between
the prediction and the measurement. And whenever data and calculations don’t agree, that
could well mean that you’ve found something that your theory can’t predict. We scientists
have a name for that. We call it a discovery.
The story of the magnetic moment of the muon is cool enough to warrant its own video. If
you want details, I got details. But there and not here.
The bottom line is that both the theory and the measurements of QED agree to parts per
trillion, making it the most precise physics theory ever proposed. And, any time you get
that level of agreement, you know you did something right.