Let's talk about the best evidence we have that the theories of quantum physics, truly represent the underlying workings of reality.

Quantum field theory is notoriously complicated.

Built from mind-bendingly abstract mathematics.

It could be that the underlying rules that govern reality are really so far from human intuition.

Or are physicists just showing off?

For better or worse, the physicists are definitely on the right track.

We know this because the predictions of quantum field theory stand up to experimental test time and time again.

Quantum field theory describes the universe filled with different quantum fields, in which particles are excitasions, quantized vibrations.

We've talked about QFT many times before, starting with the very first quantum field theory -- quantum electrodynamics.

QED talks about electromagnetic field, whose excitations give us the photon.

The calculations of QED describe how this field interacts with charged particles to give us the electromagnetic force, which binds electrons to atoms, atoms to molecules, and therefore, you know, allows you to exist.

QED is a much deeper and more complicated description of electromagnetism than a simple "opposite charges attract, like charges repel" of classical electrodynamics.

But how do we know it's right?

Well, because it makes some predictions that clash with the classical theory, and those predictions are the most precisely tested and thoroughly verified in all of physics.

Today we're gonna talk about the theory and experiments behind one of these tests -- measuring the g-factor.

Or in simple english: measuring the anomalous magnetic dipole moment of the electron.

Okay, first off, what on Earth did I just say?

What is the anomalous magnetic dipole moment?

Well, it's just like the regular magnetic dipole moment, but more anomalous.

Okay, not helpful.

Let's brake down this magnetic dipole moment thing.

Consider a bar magnet.

It has a dipole magnetic field, basicly meaning it has north and south pole -- dipole, two poles.

If we put a bar magnet in a second extrernal magnetic field, it'll feel a torque, a force causing it to rotate to align with that field.

The tendency of a dipole magnet to rotate in an external magnetic field is its magnetic dipole moment.

Anything with a dipole magnetic field has a magnetic dipole moment.

It's basically a measure of how much it would interact with an external magnetic field, if one existed.

Let's talk about this dipole thing a bit more.

Magnetic fields are produced by moving electric charges.

A perfect dipole field is produced by charges moving in circles.

For example, of loop of wire with an electric current, or the planet Earth with its dynamo core.

But in case of a bar magnet, the source of its magnetic field is a bit weirder.

It mostly comes from the summed dipole magnetic fields of individual electrons in the outer shells of its atoms.

And those electron dipole fields are indeed very weird.

As we'll see, their nature is predicted by quantum theory -- measure electron moments, and you verify your quantum picture of reality.

Electron magnetic field seem intuitive, if you think of the most tiny balls of rotating electric charge.

Except electrons aren't balls, and they aren't really rotating.

As far as we know, electrons are point-like, they have no size.

And does it make sense to think of an infinitesimal point as rotating?

None the less, electrons do have a sort of intrinsic angular momentum, a fundamental quantum spin, that is as intrinsic as mass and charge.

Despite not being the same as classical rotation, its quantum spin does grant electrons a dipole magnetic field.

So, electrons have a magnetic dipole moment, meaning they feel magnetic fields, and act as little bar magnets.

Electrons in atoms feel the magnetic fields produced by their own orbits around the atom.

This results in a subtle talk on these electrons, changing their electric states, and resulting in the fine structure splitting of electron energy levels.

The fine structure constant is named after this effect, and we've talked about this fundamental constant in an earlier episode.

Thinking of electrons as little bar magnets, or as rotating balls of charge, is a nice starting point, but in the end it's misleading.

It also gives you completely the wrong answer, if you try to calculate the electron's magnetic moment.

So, that electron diagram you did in middle school -- it's time to kill that idea, just like you killed your Tamagotchi.

In fact, weirdly, if you measure the magnetic dipole moment of an electron, you get almost exactly twice the value you'd expect for a tiny classical sphere with the same charge and angular momentum as an electron.

This difference between the quantum verus classical magnetic moments for the electron is called the g-factor.

It's the number you need to multiply the classical value by, to get the right answer.

So, apparently, g = 2.

Experiments point to this, but so does the Dirac equation.

This equation is the origin of quantum electrodynamics, and the first to correctly capture the notion of quantum spin.

It describes electrons as weird four component objects with quantum spin magnitudes of half.

That's a whole bunch of crazy we've talked about here.

So, measurement say the g-factor is around 2, and Dirac says it's exactly 2.

Case closed, right?

Wrong, oh, so very wrong.

See, even though the Dirac equation tells us how a relativistic electron would interact with an electromagnetic field, it still treats this EM-field classically.

It doesn't consider the quantum nature of the field.

Only the fully developed quantum electrodynamics -- the first true quantum field theory -- does this.

And QED tells us that the quantum electromagnetic field is a messy, messy place.

It's seas with a faint quantum buzz, infinite phantom oscillations that add infinite complication to any electromagnetic interaction.

This messiness messes with interaction of the electron and the magnetic field to shift the g-factor slightly, so it's not exactly 2, it's 2.0011614... etc.

That little bit extra is the anomaly.

And this is the anomalous magnetic dipole moment.

It's really incredible that we can even begin to calculate the effect of the messy, buzzying electromagnetic field, but in fact we can calculate it's effect extremely precisely, and test this through experiments, showing the underlying truth of quantum theory.

So, one way to think about this quantum buzz is with virtual photons.

Quantum field theory describes the interactions between particles as the sum total of all possible interactions that can lead to the same result.

In the case of electromagnetism, those interactions are mediated by virtual photons, which is just a mathematical way to describe quantum buzz.

Every interaction with virtual photons that can happen, does.

At lest in a sense.

And the sum of the infinite possible interactions defines the strenght of the one real interaction.

And if that doesn't make your head hurt, try thinking about it again.

So, yeah, quantum field theory is a type of madness.

An again, we've been down that rabbit hole.

In particular, we've looked a bit at Feynman diagrams, which are our best tool for dealing with the absurd complexity of quantum fields.

They represent the possible interactions of the quantum field by way of virtual photons.

And they tell you which interactions are the most important and which are insignificant.

So, you know, you don't have to calculate infinity of them.

A basic interaction of an electron with an EM-field is illustrated by this partial Feynman diagram.

An electron encounters a real photon that could represent an external magnetic field, and it's deflected in some way.

But the same encounter could look like this.

The electron first emits a virtual photon, then goes deflected, then reabsorbs the virtual photon.

Same particles in and out, so it leads to the same overall result.

But now the electron undergoes an additional interaction interaction with the buzzying quantum field.

We need to include this sort of secondary interaction when we calculate, say, the overall strenght of an electron's interaction with magnetic field, when we calculate the electron's magnetic dipole moment, and it's g-factor.

If we consider only the first interaction I showed, along with similar primary ones, you calculate a g-factor of exactly 2.

But if you include the secondary interaction, you get g = 2.0011614.

This correction was first calculated by American physicist Julian Schwinger in 1949.

It was an amazing result for the time, but a lot of time has passed since then, and physicists were not content to simply stop at this first correction.

See, there really are infinite ways the electron can interact with the EM-field, with crazy networks of virtual particles and virtual matter-antimatter loops between the real ingoing and outgoing particles.

The more complicated the interaction, the less it contributes to the overall effect.

But contribute they do.

Over time, physicists have included more and more corrections, refining the prediction of the g-factor to increasing precision.

For each new degree of precision the number of Feynman diagrams needed explodes.

Schwinger did his 1949 calculation by hand.

Since 2008 all calculations are done on large supercomputing clusters.

However, the ultimate arbiter of any physical theory is experiment.

To actually measure the g-factor with the same high precision as these calculations requires some cunning.

One way to do it is to watch the way electrons precess in the constant magnetic field of the cyclotron -- a type of particle accelerator.

Electron's spin axes are way slightly misaligned with an external magnetic field to do quantum uncertainty in the spin direction.

As a result they feel a torque from that field and precess like a top.

This is called Larmor precession.

And the rate of this precession tells us the electron g-factor.

And the results are staggering.

The measured g-factor agrees with the calculated value to 10 decimal places.

Now, I need to add a little subtlety here -- to get from the QED calculations to a value of a g, you also need to know the fine structure constant, that I mentioned earlier.

This is the fundamental constant galfaning the strength of the electromagnetic interaction of charged particles.

This requires an independent experimental measurement.

So, it's really the relationship between the electromagnetic moment and the fine structure constant that were verified.

But that prediction is the most accurately verified prediction in the history of physics.

At its hart, physics is the study of the natural world.

We make observations of reality and then try to find theoretical frameworks that explain those observations.

If those theories are good, they are able to predict things beyond the observations on which the theory was build.

The better these predictions, the more universal and presumably the more correct the theory.

The theory of quantum electrodynamics has been pushed to the experimental limit and come out unscathed.

That means that it and the quantum mechanical principles on which it has founded are good representations of reality.

We have to conclude that we're getting closer and closer to the truth in our search for theories to explain the underlying mechanics of space time.