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.
